A Posteriori Error Analysis and Uncertainty Quantification for Adaptive Multiscale Operator Decomposition Methods for Multiphysics Problems

DTIC Science & Technology

2013-06-24

Barrier methods for critical exponent problems in geometric analysis and mathematical physics, J. Erway and M. Hoist, Submitted for publication . • Finite...1996. [20] C. LANCZOS, Linear Differential Operators, Dover Publications , Mineola, NY, 1997. [21] G.I. MARCHUK, Adjoint Equations and Analysis of...NUMBER(S) 16. SECURITY CLASSIFICATION OF: 19b. TELEPHONE NUMBER (Include area code) The public reporting burden for this collection of information is

Influence of the Geometric Parameter on the Regimes of Natural Convection and Thermal Surface Radiation in a Closed Parallelepiped

NASA Astrophysics Data System (ADS)

Martyushev, S. G.; Miroshnichenko, I. V.; Sheremet, M. A.

2015-11-01

We have performed a numerical analysis of the stationary regimes of thermogravitational convection and thermal surface radiation in a closed differentially heated parallelepiped. The mathematical model formulated in dimensionless natural velocity-pressure-temperature variables was realized numerically in the control volume approach. Analysis of the radiative heat exchange was carried out on the basis of the surface radiation approach with the use of the balance method in the Polyak variant. We have obtained three-dimensional temperature and velocity fields, as well as dependences for the mean Nusselt number reflecting the influence of the geometric parameter, the Rayleigh number, and the reduced emissive factor of the walls on the flow structure and the heat transfer.

Nonassociative differential geometry and gravity with non-geometric fluxes

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Ćirić, Marija Dimitrijević; Szabo, Richard J.

2018-02-01

We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory.

Principal Angle Enrichment Analysis (PAEA): Dimensionally Reduced Multivariate Gene Set Enrichment Analysis Tool

PubMed Central

Clark, Neil R.; Szymkiewicz, Maciej; Wang, Zichen; Monteiro, Caroline D.; Jones, Matthew R.; Ma’ayan, Avi

2016-01-01

Gene set analysis of differential expression, which identifies collectively differentially expressed gene sets, has become an important tool for biology. The power of this approach lies in its reduction of the dimensionality of the statistical problem and its incorporation of biological interpretation by construction. Many approaches to gene set analysis have been proposed, but benchmarking their performance in the setting of real biological data is difficult due to the lack of a gold standard. In a previously published work we proposed a geometrical approach to differential expression which performed highly in benchmarking tests and compared well to the most popular methods of differential gene expression. As reported, this approach has a natural extension to gene set analysis which we call Principal Angle Enrichment Analysis (PAEA). PAEA employs dimensionality reduction and a multivariate approach for gene set enrichment analysis. However, the performance of this method has not been assessed nor its implementation as a web-based tool. Here we describe new benchmarking protocols for gene set analysis methods and find that PAEA performs highly. The PAEA method is implemented as a user-friendly web-based tool, which contains 70 gene set libraries and is freely available to the community. PMID:26848405

Principal Angle Enrichment Analysis (PAEA): Dimensionally Reduced Multivariate Gene Set Enrichment Analysis Tool.

PubMed

Clark, Neil R; Szymkiewicz, Maciej; Wang, Zichen; Monteiro, Caroline D; Jones, Matthew R; Ma'ayan, Avi

2015-11-01

Gene set analysis of differential expression, which identifies collectively differentially expressed gene sets, has become an important tool for biology. The power of this approach lies in its reduction of the dimensionality of the statistical problem and its incorporation of biological interpretation by construction. Many approaches to gene set analysis have been proposed, but benchmarking their performance in the setting of real biological data is difficult due to the lack of a gold standard. In a previously published work we proposed a geometrical approach to differential expression which performed highly in benchmarking tests and compared well to the most popular methods of differential gene expression. As reported, this approach has a natural extension to gene set analysis which we call Principal Angle Enrichment Analysis (PAEA). PAEA employs dimensionality reduction and a multivariate approach for gene set enrichment analysis. However, the performance of this method has not been assessed nor its implementation as a web-based tool. Here we describe new benchmarking protocols for gene set analysis methods and find that PAEA performs highly. The PAEA method is implemented as a user-friendly web-based tool, which contains 70 gene set libraries and is freely available to the community.

[Calculation of the partial function of the kidney with DMSA in pediatrics: is the evaluation of the geometric mean necessary?].

PubMed

Porn, U; Rossmüller, B; Alalp, S; Fischer, S; Dresel, S; Hahn, K

2001-08-01

For assessment of differential renal function (PF) by means of static renal scintigraphy with Tc-99m-dimercaptosuccinic acid (DMSA) the calculation of the geometric mean of counts from the anterior and posterior view is recommended. Of this retrospective study was to find out, if the anterior view is necessary to receive an accurate differential renal function by calculating the geometric mean compared to calculating PF using the counts of the posterior view only. 164 DMSA-scans of 151 children (86 f, 65 m) aged 16 d to 16 a (4.7 +/- 3.9 a) were reviewed. The scans were performed using a dual head gamma camera (Picker Prism 2000 XP, low energy ultra high resolution collimator, matrix 256 x 256, 300 kcts/view, Zoom: 1.6-2.0). Background corrected values from both kidneys anterior and posterior were obtained. Using region of interest technique PF was calculated using the counts of the dorsal view and compared with the calculated geometric mean [SQR(Ctsdors x Ctsventr)]. The differential function of the right kidney was significantly less when compared to the calculation of the geometric mean (p < 0.01). The mean difference between the PFgeom and the PFdors was 1.5 +/- 1.4%. A difference > or = 5% (5.0-9.5%) was obtained in only 6/164 scans (3.7%). Three of 6 patients presented with an underestimated PFdors due to dystopic kidneys on the left side in 2 patients and on the right side in one patient. The other 3 patients with a difference > 5% did not show any renal abnormality. The calculation of the PF from the posterior view only will give an underestimated value of the right kidney compared to the calculation of the geometric mean. This effect is not relevant for the calculation of the differential renal function in orthotopic kidneys, so that in these cases the anterior view is not necessary. However, geometric mean calculation to obtain reliable values for differential renal function should be applied in cases with an obvious anatomical abnormality.

Unification Principle and a Geometric Field Theory

NASA Astrophysics Data System (ADS)

Wanas, Mamdouh I.; Osman, Samah N.; El-Kholy, Reham I.

2015-08-01

In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Geometric Theory of Reduction of Nonlinear Control Systems

NASA Astrophysics Data System (ADS)

Elkin, V. I.

2018-02-01

The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

Semi-automated contour recognition using DICOMautomaton

NASA Astrophysics Data System (ADS)

Clark, H.; Wu, J.; Moiseenko, V.; Lee, R.; Gill, B.; Duzenli, C.; Thomas, S.

2014-03-01

Purpose: A system has been developed which recognizes and classifies Digital Imaging and Communication in Medicine contour data with minimal human intervention. It allows researchers to overcome obstacles which tax analysis and mining systems, including inconsistent naming conventions and differences in data age or resolution. Methods: Lexicographic and geometric analysis is used for recognition. Well-known lexicographic methods implemented include Levenshtein-Damerau, bag-of-characters, Double Metaphone, Soundex, and (word and character)-N-grams. Geometrical implementations include 3D Fourier Descriptors, probability spheres, boolean overlap, simple feature comparison (e.g. eccentricity, volume) and rule-based techniques. Both analyses implement custom, domain-specific modules (e.g. emphasis differentiating left/right organ variants). Contour labels from 60 head and neck patients are used for cross-validation. Results: Mixed-lexicographical methods show an effective improvement in more than 10% of recognition attempts compared with a pure Levenshtein-Damerau approach when withholding 70% of the lexicon. Domain-specific and geometrical techniques further boost performance. Conclusions: DICOMautomaton allows users to recognize contours semi-automatically. As usage increases and the lexicon is filled with additional structures, performance improves, increasing the overall utility of the system.

Applications of automatic differentiation in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Green, Lawrence L.; Carle, A.; Bischof, C.; Haigler, Kara J.; Newman, Perry A.

1994-01-01

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Correction of static pressure on a research aircraft in accelerated flight using differential pressure measurements

NASA Astrophysics Data System (ADS)

Rodi, A. R.; Leon, D. C.

2012-05-01

Geometric altitude data from a combined Global Navigation Satellite System (GNSS) and inertial measurement unit (IMU) system on the University of Wyoming King Air research aircraft are used to estimate acceleration effects on static pressure measurement. Using data collected during periods of accelerated flight, comparison of measured pressure with that derived from GNSS/IMU geometric altitude show that errors exceeding 150 Pa can occur which is significant in airspeed and atmospheric air motion determination. A method is developed to predict static pressure errors from analysis of differential pressure measurements from a Rosemount model 858 differential pressure air velocity probe. The method was evaluated with a carefully designed probe towed on connecting tubing behind the aircraft - a "trailing cone" - in steady flight, and shown to have a precision of about ±10 Pa over a wide range of conditions including various altitudes, power settings, and gear and flap extensions. Under accelerated flight conditions, compared to the GNSS/IMU data, this algorithm predicts corrections to a precision of better than ±20 Pa. Some limiting factors affecting the precision of static pressure measurement on a research aircraft are examined.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Analysis and design of optical systems by use of sensitivity analysis of skew ray tracing

NASA Astrophysics Data System (ADS)

Lin, Psang Dain; Lu, Chia-Hung

2004-02-01

Optical systems are conventionally evaluated by ray-tracing techniques that extract performance quantities such as aberration and spot size. Current optical analysis software does not provide satisfactory analytical evaluation functions for the sensitivity of an optical system. Furthermore, when functions oscillate strongly, the results are of low accuracy. Thus this work extends our earlier research on an advanced treatment of reflected or refracted rays, referred to as sensitivity analysis, in which differential changes of reflected or refracted rays are expressed in terms of differential changes of incident rays. The proposed sensitivity analysis methodology for skew ray tracing of reflected or refracted rays that cross spherical or flat boundaries is demonstrated and validated by the application of a cat's eye retroreflector to the design and by the image orientation of a system with noncoplanar optical axes. The proposed sensitivity analysis is projected as the nucleus of other geometrical optical computations.

Analysis and Design of Optical Systems by Use of Sensitivity Analysis of Skew Ray Tracing

NASA Astrophysics Data System (ADS)

Dain Lin, Psang; Lu, Chia-Hung

2004-02-01

Optical systems are conventionally evaluated by ray-tracing techniques that extract performance quantities such as aberration and spot size. Current optical analysis software does not provide satisfactory analytical evaluation functions for the sensitivity of an optical system. Furthermore, when functions oscillate strongly, the results are of low accuracy. Thus this work extends our earlier research on an advanced treatment of reflected or refracted rays, referred to as sensitivity analysis, in which differential changes of reflected or refracted rays are expressed in terms of differential changes of incident rays. The proposed sensitivity analysis methodology for skew ray tracing of reflected or refracted rays that cross spherical or flat boundaries is demonstrated and validated by the application of a cat ?s eye retroreflector to the design and by the image orientation of a system with noncoplanar optical axes. The proposed sensitivity analysis is projected as the nucleus of other geometrical optical computations.

Differentiation of Students' Reasoning on Linear and Quadratic Geometric Number Patterns

ERIC Educational Resources Information Center

Lin, Fou-Lai; Yang, Kai-Lin

2004-01-01

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

Theoretical analysis of the rotational barrier of ethane.

PubMed

Mo, Yirong; Gao, Jiali

2007-02-01

The understanding of the ethane rotation barrier is fundamental for structural theory and the conformational analysis of organic molecules and requires a consistent theoretical model to differentiate the steric and hyperconjugation effects. Due to recently renewed controversies over the barrier's origin, we developed a computational approach to probe the rotation barriers of ethane and its congeners in terms of steric repulsion, hyperconjugative interaction, and electronic and geometric relaxations. Our study reinstated that the conventional steric repulsion overwhelmingly dominates the barriers.

Finsler-Geometric Continuum Dynamics and Shock Compression

DTIC Science & Technology

2018-01-01

An important mathe - matical device used in the current derivations centers on the divergence theorem of Finsler geometry first presented by Rund...carbide ceramic. Philos Mag 92:2860–2893 Clayton JD (2012b)On anholonomic deformation, geometry, and differentiation. Math Mech Solids 17:702–735 Clayton... Math Phys 2015:828475 Clayton JD (2015b) Penetration resistance of armor ceramics: dimensional analysis and property correlations. Int J Impact Eng

Vehicle Concept Model Abstractions For Integrated Geometric, Inertial ,Rigid Body, Powertrain and FE Analysis

DTIC Science & Technology

2011-06-17

structure through quantitative assessment of stiffness and modal parameter changes resulting from modifications to the beam geometries and positions...power transmission assembly. If the power limit at a wheel exceeds the traction limit, then depending on the type of differential placed on the axle ...components with appropriate model connectivity instead to determine the free modal response of powertrain type components, without abstraction

Vehicle Concept Model Abstractions for Integrated Geometric, Inertial, Rigid Body, Powertrain, and FE Analysis

DTIC Science & Technology

2011-01-01

refinement of the vehicle body structure through quantitative assessment of stiffness and modal parameter changes resulting from modifications to the beam...differential placed on the axle , adjustment of the torque output to the opposite wheel may be required to obtain the correct solution. Thus...represented by simple inertial components with appropriate model connectivity instead to determine the free modal response of powertrain type

Pricing geometric Asian rainbow options under fractional Brownian motion

NASA Astrophysics Data System (ADS)

Wang, Lu; Zhang, Rong; Yang, Lin; Su, Yang; Ma, Feng

2018-03-01

In this paper, we explore the pricing of the assets of Asian rainbow options under the condition that the assets have self-similar and long-range dependence characteristics. Based on the principle of no arbitrage, stochastic differential equation, and partial differential equation, we obtain the pricing formula for two-asset rainbow options under fractional Brownian motion. Next, our Monte Carlo simulation experiments show that the derived pricing formula is accurate and effective. Finally, our sensitivity analysis of the influence of important parameters, such as the risk-free rate, Hurst exponent, and correlation coefficient, on the prices of Asian rainbow options further illustrate the rationality of our pricing model.

A rumor transmission model with incubation in social networks

NASA Astrophysics Data System (ADS)

Jia, Jianwen; Wu, Wenjiang

2018-02-01

In this paper, we propose a rumor transmission model with incubation period and constant recruitment in social networks. By carrying out an analysis of the model, we study the stability of rumor-free equilibrium and come to the local stable condition of the rumor equilibrium. We use the geometric approach for ordinary differential equations for showing the global stability of the rumor equilibrium. And when ℜ0 = 1, the new model occurs a transcritical bifurcation. Furthermore, numerical simulations are used to support the analysis. At last, some conclusions are presented.

I. Excluded volume effects in Ising cluster distributions and nuclear multifragmentation. II. Multiple-chance effects in alpha-particle evaporation

NASA Astrophysics Data System (ADS)

Breus, Dimitry Eugene

In Part I, geometric clusters of the Ising model are studied as possible model clusters for nuclear multifragmentation. These clusters may not be considered as non-interacting (ideal gas) due to excluded volume effect which predominantly is the artifact of the cluster's finite size. Interaction significantly complicates the use of clusters in the analysis of thermodynamic systems. Stillinger's theory is used as a basis for the analysis, which within the RFL (Reiss, Frisch, Lebowitz) fluid-of-spheres approximation produces a prediction for cluster concentrations well obeyed by geometric clusters of the Ising model. If thermodynamic condition of phase coexistence is met, these concentrations can be incorporated into a differential equation procedure of moderate complexity to elucidate the liquid-vapor phase diagram of the system with cluster interaction included. The drawback of increased complexity is outweighted by the reward of greater accuracy of the phase diagram, as it is demonstrated by the Ising model. A novel nuclear-cluster analysis procedure is developed by modifying Fisher's model to contain cluster interaction and employing the differential equation procedure to obtain thermodynamic variables. With this procedure applied to geometric clusters, the guidelines are developed to look for excluded volume effect in nuclear multifragmentation. In Part II, an explanation is offered for the recently observed oscillations in the energy spectra of alpha-particles emitted from hot compound nuclei. Contrary to what was previously expected, the oscillations are assumed to be caused by the multiple-chance nature of alpha-evaporation. In a semi-empirical fashion this assumption is successfully confirmed by a technique of two-spectra decomposition which treats experimental alpha-spectra as having contributions from at least two independent emitters. Building upon the success of the multiple-chance explanation of the oscillations, Moretto's single-chance evaporation theory is augmented to include multiple-chance emission and tested on experimental data to yield positive results.

Geometrical shock dynamics, formation of singularities and topological bifurcations of converging shock fronts

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.

A basis for the analysis of surface geometry of spiral bevel gears

NASA Technical Reports Server (NTRS)

Huston, R. L.; Coy, J. J.

1983-01-01

Geometrical procedures helpful in the fundamental studies of the surface geometry of spiral bevel gears are summarized. These procedures are based upon: (1) fundamental gear geometry and kinematics as exposited by Buckingham, et al; (2) formulas developed from differential geometry; and (3) geometrical concepts developed in recent papers and reports on spiral bevel gear surface geometry. Procedures which characterize the geometry so that the surface parametric equations, the principal radii of curvature, and the meshing kinematics are systematically determined are emphasized. Initially, the focus in on theoretical, logarithmic spiral bevel gears as defined by Buckingham. The gears, however, are difficult to fabricate and are sometimes considered to be too straight. Circular-cut spiral bevel gears are an alternative to this. Surface characteristics of crown circular cut gears are analyzed.

Increasing the quality of excavators’ planetary reduction gearboxes on the basis of dimensional analysis and geometrical characteristics of tooth wheels

NASA Astrophysics Data System (ADS)

Drygin, M. Yu; Kuryshkin, N. P.

2018-01-01

The article describes the problem of extending operational electrically driven excavators’ reducing gear boxes which break down nearly every six months. The main reason of the function loss is the breakdown of the bearing assembly of one of the pinions. The authors performed kinematic, dynamic and geometric calculation of gearing to detect the breakdown reasons. The main reason is that alignment condition is not provided in the differential part and in the power return gear. All toothed gear wheels must be manufactured with the positive bias of the generating rack profile, but in fact all pinions and idle gears are manufactured with negative bias. This lead to an intolerable radial clearance in the gearing and skew of the floating master gears.

Constrained variational calculus for higher order classical field theories

NASA Astrophysics Data System (ADS)

Campos, Cédric M.; de León, Manuel; Martín de Diego, David

2010-11-01

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Unified formalism for the generalized kth-order Hamilton-Jacobi problem

NASA Astrophysics Data System (ADS)

Colombo, Leonardo; de Léon, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2014-08-01

The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.

DEVELOPMENTS IN GRworkbench

NASA Astrophysics Data System (ADS)

Moylan, Andrew; Scott, Susan M.; Searle, Anthony C.

2006-02-01

The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, GRworkbench has been significantly extended to facilitate numerical experimentation in analytically-defined space-times. The numerical differential geometric engine has been rewritten using functional programming techniques, enabling objects which are normally defined as functions in the formalism of differential geometry and General Relativity to be directly represented as function variables in the C++ code of GRworkbench. The new functional differential geometric engine allows for more accurate and efficient visualisation of objects in space-times and makes new, efficient computational techniques available. Motivated by the desire to investigate a recent scientific claim using GRworkbench, new tools for numerical experimentation have been implemented, allowing for the simulation of complex physical situations.

Geometric morphometric analysis of intratrackway variability: a case study on theropod and ornithopod dinosaur trackways from Münchehagen (Lower Cretaceous, Germany).

PubMed

Lallensack, Jens N; van Heteren, Anneke H; Wings, Oliver

2016-01-01

A profound understanding of the influence of trackmaker anatomy, foot movements and substrate properties is crucial for any interpretation of fossil tracks. In this case study we analyze variability of footprint shape within one large theropod (T3), one medium-sized theropod (T2) and one ornithopod (I1) trackway from the Lower Cretaceous of Münchehagen (Lower Saxony, Germany) in order to determine the informativeness of individual features and measurements for ichnotaxonomy, trackmaker identification, and the discrimination between left and right footprints. Landmark analysis is employed based on interpretative outline drawings derived from photogrammetric data, allowing for the location of variability within the footprint and the assessment of covariation of separate footprint parts. Objective methods to define the margins of a footprint are tested and shown to be sufficiently accurate to reproduce the most important results. The lateral hypex and the heel are the most variable regions in the two theropod trackways. As indicated by principal component analysis, a posterior shift of the lateral hypex is correlated with an anterior shift of the margin of the heel. This pattern is less pronounced in the ornithopod trackway, indicating that variation patterns can differ in separate trackways. In all trackways, hypices vary independently from each other, suggesting that their relative position a questionable feature for ichnotaxonomic purposes. Most criteria commonly employed to differentiate between left and right footprints assigned to theropods are found to be reasonably reliable. The described ornithopod footprints are asymmetrical, again allowing for a left-right differentiation. Strikingly, 12 out of 19 measured footprints of the T2 trackway are stepped over the trackway midline, rendering the trackway pattern a misleading left-right criterion for this trackway. Traditional measurements were unable to differentiate between the theropod and the ornithopod trackways. Geometric morphometric analysis reveals potential for improvement of existing discriminant methods.

Geometric morphometric analysis of intratrackway variability: a case study on theropod and ornithopod dinosaur trackways from Münchehagen (Lower Cretaceous, Germany)

PubMed Central

van Heteren, Anneke H.; Wings, Oliver

2016-01-01

A profound understanding of the influence of trackmaker anatomy, foot movements and substrate properties is crucial for any interpretation of fossil tracks. In this case study we analyze variability of footprint shape within one large theropod (T3), one medium-sized theropod (T2) and one ornithopod (I1) trackway from the Lower Cretaceous of Münchehagen (Lower Saxony, Germany) in order to determine the informativeness of individual features and measurements for ichnotaxonomy, trackmaker identification, and the discrimination between left and right footprints. Landmark analysis is employed based on interpretative outline drawings derived from photogrammetric data, allowing for the location of variability within the footprint and the assessment of covariation of separate footprint parts. Objective methods to define the margins of a footprint are tested and shown to be sufficiently accurate to reproduce the most important results. The lateral hypex and the heel are the most variable regions in the two theropod trackways. As indicated by principal component analysis, a posterior shift of the lateral hypex is correlated with an anterior shift of the margin of the heel. This pattern is less pronounced in the ornithopod trackway, indicating that variation patterns can differ in separate trackways. In all trackways, hypices vary independently from each other, suggesting that their relative position a questionable feature for ichnotaxonomic purposes. Most criteria commonly employed to differentiate between left and right footprints assigned to theropods are found to be reasonably reliable. The described ornithopod footprints are asymmetrical, again allowing for a left–right differentiation. Strikingly, 12 out of 19 measured footprints of the T2 trackway are stepped over the trackway midline, rendering the trackway pattern a misleading left–right criterion for this trackway. Traditional measurements were unable to differentiate between the theropod and the ornithopod trackways. Geometric morphometric analysis reveals potential for improvement of existing discriminant methods. PMID:27330855

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

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.

Geometric constrained variational calculus. II: The second variation (Part I)

NASA Astrophysics Data System (ADS)

Massa, Enrico; Bruno, Danilo; Luria, Gianvittorio; Pagani, Enrico

2016-10-01

Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and reinterpreted in terms of Jacobi fields.

Three-dimensional (3D) geometric morphometric analysis of human premolars to assess sexual dimorphism and biological ancestry in Australian populations.

PubMed

Yong, Robin; Ranjitkar, Sarbin; Lekkas, Dimitra; Halazonetis, Demetrios; Evans, Alistair; Brook, Alan; Townsend, Grant

2018-06-01

This study aimed to investigate size and shape variation of human premolars between Indigenous Australians and Australians of European ancestry, and to assess whether sex and ancestry could be differentiated between these groups using 3D geometric morphometrics. Seventy dental casts from each group, equally subdivided by sex, were scanned using a structured-light scanner. The 3D meshes of upper and lower premolars were processed using geometric morphometric methods. Seventy-two landmarks were recorded for upper premolars and 50 landmarks for lower premolars. For each tooth type, two-way ANOVA was used to assess group differences in centroid size. Shape variations were explored using principal component analysis and visualized using 3D morphing. Two-way Procrustes ANOVA was applied to test group differences for ancestry and sex, and a "leave-one-out" discriminant function was applied to assess group assignment. Centroid size and shape did not display significant difference between the sexes. Centroid size was larger in Indigenous Australians for upper premolars and lower second premolars compared to the Australians of European ancestry. Significant shape variation was noted between the two ancestral groups for upper premolars and the lower first premolar. Correct group assignment of individual teeth to their ancestral groups ranged between 80.0 and 92.8% for upper premolars and 60.0 and 75.7% for lower premolars. Our findings provide evidence of significant size and shape variation in human premolars between the two ancestral groups. High classification rates based on shape analysis of upper premolars highlight potential application of geometric morphometrics in anthropological, bioarcheological and forensic contexts. © 2018 Wiley Periodicals, Inc.

Differential geometric methods in system theory.

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1971-01-01

Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

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

NASA Technical Reports Server (NTRS)

Hoffer, R. M.; Dean, M. E.; Knowlton, D. J.; Latty, R. S.

1982-01-01

Kershaw County, South Carolina was selected as the study site for analyzing simulated thematic mapper MSS data and dual-polarized X-band synthetic aperture radar (SAR) data. The impact of the improved spatial and spectral characteristics of the LANDSAT D thematic mapper data on computer aided analysis for forest cover type mapping was examined as well as the value of synthetic aperture radar data for differentiating forest and other cover types. The utility of pattern recognition techniques for analyzing SAR data was assessed. Topics covered include: (1) collection and of TMS and reference data; (2) reformatting, geometric and radiometric rectification, and spatial resolution degradation of TMS data; (3) development of training statistics and test data sets; (4) evaluation of different numbers and combinations of wavelength bands on classification performance; (5) comparison among three classification algorithms; and (6) the effectiveness of the principal component transformation in data analysis. The collection, digitization, reformatting, and geometric adjustment of SAR data are also discussed. Image interpretation results and classification results are presented.

Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

[Retrieval of crown closure of moso bamboo forest using unmanned aerial vehicle (UAV) remotely sensed imagery based on geometric-optical model].

PubMed

Wang, Cong; Du, Hua-qiang; Zhou, Guo-mo; Xu, Xiao-jun; Sun, Shao-bo; Gao, Guo-long

2015-05-01

This research focused on the application of remotely sensed imagery from unmanned aerial vehicle (UAV) with high spatial resolution for the estimation of crown closure of moso bamboo forest based on the geometric-optical model, and analyzed the influence of unconstrained and fully constrained linear spectral mixture analysis (SMA) on the accuracy of the estimated results. The results demonstrated that the combination of UAV remotely sensed imagery and geometric-optical model could, to some degrees, achieve the estimation of crown closure. However, the different SMA methods led to significant differentiation in the estimation accuracy. Compared with unconstrained SMA, the fully constrained linear SMA method resulted in higher accuracy of the estimated values, with the coefficient of determination (R2) of 0.63 at 0.01 level, against the measured values acquired during the field survey. Root mean square error (RMSE) of approximate 0.04 was low, indicating that the usage of fully constrained linear SMA could bring about better results in crown closure estimation, which was closer to the actual condition in moso bamboo forest.

Symbolic manipulation techniques for vibration analysis of laminated elliptic plates

NASA Technical Reports Server (NTRS)

Andersen, C. M.; Noor, A. K.

1977-01-01

A computational scheme is presented for the free vibration analysis of laminated composite elliptic plates. The scheme is based on Hamilton's principle, the Rayleigh-Ritz technique and symmetry considerations and is implemented with the aid of the MACSYMA symbolic manipulation system. The MACYSMA system, through differentiation, integration, and simplification of analytic expressions, produces highly-efficient FORTRAN code for the evaluation of the stiffness and mass coefficients. Multiple use is made of this code to obtain not only the frequencies and mode shapes of the plate, but also the derivatives of the frequencies with respect to various material and geometric parameters.

Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter.

PubMed

Yi, Sun; Nelson, Patrick W; Ulsoy, A Galip

2007-04-01

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.

Free-form geometric modeling by integrating parametric and implicit PDEs.

PubMed

Du, Haixia; Qin, Hong

2007-01-01

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.

Application of Real Options Analysis in the Valuation of Investment in Biodiesel Production

DTIC Science & Technology

2011-05-01

biodiesel) at time t, P(t) be assumed to evolve as the stochastic process given by the geometric Brownian motion (GBM). Then PdWPdtdP...Equation (3) Then in any differential time interval, dt, dX follows an arithmetic Brownian motion , which under risk neutral valuation, will be given by...valuation of American put options,” Journal of Finance 32 (May), pp.449-462. 5. Brennan, M. and E. Schwartz, 1978, “Finite difference methods and

Structure and structure-preserving algorithms for plasma physics

NASA Astrophysics Data System (ADS)

Morrison, P. J.

2016-10-01

Conventional simulation studies of plasma physics are based on numerically solving the underpinning differential (or integro-differential) equations. Usual algorithms in general do not preserve known geometric structure of the physical systems, such as the local energy-momentum conservation law, Casimir invariants, and the symplectic structure (Poincaré invariants). As a consequence, numerical errors may accumulate coherently with time and long-term simulation results may be unreliable. Recently, a series of geometric algorithms that preserve the geometric structures resulting from the Hamiltonian and action principle (HAP) form of theoretical models in plasma physics have been developed by several authors. The superiority of these geometric algorithms has been demonstrated with many test cases. For example, symplectic integrators for guiding-center dynamics have been constructed to preserve the noncanonical symplectic structures and bound the energy-momentum errors for all simulation time-steps; variational and symplectic algorithms have been discovered and successfully applied to the Vlasov-Maxwell system, MHD, and other magnetofluid equations as well. Hamiltonian truncations of the full Vlasov-Maxwell system have opened the field of discrete gyrokinetics and led to the GEMPIC algorithm. The vision that future numerical capabilities in plasma physics should be based on structure-preserving geometric algorithms will be presented. It will be argued that the geometric consequences of HAP form and resulting geometric algorithms suitable for plasma physics studies cannot be adapted from existing mathematical literature but, rather, need to be discovered and worked out by theoretical plasma physicists. The talk will review existing HAP structures of plasma physics for a variety of models, and how they have been adapted for numerical implementation. Supported by DOE DE-FG02-04ER-54742.

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

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

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

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

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

DOE PAGES

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

2016-12-15

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

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Newman, James C., III; Barnwell, Richard W.

1997-01-01

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Natural differential operations on manifolds: an algebraic approach

NASA Astrophysics Data System (ADS)

Katsylo, P. I.; Timashev, D. A.

2008-10-01

Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles \\mathscr{V},\\mathscr{W}\\to M all the natural differential operations D\\colon\\Gamma(\\mathscr{V})\\to\\Gamma(\\mathscr{W}) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds.Bibliography: 21 titles.

Fast calculation of the light differential scattering cross section of optically soft and convex bodies

NASA Astrophysics Data System (ADS)

Gruy, Frédéric

2014-02-01

Depending on the range of size and the refractive index value, an optically soft particle follows Rayleigh-Debye-Gans or RDG approximation or Van de Hulst approximation. Practically the first one is valid for small particles whereas the second one works for large particles. Klett and Sutherland (Klett JD, Sutherland RA. App. Opt. 1992;31:373) proved that the Wentzel-Kramers-Brillouin or WKB approximation leads to accurate values of the differential scattering cross section of sphere and cylinder over a wide range of size. In this paper we extend the work of Klett and Sutherland by proposing a method allowing a fast calculation of the differential scattering cross section for any shape of particle with a given orientation and illuminated by unpolarized light. Our method is based on a geometrical approximation of the particle by replacing each geometrical cross section by an ellipse and then by exactly evaluating the differential scattering cross section of the newly generated body. The latter one contains only two single integrals.

Geometric foundations of the theory of feedback equivalence

NASA Technical Reports Server (NTRS)

Hermann, R.

1987-01-01

A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. I. Foundations of Differential and Integral Calculus

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2013-04-01

Critical analysis of the standard foundations of differential and integral calculus -- as mathematical formalism of theoretical physics -- is proposed. Methodological basis of the analysis is the unity of formal logic and rational dialectics. It is shown that: (a) the foundations (i.e. d 1ptyd,;=;δ,;->;0,;δ,δ,, δ,;->;0;δ,δ,;=;δ,;->;0;f,( x;+;δ, );-;f,( x )δ,;, d,;=;δ,, d,;=;δ, where y;=;f,( x ) is a continuous function of one argument x; δ, and δ, are increments; d, and d, are differentials) not satisfy formal logic law -- the law of identity; (b) the infinitesimal quantities d,, d, are fictitious quantities. They have neither algebraic meaning, nor geometrical meaning because these quantities do not take numerical values and, therefore, have no a quantitative measure; (c) expressions of the kind x;+;d, are erroneous because x (i.e. finite quantity) and d, (i.e. infinitely diminished quantity) have different sense, different qualitative determinacy; since x;,;,,,,onst under δ,;,;,, a derivative does not contain variable quantity x and depends only on constant c. Consequently, the standard concepts ``infinitesimal quantity (uninterruptedly diminishing quantity)'', ``derivative'', ``derivative as function of variable quantity'' represent incorrect basis of mathematics and theoretical physics.

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

NASA Technical Reports Server (NTRS)

Whitcomb, J. D.; Dattaguru, B.

1984-01-01

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.

Algorithm for lens calculations in the geometrized Maxwell theory

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Sevastianov, Leonid A.; Gevorkyan, Migran N.; Demidova, Anastasia V.

2018-04-01

Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrized optics is usually not given attention. The aim of this work is to demonstrate the work of the proposed the algorithm in the framework of geometrized approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters. The methods of differential geometry are used for effective metrics construction for isotropic and anisotropic media. For effective metric space ray trajectories are obtained in the form of geodesic curves. The introduced algorithm is applied to well-known objects, Maxwell and Luneburg lenses. The similarity of results obtained by classical and geometric approach is demonstrated.

Numerical Estimation of the Curvature of Biological Surfaces

NASA Technical Reports Server (NTRS)

Todd, P. H.

1985-01-01

Many biological systems may profitably be studied as surface phenomena. A model consisting of isotropic growth of a curved surface from a flat sheet is assumed. With such a model, the Gaussian curvature of the final surface determines whether growth rate of the surface is subharmonic or superharmonic. These properties correspond to notions of convexity and concavity, and thus to local excess growth and local deficiency of growth. In biological models where the major factors controlling surface growth are intrinsic to the surface, researchers thus gained from geometrical study information on the differential growth undergone by the surface. These ideas were applied to an analysis of the folding of the cerebral cortex, a geometrically rather complex surface growth. A numerical surface curvature technique based on an approximation to the Dupin indicatrix of the surface was developed. A metric for comparing curvature estimates is introduced, and considerable numerical testing indicated the reliability of this technique.

Differentiation of δ, μ, and κ opioid receptor agonists based on pharmacophore development and computed physicochemical properties

NASA Astrophysics Data System (ADS)

Filizola, Marta; Villar, Hugo O.; Loew, Gilda H.

2001-04-01

Compounds that bind with significant affinity to the opioid receptor types, δ, μ, and κ, with different combinations of activation and inhibition at these three receptors could be promising behaviorally selective agents. Working on this hypothesis, the chemical moieties common to three different sets of opioid receptor agonists with significant affinity for each of the three receptor types δ, μ, or κ were identified. Using a distance analysis approach, common geometric arrangements of these chemical moieties were found for selected δ, μ, or κ opioid agonists. The chemical and geometric commonalities among agonists at each opioid receptor type were then compared with a non-specific opioid recognition pharmacophore recently developed. The comparison provided identification of the additional requirements for activation of δ, μ, and κ opioid receptors. The distance analysis approach was able to clearly discriminate κ-agonists, while global molecular properties for all compounds were calculated to identify additional requirements for activation of δ and μ receptors. Comparisons of the combined geometric and physicochemical properties calculated for each of the three sets of agonists allowed the determination of unique requirements for activation of each of the three opioid receptors. These results can be used to improve the activation selectivity of known opioid agonists and as a guide for the identification of novel selective opioid ligands with potential therapeutic usefulness.

Allometry and apparent paradoxes in human limb proportions: Implications for scaling factors.

PubMed

Auerbach, Benjamin M; Sylvester, Adam D

2011-03-01

It has been consistently demonstrated that human proximal limb elements exhibit negative allometry, while distal elements scale with positive allometry. Such scaling implies that longer limbs will have higher intralimb indices, a phenomenon not borne out by empirical analyses. This, therefore, creates a paradox within the limb allometry literature. This study shows that these apparently conflicting results are the product of two separate phenomena. First, the use of the geometric mean of limb elements produces allometry coefficients that are not independent, and that when using ordinary least squares regression must yield an average slope of one. This phenomenon argues against using the geometric mean as a size variable when examining limb allometry. While the employment of relevant dimensions independent of those under analysis to calculate the geometric mean--as suggested by Coleman (Am J Phys Anthropol 135 (2008) 404-415)--may be a partial method for resolving the problem, an empirically determined, independent and biologically relevant size variable is advocated. If stature is used instead of the geometric mean as an independent size variable, all major limb elements scale with positive allometry. Second, while limb allometry coefficients do indicate differential allometry in limb elements, and thus should lead to some intralimb index allometry, this pattern appears to be attenuated by other sources of limb element length variation. Copyright © 2010 Wiley-Liss, Inc.

Two solvable problems of planar geometrical optics.

PubMed

Borghero, Francesco; Bozis, George

2006-12-01

In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

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…

Algebraic and geometric structures of analytic partial differential equations

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2016-11-01

We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

Procrustes-based geometric morphometrics on MRI images: An example of inter-operator bias in 3D landmarks and its impact on big datasets.

PubMed

Daboul, Amro; Ivanovska, Tatyana; Bülow, Robin; Biffar, Reiner; Cardini, Andrea

2018-01-01

Using 3D anatomical landmarks from adult human head MRIs, we assessed the magnitude of inter-operator differences in Procrustes-based geometric morphometric analyses. An in depth analysis of both absolute and relative error was performed in a subsample of individuals with replicated digitization by three different operators. The effect of inter-operator differences was also explored in a large sample of more than 900 individuals. Although absolute error was not unusual for MRI measurements, including bone landmarks, shape was particularly affected by differences among operators, with up to more than 30% of sample variation accounted for by this type of error. The magnitude of the bias was such that it dominated the main pattern of bone and total (all landmarks included) shape variation, largely surpassing the effect of sex differences between hundreds of men and women. In contrast, however, we found higher reproducibility in soft-tissue nasal landmarks, despite relatively larger errors in estimates of nasal size. Our study exemplifies the assessment of measurement error using geometric morphometrics on landmarks from MRIs and stresses the importance of relating it to total sample variance within the specific methodological framework being used. In summary, precise landmarks may not necessarily imply negligible errors, especially in shape data; indeed, size and shape may be differentially impacted by measurement error and different types of landmarks may have relatively larger or smaller errors. Importantly, and consistently with other recent studies using geometric morphometrics on digital images (which, however, were not specific to MRI data), this study showed that inter-operator biases can be a major source of error in the analysis of large samples, as those that are becoming increasingly common in the 'era of big data'.

Procrustes-based geometric morphometrics on MRI images: An example of inter-operator bias in 3D landmarks and its impact on big datasets

PubMed Central

Ivanovska, Tatyana; Bülow, Robin; Biffar, Reiner; Cardini, Andrea

2018-01-01

Using 3D anatomical landmarks from adult human head MRIs, we assessed the magnitude of inter-operator differences in Procrustes-based geometric morphometric analyses. An in depth analysis of both absolute and relative error was performed in a subsample of individuals with replicated digitization by three different operators. The effect of inter-operator differences was also explored in a large sample of more than 900 individuals. Although absolute error was not unusual for MRI measurements, including bone landmarks, shape was particularly affected by differences among operators, with up to more than 30% of sample variation accounted for by this type of error. The magnitude of the bias was such that it dominated the main pattern of bone and total (all landmarks included) shape variation, largely surpassing the effect of sex differences between hundreds of men and women. In contrast, however, we found higher reproducibility in soft-tissue nasal landmarks, despite relatively larger errors in estimates of nasal size. Our study exemplifies the assessment of measurement error using geometric morphometrics on landmarks from MRIs and stresses the importance of relating it to total sample variance within the specific methodological framework being used. In summary, precise landmarks may not necessarily imply negligible errors, especially in shape data; indeed, size and shape may be differentially impacted by measurement error and different types of landmarks may have relatively larger or smaller errors. Importantly, and consistently with other recent studies using geometric morphometrics on digital images (which, however, were not specific to MRI data), this study showed that inter-operator biases can be a major source of error in the analysis of large samples, as those that are becoming increasingly common in the 'era of big data'. PMID:29787586

Cellular self-organization by autocatalytic alignment feedback

PubMed Central

Junkin, Michael; Leung, Siu Ling; Whitman, Samantha; Gregorio, Carol C.; Wong, Pak Kin

2011-01-01

Myoblasts aggregate, differentiate and fuse to form skeletal muscle during both embryogenesis and tissue regeneration. For proper muscle function, long-range self-organization of myoblasts is required to create organized muscle architecture globally aligned to neighboring tissue. However, how the cells process geometric information over distances considerably longer than individual cells to self-organize into well-ordered, aligned and multinucleated myofibers remains a central question in developmental biology and regenerative medicine. Using plasma lithography micropatterning to create spatial cues for cell guidance, we show a physical mechanism by which orientation information can propagate for a long distance from a geometric boundary to guide development of muscle tissue. This long-range alignment occurs only in differentiating myoblasts, but not in non-fusing myoblasts perturbed by microfluidic disturbances or other non-fusing cell types. Computational cellular automata analysis of the spatiotemporal evolution of the self-organization process reveals that myogenic fusion in conjunction with rotational inertia functions in a self-reinforcing manner to enhance long-range propagation of alignment information. With this autocatalytic alignment feedback, well-ordered alignment of muscle could reinforce existing orientations and help promote proper arrangement with neighboring tissue and overall organization. Such physical self-enhancement might represent a fundamental mechanism for long-range pattern formation during tissue morphogenesis. PMID:22193956

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 \

The Emergence and Propagation of a Phase Boundary in an Elastic Bar.

DTIC Science & Technology

1983-06-01

differential- delay equations, where the delay 1s unknown. We first present a short- time analysis of this system in order to describe the emergence and Initial...ft, which arise on x=0 at progressively earlier times ; see Fig. 8. This geometric state of affairs is described by the inequalities : TT^"^^WF...t))) < 0 , (6.7) so that e(s(t)~,t) and v(s(t)",t) are decreasing with time . We have already observed that the first Inequality In (6.2

Geometric approach to nuclear pasta phases

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2016-12-01

By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The β equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

A Comprehensive Comparison of Multiparty Secure Additions with Differential Privacy

PubMed Central

Goryczka, Slawomir; Xiong, Li

2016-01-01

This paper considers the problem of secure data aggregation (mainly summation) in a distributed setting, while ensuring differential privacy of the result. We study secure multiparty addition protocols using well known security schemes: Shamir’s secret sharing, perturbation-based, and various encryptions. We supplement our study with our new enhanced encryption scheme EFT, which is efficient and fault tolerant. Differential privacy of the final result is achieved by either distributed Laplace or Geometric mechanism (respectively DLPA or DGPA), while approximated differential privacy is achieved by diluted mechanisms. Distributed random noise is generated collectively by all participants, which draw random variables from one of several distributions: Gamma, Gauss, Geometric, or their diluted versions. We introduce a new distributed privacy mechanism with noise drawn from the Laplace distribution, which achieves smaller redundant noise with efficiency. We compare complexity and security characteristics of the protocols with different differential privacy mechanisms and security schemes. More importantly, we implemented all protocols and present an experimental comparison on their performance and scalability in a real distributed environment. Based on the evaluations, we identify our security scheme and Laplace DLPA as the most efficient for secure distributed data aggregation with privacy. PMID:28919841

A Comprehensive Comparison of Multiparty Secure Additions with Differential Privacy.

PubMed

Goryczka, Slawomir; Xiong, Li

2017-01-01

This paper considers the problem of secure data aggregation (mainly summation) in a distributed setting, while ensuring differential privacy of the result. We study secure multiparty addition protocols using well known security schemes: Shamir's secret sharing, perturbation-based, and various encryptions. We supplement our study with our new enhanced encryption scheme EFT, which is efficient and fault tolerant. Differential privacy of the final result is achieved by either distributed Laplace or Geometric mechanism (respectively DLPA or DGPA), while approximated differential privacy is achieved by diluted mechanisms. Distributed random noise is generated collectively by all participants, which draw random variables from one of several distributions: Gamma, Gauss, Geometric, or their diluted versions. We introduce a new distributed privacy mechanism with noise drawn from the Laplace distribution, which achieves smaller redundant noise with efficiency. We compare complexity and security characteristics of the protocols with different differential privacy mechanisms and security schemes. More importantly, we implemented all protocols and present an experimental comparison on their performance and scalability in a real distributed environment. Based on the evaluations, we identify our security scheme and Laplace DLPA as the most efficient for secure distributed data aggregation with privacy.

Some properties for integro-differential operator defined by a fractional formal.

PubMed

Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

2016-01-01

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

What Differential Weighting of Subsets of Items Does and Does Not Accomplish: Geometric Explanation. Research Report. ETS RR-14-20

ERIC Educational Resources Information Center

Carlson, James E.

2014-01-01

A little-known theorem, a generalization of Pythagoras's theorem, due to Pappus, is used to present a geometric explanation of various definitions of the contribution of component tests to their composite. I show that an unambiguous definition of the unique contribution of a component to the composite score variance is present if and only if the…

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

ERIC Educational Resources Information Center

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

2009-01-01

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

Knot soliton in DNA and geometric structure of its free-energy density.

PubMed

Wang, Ying; Shi, Xuguang

2018-03-01

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Differential geometric treewidth estimation in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Wang, Chi; Jonckheere, Edmond; Brun, Todd

2016-10-01

The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.

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.

Assessment of Arterial Wall Enhancement for Differentiation of Parent Artery Disease from Small Artery Disease: Comparison between Histogram Analysis and Visual Analysis on 3-Dimensional Contrast-Enhanced T1-Weighted Turbo Spin Echo MR Images at 3T.

PubMed

Jang, Jinhee; Kim, Tae-Won; Hwang, Eo-Jin; Choi, Hyun Seok; Koo, Jaseong; Shin, Yong Sam; Jung, So-Lyung; Ahn, Kook-Jin; Kim, Bum-Soo

2017-01-01

The purpose of this study was to compare the histogram analysis and visual scores in 3T MRI assessment of middle cerebral arterial wall enhancement in patients with acute stroke, for the differentiation of parent artery disease (PAD) from small artery disease (SAD). Among the 82 consecutive patients in a tertiary hospital for one year, 25 patients with acute infarcts in middle cerebral artery (MCA) territory were included in this study including 15 patients with PAD and 10 patients with SAD. Three-dimensional contrast-enhanced T1-weighted turbo spin echo MR images with black-blood preparation at 3T were analyzed both qualitatively and quantitatively. The degree of MCA stenosis, and visual and histogram assessments on MCA wall enhancement were evaluated. A statistical analysis was performed to compare diagnostic accuracy between qualitative and quantitative metrics. The degree of stenosis, visual enhancement score, geometric mean (GM), and the 90th percentile (90P) value from the histogram analysis were significantly higher in PAD than in SAD ( p = 0.006 for stenosis, < 0.001 for others). The receiver operating characteristic curve area of GM and 90P were 1 (95% confidence interval [CI], 0.86-1.00). A histogram analysis of a relevant arterial wall enhancement allows differentiation between PAD and SAD in patients with acute stroke within the MCA territory.

Geometric morphometrics reveals sex-differential shape allometry in a spider.

PubMed

Fernández-Montraveta, Carmen; Marugán-Lobón, Jesús

2017-01-01

Common scientific wisdom assumes that spider sexual dimorphism (SD) mostly results from sexual selection operating on males. However, testing predictions from this hypothesis, particularly male size hyperallometry, has been restricted by methodological constraints. Here, using geometric morphometrics (GMM) we studied for the first time sex-differential shape allometry in a spider ( Donacosa merlini , Araneae: Lycosidae) known to exhibit the reverse pattern (i.e., male-biased) of spider sexual size dimorphism. GMM reveals previously undetected sex-differential shape allometry and sex-related shape differences that are size independent (i.e., associated to the y-intercept, and not to size scaling). Sexual shape dimorphism affects both the relative carapace-to-opisthosoma size and the carapace geometry, arguably resulting from sex differences in both reproductive roles (female egg load and male competition) and life styles (wandering males and burrowing females). Our results demonstrate that body portions may vary modularly in response to different selection pressures, giving rise to sex differences in shape, which reconciles previously considered mutually exclusive interpretations about the origins of spider SD.

Differential geometry based solvation model II: Lagrangian formulation.

PubMed

Chen, Zhan; Baker, Nathan A; Wei, G W

2011-12-01

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature. © Springer-Verlag 2011

Differential geometry based solvation model II: Lagrangian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface (MMS) and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature. PMID:21279359

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

Sheng, Y; Ge, Y; Yuan, L

Purpose: To investigate the impact of outliers on knowledge modeling in radiation therapy, and develop a systematic workflow for identifying and analyzing geometric and dosimetric outliers using pelvic cases. Methods: Four groups (G1-G4) of pelvic plans were included: G1 (37 prostate cases), G2 (37 prostate plus lymph node cases), and G3 (37 prostate bed cases) are all clinical IMRT cases. G4 are 10 plans outside G1 re-planned with dynamic-arc to simulate dosimetric outliers. The workflow involves 2 steps: 1. identify geometric outliers, assess impact and clean up; 2. identify dosimetric outliers, assess impact and clean up.1. A baseline model wasmore » trained with all G1 cases. G2/G3 cases were then individually added to the baseline model as geometric outliers. The impact on the model was assessed by comparing leverage statistic of inliers (G1) and outliers (G2/G3). Receiver-operating-characteristics (ROC) analysis was performed to determine optimal threshold. 2. A separate baseline model was trained with 32 G1 cases. Each G4 case (dosimetric outliers) was then progressively added to perturb this model. DVH predictions were performed using these perturbed models for remaining 5 G1 cases. Normal tissue complication probability (NTCP) calculated from predicted DVH were used to evaluate dosimetric outliers’ impact. Results: The leverage of inliers and outliers was significantly different. The Area-Under-Curve (AUC) for differentiating G2 from G1 was 0.94 (threshold: 0.22) for bladder; and 0.80 (threshold: 0.10) for rectum. For differentiating G3 from G1, the AUC (threshold) was 0.68 (0.09) for bladder, 0.76 (0.08) for rectum. Significant increase in NTCP started from models with 4 dosimetric outliers for bladder (p<0.05), and with only 1 dosimetric outlier for rectum (p<0.05). Conclusion: We established a systematic workflow for identifying and analyzing geometric and dosimetric outliers, and investigated statistical metrics for detecting. Results validated the necessity for outlier detection and clean-up to enhance model quality in clinical practice. Research Grant: Varian master research grant.« less

On the geometry of inhomogeneous quantum groups

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

Aschieri, Paolo

1998-01-01

The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields. Equivalent definitions of bicovariant differential calculus are studied and their geometrical interpretation is explained. From these data he constructs and analyzes the space of vectorfields, and naturally introduces a contraction operator and a Lie derivative. Their properties are discussed.

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Parametric FEM for geometric biomembranes

NASA Astrophysics Data System (ADS)

Bonito, Andrea; Nochetto, Ricardo H.; Sebastian Pauletti, M.

2010-05-01

We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.

On the numeric integration of dynamic attitude equations

NASA Technical Reports Server (NTRS)

Crouch, P. E.; Yan, Y.; Grossman, Robert

1992-01-01

We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.

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

Separation of plastic waste via the hydraulic separator Multidune under different geometric configurations.

PubMed

La Marca, Floriana; Moroni, Monica; Cherubini, Lorenzo; Lupo, Emanuela; Cenedese, Antonio

2012-07-01

The recovery of high-quality plastic materials is becoming an increasingly challenging issue for the recycling sector. Technologies for plastic recycling have to guarantee high-quality secondary raw material, complying with specific standards, for use in industrial applications. The variability in waste plastics does not always correspond to evident differences in physical characteristics, making traditional methodologies ineffective for plastic separation. The Multidune separator is a hydraulic channel allowing the sorting of solid particles on the basis of differential transport mechanisms by generating particular fluid dynamic conditions due to its geometric configuration and operational settings. In this paper, the fluid dynamic conditions were investigated by an image analysis technique, allowing the reconstruction of velocity fields generated inside the Multidune, considering two different geometric configurations of the device, Configuration A and Configuration B. Furthermore, tests on mono- and bi-material samples were completed with varying operational conditions under both configurations. In both series of experiments, the bi-material samples were composed of differing proportions (85% vs. 15%) to simulate real conditions in an industrial plant for the purifying of a useful fraction from a contaminating fraction. The separation results were evaluated in terms of grade and recovery of the useful fraction. Copyright © 2012 Elsevier Ltd. All rights reserved.

Multiscale Path Metrics for the Analysis of Discrete Geometric Structures

DTIC Science & Technology

2017-11-30

Report: Multiscale Path Metrics for the Analysis of Discrete Geometric Structures The views, opinions and/or findings contained in this report are those...Analysis of Discrete Geometric Structures Report Term: 0-Other Email: tomasi@cs.duke.edu Distribution Statement: 1-Approved for public release

On the geometric analysis and adjustment of optical satellite observations. M.S. Thesis

NASA Technical Reports Server (NTRS)

Tsimis, E.

1972-01-01

Satellite geodesy methods were catagorized into three divisions: geometric, dynamic, and mixed. These catagories furnish the basis for distinction between geometric and dynamic satellite geodesy. The dual adjustment, geometric analysis, and Cartesian coodinate determination are examined for two observing stations. Similar illustrations are given when more than two observing stations are used.

Automated image alignment for 2D gel electrophoresis in a high-throughput proteomics pipeline.

PubMed

Dowsey, Andrew W; Dunn, Michael J; Yang, Guang-Zhong

2008-04-01

The quest for high-throughput proteomics has revealed a number of challenges in recent years. Whilst substantial improvements in automated protein separation with liquid chromatography and mass spectrometry (LC/MS), aka 'shotgun' proteomics, have been achieved, large-scale open initiatives such as the Human Proteome Organization (HUPO) Brain Proteome Project have shown that maximal proteome coverage is only possible when LC/MS is complemented by 2D gel electrophoresis (2-DE) studies. Moreover, both separation methods require automated alignment and differential analysis to relieve the bioinformatics bottleneck and so make high-throughput protein biomarker discovery a reality. The purpose of this article is to describe a fully automatic image alignment framework for the integration of 2-DE into a high-throughput differential expression proteomics pipeline. The proposed method is based on robust automated image normalization (RAIN) to circumvent the drawbacks of traditional approaches. These use symbolic representation at the very early stages of the analysis, which introduces persistent errors due to inaccuracies in modelling and alignment. In RAIN, a third-order volume-invariant B-spline model is incorporated into a multi-resolution schema to correct for geometric and expression inhomogeneity at multiple scales. The normalized images can then be compared directly in the image domain for quantitative differential analysis. Through evaluation against an existing state-of-the-art method on real and synthetically warped 2D gels, the proposed analysis framework demonstrates substantial improvements in matching accuracy and differential sensitivity. High-throughput analysis is established through an accelerated GPGPU (general purpose computation on graphics cards) implementation. Supplementary material, software and images used in the validation are available at http://www.proteomegrid.org/rain/.

Final Report for Geometric Analysis for Data Reduction and Structure Discovery DE-FG02-10ER25983, STRIPES award # DE-SC0004096

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

Vixie, Kevin R.

This is the final report for the project "Geometric Analysis for Data Reduction and Structure Discovery" in which insights and tools from geometric analysis were developed and exploited for their potential to large scale data challenges.

Learning Extrema Problems Using a Non-Differential Approach in a Digital Dynamic Environment: The Case of High-Track yet Low-Achievers

ERIC Educational Resources Information Center

Dvir, Assaf; Tabach, Michal

2017-01-01

High schools commonly use a differential approach to teach minima and maxima geometric problems. Although calculus serves as a systematic and powerful technique, this rigorous instrument might hinder students' ability to understand the behavior and constraints of the objective function. The proliferation of digital environments allowed us to adopt…

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

PubMed Central

Eshraghi, Iman; Jalali, Seyed K.; Pugno, Nicola Maria

2016-01-01

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs. PMID:28773911

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.

2013-05-01

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Computation and visualization of geometric partial differential equations

NASA Astrophysics Data System (ADS)

Tiee, Christopher L.

The chief goal of this work is to explore a modern framework for the study and approximation of partial differential equations, recast common partial differential equations into this framework, and prove theorems about such equations and their approximations. A central motivation is to recognize and respect the essential geometric nature of such problems, and take it into consideration when approximating. The hope is that this process will lead to the discovery of more refined algorithms and processes and apply them to new problems. In the first part, we introduce our quantities of interest and reformulate traditional boundary value problems in the modern framework. We see how Hilbert complexes capture and abstract the most important properties of such boundary value problems, leading to generalizations of important classical results such as the Hodge decomposition theorem. They also provide the proper setting for numerical approximations. We also provide an abstract framework for evolution problems in these spaces: Bochner spaces. We next turn to approximation. We build layers of abstraction, progressing from functions, to differential forms, and finally, to Hilbert complexes. We explore finite element exterior calculus (FEEC), which allows us to approximate solutions involving differential forms, and analyze the approximation error. In the second part, we prove our central results. We first prove an extension of current error estimates for the elliptic problem in Hilbert complexes. This extension handles solutions with nonzero harmonic part. Next, we consider evolution problems in Hilbert complexes and prove abstract error estimates. We apply these estimates to the problem for Riemannian hypersurfaces in R. {n+1},generalizing current results for open subsets of R. {n}. Finally, we applysome of the concepts to a nonlinear problem, the Ricci flow on surfaces, and use tools from nonlinear analysis to help develop and analyze the equations. In the appendices, we detail some additional motivation and a source for further examples: canonical geometries that are realized as steady-state solutions to parabolic equations similar to that of Ricci flow. An eventual goal is to compute such solutions using the methods of the previous chapters.

How long does it take to boil an egg? A simple approach to the energy transfer equation

NASA Astrophysics Data System (ADS)

Roura, P.; Fort, J.; Saurina, J.

2000-01-01

The heating of simple geometric objects immersed in an isothermal bath is analysed qualitatively through Fourier's law. The approximate temperature evolution is compared with the exact solution obtained by solving the transport differential equation, the discrepancies being smaller than 20%. Our method succeeds in giving the solution as a function of the Fourier modulus so that the scale laws hold. It is shown that the time needed to homogenize temperature variations that extend over mean distances xm is approximately xm2/icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/>, where icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/> is the thermal diffusivity. This general relationship also applies to atomic diffusion. Within the approach presented there is no need to write down any differential equation. As an example, the analysis is applied to the process of boiling an egg.

Geometric algebra description of polarization mode dispersion, polarization-dependent loss, and Stokes tensor transformations.

PubMed

Soliman, George; Yevick, David; Jessop, Paul

2014-09-01

This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.

Evidence of at least two evolutionary lineages in Melipona subnitida (Apidae, Meliponini) suggested by mtDNA variability and geometric morphometrics of forewings.

PubMed

Bonatti, Vanessa; Simões, Zilá Luz Paulino; Franco, Fernando Faria; Francoy, Tiago Mauricio

2014-01-01

Melipona subnitida, a tropical stingless bee, is an endemic species of the Brazilian northeast and exhibits great potential for honey and pollen production in addition to its role as one of the main pollinators of the Caatinga biome. To understand the genetic structure and better assist in the conservation of this species, we characterized the population variability of M. subnitida using geometric morphometrics of the forewing and cytochrome c oxidase I gene fragment sequencing. We collected workers from six localities in the northernmost distribution. Both methodologies indicated that the variability among the sampled populations is related both to the environment in which samples were collected and the geographical distance between the sampling sites, indicating that differentiation among the populations is due to the existence of at least evolutionary lineages. Molecular clock data suggest that this differentiation may have begun in the middle Pleistocene, approximately 396 kya. The conservation of all evolutionary lineages is important since they can present differential resistance to environmental changes, as resistance to drought and diseases.

Evidence of at least two evolutionary lineages in Melipona subnitida (Apidae, Meliponini) suggested by mtDNA variability and geometric morphometrics of forewings

NASA Astrophysics Data System (ADS)

Bonatti, Vanessa; Simões, Zilá Luz Paulino; Franco, Fernando Faria; Francoy, Tiago Mauricio

2014-01-01

Melipona subnitida, a tropical stingless bee, is an endemic species of the Brazilian northeast and exhibits great potential for honey and pollen production in addition to its role as one of the main pollinators of the Caatinga biome. To understand the genetic structure and better assist in the conservation of this species, we characterized the population variability of M. subnitida using geometric morphometrics of the forewing and cytochrome c oxidase I gene fragment sequencing. We collected workers from six localities in the northernmost distribution. Both methodologies indicated that the variability among the sampled populations is related both to the environment in which samples were collected and the geographical distance between the sampling sites, indicating that differentiation among the populations is due to the existence of at least evolutionary lineages. Molecular clock data suggest that this differentiation may have begun in the middle Pleistocene, approximately 396 kya. The conservation of all evolutionary lineages is important since they can present differential resistance to environmental changes, as resistance to drought and diseases.

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Newman, James C., III; Barnwell, Richard W.; Taylor, Arthur C., III; Hou, Gene J.-W.

1998-01-01

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Probing Mechanoregulation of Neuronal Differentiation by Plasma Lithography Patterned Elastomeric Substrates

NASA Astrophysics Data System (ADS)

Nam, Ki-Hwan; Jamilpour, Nima; Mfoumou, Etienne; Wang, Fei-Yue; Zhang, Donna D.; Wong, Pak Kin

2014-11-01

Cells sense and interpret mechanical cues, including cell-cell and cell-substrate interactions, in the microenvironment to collectively regulate various physiological functions. Understanding the influences of these mechanical factors on cell behavior is critical for fundamental cell biology and for the development of novel strategies in regenerative medicine. Here, we demonstrate plasma lithography patterning on elastomeric substrates for elucidating the influences of mechanical cues on neuronal differentiation and neuritogenesis. The neuroblastoma cells form neuronal spheres on plasma-treated regions, which geometrically confine the cells over two weeks. The elastic modulus of the elastomer is controlled simultaneously by the crosslinker concentration. The cell-substrate mechanical interactions are also investigated by controlling the size of neuronal spheres with different cell seeding densities. These physical cues are shown to modulate with the formation of focal adhesions, neurite outgrowth, and the morphology of neuroblastoma. By systematic adjustment of these cues, along with computational biomechanical analysis, we demonstrate the interrelated mechanoregulatory effects of substrate elasticity and cell size. Taken together, our results reveal that the neuronal differentiation and neuritogenesis of neuroblastoma cells are collectively regulated via the cell-substrate mechanical interactions.

The shape of a long leaf

PubMed Central

Liang, Haiyi; Mahadevan, L.

2009-01-01

Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology. PMID:19966215

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1994-01-01

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent flow example; both geometric-shape and flow-condition design variables are considered. Several methods are tested; results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method; for six independent variables, it is at least two to four times faster than central finite differences and requires only 60 percent more memory than the original code; the performance is expected to improve further in the future.

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.

[Differentiation by geometric morphometrics among 11 Anopheles (Nyssorhynchus) in Colombia].

PubMed

Calle, David Alonso; Quiñones, Martha Lucía; Erazo, Holmes Francisco; Jaramillo, Nicolás

2008-09-01

The correct identification of the Anopheles species of the subgenus Nyssorhynchus is important because this subgenus includes the main malaria vectors in Colombia. This information is necessary for focusing a malaria control program. Geometric morphometrics were used to evaluate morphometric variation of 11 species of subgenus Nyssorhynchus present in Colombia and to distinguish females of each species. Materials and methods. The specimens were obtained from series and family broods from females collected with protected human hosts as attractants. The field collected specimens and their progeny were identified at each of the associated stages by conventional keys. For some species, wild females were used. Landmarks were selected on wings from digital pictures from 336 individuals, and digitized with coordinates. The coordinate matrix was processed by generalized Procrustes analysis which generated size and shape variables, free of non-biological variation. Size and shape variables were analyzed by univariate and multivariate statistics. The subdivision of subgenus Nyssorhynchus in sections is not correlated with wing shape. Discriminant analyses correctly classified 97% of females in the section Albimanus and 86% in the section Argyritarsis. In addition, these methodologies allowed the correct identification of 3 sympatric species from Putumayo which have been difficult to identify in the adult female stage. The geometric morphometrics were demonstrated to be a very useful tool as an adjunct to taxonomy of females the use of this method is recommended in studies of the subgenus Nyssorhynchus in Colombia.

The analysis of control trajectories using symbolic and database computing

NASA Technical Reports Server (NTRS)

Grossman, Robert

1995-01-01

This final report comprises the formal semi-annual status reports for this grant for the periods June 30-December 31, 1993, January 1-June 30, 1994, and June 1-December 31, 1994. The research supported by this grant is broadly concerned with the symbolic computation, mixed numeric-symbolic computation, and database computation of trajectories of dynamical systems, especially control systems. A review of work during the report period covers: trajectories and approximating series, the Cayley algebra of trees, actions of differential operators, geometrically stable integration algorithms, hybrid systems, trajectory stores, PTool, and other activities. A list of publications written during the report period is attached.

Manifolds, Tensors, and Forms

NASA Astrophysics Data System (ADS)

Renteln, Paul

2013-11-01

Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.

Systems of conservation laws with third-order Hamiltonian structures

NASA Astrophysics Data System (ADS)

Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

2018-06-01

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2, classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

Profound Effect of Profiling Platform and Normalization Strategy on Detection of Differentially Expressed MicroRNAs – A Comparative Study

PubMed Central

Meyer, Swanhild U.; Kaiser, Sebastian; Wagner, Carola; Thirion, Christian; Pfaffl, Michael W.

2012-01-01

Background Adequate normalization minimizes the effects of systematic technical variations and is a prerequisite for getting meaningful biological changes. However, there is inconsistency about miRNA normalization performances and recommendations. Thus, we investigated the impact of seven different normalization methods (reference gene index, global geometric mean, quantile, invariant selection, loess, loessM, and generalized procrustes analysis) on intra- and inter-platform performance of two distinct and commonly used miRNA profiling platforms. Methodology/Principal Findings We included data from miRNA profiling analyses derived from a hybridization-based platform (Agilent Technologies) and an RT-qPCR platform (Applied Biosystems). Furthermore, we validated a subset of miRNAs by individual RT-qPCR assays. Our analyses incorporated data from the effect of differentiation and tumor necrosis factor alpha treatment on primary human skeletal muscle cells and a murine skeletal muscle cell line. Distinct normalization methods differed in their impact on (i) standard deviations, (ii) the area under the receiver operating characteristic (ROC) curve, (iii) the similarity of differential expression. Loess, loessM, and quantile analysis were most effective in minimizing standard deviations on the Agilent and TLDA platform. Moreover, loess, loessM, invariant selection and generalized procrustes analysis increased the area under the ROC curve, a measure for the statistical performance of a test. The Jaccard index revealed that inter-platform concordance of differential expression tended to be increased by loess, loessM, quantile, and GPA normalization of AGL and TLDA data as well as RGI normalization of TLDA data. Conclusions/Significance We recommend the application of loess, or loessM, and GPA normalization for miRNA Agilent arrays and qPCR cards as these normalization approaches showed to (i) effectively reduce standard deviations, (ii) increase sensitivity and accuracy of differential miRNA expression detection as well as (iii) increase inter-platform concordance. Results showed the successful adoption of loessM and generalized procrustes analysis to one-color miRNA profiling experiments. PMID:22723911

Analysis of Geometric Thinking Students’ and Process-Guided Inquiry Learning Model

NASA Astrophysics Data System (ADS)

Hardianti, D.; Priatna, N.; Priatna, B. A.

2017-09-01

This research aims to analysis students’ geometric thinking ability and theoretically examine the process-oriented guided iquiry (POGIL) model. This study uses qualitative approach with descriptive method because this research was done without any treatment on subjects. Data were collected naturally. This study was conducted in one of the State Junior High School in Bandung. The population was second grade students and the sample was 32 students. Data of students’ geometric thinking ability were collected through geometric thinking test. These questions are made based on the characteristics of geometry thinking based on van hiele’s theory. Based on the results of the analysis and discussion, students’ geometric thinking ability is still low so it needs to be improved. Therefore, an effort is needed to overcome the problems related to students’ geometric thinking ability. One of the efforts that can be done by doing the learning that can facilitate the students to construct their own geometry concept, especially quadrilateral’s concepts so that students’ geometric thinking ability can enhance maximally. Based on study of the theory, one of the learning models that can enhance the students’ geometric thinking ability is POGIL model.

Simplified and refined finite element approaches for determining stresses and internal forces in geometrically nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Robinson, J. C.

1979-01-01

Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.

Geometric analysis and restitution of digital multispectral scanner data arrays

NASA Technical Reports Server (NTRS)

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

1975-01-01

An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.

Selection of reference genes for expression studies with fish myogenic cell cultures.

PubMed

Bower, Neil I; Johnston, Ian A

2009-08-10

Relatively few studies have used cell culture systems to investigate gene expression and the regulation of myogenesis in fish. To produce robust data from quantitative real-time PCR mRNA levels need to be normalised using internal reference genes which have stable expression across all experimental samples. We have investigated the expression of eight candidate genes to identify suitable reference genes for use in primary myogenic cell cultures from Atlantic salmon (Salmo salar L.). The software analysis packages geNorm, Normfinder and Best keeper were used to rank genes according to their stability across 42 samples during the course of myogenic differentiation. Initial results showed several of the candidate genes exhibited stable expression throughout myogenic culture while Sdha was identified as the least stable gene. Further analysis with geNorm, Normfinder and Bestkeeper identified Ef1alpha, Hprt1, Ppia and RNApolII as stably expressed. Comparison of data normalised with the geometric average obtained from combinations of any three of these genes showed no significant differences, indicating that any combination of these genes is valid. The geometric average of any three of Hprt1, Ef1alpha, Ppia and RNApolII is suitable for normalisation of gene expression data in primary myogenic cultures from Atlantic salmon.

A new approach for shaping of dual-reflector antennas

NASA Technical Reports Server (NTRS)

Lee, Teh-Hong; Burnside, W. D.; Rudduck, Roger C.

1987-01-01

The shaping of 2-D dual-reflector antenna systems to generate a prescribed distribution with uniform phase at the aperture of the second reflector is examined. This method is based on the geometrical nature of Cassegrain and Gregorian dual-reflector antennas. The method of syntheses satisfies the principles of geometrical optics which are the foundations of dual-reflector designs. Instead of setting up differential equations or heuristically designing the subreflector, a set of algebraic equations is formulated and solved numerically to obtain the desired surfaces. The caustics of the reflected rays from the subreflector can be obtained and examined. Several examples of 2-D dual-reflector shaping are shown to validate the study. Geometrical optics and physical optics are used to calculate the scattered fields from the reflectors.

Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

NASA Astrophysics Data System (ADS)

Farajpour, Ali; Arab Solghar, Alireza; Shahidi, Alireza

2013-01-01

In this article, the nonlinear buckling characteristics of multi-layered graphene sheets are investigated. The graphene sheet is modeled as an orthotropic nanoplate with size-dependent material properties. The graphene film is subjected by non-uniformly distributed in-plane load through its thickness. To include the small scale and the geometrical nonlinearity effects, the governing differential equations are derived based on the nonlocal elasticity theory in conjunction with the von Karman geometrical model. Explicit expressions for the postbuckling loads of single- and double-layered graphene sheets with simply supported edges under biaxial compression are obtained. For numerical results, six types of armchair and zigzag graphene sheets with different aspect ratio are considered. The present formulation and method of solution are validated by comparing the results, in the limit cases, with those available in the open literature. Excellent agreement between the obtained and available results is observed. Finally, the effects of nonlocal parameter, buckling mode number, compression ratio and non-uniform parameter on the postbuckling behavior of multi-layered graphene sheets are studied.

Polymeric Helical Microactuators: Achieving High Speed and High Extension.

NASA Astrophysics Data System (ADS)

Kim, Yongjin; Crosby, Alfred

We proposed novel concepts of actuation mechanism and fabrication method to induce fast and highly extensional motion in polymeric actuators. Exceptionally high extensional strain over 1400% was realized by the geometric transformation from a helix to a stretched ribbon in a responsive and reversible manner. As a model system, sub-micron sized helices were fabricated from a self-assembled, UV-cured, thermo-responsive polymer. By controlling the size and the geometrical asymmetries in the system, a combined effect of surface tension and differential volumetric strain during the transition between swollen-deswollen state induced by phase transition of the material was successfully utilized to generate torsional stresses in the system. For the full understanding of the results, a finite element analysis and measurements on the poroelastic properties of the material were conducted as well as a demonstration on macroscopic system made with PDMS. Finally, remaining questions on the chirality of helices were presented. This material is based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/Grant Number W911NF-15-1-0358.

Domain decomposition for aerodynamic and aeroacoustic analyses, and optimization

NASA Technical Reports Server (NTRS)

Baysal, Oktay

1995-01-01

The overarching theme was the domain decomposition, which intended to improve the numerical solution technique for the partial differential equations at hand; in the present study, those that governed either the fluid flow, or the aeroacoustic wave propagation, or the sensitivity analysis for a gradient-based optimization. The role of the domain decomposition extended beyond the original impetus of discretizing geometrical complex regions or writing modular software for distributed-hardware computers. It induced function-space decompositions and operator decompositions that offered the valuable property of near independence of operator evaluation tasks. The objectives have gravitated about the extensions and implementations of either the previously developed or concurrently being developed methodologies: (1) aerodynamic sensitivity analysis with domain decomposition (SADD); (2) computational aeroacoustics of cavities; and (3) dynamic, multibody computational fluid dynamics using unstructured meshes.

Delay differential analysis of time series.

PubMed

Lainscsek, Claudia; Sejnowski, Terrence J

2015-03-01

Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Dose impact in radiographic lung injury following lung SBRT: Statistical analysis and geometric interpretation

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

Yu, Victoria; Kishan, Amar U.; Cao, Minsong

2014-03-15

Purpose: To demonstrate a new method of evaluating dose response of treatment-induced lung radiographic injury post-SBRT (stereotactic body radiotherapy) treatment and the discovery of bimodal dose behavior within clinically identified injury volumes. Methods: Follow-up CT scans at 3, 6, and 12 months were acquired from 24 patients treated with SBRT for stage-1 primary lung cancers or oligometastic lesions. Injury regions in these scans were propagated to the planning CT coordinates by performing deformable registration of the follow-ups to the planning CTs. A bimodal behavior was repeatedly observed from the probability distribution for dose values within the deformed injury regions. Basedmore » on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the critical dose level that is potentially inductive of post-SBRT lung injury. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the injury volume with good consistency. The average Kullback-Leibler divergence values between the empirical differential dose volume histogram and the EM-obtained Gaussian mixture distribution were calculated to be 0.069, 0.063, and 0.092 for the 3, 6, and 12 month follow-up groups, respectively. The lower Gaussian component was located at approximately 70% prescription dose (35 Gy) for all three follow-up time points. The higher Gaussian component, contributed by the dose received by planning target volume, was located at around 107% of the prescription dose. Geometrical analysis suggests the mean of the lower Gaussian component, located at 35 Gy, as a possible indicator for a critical dose that induces lung injury after SBRT. Conclusions: An innovative and improved method for analyzing the correspondence between lung radiographic injury and SBRT treatment dose has been demonstrated. Bimodal behavior was observed in the dose distribution of lung injury after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak at approximately 35 Gy, or 70% prescription dose, is a good indication of a critical dose for injury. The determined critical dose of 35 Gy resembles the critical dose volume limit of 30 Gy for ipsilateral bronchus in RTOG 0618 and results from previous studies. The authors seek to further extend this improved analysis method to a larger cohort to better understand the interpatient variation in radiographic lung injury dose response post-SBRT.« less

3D Facial Pattern Analysis for Autism

DTIC Science & Technology

2010-07-01

each individual’s data were scaled by the geometric mean of all possible linear distances between landmarks, following. The first two principal...over traditional template matching in that it can represent geometrical and non- geometrical changes of an object in the parametric template space...set of vertex templates can be generated from the root template by geometric or non- geometric transformation. Let Mtt ,...1 be M normalized vertex

Geometric Analysis of Wing Sections

DOT National Transportation Integrated Search

1995-04-01

This paper describes a new geometric analysis procedure for wing sections. This procedure is based on the normal mode analysis for continuous functions. A set of special shape functions is introduced to represent the geometry of the wing section. The...

Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

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

De Nittis, Giuseppe, E-mail: gidenittis@mat.puc.cl; Gomi, Kiyonori, E-mail: kgomi@math.shinshu-u.ac.jp

2016-05-15

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related “Real” (resp. “Quaternionic”) Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] for the “Quaternionic” case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. Demore » Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the “Real” case we generalize the Chern-Weil theory and we show that the assignment of a “Real” connection, along with the related differential Chern class and its holonomy, suffices for the classification of “Real” vector bundles in low dimensions.« less

Genetic and Morphological Differentiation of the Semiterrestrial Crab Armases angustipes (Brachyura: Sesarmidae) along the Brazilian Coast.

PubMed

Marochi, Murilo Zanetti; Masunari, Setuko; Schubart, Christoph D

2017-02-01

The genetic and morphometric population structures of the semiterrestrial crab Armases angustipes from along the Brazilian coast were examined. The influence of the Central South Equatorial Current on larval dispersal of A. angustipes also was evaluated. Six populations were sampled from estuarine areas in São Luis do Maranhão, Maranhão; Natal, Rio Grande do Norte; Maceió, Alagoas; Ilhéus, Bahia; Aracruz, Espírito Santo; and Guaratuba, Paraná. Patterns of genetic differentiation were assessed using DNA sequence data corresponding to parts of the mitochondrial cytochrome c oxidase subunit 1. Geometric morphometric techniques were used to evaluate morphological variation in shape and size of the carapace and right cheliped propodus. Our results revealed low genetic variability and lack of phylogeographic structure; geometric morphometrics showed statistically significant morphological differentiation and geographic structuring. Our data indicate the absence of possible barriers to gene flow for this mobile species, and no clear correlation of morphological or genetic variation with ocean currents and/or geographic distance. Our results also suggest that historical geological and climatological events and/or possible bottleneck effects influenced the current low genetic variability among the populations of A. angustipes.

Geometric, Kinematic and Radiometric Aspects of Image-Based Measurements

NASA Technical Reports Server (NTRS)

Liu, Tianshu

2002-01-01

This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.

Nonlinear Geometric and Differential Geometric Guidance of UAVs with Vision Sensing for Reactive Obstacle Avoidance

DTIC Science & Technology

2010-09-29

1 1 1 2 2 2ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ0 0 0 0 0 0 0 0 0 0 T r ob ob ob ob ob ob tr tr trX r r rθ φ θ φ θ φ= (3.28) 29...ˆ ˆ ˆ ˆˆ ˆ ˆ0 0 0 0 0 0 0 T r ob ob ob tr tr trX r rθ φ θ φ⎡ ⎤= ⎣ ⎦ (3.29) Since obstacles are assumed to be point obstacles, it

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.

Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

NASA Astrophysics Data System (ADS)

Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

2018-05-01

A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Integrated multidisciplinary design optimization using discrete sensitivity analysis for geometrically complex aeroelastic configurations

NASA Astrophysics Data System (ADS)

Newman, James Charles, III

1997-10-01

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the time-dependent, nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional cases and a Gauss-Seidel algorithm for the three-dimensional; at steady-state, similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Various surface parameterization techniques have been employed in the current study to control the shape of the design surface. Once this surface has been deformed, the interior volume of the unstructured grid is adapted by considering the mesh as a system of interconnected tension springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR, an advanced automatic-differentiation software tool. To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for several two- and three-dimensional cases. In twodimensions, an initially symmetric NACA-0012 airfoil and a high-lift multielement airfoil were examined. For the three-dimensional configurations, an initially rectangular wing with uniform NACA-0012 cross-sections was optimized; in addition, a complete Boeing 747-200 aircraft was studied. Furthermore, the current study also examines the effect of inconsistency in the order of spatial accuracy between the nonlinear fluid and linear shape sensitivity equations. The second step was to develop a computationally efficient, high-fidelity, integrated static aeroelastic analysis procedure. To accomplish this, a structural analysis code was coupled with the aforementioned unstructured grid aerodynamic analysis solver. The use of an unstructured grid scheme for the aerodynamic analysis enhances the interaction compatibility with the wing structure. The structural analysis utilizes finite elements to model the wing so that accurate structural deflections may be obtained. In the current work, parameters have been introduced to control the interaction of the computational fluid dynamics and structural analyses; these control parameters permit extremely efficient static aeroelastic computations. To demonstrate and evaluate this procedure, static aeroelastic analysis results for a flexible wing in low subsonic, high subsonic (subcritical), transonic (supercritical), and supersonic flow conditions are presented.

Surface Curvature Differentially Regulates Stem Cell Migration and Differentiation via Altered Attachment Morphology and Nuclear Deformation

PubMed Central

Werner, Maike; Blanquer, Sébastien B. G.; Haimi, Suvi P.; Korus, Gabriela; Dunlop, John W. C.; Duda, Georg N.; Grijpma, Dirk. W.

2016-01-01

Signals from the microenvironment around a cell are known to influence cell behavior. Material properties, such as biochemical composition and substrate stiffness, are today accepted as significant regulators of stem cell fate. The knowledge of how cell behavior is influenced by 3D geometric cues is, however, strongly limited despite its potential relevance for the understanding of tissue regenerative processes and the design of biomaterials. Here, the role of surface curvature on the migratory and differentiation behavior of human mesenchymal stem cells (hMSCs) has been investigated on 3D surfaces with well‐defined geometric features produced by stereolithography. Time lapse microscopy reveals a significant increase of cell migration speed on concave spherical compared to convex spherical structures and flat surfaces resulting from an upward‐lift of the cell body due to cytoskeletal forces. On convex surfaces, cytoskeletal forces lead to substantial nuclear deformation, increase lamin‐A levels and promote osteogenic differentiation. The findings of this study demonstrate a so far missing link between 3D surface curvature and hMSC behavior. This will not only help to better understand the role of extracellular matrix architecture in health and disease but also give new insights in how 3D geometries can be used as a cell‐instructive material parameter in the field of biomaterial‐guided tissue regeneration. PMID:28251054

Identifying phase-space boundaries with Voronoi tessellations

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

Debnath, Dipsikha; Gainer, James S.; Kilic, Can

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here in this paper we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be usedmore » to corroborate a new physics discovery based on a cut-and-count analysis.« less

Dynamic characteristics of organic bulk-heterojunction solar cells

NASA Astrophysics Data System (ADS)

Babenko, S. D.; Balakai, A. A.; Moskvin, Yu. L.; Simbirtseva, G. V.; Troshin, P. A.

2010-12-01

Transient characteristics of organic bulk-heterojunction solar cells have been studied using pulsed laser probing. An analysis of the photoresponse waveforms of a typical solar cell measured by varying load resistance within broad range at different values of the bias voltage provided detailed information on the photocell parameters that characterize electron-transport properties of active layers. It is established that the charge carrier mobility is sufficient to ensure high values of the fill factor (˜0.6) in the obtained photocells. On approaching the no-load voltage, the differential capacitance of the photocell exhibits a sixfold increase as compared to the geometric capacitance. A possible mechanism of recombination losses in the active medium is proposed.

Identifying phase-space boundaries with Voronoi tessellations

DOE PAGES

Debnath, Dipsikha; Gainer, James S.; Kilic, Can; ...

2016-11-24

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here in this paper we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be usedmore » to corroborate a new physics discovery based on a cut-and-count analysis.« less

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

PubMed

Gruenert, Gerd; Ibrahim, Bashar; Lenser, Thorsten; Lohel, Maiko; Hinze, Thomas; Dittrich, Peter

2010-06-07

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly. PMID:20529264

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Green, Lawrence L.; Newman, Perry A.; Putko, Michele M.

2003-01-01

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Green, Lawrence L.; Newman, Perry A.; Putko, Michele M.

2001-01-01

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Differentiation of fibroblastic meningiomas from other benign subtypes using diffusion tensor imaging.

PubMed

Tropine, Andrei; Dellani, Paulo D; Glaser, Martin; Bohl, Juergen; Plöner, Till; Vucurevic, Goran; Perneczky, Axel; Stoeter, Peter

2007-04-01

To differentiate fibroblastic meningiomas, usually considered to be of a hard consistency, from other benign subtypes using diffusion tensor imaging (DTI). From DTI data sets of 30 patients with benign meningiomas, we calculated diffusion tensors and mean diffusivity (MD) and fractional anisotropy (FA) maps as well as barycentric maps representing the geometrical shape of the tensors. The findings were compared to postoperative histology. The study was approved by the local ethics committee, and informed consent was given by the patients. According to one-way analysis of variance (ANOVA), FA was the best parameter to differentiate between the subtypes (F=32.2; p<0.0001). Regarding tensor shape, endothelial meningiomas were represented by spherical tensors (80%) corresponding to isotropic diffusion, whereas the fibroblastic meningiomas showed a high percentage (43%) of nonspherical tensors, indicating planar or longitudinal diffusion. The difference was highly significant (F=28.4; p<0.0001) and may be due to the fascicular arrangement of long spindle-shaped tumor cells and the high content of intra- and interfascicular fibers as shown in the histology. In addition, a capsule-like rim of the in-plane diffusion surrounded most meningiomas irrespective of their histological type. If these results correlate to the intraoperative findings of meningioma consistency, DTI-based measurement of FA and analysis of the shape of the diffusion tensor is a promising method to differentiate between fibroblastic and other subtypes of benign meningiomas in order to get information about their "hard" or "soft" consistency prior to removal. Copyright (c) 2007 Wiley-Liss, Inc.

Simple agarose micro-confinement array and machine-learning-based classification for analyzing the patterned differentiation of mesenchymal stem cells

PubMed Central

Sato, Asako; Vogel, Viola; Tanaka, Yo

2017-01-01

The geometrical confinement of small cell colonies gives differential cues to cells sitting at the periphery versus the core. To utilize this effect, for example to create spatially graded differentiation patterns of human mesenchymal stem cells (hMSCs) in vitro or to investigate underpinning mechanisms, the confinement needs to be robust for extended time periods. To create highly repeatable micro-fabricated structures for cellular patterning and high-throughput data mining, we employed here a simple casting method to fabricate more than 800 adhesive patches confined by agarose micro-walls. In addition, a machine learning based image processing software was developed (open code) to detect the differentiation patterns of the population of hMSCs automatically. Utilizing the agarose walls, the circular patterns of hMSCs were successfully maintained throughout 15 days of cell culture. After staining lipid droplets and alkaline phosphatase as the markers of adipogenic and osteogenic differentiation, respectively, the mega-pixels of RGB color images of hMSCs were processed by the software on a laptop PC within several minutes. The image analysis successfully showed that hMSCs sitting on the more central versus peripheral sections of the adhesive circles showed adipogenic versus osteogenic differentiation as reported previously, indicating the compatibility of patterned agarose walls to conventional microcontact printing. In addition, we found a considerable fraction of undifferentiated cells which are preferentially located at the peripheral part of the adhesive circles, even in differentiation-inducing culture media. In this study, we thus successfully demonstrated a simple framework for analyzing the patterned differentiation of hMSCs in confined microenvironments, which has a range of applications in biology, including stem cell biology. PMID:28380036

Bisimulation equivalence of differential-algebraic systems

NASA Astrophysics Data System (ADS)

Megawati, Noorma Yulia; Schaft, Arjan van der

2018-01-01

In this paper, the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterisation of bisimulation relations, and an algorithm for computing the maximal bisimulation relation between two linear DAE systems. The general definition is specialised to the case where the matrix pencil sE - A is regular. Furthermore, by developing a one-sided version of bisimulation, characterisations of simulation and abstraction are obtained.

Analysis of hysteresis effect on the vibration motion of a bimodal non-uniform micro-cantilever using MCS theory

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Korayem, A. H.; Hosseini Hashemi, Sh.

2016-02-01

Nowadays, to enhance the performance of atomic force microscopy (AFM) micro-cantilevers (MCs) during imaging, reduce costs and increase the surface topography precision, advanced MCs equipped with piezoelectric layers are utilized. Using the modified couple stress (MCS) theory not only makes the modeling more exhaustive, but also increases the accuracy of prediction of the vibration behavior of the system. In this paper, Hamilton's principle by consideration of the MCS theory has been used to extract the equations. In addition, to discretize the equations, differential quadrature method has been adopted. Analysis of the hysteresis effect on the vibration behavior of the AFM MC is of significant importance. Thus, to model the hysteresis effect, Bouc-Wen method, which is solved simultaneously with the vibration equations of non-uniform Timoshenko beam, has been utilized. Furthermore, a bimodal excitation of the MC has been considered. The results reveal that the hysteresis effect appears as a phase difference in the time response. Finally, the effect of the geometric parameters on the vibration frequency of the system which is excited by combination of the first two vibration modes of the non-uniform piezoelectric MC has been examined. The results indicate the considerable effect of the MC length in comparison with other geometric parameters such as the MC width and thickness.

Comparison of Interferometric Time-Series Analysis Techniques with Implications for Future Mission Design

NASA Astrophysics Data System (ADS)

Werner, C. L.; Wegmuller, U.; Strozzi, T.; Wiesmann, A.

2006-12-01

Principle contributors to the noise in differential SAR interferograms are temporal phase stability of the surface, geometry relating to baseline and surface slope, and propagation path delay variations due to tropospheric water vapor and the ionosphere. Time series analysis of multiple interferograms generated from a stack of SAR SLC images seeks to determine the deformation history of the surface while reducing errors. Only those scatterers within a resolution element that are stable and coherent for each interferometric pair contribute to the desired deformation signal. Interferograms with baselines exceeding 1/3 the critical baseline have substantial geometrical decorrelation for distributed targets. Short baseline pairs with multiple reference scenes can be combined using least-squares estimation to obtain a global deformation solution. Alternately point-like persistent scatterers can be identified in scenes that do not exhibit geometrical decorrelation associated with large baselines. In this approach interferograms are formed from a stack of SAR complex images using a single reference scene. Stable distributed scatter pixels are excluded however due to the presence of large baselines. We apply both point- based and short-baseline methodologies and compare results for a stack of fine-beam Radarsat data acquired in 2002-2004 over a rapidly subsiding oil field near Lost Hills, CA. We also investigate the density of point-like scatters with respect to image resolution. The primary difficulty encountered when applying time series methods is phase unwrapping errors due to spatial and temporal gaps. Phase unwrapping requires sufficient spatial and temporal sampling. Increasing the SAR range bandwidth increases the range resolution as well as increasing the critical interferometric baseline that defines the required satellite orbital tube diameter. Sufficient spatial sampling also permits unwrapping because of the reduced phase/pixel gradient. Short time intervals further reduce the differential phase due to deformation when the deformation is continuous. Lower frequency systems (L- vs. C-Band) substantially improve the ability to unwrap the phase correctly by directly reducing both interferometric phase amplitude and temporal decorrelation.

Comment on Schuster's Technique for Focusing the Prism Spectrometer.

ERIC Educational Resources Information Center

Beynon, John

1991-01-01

Discussed is the physics that underpins Schuster's technique for obtaining a parallel light beam for use in various prism and grating experiments. Basic physics concepts using geometrical optics of prism, together with elementary differential calculus are explained as well as the mechanics of Schuster's technique. (KR)

Fractal Analysis in Agrophysics

USDA-ARS?s Scientific Manuscript database

The geometric irregularity is an intrinsic property of soils and plants. This geometric irregularity is easy to perceive and observe, but quantifying it has long presented a daunting challenge. Such quantifying is imperative because the geometric irregularity is the cause and the reflection of spati...

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.

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.

Propagation of Polarization Modulated Beams Through a Turbulent Atmosphere

DTIC Science & Technology

2014-11-24

Clifford Algebra to Geometric Calculus , Reidel, 1984. Hirschfelder, J.O., Curtiss, C.F. & Bird, R.B., Molecular Theory of Gases and Liquids, Wiley, 1954...are made explicit in a Poincaré sphere and geometric (Clifford) algebra representation. Section 5.0 of this report provides the evidence supporting...MEDIA 4.0 LABORATORY TEST CONFIGURATIONS 5.0 TEST RESULTS 5.1 DATA ANALYSIS METHODS 5.2 DATA ANALYSIS 6.0 GEOMETRIC ALGEBRA 6.1 INTRODUCTION

Geometric Theory of Moving Grid Wavefront Sensor

DTIC Science & Technology

1977-06-30

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

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.

Differential segregation in a cell-cell contact interface: the dynamics of the immunological synapse.

PubMed Central

Burroughs, Nigel John; Wülfing, Christoph

2002-01-01

Receptor-ligand couples in the cell-cell contact interface between a T cell and an antigen-presenting cell form distinct geometric patterns and undergo spatial rearrangement within the contact interface. Spatial segregation of the antigen and adhesion receptors occurs within seconds of contact, central aggregation of the antigen receptor then occurring over 1-5 min. This structure, called the immunological synapse, is becoming a paradigm for localized signaling. However, the mechanisms driving its formation, in particular spatial segregation, are currently not understood. With a reaction diffusion model incorporating thermodynamics, elasticity, and reaction kinetics, we examine the hypothesis that differing bond lengths (extracellular domain size) is the driving force behind molecular segregation. We derive two key conditions necessary for segregation: a thermodynamic criterion on the effective bond elasticity and a requirement for the seeding/nucleation of domains. Domains have a minimum length scale and will only spontaneously coalesce/aggregate if the contact area is small or the membrane relaxation distance large. Otherwise, differential attachment of receptors to the cytoskeleton is required for central aggregation. Our analysis indicates that differential bond lengths have a significant effect on synapse dynamics, i.e., there is a significant contribution to the free energy of the interaction, suggesting that segregation by differential bond length is important in cell-cell contact interfaces and the immunological synapse. PMID:12324401

A Genetic Analysis of Taoyuan Pig and Its Phylogenetic Relationship to Eurasian Pig Breeds

PubMed Central

Li, Kuan-Yi; Li, Kuang-Ti; Cheng, Chun-Chun; Chen, Chia-Hsuan; Hung, Chien-Yi; Ju, Yu-Ten

2015-01-01

Taoyuan pig is a native Taiwan breed. According to the historical record, the breed was first introduced to Taiwan from Guangdong province, Southern China, around 1877. The breed played an important role in Taiwan’s early swine industry. It was classified as an indigenous breed in 1986. After 1987, a conserved population of Taoyuan pig was collected and reared in isolation. In this study, mitochondrial DNA sequences and 18 microsatellite markers were used to investigate maternal lineage and genetic diversity within the Taoyuan pig population. Population differentiation among Taoyuan, Asian type, and European type pig breeds was also evaluated using differentiation indices. Only one D-loop haplotype of the Taoyuan pig was found. It clustered with Lower Changjiang River Basin and Central China Type pig breeds. Based on the polymorphism of microsatellite markers, a positive fixation index value (FIS) indicates that the conserved Taoyuan population suffers from inbreeding. In addition, high FST values (>0.2105) were obtained, revealing high differentiation among these breeds. Non-metric multi-dimensional scaling showed a clear geometric structure among 7 breeds. Together these results indicate that maternally Taoyuan pig originated in the Lower Changjiang River Basin and Central China; however, since being introduced to Taiwan differentiation has occurred. In addition, Taoyuan pig has lost genetic diversity in both its mitochondrial and nuclear genomes. PMID:25656199

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

NASA Astrophysics Data System (ADS)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-07-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+-up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Genetic and Morphological Variation of the Forkbeard, Phycis phycis (Pisces, Phycidae): Evidence of Panmixia and Recent Population Expansion along Its Distribution Area

PubMed Central

Rodrigues, Ana Sofia B.; Sequeira, Vera; Neves, Ana; Paiva, Rafaela Barros

2016-01-01

The knowledge of population structure of a species is essential to effectively assess and manage fisheries. In the present study, genetics, by mitochondrial DNA cytochrome b sequence analysis, and body geometric morphometrics were used to evaluate the existence of distinct populations of the forkbeard (Phycis phycis), an important commercial species in several European countries, especially Portugal and Spain. For geometric morphometric analysis, specimens were collected in the Northeast Atlantic Ocean—Azores, Madeira and mainland Portugal, and for genetic analysis, these samples were complemented with samples collected in the Mediterranean Sea—Spain, Italy and Croatia, in order to cover the entire distribution area of the species. Body shape of the forkbeard from the Northeast Atlantic was found to be highly variable. This variation was probably associated with different environmental factors between the study areas. Despite morphological variation, a low genetic differentiation between samples from different areas was found, most likely due to gene flow that occurred in the past or with the demographic history of the species. Moreover, the presence of unique haplotypes in the Northeast Atlantic and in the Mediterranean suggests that recent gene flow between populations from these areas should be limited. Altogether, a high haplotype diversity, a low nucleotide diversity, a “star-like” network and the results of the mismatch distribution, indicate a possible signature of recent population expansions, which probably started during the end of the Last Glacial Maximum and led to the colonization of the Northeast Atlantic and the Mediterranean. PMID:27941988

Determination of fucoxanthin isomers in microalgae (Isochrysis sp.) by high-performance liquid chromatography coupled with diode-array detector multistage mass spectrometry coupled with positive electrospray ionization.

PubMed

Crupi, Pasquale; Toci, Aline Theodore; Mangini, Silvio; Wrubl, Federico; Rodolfi, Liliana; Tredici, Mario R; Coletta, Antonio; Antonacci, Donato

2013-05-15

Due to their health benefits, there is growing interest in the production and use of carotenoids from natural sources, e.g. microalgae. To date, only Haematococcus pluvialis and Dunaliella, that accumulate, respectively, astaxanthin and β-carotene in large quantities, are grown commercially. However, interest is also being focused on other xanthophylls, such as (all-E)-fucoxanthin characterized by anti-obesity and anti-carcinogenic effects. In this regard, rigorous chemical and analytical techniques following preparative isolation of components are needed to unequivocally identify individual carotenoids in microalgae. The carotenoid profile of Isochrysis sp. biomass, produced in closed photobioreactors, was determined by reversed-phase C30 (RP-30) high-performance liquid chromatography coupled with diode-array detector mass spectrometry using positive electrospray ionization (HPLC/DAD-MS/ESI(+) ) analysis. Additionally, multistage mass spectrometry (MS(n) ) analyses, together with fine structures of the UV-vis spectra, were used to differentiate structural and geometrical isomers. This technique allowed the simultaneous determination of geometrical, isomers of fucoxanthin (all-E-fucoxanthin, 13Z-, 13'Z- and 9'Z-fucoxanthin), diatoxanthin and 5,8-epoxydiadinoxanthin diasteroisomers (R/S). The analyzed extracts contained fucoxanthin isomers as the major carotenoids and, in particular, (all-E)-fucoxanthin was the main geometrical isomer (~85%) found at a concentration of 17 mg/g of the lyophilized biomass. Considering the high content of fucoxanthin in Isochrysis sp. biomass, the microalga could be proposed as a source of this compound for nutraceutical and pharmaceutical applications. Copyright © 2013 John Wiley & Sons, Ltd.

To 3D or Not to 3D, That Is the Question: Do 3D Surface Analyses Improve the Ecomorphological Power of the Distal Femur in Placental Mammals?

PubMed Central

Gould, Francois D. H.

2014-01-01

Improvements in three-dimensional imaging technologies have renewed interest in the study of functional and ecological morphology. Quantitative approaches to shape analysis are used increasingly to study form-function relationships. These methods are computationally intensive, technically demanding, and time-consuming, which may limit sampling potential. There have been few side-by-side comparisons of the effectiveness of such approaches relative to more traditional analyses using linear measurements and ratios. Morphological variation in the distal femur of mammals has been shown to reflect differences in locomotor modes across clades. Thus I tested whether a geometric morphometric analysis of surface shape was superior to a multivariate analysis of ratios for describing ecomorphological patterns in distal femoral variation. A sample of 164 mammalian specimens from 44 genera was assembled. Each genus was assigned to one of six locomotor categories. The same hypotheses were tested using two methods. Six linear measurements of the distal femur were taken with calipers, from which four ratios were calculated. A 3D model was generated with a laser scanner, and analyzed using three dimensional geometric morphometrics. Locomotor category significantly predicted variation in distal femoral morphology in both analyses. Effect size was larger in the geometric morphometric analysis than in the analysis of ratios. Ordination reveals a similar pattern with arboreal and cursorial taxa as extremes on a continuum of morphologies in both analyses. Discriminant functions calculated from the geometric morphometric analysis were more accurate than those calculated from ratios. Both analysis of ratios and geometric morphometric surface analysis reveal similar, biologically meaningful relationships between distal femoral shape and locomotor mode. The functional signal from the morphology is slightly higher in the geometric morphometric analysis. The practical costs of conducting these sorts of analyses should be weighed against potentially slight increases in power when designing protocols for ecomorphological studies. PMID:24633081

Practical quality control tools for curves and surfaces

NASA Technical Reports Server (NTRS)

Small, Scott G.

1992-01-01

Curves (geometry) and surfaces created by Computer Aided Geometric Design systems in the engineering environment must satisfy two basic quality criteria: the geometric shape must have the desired engineering properties; and the objects must be parameterized in a way which does not cause computational difficulty for geometric processing and engineering analysis. Interactive techniques are described which are in use at Boeing to evaluate the quality of aircraft geometry prior to Computational Fluid Dynamic analysis, including newly developed methods for examining surface parameterization and its effects.

LOCAL ORTHOGONAL CUTTING METHOD FOR COMPUTING MEDIAL CURVES AND ITS BIOMEDICAL APPLICATIONS

PubMed Central

Einstein, Daniel R.; Dyedov, Vladimir

2010-01-01

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method called local orthogonal cutting (LOC) for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stability and consistency tests. These concepts lend themselves to robust numerical techniques and result in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods. PMID:20628546

Annealing of aromatic polyimide precursors

NASA Technical Reports Server (NTRS)

Wakelyn, N. T.

1975-01-01

A study has been made of the thermal behavior of polyimide precursors: an isomeric pair of crystals of the complex formed by p-phenylenediamine with the separated isomers of the di-isopropyl ester of pyromellitic acid. Specimens of this material were isothermally annealed in the temperature range 120 C to 170 C for periods of time up to 1 week. Although this temperature range is well below that customarily used for imidizations, the working hypothesis was that it would be more likely that a polymer embodying at least part of the precursor structure could be formed if the molecular motion was minimized to that actually required for the formation of the imide linkage. The progress of the annealing was followed by: infrared spectroscopy, differential thermal analysis, powder X-ray diffraction, and thermal gravimetric analysis. Single crystal X-ray analysis of the meta monomer yields a structure of chains of alternating acid and base and suggests that this monomer is amenable to polymerization with a minimum of geometrical disruption.

Prospective Middle School Mathematics Teachers' Preconceptions of Geometric Translations

ERIC Educational Resources Information Center

Yanik, H. Bahadir

2011-01-01

This article reports an analysis of 44 prospective middle school mathematics teachers' pre-existing knowledge of rigid geometric transformations, specifically the geometric translations. The main data source for this study was the participants' responses to the tasks that were presented during semi-structured clinical interviews. The findings of…

From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

2012-12-01

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, such that each Gn is simply connected. We use the 1-jet of the classifying space W¯ G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The result can be seen as a geometric interpretation of Quillen's (purely algebraic) construction of the adjunction between simplicial Lie algebras and dg-Lie algebras.

On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schlieker, M.

1995-07-01

In this paper explicitly natural (from the geometrical point of view) Fock-space representations (contragradient Verma modules) of the quantized enveloping algebras are constructed. In order to do so, one starts from the Gauss decomposition of the quantum group and introduces the differential operators on the corresponding q-deformed flag manifold (assumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group are expressed as first-order differential operators on the q-deformed flag manifold.

Some methods to regulate low-bias negative differential resistance in σ barrier separating nanoscale molecular transport systems

NASA Astrophysics Data System (ADS)

Shen, Ji-Mei; Liu, Jing; Min, Yi; Zhou, Li-Ping

2016-12-01

Using the first-principles method which combines the nonequilibrium Green’s function (NEGF) with density functional theory (DFT), the role of defect, dopant, barrier length and geometric deformation for low-bias negative differential resistance (NDR) in two capped armchair carbon nanotubes (CNTs) sandwiching σ barrier are systematically analyzed. We found that this method can regulate the negative differential resistance (NDR) effects such as current peak and peak position. The adjusting mechanism may originate from orbital interaction and orbital reconstruction. Our calculations try to manipulate the transport characteristics in energy space by simply manipulating the structure in real space, which may promise the potential applications in nanomolecular-electronics in the future.

Self-similarity in the inertial region of wall turbulence.

PubMed

Klewicki, J; Philip, J; Marusic, I; Chauhan, K; Morrill-Winter, C

2014-12-01

The inverse of the von Kármán constant κ is the leading coefficient in the equation describing the logarithmic mean velocity profile in wall bounded turbulent flows. Klewicki [J. Fluid Mech. 718, 596 (2013)] connects the asymptotic value of κ with an emerging condition of dynamic self-similarity on an interior inertial domain that contains a geometrically self-similar hierarchy of scaling layers. A number of properties associated with the asymptotic value of κ are revealed. This is accomplished using a framework that retains connection to invariance properties admitted by the mean statement of dynamics. The development leads toward, but terminates short of, analytically determining a value for κ. It is shown that if adjacent layers on the hierarchy (or their adjacent positions) adhere to the same self-similarity that is analytically shown to exist between any given layer and its position, then κ≡Φ(-2)=0.381966..., where Φ=(1+√5)/2 is the golden ratio. A number of measures, derived specifically from an analysis of the mean momentum equation, are subsequently used to empirically explore the veracity and implications of κ=Φ(-2). Consistent with the differential transformations underlying an invariant form admitted by the governing mean equation, it is demonstrated that the value of κ arises from two geometric features associated with the inertial turbulent motions responsible for momentum transport. One nominally pertains to the shape of the relevant motions as quantified by their area coverage in any given wall-parallel plane, and the other pertains to the changing size of these motions in the wall-normal direction. In accord with self-similar mean dynamics, these two features remain invariant across the inertial domain. Data from direct numerical simulations and higher Reynolds number experiments are presented and discussed relative to the self-similar geometric structure indicated by the analysis, and in particular the special form of self-similarity shown to correspond to κ=Φ(-2).

Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory

PubMed Central

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS. PMID:24860602

Geometric morphometric analysis of mandibular shape diversity in Pan.

PubMed

Robinson, Chris

2012-07-01

The aim of this research is to determine whether geometric morphometric (GM) techniques can provide insights into how the shape of the mandibular corpus differs between bonobos and chimpanzees and to explore the potential implications of those results for our understanding of hominin evolution. We focused on this region of the mandible because of the relative frequency with which it has been recovered in the hominin fossil record. In addition, no previous study had explored in-depth three-dimensional (3D) mandibular corpus shape differences between adults of the two Pan species using geometric morphometrics. GM methods enable researchers to quantitatively analyze and visualize 3D shape changes in skeletal elements and provide an important compliment to traditional two-dimensional analyses. Eighteen mandibular landmarks were collected using a Microscribe 3DX portable digitizer. Specimen configurations were superimposed using Generalized Procrustes analysis and the projections of the fitted coordinates to tangent space were analyzed using multivariate statistics. The size-adjusted corpus shapes of Pan paniscus and Pan troglodytes could be assigned to species with approximately 93% accuracy and the Procrustes distance between the two species was significant. Analyses of the residuals from a multivariate linear regression of the data on centroid size suggested that much of the shape difference between the species is size-related. Chimpanzee subspecies and a small sample of Australopithecus specimens could be correctly identified to taxon, at best, only 75% of the time, although the Procrustes distances between these taxa were significant. The shape of the mandibular symphysis was identified as especially useful in differentiating Pan species from one another. This suggests that this region of the mandible has the potential to be informative for taxonomic analyses of fossil hominoids, including hominins. The results also have implications for phylogenetic hypotheses of hominoid evolution. Copyright © 2012 Elsevier Ltd. All rights reserved.

Density estimation using the trapping web design: A geometric analysis

USGS Publications Warehouse

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

1994-01-01

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

Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing

DTIC Science & Technology

1994-04-15

1991. [40] D. G. Lowe, "Organization of smooth image curves at multiple scales," International Journal of Computer Vision 3, pp. 119-130, 1989. [41] E ... Lutwak , "On some affine isoperimetric inequalities," J. Differential Geometry 23, pp. 1-13, 1986. [42] F. Mokhatarian and A. Mackworth, "A theory of

Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics

NASA Astrophysics Data System (ADS)

Baskin, E.; Iomin, A.

2011-12-01

We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional integro-differentiation. The method is based on fractional calculus and permits to obtain analytical expressions for the electric-field enhancement.

Families of Ellipses and their Orthogonal Trajectories

ERIC Educational Resources Information Center

Ayoub, Ayoub B.

2004-01-01

The topic of orthogonal trajectories is taught as a geometric application of first order differential equations. Instructors usually elaborate on the concept of a family of curves to emphasize that they are different even if their members are of the same type. In this article the author considers five families of ellipses, discusses their…

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

NASA Astrophysics Data System (ADS)

Krishna, S.; Shukla, D.; Malik, R. P.

2016-07-01

In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.

Permeability of Two Parachute Fabrics: Measurements, Modeling, and Application

NASA Technical Reports Server (NTRS)

Cruz, Juan R.; O'Farrell, Clara; Hennings, Elsa; Runnells, Paul

2017-01-01

Two parachute fabrics, described by Parachute Industry Specifications PIA-C-7020D Type I and PIA-C-44378D Type I, were tested to obtain their permeabilities in air (i.e., flow-through volume of air per area per time) over the range of differential pressures from 0.146 psf (7 Pa) to 25 psf (1197 Pa). Both fabrics met their specification permeabilities at the standard differential pressure of 0.5 inch of water (2.60 psf, 124 Pa). The permeability results were transformed into an effective porosity for use in calculations related to parachutes. Models were created that related the effective porosity to the unit Reynolds number for each of the fabrics. As an application example, these models were used to calculate the total porosities for two geometrically-equivalent subscale Disk-Gap-Band (DGB) parachutes fabricated from each of the two fabrics, and tested at the same operating conditions in a wind tunnel. Using the calculated total porosities and the results of the wind tunnel tests, the drag coefficient of a geometrically-equivalent full-scale DGB operating on Mars was estimated.

Permeability of Two Parachute Fabrics - Measurements, Modeling, and Application

NASA Technical Reports Server (NTRS)

Cruz, Juan R.; O'Farrell, Clara; Hennings, Elsa; Runnells, Paul

2016-01-01

Two parachute fabrics, described by Parachute Industry Specifications PIA-C-7020D Type I and PIA-C-44378D Type I, were tested to obtain their permeabilities in air (i.e., flow-through volume of air per area per time) over the range of differential pressures from 0.146 psf (7 Pa) to 25 psf (1197 Pa). Both fabrics met their specification permeabilities at the standard differential pressure of 0.5 inch of water (2.60 psf, 124 Pa). The permeability results were transformed into an effective porosity for use in calculations related to parachutes. Models were created that related the effective porosity to the unit Reynolds number for each of the fabrics. As an application example, these models were used to calculate the total porosities for two geometrically-equivalent subscale Disk-Gap-Band (DGB) parachutes fabricated from each of the two fabrics, and tested at the same operating conditions in a wind tunnel. Using the calculated total porosities and the results of the wind tunnel tests, the drag coefficient of a geometrically-equivalent full-scale DGB operating on Mars was estimated.

Evaluation of grid generation technologies from an applied perspective

NASA Technical Reports Server (NTRS)

Hufford, Gary S.; Harrand, Vincent J.; Patel, Bhavin C.; Mitchell, Curtis R.

1995-01-01

An analysis of the grid generation process from the point of view of an applied CFD engineer is given. Issues addressed include geometric modeling, structured grid generation, unstructured grid generation, hybrid grid generation and use of virtual parts libraries in large parametric analysis projects. The analysis is geared towards comparing the effective turn around time for specific grid generation and CFD projects. The conclusion was made that a single grid generation methodology is not universally suited for all CFD applications due to both limitations in grid generation and flow solver technology. A new geometric modeling and grid generation tool, CFD-GEOM, is introduced to effectively integrate the geometric modeling process to the various grid generation methodologies including structured, unstructured, and hybrid procedures. The full integration of the geometric modeling and grid generation allows implementation of extremely efficient updating procedures, a necessary requirement for large parametric analysis projects. The concept of using virtual parts libraries in conjunction with hybrid grids for large parametric analysis projects is also introduced to improve the efficiency of the applied CFD engineer.

A protocol for the creation of useful geometric shape metrics illustrated with a newly derived geometric measure of leaf circularity.

PubMed

Krieger, Jonathan D

2014-08-01

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

Instability in strongly magnetized accretion discs: a global perspective

NASA Astrophysics Data System (ADS)

Das, Upasana; Begelman, Mitchell C.; Lesur, Geoffroy

2018-01-01

We examine the properties of strongly magnetized accretion discs in a global framework, with particular focus on the evolution of magnetohydrodynamic instabilities such as the magnetorotational instability (MRI). Work by Pessah & Psaltis showed that MRI is stabilized beyond a critical toroidal field in compressible, differentially rotating flows and, also, reported the appearance of two new instabilities beyond this field. Their results stemmed from considering geometric curvature effects due to the suprathermal background toroidal field, which had been previously ignored in weak-field studies. However, their calculations were performed under the local approximation, which poses the danger of introducing spurious behaviour due to the introduction of global geometric terms in an otherwise local framework. In order to avoid this, we perform a global eigenvalue analysis of the linearized MHD equations in cylindrical geometry. We confirm that MRI indeed tends to be highly suppressed when the background toroidal field attains the Pessah-Psaltis limit. We also observe the appearance of two new instabilities that emerge in the presence of highly suprathermal toroidal fields. These results were additionally verified using numerical simulations in PLUTO. There are, however, certain differences between the the local and global results, especially in the vertical wavenumber occupancies of the various instabilities, which we discuss in detail. We also study the global eigenfunctions of the most unstable modes in the suprathermal regime, which are inaccessible in the local analysis. Overall, our findings emphasize the necessity of a global treatment for accurately modelling strongly magnetized accretion discs.

Blind Forensics of Successive Geometric Transformations in Digital Images Using Spectral Method: Theory and Applications.

PubMed

Chen, Chenglong; Ni, Jiangqun; Shen, Zhaoyi; Shi, Yun Qing

2017-06-01

Geometric transformations, such as resizing and rotation, are almost always needed when two or more images are spliced together to create convincing image forgeries. In recent years, researchers have developed many digital forensic techniques to identify these operations. Most previous works in this area focus on the analysis of images that have undergone single geometric transformations, e.g., resizing or rotation. In several recent works, researchers have addressed yet another practical and realistic situation: successive geometric transformations, e.g., repeated resizing, resizing-rotation, rotation-resizing, and repeated rotation. We will also concentrate on this topic in this paper. Specifically, we present an in-depth analysis in the frequency domain of the second-order statistics of the geometrically transformed images. We give an exact formulation of how the parameters of the first and second geometric transformations influence the appearance of periodic artifacts. The expected positions of characteristic resampling peaks are analytically derived. The theory developed here helps to address the gap left by previous works on this topic and is useful for image security and authentication, in particular, the forensics of geometric transformations in digital images. As an application of the developed theory, we present an effective method that allows one to distinguish between the aforementioned four different processing chains. The proposed method can further estimate all the geometric transformation parameters. This may provide useful clues for image forgery detection.

Once upon Multivariate Analyses: When They Tell Several Stories about Biological Evolution.

PubMed

Renaud, Sabrina; Dufour, Anne-Béatrice; Hardouin, Emilie A; Ledevin, Ronan; Auffray, Jean-Christophe

2015-01-01

Geometric morphometrics aims to characterize of the geometry of complex traits. It is therefore by essence multivariate. The most popular methods to investigate patterns of differentiation in this context are (1) the Principal Component Analysis (PCA), which is an eigenvalue decomposition of the total variance-covariance matrix among all specimens; (2) the Canonical Variate Analysis (CVA, a.k.a. linear discriminant analysis (LDA) for more than two groups), which aims at separating the groups by maximizing the between-group to within-group variance ratio; (3) the between-group PCA (bgPCA) which investigates patterns of between-group variation, without standardizing by the within-group variance. Standardizing within-group variance, as performed in the CVA, distorts the relationships among groups, an effect that is particularly strong if the variance is similarly oriented in a comparable way in all groups. Such shared direction of main morphological variance may occur and have a biological meaning, for instance corresponding to the most frequent standing genetic variation in a population. Here we undertake a case study of the evolution of house mouse molar shape across various islands, based on the real dataset and simulations. We investigated how patterns of main variance influence the depiction of among-group differentiation according to the interpretation of the PCA, bgPCA and CVA. Without arguing about a method performing 'better' than another, it rather emerges that working on the total or between-group variance (PCA and bgPCA) will tend to put the focus on the role of direction of main variance as line of least resistance to evolution. Standardizing by the within-group variance (CVA), by dampening the expression of this line of least resistance, has the potential to reveal other relevant patterns of differentiation that may otherwise be blurred.

Parametric instability analysis of truncated conical shells using the Haar wavelet method

NASA Astrophysics Data System (ADS)

Dai, Qiyi; Cao, Qingjie

2018-05-01

In this paper, the Haar wavelet method is employed to analyze the parametric instability of truncated conical shells under static and time dependent periodic axial loads. The present work is based on the Love first-approximation theory for classical thin shells. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. Then the partial differential equations are reduced into a system of coupled Mathieu-type ordinary differential equations describing dynamic instability behavior of the shell. Using Bolotin's method, the first-order and second-order approximations of principal instability regions are determined. The correctness of present method is examined by comparing the results with those in the literature and very good agreement is observed. The difference between the first-order and second-order approximations of principal instability regions for tensile and compressive loads is also investigated. Finally, numerical results are presented to bring out the influences of various parameters like static load factors, boundary conditions and shell geometrical characteristics on the domains of parametric instability of conical shells.

A new design approach based on differential evolution algorithm for geometric optimization of magnetorheological brakes

NASA Astrophysics Data System (ADS)

Le-Duc, Thang; Ho-Huu, Vinh; Nguyen-Thoi, Trung; Nguyen-Quoc, Hung

2016-12-01

In recent years, various types of magnetorheological brakes (MRBs) have been proposed and optimized by different optimization algorithms that are integrated in commercial software such as ANSYS and Comsol Multiphysics. However, many of these optimization algorithms often possess some noteworthy shortcomings such as the trap of solutions at local extremes, or the limited number of design variables or the difficulty of dealing with discrete design variables. Thus, to overcome these limitations and develop an efficient computation tool for optimal design of the MRBs, an optimization procedure that combines differential evolution (DE), a gradient-free global optimization method with finite element analysis (FEA) is proposed in this paper. The proposed approach is then applied to the optimal design of MRBs with different configurations including conventional MRBs and MRBs with coils placed on the side housings. Moreover, to approach a real-life design, some necessary design variables of MRBs are considered as discrete variables in the optimization process. The obtained optimal design results are compared with those of available optimal designs in the literature. The results reveal that the proposed method outperforms some traditional approaches.

A computational model of cerebral cortex folding.

PubMed

Nie, Jingxin; Guo, Lei; Li, Gang; Faraco, Carlos; Stephen Miller, L; Liu, Tianming

2010-05-21

The geometric complexity and variability of the human cerebral cortex have long intrigued the scientific community. As a result, quantitative description of cortical folding patterns and the understanding of underlying folding mechanisms have emerged as important research goals. This paper presents a computational 3D geometric model of cerebral cortex folding initialized by MRI data of a human fetal brain and deformed under the governance of a partial differential equation modeling cortical growth. By applying different simulation parameters, our model is able to generate folding convolutions and shape dynamics of the cerebral cortex. The simulations of this 3D geometric model provide computational experimental support to the following hypotheses: (1) Mechanical constraints of the skull regulate the cortical folding process. (2) The cortical folding pattern is dependent on the global cell growth rate of the whole cortex. (3) The cortical folding pattern is dependent on relative rates of cell growth in different cortical areas. (4) The cortical folding pattern is dependent on the initial geometry of the cortex. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Relative impact of uniaxial alignment vs. form-induced stress on differentiation of human adipose derived stem cells

PubMed Central

Huang, Samuel; Li, Julie Yi-Shuan; Chien, Shu; Zhang, Kang; Chen, Shaochen

2013-01-01

ADSCs are a great cell source for tissue engineering and regenerative medicine. However, the development of methods to appropriately manipulate these cells in vitro remains a challenge. Here the proliferation and differentiation of ADSCs on microfabricated surfaces with varying geometries were investigated. To create the patterned substrates, a maskless biofabrication method was developed based on dynamic optical projection stereolithography. Proliferation and early differentiation of ADSCs were compared across three distinct multicellular patterns, namely stripes (ST), symmetric fork (SF), and asymmetric fork (AF). The ST pattern was designed for uniaxial cell alignment while the SF and AF pattern were designed with altered cell directionality to different extents. The SF and AF patterns generated similar levels of regional peak stress, which were both significantly higher than those within the ST pattern. No significant difference in ADSC proliferation was observed among the three patterns. In comparison to the ST pattern, higher peak stress levels of the SF and AF patterns were associated with up-regulation of the chondrogenic and osteogenic markers SOX9 and RUNX2. Interestingly, uniaxial cell alignment in the ST pattern seemed to increase the expression of SM22α and smooth muscle α-actin, suggesting an early smooth muscle lineage progression. These results indicate that geometric cues that promote uniaxial alignment might be more potent for myogenesis than those with increased peak stress. Overall, the use of these patterned geometric cues for modulating cell alignment and form-induced stress can serve as a powerful and versatile technique towards controlling differentiation in ADSCs. PMID:24060419

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

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.

Device-Free Localization via an Extreme Learning Machine with Parameterized Geometrical Feature Extraction.

PubMed

Zhang, Jie; Xiao, Wendong; Zhang, Sen; Huang, Shoudong

2017-04-17

Device-free localization (DFL) is becoming one of the new technologies in wireless localization field, due to its advantage that the target to be localized does not need to be attached to any electronic device. In the radio-frequency (RF) DFL system, radio transmitters (RTs) and radio receivers (RXs) are used to sense the target collaboratively, and the location of the target can be estimated by fusing the changes of the received signal strength (RSS) measurements associated with the wireless links. In this paper, we will propose an extreme learning machine (ELM) approach for DFL, to improve the efficiency and the accuracy of the localization algorithm. Different from the conventional machine learning approaches for wireless localization, in which the above differential RSS measurements are trivially used as the only input features, we introduce the parameterized geometrical representation for an affected link, which consists of its geometrical intercepts and differential RSS measurement. Parameterized geometrical feature extraction (PGFE) is performed for the affected links and the features are used as the inputs of ELM. The proposed PGFE-ELM for DFL is trained in the offline phase and performed for real-time localization in the online phase, where the estimated location of the target is obtained through the created ELM. PGFE-ELM has the advantages that the affected links used by ELM in the online phase can be different from those used for training in the offline phase, and can be more robust to deal with the uncertain combination of the detectable wireless links. Experimental results show that the proposed PGFE-ELM can improve the localization accuracy and learning speed significantly compared with a number of the existing machine learning and DFL approaches, including the weighted K-nearest neighbor (WKNN), support vector machine (SVM), back propagation neural network (BPNN), as well as the well-known radio tomographic imaging (RTI) DFL approach.

Device-Free Localization via an Extreme Learning Machine with Parameterized Geometrical Feature Extraction

PubMed Central

Zhang, Jie; Xiao, Wendong; Zhang, Sen; Huang, Shoudong

2017-01-01

Device-free localization (DFL) is becoming one of the new technologies in wireless localization field, due to its advantage that the target to be localized does not need to be attached to any electronic device. In the radio-frequency (RF) DFL system, radio transmitters (RTs) and radio receivers (RXs) are used to sense the target collaboratively, and the location of the target can be estimated by fusing the changes of the received signal strength (RSS) measurements associated with the wireless links. In this paper, we will propose an extreme learning machine (ELM) approach for DFL, to improve the efficiency and the accuracy of the localization algorithm. Different from the conventional machine learning approaches for wireless localization, in which the above differential RSS measurements are trivially used as the only input features, we introduce the parameterized geometrical representation for an affected link, which consists of its geometrical intercepts and differential RSS measurement. Parameterized geometrical feature extraction (PGFE) is performed for the affected links and the features are used as the inputs of ELM. The proposed PGFE-ELM for DFL is trained in the offline phase and performed for real-time localization in the online phase, where the estimated location of the target is obtained through the created ELM. PGFE-ELM has the advantages that the affected links used by ELM in the online phase can be different from those used for training in the offline phase, and can be more robust to deal with the uncertain combination of the detectable wireless links. Experimental results show that the proposed PGFE-ELM can improve the localization accuracy and learning speed significantly compared with a number of the existing machine learning and DFL approaches, including the weighted K-nearest neighbor (WKNN), support vector machine (SVM), back propagation neural network (BPNN), as well as the well-known radio tomographic imaging (RTI) DFL approach. PMID:28420187

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

PubMed

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

2010-01-01

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

Local Orthogonal Cutting Method for Computing Medial Curves and Its Biomedical Applications

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

Jiao, Xiangmin; Einstein, Daniel R.; Dyedov, Volodymyr

2010-03-24

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stabilitymore » and consistency tests. These concepts lend themselves to robust numerical techniques including eigenvalue analysis, weighted least squares approximations, and numerical minimization, resulting in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods.« less

Differential Kinematics Of Contemporary Industrial Robots

NASA Astrophysics Data System (ADS)

Szkodny, T.

2014-08-01

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

GMPR: A robust normalization method for zero-inflated count data with application to microbiome sequencing data.

PubMed

Chen, Li; Reeve, James; Zhang, Lujun; Huang, Shengbing; Wang, Xuefeng; Chen, Jun

2018-01-01

Normalization is the first critical step in microbiome sequencing data analysis used to account for variable library sizes. Current RNA-Seq based normalization methods that have been adapted for microbiome data fail to consider the unique characteristics of microbiome data, which contain a vast number of zeros due to the physical absence or under-sampling of the microbes. Normalization methods that specifically address the zero-inflation remain largely undeveloped. Here we propose geometric mean of pairwise ratios-a simple but effective normalization method-for zero-inflated sequencing data such as microbiome data. Simulation studies and real datasets analyses demonstrate that the proposed method is more robust than competing methods, leading to more powerful detection of differentially abundant taxa and higher reproducibility of the relative abundances of taxa.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Landsat 4 results and their implications for agricultural surveys

NASA Technical Reports Server (NTRS)

Erickson, J. D.; Bizzell, R. M.; Pitts, D. E.; Thompson, D. R.

1983-01-01

Progress on defining the minimum Landsat-4 data characteristics needed for agricultural information in the U.S. and assessing the value-added capability of current technology to extract that level of information is reported. Emphasis is laid on the thematic mapper (TM) data and the ground processing facilities. TM data from all 7 bands for a rural Arkansas scene were examined in terms of radiometric, spatial, and geometric fidelity characteristics. Another scene sensed over Iowa was analyzed using three two-channel data sets. Although the TM data were an improvement over MSS data, no value differential was perceived. However, the development of further analysis techniques is still necessary to determine the actual worth of the improved sensor capabilities available with the TM, which actually has an MSS within itself.

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

Structural Characterisation and Mechanical FE Analysis of Conventional and M-Wire Ni-Ti Alloys Used in Endodontic Rotary Instruments

PubMed Central

Montalvão, Diogo; Alçada, Francisca Sena; Braz Fernandes, Francisco Manuel; de Vilaverde-Correia, Sancho

2014-01-01

The purpose of this study is to understand how the M-Wire alloy conditions the mechanical flexibility of endodontic rotary files at body temperature.Two different rotary instruments, a Profile GT 20/.06 and a Profile GT Series X 20/.06, were selected due to their geometrical similarity and their different constituent alloy. GT series X files are made from M-Wire, a Ni-Ti alloy allegedly having higher flexibility at body temperature. Both files were analysed by X-Ray Diffraction and Differential Scanning Calorimetry to investigate phase transformations and the effects of working temperature on these different alloys. Mechanical behaviour was assessed by means of static bending and torsional Finite Element simulations, taking into account the nonlinear superelastic behaviour of Ni-Ti materials. It was found that GT files present austenitic phase at body temperature, whereas GT series X present R-phase at temperatures under 40°C with a potential for larger flexibility. For the same load conditions, simulations showed that the slight geometrical differences between the two files do not introduce great disagreement in the instruments' mechanical response. It was confirmed that M-Wire increases the instrument's flexibility, mainly due to the presence of R-phase at body temperature. PMID:24574937

Structural characterisation and mechanical FE analysis of conventional and M-Wire Ni-Ti alloys used in endodontic rotary instruments.

PubMed

Montalvão, Diogo; Alçada, Francisca Sena; Braz Fernandes, Francisco Manuel; de Vilaverde-Correia, Sancho

2014-01-01

The purpose of this study is to understand how the M-Wire alloy conditions the mechanical flexibility of endodontic rotary files at body temperature.Two different rotary instruments, a Profile GT 20/.06 and a Profile GT Series X 20/.06, were selected due to their geometrical similarity and their different constituent alloy. GT series X files are made from M-Wire, a Ni-Ti alloy allegedly having higher flexibility at body temperature. Both files were analysed by X-Ray Diffraction and Differential Scanning Calorimetry to investigate phase transformations and the effects of working temperature on these different alloys. Mechanical behaviour was assessed by means of static bending and torsional Finite Element simulations, taking into account the nonlinear superelastic behaviour of Ni-Ti materials. It was found that GT files present austenitic phase at body temperature, whereas GT series X present R-phase at temperatures under 40 °C with a potential for larger flexibility. For the same load conditions, simulations showed that the slight geometrical differences between the two files do not introduce great disagreement in the instruments' mechanical response. It was confirmed that M-Wire increases the instrument's flexibility, mainly due to the presence of R-phase at body temperature.

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

Missing dimer defects investigated by adsorption of nitric oxide (NO) on silicon (100) 2 × 1

NASA Astrophysics Data System (ADS)

Sasse, A. G. B. M.; Kleinherenbrink, P. M.; Van Silfhout, A.

This paper describes a study concerning the interaction of nitric oxide (NO) with the clean Si(100)2×1 surface in ultra-high vacuum at room temperature. Differential reflectometry (DR) in the photon energy range of 2.4-4.4 eV. Auger electron spectroscopy (AES) and low energy electron diffraction (LEED) have been used to investigate the chemisorption of NO on Si(100)2×1. With this combination of techniques it is possible to make an analysis of the geometric and electronic structure and chemical composition of the surface layer. The aim of the present study was to explain the experimental results of the adsorption of NO on the clean Si(100)2×1 at 300 K. Analysing the electronic and geometric structure of a simplified stepped 2×1 reconstructed Si(100) surface and of the NO molecule in combination with the use of Woodward-Hoffmann rules (WHR) we were able to model a surface defect specific adsorption mechanism. Surface defects such as missing dimer defects seem to play an important role in the adsorption mechanism of NO on the silicon surface. The experimental results are consistent with this developed model. We also suggest a relation between the missing dimer defects and the number of steps on the silicon surface.

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.

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

Nute, J; Jacobsen, M; Popnoe, D

Purpose: Intracranial hemorrhage and calcification with Single-Energy CT (SECT) attenuation below 100HU cannot be reliably identified using currently clinically available means. Calcification is typically benign but hemorrhage can carry a risk of intracranial bleeding and contraindicate use of anticoagulant therapies. A biologically-relevant phantom was used to investigate identification of unknown intracranial lesions using dual-energy CT (DECT) as a verification of prior lesion differentiation results. Methods: Prior phantom work investigating calcification and hemorrhage differentiation resulted in 3D-DECT raw data (water density, calcium density, 68keV) for a range of DECT protocol variations: image thicknesses (1.25, 2.5, 3.75, 5mm), CTDIvol (36.7 to 132.6mGy)more » and reconstruction algorithms (Soft, Standard, Detail). Acquisition-specific raw data were used to create a plane of optimal differentiation based on the geometric bisector of 3D-linear regression of the two lesion distributions. Verification hemorrhage and calcification lesions, ranging in size from 0.5 to 1.5cm, were created at varying attenuation from 50 to 100HU. Lesions were inserted into a biologically-relevant brain phantom and scanned using SECT (3.75mm images, Standard, 67mGy) and a range of DECT protocols (3.75mm images, Standard, [67, 105.6, 132.6mGy]). 3D-DECT data were collected and blinded for analysis. The 3D-DECT distribution of the lesion was then compared to the acquisition-matched geometric bisector plane and the mean lesion value’s position relative to the plane, indicating lesion identity, and the percentage of voxels on the identified side of the plane, indicating identification confidence, were derived. Results: 98% of the 120 lesions investigated were identified correctly as hemorrhage or calcification. 74% were identified with greater than 80% confidence. Increases in CTDIvol and lesion diameter were associated with increased identification confidence. Conclusion: Intracranial lesions of unknown etiology were identified with 80% confidence for 74% of lesions investigated. These phantom data suggest that the identification of intracranial lesions below 100HU is clinically feasible using DECT. This research was conducted at the MD Anderson Center for Advanced Biomedical Imaging in-part with equipment support from General Electric Healthcare.« less

Process for computing geometric perturbations for probabilistic analysis

DOEpatents

Fitch, Simeon H. K. [Charlottesville, VA; Riha, David S [San Antonio, TX; Thacker, Ben H [San Antonio, TX

2012-04-10

A method for computing geometric perturbations for probabilistic analysis. The probabilistic analysis is based on finite element modeling, in which uncertainties in the modeled system are represented by changes in the nominal geometry of the model, referred to as "perturbations". These changes are accomplished using displacement vectors, which are computed for each node of a region of interest and are based on mean-value coordinate calculations.

A framework for qualitative reasoning about solid objects

NASA Technical Reports Server (NTRS)

Davis, E.

1987-01-01

Predicting the behavior of a qualitatively described system of solid objects requires a combination of geometrical, temporal, and physical reasoning. Methods based upon formulating and solving differential equations are not adequate for robust prediction, since the behavior of a system over extended time may be much simpler than its behavior over local time. A first-order logic, in which one can state simple physical problems and derive their solution deductively, without recourse to solving the differential equations, is discussed. This logic is substantially more expressive and powerful than any previous AI representational system in this domain.

A Hamilton-Jacobi theory for implicit differential systems

NASA Astrophysics Data System (ADS)

Esen, Oǧul; de León, Manuel; Sardón, Cristina

2018-02-01

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of TT*Q generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton-Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to singular Lagrangians by employing the construction of special symplectic structures.

Theory of liquid crystal elastomers and polymer networks : Connection between neoclassical theory and differential geometry.

PubMed

Nguyen, Thanh-Son; Selinger, Jonathan V

2017-09-01

In liquid crystal elastomers and polymer networks, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymers. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation gradient tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.

Enhancements to NURBS-Based FEA Airfoil Modeler: SABER

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Trowbridge, D. A.

2003-01-01

NURBS (Non-Uniform Rational B-Splines) have become a common way for CAD programs to fit a smooth surface to discrete geometric data. This concept has been extended to allow for the fitting of analysis data in a similar manner and "attaching" the analysis data to the geometric definition of the structure. The "attaching" of analysis data to the geometric definition allows for a more seamless sharing of data between analysis disciplines. NURBS have become a useful tool in the modeling of airfoils. The use of NURBS has allowed for the development of software that easily and consistently generates plate finite element models of the midcamber surface of a given airfoil. The resulting displacements can then be applied to the original airfoil surface and the deformed shape calculated.

Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures

NASA Technical Reports Server (NTRS)

Mangalgiri, P. D.; Prabhakaran, R.

1986-01-01

An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.

Using EIGER for Antenna Design and Analysis

NASA Technical Reports Server (NTRS)

Champagne, Nathan J.; Khayat, Michael; Kennedy, Timothy F.; Fink, Patrick W.

2007-01-01

EIGER (Electromagnetic Interactions GenERalized) is a frequency-domain electromagnetics software package that is built upon a flexible framework, designed using object-oriented techniques. The analysis methods used include moment method solutions of integral equations, finite element solutions of partial differential equations, and combinations thereof. The framework design permits new analysis techniques (boundary conditions, Green#s functions, etc.) to be added to the software suite with a sensible effort. The code has been designed to execute (in serial or parallel) on a wide variety of platforms from Intel-based PCs and Unix-based workstations. Recently, new potential integration scheme s that avoid singularity extraction techniques have been added for integral equation analysis. These new integration schemes are required for facilitating the use of higher-order elements and basis functions. Higher-order elements are better able to model geometrical curvature using fewer elements than when using linear elements. Higher-order basis functions are beneficial for simulating structures with rapidly varying fields or currents. Results presented here will demonstrate curren t and future capabilities of EIGER with respect to analysis of installed antenna system performance in support of NASA#s mission of exploration. Examples include antenna coupling within an enclosed environment and antenna analysis on electrically large manned space vehicles.

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.

Morphometric variability among the species of the Sordida subcomplex (Hemiptera: Reduviidae: Triatominae): evidence for differentiation across the distribution range of Triatoma sordida.

PubMed

Nattero, Julieta; Piccinali, Romina Valeria; Macedo Lopes, Catarina; Hernández, María Laura; Abrahan, Luciana; Lobbia, Patricia Alejandra; Rodríguez, Claudia Susana; Carbajal de la Fuente, Ana Laura

2017-09-06

The Sordida subcomplex (Triatominae) comprises four species, Triatoma garciabesi, T. guasayana, T. patagonica and T. sordida, which differ in epidemiological importance and adaptations to human environments. Some morphological similarities among species make taxonomic identification, population differentiation and species delimitation controversial. Triatoma garciabesi and T. sordida are the most similar species, having been considered alternatively two and a single species until T. garciabesi was re-validated, mostly based on the morphology of male genitalia. More recently, T. sordida from Argentina has been proposed as a new cryptic species distinguishable from T. sordida from Brazil, Bolivia and Paraguay by cytogenetics. We studied linear and geometric morphometry of the head, wings and pronotum in populations of these species aiming to find phenotypic markers for their discrimination, especially between T. sordida and T. garciabesi, and if any set of variables that validates T. sordida from Argentina as a new species. Head width and pronotum length were the linear variables that best differentiated species. Geometric morphometry revealed significant Mahalanobis distances in wing shape between all pairwise comparisons. Triatoma patagonica exhibited the best discrimination and T. garciabesi overlapped the distribution of the other species in the morphometric space of the first two DFA axes. Head shape showed differentiation between all pairs of species except for T. garciabesi and T. sordida. Pronotum shape did not differentiate T. garciabesi from T. guasayana. The comparison between T. garciabesi and T. sordida from Argentina and T. sordida from Brazil and Bolivia revealed low differentiation based on head and pronotum linear measurements. Pronotum and wing shape were different between T. garciabesi and T. sordida from Brazil and Bolivia and T. sordida from Argentina. Head shape did not differentiate T. garciabesi from T. sordida from Argentina. Wing shape best delimited the four species phenotypically. The proposed cryptic species, T. sordida from Argentina, differed from T. sordida from Brazil and Bolivia in all measured shape traits, suggesting that the putative new species may not be cryptic. Additional studies integrating cytogenetic, phenotypic and molecular markers, as well as cross-breeding experiments are needed to confirm if these three entities represent true biological species.

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

NASA Technical Reports Server (NTRS)

Burnside, W. D.

1976-01-01

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

An Analysis of Pre-Service Elementary School Teachers' Skills in Geometrical Drawing Using Isometric Paper

ERIC Educational Resources Information Center

Toptas, Veli; Karaca, Elif Tugçe

2017-01-01

The aim of this study was to determine pre-service elementary school teachers' capabilities of deciding the viewpoint and perspective in geometrical drawing. The study examined geometrical drawings the participants did on isometric paper. This is a case study, a qualitative study method, and the study data were analyzed using written documents.…

Effect of Geometrical Imperfection on Buckling Failure of ITER VVPSS Tank

NASA Astrophysics Data System (ADS)

Jha, Saroj Kumar; Gupta, Girish Kumar; Pandey, Manish Kumar; Bhattacharya, Avik; Jogi, Gaurav; Bhardwaj, Anil Kumar

2017-04-01

The ‘Vacuum Vessel Pressure Suppression System’ (VVPSS) is part of ITER machine, which is designed to protect the ITER Vacuum Vessel and its connected systems, from an over-pressure situation. It is comprised of a partially evacuated tank of stainless steel approximately 46 m long and 6 m in diameter and thickness 30 mm. It is to hold approximately 675 tonnes of water at room temperature to condense the steam resulting from the adverse water leakage into the Vacuum Vessel chamber. For any vacuum vessel, geometrical imperfection has significant effect on buckling failure and structural integrity. Major geometrical imperfection in VVPSS tank depends on form tolerances. To study the effect of geometrical imperfection on buckling failure of VVPSS tank, finite element analysis (FEA) has been performed in line with ASME section VIII division 2 part 5 [1], ‘design by analysis method’. Linear buckling analysis has been performed to get the buckled shape and displacement. Geometrical imperfection due to form tolerance is incorporated in FEA model of VVPSS tank by scaling the resulted buckled shape by a factor ‘60’. This buckled shape model is used as input geometry for plastic collapse and buckling failure assessment. Plastic collapse and buckling failure of VVPSS tank has been assessed by using the elastic-plastic analysis method. This analysis has been performed for different values of form tolerance. The results of analysis show that displacement and load proportionality factor (LPF) vary inversely with form tolerance. For higher values of form tolerance LPF reduces significantly with high values of displacement.

Music of the 7Ts: Predicting and Decoding Multivoxel fMRI Responses with Acoustic, Schematic, and Categorical Music Features

PubMed Central

Casey, Michael A.

2017-01-01

Underlying the experience of listening to music are parallel streams of auditory, categorical, and schematic qualia, whose representations and cortical organization remain largely unresolved. We collected high-field (7T) fMRI data in a music listening task, and analyzed the data using multivariate decoding and stimulus-encoding models. Twenty subjects participated in the experiment, which measured BOLD responses evoked by naturalistic listening to twenty-five music clips from five genres. Our first analysis applied machine classification to the multivoxel patterns that were evoked in temporal cortex. Results yielded above-chance levels for both stimulus identification and genre classification–cross-validated by holding out data from multiple of the stimuli during model training and then testing decoding performance on the held-out data. Genre model misclassifications were significantly correlated with those in a corresponding behavioral music categorization task, supporting the hypothesis that geometric properties of multivoxel pattern spaces underlie observed musical behavior. A second analysis employed a spherical searchlight regression analysis which predicted multivoxel pattern responses to music features representing melody and harmony across a large area of cortex. The resulting prediction-accuracy maps yielded significant clusters in the temporal, frontal, parietal, and occipital lobes, as well as in the parahippocampal gyrus and the cerebellum. These maps provide evidence in support of our hypothesis that geometric properties of music cognition are neurally encoded as multivoxel representational spaces. The maps also reveal a cortical topography that differentially encodes categorical and absolute-pitch information in distributed and overlapping networks, with smaller specialized regions that encode tonal music information in relative-pitch representations. PMID:28769835

Classical and sequential limit analysis revisited

NASA Astrophysics Data System (ADS)

Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

2018-04-01

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

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.

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Small, Des; Wiggins, Stephen

2006-12-01

In the past 15 years the framework and ideas from dynamical systems theory have been applied to a variety of transport and mixing problems in oceanic flows. The motivation for this approach comes directly from advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.) which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. In this tutorial, we motivate this approach by showing the relationship between fluid transport in two-dimensional time-periodic incompressible flows and the geometrical structures that exist for two-dimensional area-preserving maps, such as hyperbolic periodic orbits, their stable and unstable manifolds and KAM (Kolmogorov-Arnold-Moser) tori. This serves to set the stage for the attempt to “transfer” this approach to more realistic flows modelling the ocean. However, in order to accomplish this several difficulties must be overcome. The first difficulty that confronts us that any attempt to carry out a dynamical systems approach to transport requires us to obtain the appropriate “dynamical system”, which is the velocity field describing the fluid flow. In general, adequate model velocity fields are obtained by numerical solution of appropriate partial differential equations describing the dynamical evolution of the velocity field. Numerical solution of the partial differential equations can only be done for a finite time interval, and since the ocean is generally not time-periodic, this leads to a new type of dynamical system: a finite-time, aperiodically time-dependent velocity field defined as a data set on a space-time grid. The global, geometrical analysis of transport in such dynamical systems requires both new concepts and new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. The purpose of this tutorial is to describe these new concepts and analytical tools first using simple dynamical systems where quantities can be computed exactly. We then discuss their computational implications and implementation in the context of a model geophysical flow: a turbulent wind-driven double-gyre in the quasigeostrophic approximation.

Fused Traditional and Geometric Morphometrics Demonstrate Pinniped Whisker Diversity

PubMed Central

Ginter, Carly C.; DeWitt, Thomas J.; Fish, Frank E.; Marshall, Christopher D.

2012-01-01

Vibrissae (whiskers) are important components of the mammalian tactile sensory system, and primarily function as detectors of vibrotactile information from the environment. Pinnipeds possess the largest vibrissae among mammals and their vibrissal hair shafts demonstrate a diversity of shapes. The vibrissae of most phocid seals exhibit a beaded morphology with repeating sequences of crests and troughs along their length. However, there are few detailed analyses of pinniped vibrissal morphology, and these are limited to a few species. Therefore, we comparatively characterized differences in vibrissal hair shaft morphologies among phocid species with a beaded profile, phocid species with a smooth profile, and otariids with a smooth profile using traditional and geometric morphometric methods. Traditional morphometric measurements (peak-to-peak distance, crest width, trough width and total length) were collected using digital photographs. Elliptic Fourier analysis (geometric morphometrics) was used to quantify the outlines of whole vibrissae. The traditional and geometric morphometric datasets were subsequently combined by mathematically scaling each to true rank, followed by a single eigendecomposition. Quadratic discriminant function analysis demonstrated that 79.3, 97.8 and 100% of individuals could be correctly classified to their species based on vibrissal shape variables in the traditional, geometric and combined morphometric analyses, respectively. Phocids with beaded vibrissae, phocids with smooth vibrissae, and otariids each occupied distinct morphospace in the geometric morphometric and combined data analyses. Otariids split into two groups in the geometric morphometric analysis and gray seals appeared intermediate between beaded- and smooth-whiskered species in the traditional and combined analyses. Vibrissal hair shafts modulate the transduction of environmental stimuli to the mechanoreceptors in the follicle-sinus complex (F-SC), which results in vibrotactile reception, but it is currently unclear how the diversity of shapes affects environmental signal modulation. PMID:22509310

The influence of geometric imperfections on the stability of three-layer beams with foam core

NASA Astrophysics Data System (ADS)

Wstawska, Iwona

2017-01-01

The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.

Symmetry analysis of talus bone: A Geometric morphometric approach.

PubMed

Islam, K; Dobbe, A; Komeili, A; Duke, K; El-Rich, M; Dhillon, S; Adeeb, S; Jomha, N M

2014-01-01

The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139-45.

Exotic differentiable structures and general relativity

NASA Astrophysics Data System (ADS)

Brans, Carl H.; Randall, Duane

1993-02-01

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (“fake” or “exotic”) differentiable structures on topologically simple manifolds such asS 7, ℝ4 andS 3 X ℝ1. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.

Stress analysis of the cracked-lap-shear specimen - An ASTM round-robin

NASA Technical Reports Server (NTRS)

Johnson, W. S.

1987-01-01

This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

Stress analysis of the cracked lap shear specimens: An ASTM round robin

NASA Technical Reports Server (NTRS)

Johnson, W. S.

1986-01-01

This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

Minigrant Program. A Differential Geometric Approach to Electromagnetic Lens Design.

DTIC Science & Technology

1984-06-01

34,___" ,. --. 5 %’’ %, ;_-- - .-.- -. ...’ .¢ MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS-1963-A _"O i ’,... • . , w .T..rm,..p,. .. , .e W...ORGANIZATION REPORT NU,/dEHj) AD"A144 239 AFOSRTR- 3 4 - 0 5 9 6 aNIAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 74. NAME OF MONITORING ORGANIZATION

Role of geometrical cues in bone marrow-derived mesenchymal stem cell survival, growth and osteogenic differentiation.

PubMed

Gupta, Dhanak; Grant, David M; Zakir Hossain, Kazi M; Ahmed, Ifty; Sottile, Virginie

2018-02-01

Mesenchymal stem cells play a vital role in bone formation process by differentiating into osteoblasts, in a tissue that offers not a flat but a discontinuous three-dimensional (3D) topography in vivo. In order to understand how geometry may be affecting mesenchymal stem cells, this study explored the influence of 3D geometry on mesenchymal stem cell-fate by comparing cell growth, viability and osteogenic potential using monolayer (two-dimensional, 2D) with microsphere (3D) culture systems normalised to surface area. The results suggested lower cell viability and reduced cell growth in 3D. Alkaline phosphatase activity was higher in 3D; however, both collagen and mineral deposition appeared significantly lower in 3D, even after osteogenic supplementation. Also, there were signs of patchy mineralisation in 3D with or without osteogenic supplementation as early as day 7. These results suggest that the convex surfaces on microspheres and inter-particulate porosity may have led to variable cell morphology and fate within the 3D culture. This study provides deeper insights into geometrical regulation of mesenchymal stem cell responses applicable for bone tissue engineering.

Spin effects in transport through triangular quantum dot molecule in different geometrical configurations

NASA Astrophysics Data System (ADS)

Wrześniewski, Kacper; Weymann, Ireneusz

2015-07-01

We analyze the spin-resolved transport properties of a triangular quantum dot molecule weakly coupled to external ferromagnetic leads. The calculations are performed by using the real-time diagrammatic technique up to the second-order of perturbation theory, which enables a description of both the sequential and cotunneling processes. We study the behavior of the current and differential conductance in the parallel and antiparallel magnetic configurations, as well as the tunnel magnetoresistance (TMR) and the Fano factor in both the linear and nonlinear response regimes. It is shown that the transport characteristics depend greatly on how the system is connected to external leads. Two specific geometrical configurations of the device are considered—the mirror one, which possesses the reflection symmetry with respect to the current flow direction and the fork one, in which this symmetry is broken. In the case of first configuration we show that, depending on the bias and gate voltages, the system exhibits both enhanced TMR and super-Poissonian shot noise. On the other hand, when the system is in the second configuration, we predict a negative TMR and a negative differential conductance in certain transport regimes. The mechanisms leading to those effects are thoroughly discussed.

Use of UV Sources for Detection and Identification of Explosives

NASA Technical Reports Server (NTRS)

Hug, William; Reid, Ray; Bhartia, Rohit; Lane, Arthur

2009-01-01

Measurement of Raman and native fluorescence emission using ultraviolet (UV) sources (<400 nm) on targeted materials is suitable for both sensitive detection and accurate identification of explosive materials. When the UV emission data are analyzed using a combination of Principal Component Analysis (PCA) and cluster analysis, chemicals and biological samples can be differentiated based on the geometric arrangement of molecules, the number of repeating aromatic rings, associated functional groups (nitrogen, sulfur, hydroxyl, and methyl), microbial life cycles (spores vs. vegetative cells), and the number of conjugated bonds. Explosive materials can be separated from one another as well as from a range of possible background materials, which includes microbes, car doors, motor oil, and fingerprints on car doors, etc. Many explosives are comprised of similar atomic constituents found in potential background samples such as fingerprint oils/skin, motor oil, and soil. This technique is sensitive to chemical bonds between the elements that lead to the discriminating separability between backgrounds and explosive materials.

Electron Backscatter Diffraction (EBSD) Analysis and U-Pb Geochronology of the Oldest Lunar Zircon: Constraining Early Lunar Differentiation and Dating Impact-Related Deformation

NASA Technical Reports Server (NTRS)

Timms, Nick; Nemchin, Alexander; Grange, Marion; Reddy, Steve; Pidgeon, Bob; Geisler, Thorsten; Meyer, Chuck

2009-01-01

The evolution of the early moon was dominated by two processes (i) crystallization of the Lunar Magma Ocean (LMO) and differentiation of potassium-rare earth element-phosphorous-rich residual magma reservoir referred to as KREEP, and (ii) an intense meteorite bombardment referred to as lunar cataclysm . The exact timing of these processes is disputed, and resolution relies on collection and interpretation of precise age data. This study examines the microstructure and geochronology of zircon from lunar impact breccias collected during the Apollo 17 mission. A large zircon clast within lunar breccia 72215,195 shows sector zoning in optical microscopy, cathodoluminescence (CL) imaging and Raman mapping, and indicates that it was a relict fragment of a much larger magmatic grain. Sensitive high resolution ion microprobe (SHRIMP) U-Pb analysis of the zircon shows that U and Th concentration correlate with sector zoning, with darkest CL domains corresponding with high-U and Th (approx.150 and approx.100 ppm respectively), and the brightest-CL sectors containing approx.30-50 ppm U and approx.10-20 ppm Th. This indicates that variations in optical CL and Raman properties correspond to differential accumulation of alpha-radiation damage in each sector. Electron backscatter diffraction (EBSD) mapping shows that the quality of electron backscatter patterns (band contrast) varies with sector zoning, with the poorest quality patterns obtained from high-U and Th, dark-CL zones. EBSD mapping also reveals a deformation microstructure that is cryptic in optical, CL and Raman imaging. Two orthogonal sets of straight discrete and gradational low-angle boundaries accommodate approx.12 misorientation across the grain. The deformation bands are parallel to the crystallographic {a}-planes of the zircon, have misorientation axes parallel to the c-axis, and are geometrically consistent with formation by dislocation creep associated with <100>{010} slip. The deformation bands are unlike curved morphology of crystal-plastic microstructures in tectonically deformed terrestrial zircon, and geometrically similar to dislocation microstructures reported in experimentally shocked zircon. We interpret these crystal-plastic deformation microstructures to have resulted from a significant impact, either directly from impact shock, or during ductile flow directly following the impact. The deformation bands appear to continue undeflected through the non-indexed, radiation-damaged areas of the grain, which suggests that the orientation variation predates any significant mechanical weakening from radiation damage in the grain, and therefore occurred early in its history.

Differential characters and cohomology of the moduli of flat connections

NASA Astrophysics Data System (ADS)

Castrillón López, Marco; Ferreiro Pérez, Roberto

2018-05-01

Let π {:} P→ M be a principal bundle and p an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern-Simons differential characters is exploited to define a homology map χ k {:} H_{2r-k-1}(M)× Hk(F/G)→ R/Z , for k

Aerodynamic shape optimization using control theory

NASA Technical Reports Server (NTRS)

Reuther, James

1996-01-01

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Simple and practical approach for computing the ray Hessian matrix in geometrical optics.

PubMed

Lin, Psang Dain

2018-02-01

A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.

Surface Aesthetics and Analysis.

PubMed

Çakır, Barış; Öreroğlu, Ali Rıza; Daniel, Rollin K

2016-01-01

Surface aesthetics of an attractive nose result from certain lines, shadows, and highlights with specific proportions and breakpoints. Analysis emphasizes geometric polygons as aesthetic subunits. Evaluation of the complete nasal surface aesthetics is achieved using geometric polygons to define the existing deformity and aesthetic goals. The relationship between the dome triangles, interdomal triangle, facet polygons, and infralobular polygon are integrated to form the "diamond shape" light reflection on the nasal tip. The principles of geometric polygons allow the surgeon to analyze the deformities of the nose, define an operative plan to achieve specific goals, and select the appropriate operative technique. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

All-digital precision processing of ERTS images

NASA Technical Reports Server (NTRS)

Bernstein, R. (Principal Investigator)

1975-01-01

The author has identified the following significant results. Digital techniques have been developed and used to apply precision-grade radiometric and geometric corrections to ERTS MSS and RBV scenes. Geometric accuracies sufficient for mapping at 1:250,000 scale have been demonstrated. Radiometric quality has been superior to ERTS NDPF precision products. A configuration analysis has shown that feasible, cost-effective all-digital systems for correcting ERTS data are easily obtainable. This report contains a summary of all results obtained during this study and includes: (1) radiometric and geometric correction techniques, (2) reseau detection, (3) GCP location, (4) resampling, (5) alternative configuration evaluations, and (6) error analysis.

Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

DOEpatents

Blacker, Teddy D.

1994-01-01

An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.

Structural changes in cross-border liabilities: A multidimensional approach

NASA Astrophysics Data System (ADS)

Araújo, Tanya; Spelta, Alessandro

2014-01-01

We study the international interbank market through a geometric analysis of empirical data. The geometric analysis of the time series of cross-country liabilities shows that the systematic information of the interbank international market is contained in a space of small dimension. Geometric spaces of financial relations across countries are developed, for which the space volume, multivariate skewness and multivariate kurtosis are computed. The behavior of these coefficients reveals an important modification acting in the financial linkages since 1997 and allows us to relate the shape of the geometric space that emerges in recent years to the globally turbulent period that has characterized financial systems since the late 1990s. Here we show that, besides a persistent decrease in the volume of the geometric space since 1997, the observation of a generalized increase in the values of the multivariate skewness and kurtosis sheds some light on the behavior of cross-border interdependencies during periods of financial crises. This was found to occur in such a systematic fashion, that these coefficients may be used as a proxy for systemic risk.

Quantitative Analysis of Bone Microstructure Using Tomosynthesis

DTIC Science & Technology

2013-10-01

resolution of separation, thickness, distances, in-plane and out-of-plane geometric distortion, and density linearity. 5 To assess the minimum spacing... geometric accuracy phantom was created using four 1 mm beads, placed in four corners at 35 mm apart (Figure 1f). An embedded human vertebra was also...included in the phantom as a realistic reference material (Figure 1g). Figure 1: Tray of phantoms to assess DTS resolution, geometric distortion

Quantitative Analysis of Bone Microstructure Using Tomosynthesis

DTIC Science & Technology

2012-10-01

resolution of separation, thickness, distances, in-plane and out-of-plane geometric distortion, and density linearity. To assess the minimum spacing...volume, a geometric accuracy phantom was created using four 1 mm beads, placed in four corners at 35 mm apart (Figure 1f). An embedded human vertebra...was also included in the phantom as a realistic reference material (Figure 1g). Figure 1: Tray of phantoms to assess DTS resolution, geometric

Higuchi’s Method applied to detection of changes in timbre of digital sound synthesis of string instruments with the functional transformation method

NASA Astrophysics Data System (ADS)

Kanjanapen, Manorth; Kunsombat, Cherdsak; Chiangga, Surasak

2017-09-01

The functional transformation method (FTM) is a powerful tool for detailed investigation of digital sound synthesis by the physical modeling method, the resulting sound or measured vibrational characteristics at discretized points on real instruments directly solves the underlying physical effect of partial differential equation (PDE). In this paper, we present the Higuchi’s method to examine the difference between the timbre of tone and estimate fractal dimension of musical signals which contains information about their geometrical structure that synthesizes by FTM. With the Higuchi’s method we obtain the whole process is not complicated, fast processing, with the ease of analysis without expertise in the physics or virtuoso musicians and the easiest way for the common people can judge that sounds similarly presented.

Geometric constrained variational calculus. III: The second variation (Part II)

NASA Astrophysics Data System (ADS)

Massa, Enrico; Luria, Gianvittorio; Pagani, Enrico

2016-03-01

The problem of minimality for constrained variational calculus is analyzed within the class of piecewise differentiable extremaloids. A fully covariant representation of the second variation of the action functional based on a family of local gauge transformations of the original Lagrangian is proposed. The necessity of pursuing a local adaptation process, rather than the global one described in [1] is seen to depend on the value of certain scalar attributes of the extremaloid, here called the corners’ strengths. On this basis, both the necessary and the sufficient conditions for minimality are worked out. In the discussion, a crucial role is played by an analysis of the prolongability of the Jacobi fields across the corners. Eventually, in the appendix, an alternative approach to the concept of strength of a corner, more closely related to Pontryagin’s maximum principle, is presented.

Geometric morphometric analysis reveals age-related differences in the distal femur of Europeans.

PubMed

Cavaignac, Etienne; Savall, Frederic; Chantalat, Elodie; Faruch, Marie; Reina, Nicolas; Chiron, Philippe; Telmon, Norbert

2017-12-01

Few studies have looked into age-related variations in femur shape. We hypothesized that three-dimensional (3D) geometric morphometric analysis of the distal femur would reveal age-related differences. The purpose of this study was to show that differences in distal femur shape related to age could be identified, visualized, and quantified using three-dimensional (3D) geometric morphometric analysis. Geometric morphometric analysis was carried out on CT scans of the distal femur of 256 subjects living in the south of France. Ten landmarks were defined on 3D reconstructions of the distal femur. Both traditional metric and geometric morphometric analyses were carried out on these bone reconstructions. These analyses were used to identify trends in bone shape in various age-based subgroups (<40, 40-60, >60). Only the average bone shape of the < 40-year subgroup was statistically different from that of the other two groups. When the population was divided into two subgroups using 40 years of age as a threshold, the subject's age was correctly assigned 80% of the time. Age-related differences are present in this bone segment. This reliable, accurate method could be used for virtual autopsy and to perform diachronic and interethnic comparisons. Moreover, this study provides updated morphometric data for a modern population in the south of France. Manufacturers of knee replacement implants will have to adapt their prosthesis models as the population evolves over time.

Complex Ordered Patterns in Mechanical Instability Induced Geometrically Frustrated Triangular Cellular Structures

NASA Astrophysics Data System (ADS)

Kang, Sung Hoon; Shan, Sicong; Košmrlj, Andrej; Noorduin, Wim L.; Shian, Samuel; Weaver, James C.; Clarke, David R.; Bertoldi, Katia

2014-03-01

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

APPROACHES TO GEOMETRIC DATA ANALYSIS ON BIG AREA ADDITIVELY MANUFACTURED (BAAM) PARTS

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

Dreifus, Gregory D; Ally, Nadya R; Post, Brian K

The promise of additive manufacturing is that a user can design and print complex geometries that are very difficult, if not impossible, to machine. The capabilities of 3D printing are restricted by a number of factors, including properties of the build material, time constraints, and geometric design restrictions. In this paper, a thorough accounting and study of the geometric restrictions that exist in the current iteration of additive manufacturing (AM) fused deposition modeling (FDM) technologies are discussed. Offline and online methodologies for collecting data sets for qualitative analysis of large scale AM, in particular Oak Ridge National Laboratory s (ORNL)more » big area additive manufacturing (BAAM) system, are summarized. In doing so, a survey of tools for designers and software developers is provided. In particular, strategies in which geometric data can be used as training sets for smarter AM technologies in the future are explained as well.« less

Geometric Constraints and the Anatomical Interpretation of Twisted Plant Organ Phenotypes

PubMed Central

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

2011-01-01

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

Acoustic streaming related to minor loss phenomenon in differentially heated elements of thermoacoustic devices

NASA Astrophysics Data System (ADS)

Mironov, Mikhail; Gusev, Vitalyi; Auregan, Yves; Lotton, Pierrick; Bruneau, Michel; Piatakov, Pavel

2002-08-01

It is demonstrated that the differentially heated stack, the heart of all thermoacoustic devices, provides a source of streaming additional to those associated with Reynolds stresses in quasi-unidirectional gas flow. This source of streaming is related to temperature-induced asymmetry in the generation of vortices and turbulence near the stack ends. The asymmetry of the hydrodynamic effects in an otherwise geometrically symmetric stack is due to the temperature difference between stack ends. The proposed mechanism of streaming excitation in annular thermoacoustic devices operates even in the absence of thermo-viscous interaction of sound waves with resonator walls. copyright 2002 Acoustical Society of America.

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.

Parametric Study on the Response of Compression-Loaded Composite Shells With Geometric and Material Imperfections

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2004-01-01

The results of a parametric study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thinwalled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The imperfections considered include initial geometric shell-wall midsurface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these imperfections on the nonlinear responses and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable response characteristics.

Geometric Modelling of Tree Roots with Different Levels of Detail

NASA Astrophysics Data System (ADS)

Guerrero Iñiguez, J. I.

2017-09-01

This paper presents a geometric approach for modelling tree roots with different Levels of Detail, suitable for analysis of the tree anchoring, potentially occupied underground space, interaction with urban elements and damage produced and taken in the built-in environment. Three types of tree roots are considered to cover several species: tap root, heart shaped root and lateral roots. Shrubs and smaller plants are not considered, however, a similar approach can be considered if the information is available for individual species. The geometrical approach considers the difficulties of modelling the actual roots, which are dynamic and almost opaque to direct observation, proposing generalized versions. For each type of root, different geometric models are considered to capture the overall shape of the root, a simplified block model, and a planar or surface projected version. Lower detail versions are considered as compatibility version for 2D systems while higher detail models are suitable for 3D analysis and visualization. The proposed levels of detail are matched with CityGML Levels of Detail, enabling both analysis and aesthetic views for urban modelling.

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

NASA Technical Reports Server (NTRS)

Thomas, A. M.; Tiwari, S. N.

1997-01-01

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1985-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1986-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Towards spectral geometric methods for Euclidean quantum gravity

NASA Astrophysics Data System (ADS)

Panine, Mikhail; Kempf, Achim

2016-04-01

The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.

A New (?) Physiological Effect in a Demonstration Experiment in Geometrical Optics

ERIC Educational Resources Information Center

Ganci, S.

2018-01-01

A surprising phenomenology from a traditional demonstration experiment in Geometrical Optics reveals here an interesting matter of discussion and analysis. Hence, the main focus of this paper is to observe and discuss such an innovative phenomenology.

Theory for computing the size and shape of a region of influence associated with a maneuvering vehicle

NASA Technical Reports Server (NTRS)

Barger, R. L.

1980-01-01

A general procedure for computing the region of influence of a maneuvering vehicle is described. Basic differential geometric relations, including the use of a general trajectory parameter and the introduction of auxiliary variables in the envelope theory are presented. To illustrate the application of the method, the destruct region for a maneuvering fighter firing missiles is computed.

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.

New Geologic Map and Structural Cross Sections of the Death Valley Extended Terrain (southern Sierra Nevada, California to Spring Mountains, Nevada): Toward 3D Kinematic Reconstructions

NASA Astrophysics Data System (ADS)

Lutz, B. M.; Axen, G. J.; Phillips, F. M.

2017-12-01

Tectonic reconstructions for the Death Valley extended terrain (S. Sierra Nevada to Spring Mountains) have evolved to include a growing number of offset markers for strike-slip fault systems but are mainly map view (2D) and do not incorporate a wealth of additional constraints. We present a new 1:300,000 digital geologic map and structural cross sections, which provide a geometric framework for stepwise 3D reconstructions of Late Cenozoic extension and transtension. 3D models will decipher complex relationships between strike-slip, normal, and detachment faults and their role in accommodating large magnitude extension/rigid block rotation. Fault coordination is key to understanding how extensional systems and transform margins evolve with changing boundary conditions. 3D geometric and kinematic analysis adds key strain compatibility unavailable in 2D reconstructions. The stratigraphic framework of Fridrich and Thompson (2011) is applied to rocks outside of Death Valley. Cenozoic basin deposits are grouped into 6 assemblages differentiated by age, provenance, and bounding unconformities, which reflect Pacific-North American plate boundary events. Pre-Cenozoic rocks are grouped for utility: for example, Cararra Formation equivalents are grouped because they form a Cordilleran thrust decollement zone. Offset markers are summarized in the associated tectonic map. Other constraints include fault geometries and slip rates, age, geometry and provenance of Cenozoic basins, gravity, cooling histories of footwalls, and limited seismic/well data. Cross sections were constructed parallel to net-transport directions of fault blocks. Surface fault geometries were compiled from previous mapping and projected to depth using seismic/gravity data. Cooling histories of footwalls guided geometric interpretation of uplifted detachment footwalls. Mesh surfaces will be generated from 2D section lines to create a framework for stepwise 3D reconstruction of extension and transtension in the study area. Analysis of all available data in a seamless 3D framework should force more unique solutions to outstanding kinematic problems, provide a better understanding of the Cordilleran thrust belt, and constrain the mechanisms of strain partitioning between the upper and lower crust.

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.

On the simulation and mitigation of anisoplanatic optical turbulence for long range imaging

NASA Astrophysics Data System (ADS)

Hardie, Russell C.; LeMaster, Daniel A.

2017-05-01

We describe a numerical wave propagation method for simulating long range imaging of an extended scene under anisoplanatic conditions. Our approach computes an array of point spread functions (PSFs) for a 2D grid on the object plane. The PSFs are then used in a spatially varying weighted sum operation, with an ideal image, to produce a simulated image with realistic optical turbulence degradation. To validate the simulation we compare simulated outputs with the theoretical anisoplanatic tilt correlation and differential tilt variance. This is in addition to comparing the long- and short-exposure PSFs, and isoplanatic angle. Our validation analysis shows an excellent match between the simulation statistics and the theoretical predictions. The simulation tool is also used here to quantitatively evaluate a recently proposed block- matching and Wiener filtering (BMWF) method for turbulence mitigation. In this method block-matching registration algorithm is used to provide geometric correction for each of the individual input frames. The registered frames are then averaged and processed with a Wiener filter for restoration. A novel aspect of the proposed BMWF method is that the PSF model used for restoration takes into account the level of geometric correction achieved during image registration. This way, the Wiener filter is able fully exploit the reduced blurring achieved by registration. The BMWF method is relatively simple computationally, and yet, has excellent performance in comparison to state-of-the-art benchmark methods.

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.

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Dual nozzle aerodynamic and cooling analysis study. [dual throat and dual expander nozzles

NASA Technical Reports Server (NTRS)

Meagher, G. M.

1980-01-01

Geometric, aerodynamic flow field, performance prediction, and heat transfer analyses are considered for two advanced chamber nozzle concepts applicable to Earth-to-orbit engine systems. Topics covered include improvements to the dual throat aerodynamic and performance prediction program; geometric and flow field analyses of the dual expander concept; heat transfer analysis of both concepts, and engineering analysis of data from the NASA/MSFC hot-fire testing of a dual throat thruster model thrust chamber assembly. Preliminary results obtained are presented in graphs.

Ultimate boundedness stability and controllability of hereditary systems

NASA Technical Reports Server (NTRS)

Chukwu, E. N.

1979-01-01

By generalizing the Liapunov-Yoshizawa techniques, necessary and sufficient conditions are given for uniform boundedness and uniform ultimate boundedness of a rather general class of nonlinear differential equations of neutral type. Among the applications treated by the methods are the Lienard equation of neutral type and hereditary systems of Lurie type. The absolute stability of this later equation is also investigated. A certain existence result of a solution of a neutral functional differential inclusion with two point boundary values is applied to study the exact function space controllability of a nonlinear neutral functional differential control system. A geometric growth condition is used to characterize both the function space and Euclidean controllability of another nonlinear delay system which has a compact and convex control set. This yields conditions under which perturbed nonlinear delay controllable systems are controllable.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

NASA Astrophysics Data System (ADS)

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

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Sensitivity analysis of static resistance of slender beam under bending

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

Valeš, Jan

2016-06-08

The paper deals with statical and sensitivity analyses of resistance of simply supported I-beams under bending. The resistance was solved by geometrically nonlinear finite element method in the programme Ansys. The beams are modelled with initial geometrical imperfections following the first eigenmode of buckling. Imperfections were, together with geometrical characteristics of cross section, and material characteristics of steel, considered as random quantities. The method Latin Hypercube Sampling was applied to evaluate statistical and sensitivity resistance analyses.

3D tomographic reconstruction using geometrical models

NASA Astrophysics Data System (ADS)

Battle, Xavier L.; Cunningham, Gregory S.; Hanson, Kenneth M.

1997-04-01

We address the issue of reconstructing an object of constant interior density in the context of 3D tomography where there is prior knowledge about the unknown shape. We explore the direct estimation of the parameters of a chosen geometrical model from a set of radiographic measurements, rather than performing operations (segmentation for example) on a reconstructed volume. The inverse problem is posed in the Bayesian framework. A triangulated surface describes the unknown shape and the reconstruction is computed with a maximum a posteriori (MAP) estimate. The adjoint differentiation technique computes the derivatives needed for the optimization of the model parameters. We demonstrate the usefulness of the approach and emphasize the techniques of designing forward and adjoint codes. We use the system response of the University of Arizona Fast SPECT imager to illustrate this method by reconstructing the shape of a heart phantom.

Functional Heart Valve Scaffolds Obtained by Complete Decellularization of Porcine Aortic Roots in a Novel Differential Pressure Gradient Perfusion System

PubMed Central

Sierad, Leslie Neil; Shaw, Eliza Laine; Bina, Alexander; Brazile, Bryn; Rierson, Nicholas; Patnaik, Sourav S.; Kennamer, Allison; Odum, Rebekah; Cotoi, Ovidiu; Terezia, Preda; Branzaniuc, Klara; Smallwood, Harrison; Deac, Radu; Egyed, Imre; Pavai, Zoltan; Szanto, Annamaria; Harceaga, Lucian; Suciu, Horatiu; Raicea, Victor; Olah, Peter; Simionescu, Agneta; Liao, Jun; Movileanu, Ionela

2015-01-01

There is a great need for living valve replacements for patients of all ages. Such constructs could be built by tissue engineering, with perspective of the unique structure and biology of the aortic root. The aortic valve root is composed of several different tissues, and careful structural and functional consideration has to be given to each segment and component. Previous work has shown that immersion techniques are inadequate for whole-root decellularization, with the aortic wall segment being particularly resistant to decellularization. The aim of this study was to develop a differential pressure gradient perfusion system capable of being rigorous enough to decellularize the aortic root wall while gentle enough to preserve the integrity of the cusps. Fresh porcine aortic roots have been subjected to various regimens of perfusion decellularization using detergents and enzymes and results compared to immersion decellularized roots. Success criteria for evaluation of each root segment (cusp, muscle, sinus, wall) for decellularization completeness, tissue integrity, and valve functionality were defined using complementary methods of cell analysis (histology with nuclear and matrix stains and DNA analysis), biomechanics (biaxial and bending tests), and physiologic heart valve bioreactor testing (with advanced image analysis of open–close cycles and geometric orifice area measurement). Fully acellular porcine roots treated with the optimized method exhibited preserved macroscopic structures and microscopic matrix components, which translated into conserved anisotropic mechanical properties, including bending and excellent valve functionality when tested in aortic flow and pressure conditions. This study highlighted the importance of (1) adapting decellularization methods to specific target tissues, (2) combining several methods of cell analysis compared to relying solely on histology, (3) developing relevant valve-specific mechanical tests, and (4) in vitro testing of valve functionality. PMID:26467108

Nondynamic Tracking Using The Global Positioning System

NASA Technical Reports Server (NTRS)

Yunck, T. P.; Wu, Sien-Chong

1988-01-01

Report describes technique for using Global Positioning System (GPS) to determine position of low Earth orbiter without need for dynamic models. Differential observing strategy requires GPS receiver on user vehicle and network of six ground receivers. Computationally efficient technique delivers decimeter accuracy on orbits down to lowest altitudes. New technique nondynamic long-arc strategy having potential for accuracy of best dynamic techniques while retaining much of computational simplicity of geometric techniques.

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

Argo, P.E.; DeLapp, D.; Sutherland, C.D.

TRACKER is an extension of a three-dimensional Hamiltonian raytrace code developed some thirty years ago by R. Michael Jones. Subsequent modifications to this code, which is commonly called the {open_quotes}Jones Code,{close_quotes} were documented by Jones and Stephensen (1975). TRACKER incorporates an interactive user`s interface, modern differential equation integrators, graphical outputs, homing algorithms, and the Ionospheric Conductivity and Electron Density (ICED) ionosphere. TRACKER predicts the three-dimensional paths of radio waves through model ionospheres by numerically integrating Hamilton`s equations, which are a differential expression of Fermat`s principle of least time. By using continuous models, the Hamiltonian method avoids false caustics and discontinuousmore » raypath properties often encountered in other raytracing methods. In addition to computing the raypath, TRACKER also calculates the group path (or pulse travel time), the phase path, the geometrical (or {open_quotes}real{close_quotes}) pathlength, and the Doppler shift (if the time variation of the ionosphere is explicitly included). Computational speed can be traded for accuracy by specifying the maximum allowable integration error per step in the integration. Only geometrical optics are included in the main raytrace code; no partial reflections or diffraction effects are taken into account. In addition, TRACKER does not lend itself to statistical descriptions of propagation -- it requires a deterministic model of the ionosphere.« less

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

NASA Technical Reports Server (NTRS)

Johnson, W. L.

2009-01-01

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

From face to interface recognition: a differential geometric approach to distinguish DNA from RNA binding surfaces.

PubMed

Shazman, Shula; Elber, Gershon; Mandel-Gutfreund, Yael

2011-09-01

Protein nucleic acid interactions play a critical role in all steps of the gene expression pathway. Nucleic acid (NA) binding proteins interact with their partners, DNA or RNA, via distinct regions on their surface that are characterized by an ensemble of chemical, physical and geometrical properties. In this study, we introduce a novel methodology based on differential geometry, commonly used in face recognition, to characterize and predict NA binding surfaces on proteins. Applying the method on experimentally solved three-dimensional structures of proteins we successfully classify double-stranded DNA (dsDNA) from single-stranded RNA (ssRNA) binding proteins, with 83% accuracy. We show that the method is insensitive to conformational changes that occur upon binding and can be applicable for de novo protein-function prediction. Remarkably, when concentrating on the zinc finger motif, we distinguish successfully between RNA and DNA binding interfaces possessing the same binding motif even within the same protein, as demonstrated for the RNA polymerase transcription-factor, TFIIIA. In conclusion, we present a novel methodology to characterize protein surfaces, which can accurately tell apart dsDNA from an ssRNA binding interfaces. The strength of our method in recognizing fine-tuned differences on NA binding interfaces make it applicable for many other molecular recognition problems, with potential implications for drug design.

Selection of the best features for leukocytes classification in blood smear microscopic images

NASA Astrophysics Data System (ADS)

Sarrafzadeh, Omid; Rabbani, Hossein; Talebi, Ardeshir; Banaem, Hossein Usefi

2014-03-01

Automatic differential counting of leukocytes provides invaluable information to pathologist for diagnosis and treatment of many diseases. The main objective of this paper is to detect leukocytes from a blood smear microscopic image and classify them into their types: Neutrophil, Eosinophil, Basophil, Lymphocyte and Monocyte using features that pathologists consider to differentiate leukocytes. Features contain color, geometric and texture features. Colors of nucleus and cytoplasm vary among the leukocytes. Lymphocytes have single, large, round or oval and Monocytes have singular convoluted shape nucleus. Nucleus of Eosinophils is divided into 2 segments and nucleus of Neutrophils into 2 to 5 segments. Lymphocytes often have no granules, Monocytes have tiny granules, Neutrophils have fine granules and Eosinophils have large granules in cytoplasm. Six color features is extracted from both nucleus and cytoplasm, 6 geometric features only from nucleus and 6 statistical features and 7 moment invariants features only from cytoplasm of leukocytes. These features are fed to support vector machine (SVM) classifiers with one to one architecture. The results obtained by applying the proposed method on blood smear microscopic image of 10 patients including 149 white blood cells (WBCs) indicate that correct rate for all classifiers are above 93% which is in a higher level in comparison with previous literatures.

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.

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

NASA Astrophysics Data System (ADS)

Dion, Marc; Kashyap, Satish; Louie, Aloisius

1991-06-01

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

SMP: A solid modeling program version 2.0

NASA Technical Reports Server (NTRS)

Randall, D. P.; Jones, K. H.; Vonofenheim, W. H.; Gates, R. L.; Matthews, C. G.

1986-01-01

The Solid Modeling Program (SMP) provides the capability to model complex solid objects through the composition of primitive geometric entities. In addition to the construction of solid models, SMP has extensive facilities for model editing, display, and analysis. The geometric model produced by the software system can be output in a format compatible with existing analysis programs such as PATRAN-G. The present version of the SMP software supports six primitives: boxes, cones, spheres, paraboloids, tori, and trusses. The details for creating each of the major primitive types is presented. The analysis capabilities of SMP, including interfaces to existing analysis programs, are discussed.

Analytical study on the thermal performance of a partially wet constructal T-shaped fin

NASA Astrophysics Data System (ADS)

Hazarika, Saheera Azmi; Zeeshan, Mohd; Bhanja, Dipankar; Nath, Sujit

2017-07-01

The present paper addresses the thermal analysis of a T-shaped fin under partially wet condition by adopting a cubic variation of the humidity ratio of saturated air with the corresponding fin surface temperature. The point separating the dry and wet parts may lie either in the flange or stem part of the fin and so, two different cases having different governing equations and boundary conditions are analyzed in this paper. Since the governing equations are highly non-linear, they are solved by using an analytical technique called the Differential Transform Method and subsequently, the dry fin length, temperature distribution and fin performances are evaluated and analyzed for a wide range of the various psychometric, geometric and thermo-physical parameters. Finally, it can be highlighted that relative humidity has a pronounced effect on the performance parameters when the fin surface is partially wet whereas this effect is marginally small for fully wet surface.

The Effect of Basis Selection on Static and Random Acoustic Response Prediction Using a Nonlinear Modal Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2005-01-01

An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.

Enhanced LOD Concepts for Virtual 3d City Models

NASA Astrophysics Data System (ADS)

Benner, J.; Geiger, A.; Gröger, G.; Häfele, K.-H.; Löwner, M.-O.

2013-09-01

Virtual 3D city models contain digital three dimensional representations of city objects like buildings, streets or technical infrastructure. Because size and complexity of these models continuously grow, a Level of Detail (LoD) concept effectively supporting the partitioning of a complete model into alternative models of different complexity and providing metadata, addressing informational content, complexity and quality of each alternative model is indispensable. After a short overview on various LoD concepts, this paper discusses the existing LoD concept of the CityGML standard for 3D city models and identifies a number of deficits. Based on this analysis, an alternative concept is developed and illustrated with several examples. It differentiates between first, a Geometric Level of Detail (GLoD) and a Semantic Level of Detail (SLoD), and second between the interior building and its exterior shell. Finally, a possible implementation of the new concept is demonstrated by means of an UML model.

Configuration color vision tests: the interaction between aging and the complexity of figure-ground segregation.

PubMed

Stanford, T; Pollack, R H

1984-09-01

A cross-sectional study comparing response time and the percentage of items correctly identified in three color vision tests (Pflügertrident, HRR-AO pseudoisochromatic plates, and AO pseudoisochromatic plates) was carried out on 72 women (12 in each decade) ranging from ages 20 to 79 years. Overall, time scores increased across the age groups. Analysis of the correctness scores indicated that the AO pseudoisochromatic plates requiring the identification of numbers was more difficult than the other tests which consisted of geometric forms or the letter E. This differential difficulty increased as a function of age. There was no indication of color defect per se which led to the conclusion that figure complexity may be the key variable determining performance. The results were similar to those obtained by Lee and Pollack (1978) in their study of the Embedded Figures Test.

STELLTRANS: A Transport Analysis Suite for Stellarators

NASA Astrophysics Data System (ADS)

Mittelstaedt, Joseph; Lazerson, Samuel; Pablant, Novimir; Weir, Gavin; W7-X Team

2016-10-01

The stellarator transport code STELLTRANS allows us to better analyze the power balance in W7-X. Although profiles of temperature and density are measured experimentally, geometrical factors are needed in conjunction with these measurements to properly analyze heat flux densities in stellarators. The STELLTRANS code interfaces with VMEC to find an equilibrium flux surface configuration and with TRAVIS to determine the RF heating and current drive in the plasma. Stationary transport equations are then considered which are solved using a boundary value differential equation solver. The equations and quantities considered are averaged over flux surfaces to reduce the system to an essentially one dimensional problem. We have applied this code to data from W-7X and were able to calculate the heat flux coefficients. We will also present extensions of the code to a predictive capacity which would utilize DKES to find neoclassical transport coefficients to update the temperature and density profiles.

On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis

NASA Astrophysics Data System (ADS)

Shao, S.; Gao, Z.

2017-10-01

Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.

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.

GOATS Image Projection Component

NASA Technical Reports Server (NTRS)

Haber, Benjamin M.; Green, Joseph J.

2011-01-01

When doing mission analysis and design of an imaging system in orbit around the Earth, answering the fundamental question of imaging performance requires an understanding of the image products that will be produced by the imaging system. GOATS software represents a series of MATLAB functions to provide for geometric image projections. Unique features of the software include function modularity, a standard MATLAB interface, easy-to-understand first-principles-based analysis, and the ability to perform geometric image projections of framing type imaging systems. The software modules are created for maximum analysis utility, and can all be used independently for many varied analysis tasks, or used in conjunction with other orbit analysis tools.

Transactions of the Army Conference on Applied Mathematics and Computing (1st) Held at Washington, DC on 9-11 May 1983

DTIC Science & Technology

1984-02-01

I . . . . . . An Introduction to Geometric Programming Patrick D. Allen and David W. Baker . . . . . . , . . . . . . . Space and Time...Zarwyn, US-Army Electronics R & D Comhiand GEOMETRIC PROGRAMING SPACE AND TIFFE ANALYSIS IN DYNAMIC PROGRAMING ALGORITHMS Renne..tf Stizti, AkeanXa...physical and parameter space can be connected by asymptotic matching. The purpose of the asymptotic analysis is to define the simplest problems

Artefacts in geometric phase analysis of compound materials.

PubMed

Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M

2015-10-01

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. Copyright © 2015 Elsevier B.V. All rights reserved.

Analysis for delamination initiation in postbuckled dropped-ply laminates

NASA Technical Reports Server (NTRS)

Davila, Carlos G.; Johnson, Eric R.

1992-01-01

The compression strength of dropped-ply, graphite-epoxy laminated plates for the delamination mode of failure is studied by analysis and corroborated with experiments. The nonlinear response of the test specimens is modeled by a geometrically nonlinear finite element analysis. The methodology for predicting delamination is based on a quadratic interlaminar stress criterion evaluated at a characteristic distance from the ply drop-off. The compression strength of specimens exhibiting a linear response is greater than the compression strength of specimens with the same layup exhibiting a geometrically nonlinear response. The analyses for both linear and nonlinear response show that severe interlaminar stress gradients occur in the interfaces at the drop-off because of the thickness/stiffness discontinuity. However, these interlaminar stress distributions are altered in the geometrically nonlinear response such that, with increasing load, their growth at the center of the laminate is retarded while their growth near the unloaded supported edge is increased.

Hyperspectral target detection analysis of a cluttered scene from a virtual airborne sensor platform using MuSES

NASA Astrophysics Data System (ADS)

Packard, Corey D.; Viola, Timothy S.; Klein, Mark D.

2017-10-01

The ability to predict spectral electro-optical (EO) signatures for various targets against realistic, cluttered backgrounds is paramount for rigorous signature evaluation. Knowledge of background and target signatures, including plumes, is essential for a variety of scientific and defense-related applications including contrast analysis, camouflage development, automatic target recognition (ATR) algorithm development and scene material classification. The capability to simulate any desired mission scenario with forecast or historical weather is a tremendous asset for defense agencies, serving as a complement to (or substitute for) target and background signature measurement campaigns. In this paper, a systematic process for the physical temperature and visible-through-infrared radiance prediction of several diverse targets in a cluttered natural environment scene is presented. The ability of a virtual airborne sensor platform to detect and differentiate targets from a cluttered background, from a variety of sensor perspectives and across numerous wavelengths in differing atmospheric conditions, is considered. The process described utilizes the thermal and radiance simulation software MuSES and provides a repeatable, accurate approach for analyzing wavelength-dependent background and target (including plume) signatures in multiple band-integrated wavebands (multispectral) or hyperspectrally. The engineering workflow required to combine 3D geometric descriptions, thermal material properties, natural weather boundary conditions, all modes of heat transfer and spectral surface properties is summarized. This procedure includes geometric scene creation, material and optical property attribution, and transient physical temperature prediction. Radiance renderings, based on ray-tracing and the Sandford-Robertson BRDF model, are coupled with MODTRAN for the inclusion of atmospheric effects. This virtual hyperspectral/multispectral radiance prediction methodology has been extensively validated and provides a flexible process for signature evaluation and algorithm development.

A new look at the Feynman ‘hodograph’ approach to the Kepler first law

NASA Astrophysics Data System (ADS)

Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano

2016-03-01

Hodographs for the Kepler problem are circles. This fact, known for almost two centuries, still provides the simplest path to derive the Kepler first law. Through Feynman’s ‘lost lecture’, this derivation has now reached a wider audience. Here we look again at Feynman’s approach to this problem, as well as the recently suggested modification by van Haandel and Heckman (vHH), with two aims in mind, both of which extend the scope of the approach. First we review the geometric constructions of the Feynman and vHH approaches (that prove the existence of elliptic orbits without making use of integral calculus or differential equations) and then extend the geometric approach to also cover the hyperbolic orbits (corresponding to E\\gt 0). In the second part we analyse the properties of the director circles of the conics, which are used to simplify the approach, and we relate with the properties of the hodographs and Laplace-Runge-Lenz vector the constant of motion specific to the Kepler problem. Finally, we briefly discuss the generalisation of the geometric method to the Kepler problem in configuration spaces of constant curvature, i.e. in the sphere and the hyperbolic plane.

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

NASA Astrophysics Data System (ADS)

Mylonas, Dionysios; Schupp, Peter; Szabo, Richard J.

2014-12-01

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting, nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.

Stock price prediction using geometric Brownian motion

NASA Astrophysics Data System (ADS)

Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM

2018-03-01

Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.

Symmetry analysis of talus bone

PubMed Central

Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.

2014-01-01

Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391

3D volumetry comparison using 3T magnetic resonance imaging between normal and adenoma-containing pituitary glands.

PubMed

Roldan-Valadez, Ernesto; Garcia-Ulloa, Ana Cristina; Gonzalez-Gutierrez, Omar; Martinez-Lopez, Manuel

2011-01-01

Computed-assisted three-dimensional data (3D) allows for an accurate evaluation of volumes compared with traditional measurements. An in vitro method comparison between geometric volume and 3D volumetry to obtain reference data for pituitary volumes in normal pituitary glands (PGs) and PGs containing adenomas. Prospective, transverse, analytical study. Forty-eight subjects underwent brain magnetic resonance imaging (MRI) with 3D sequencing for computer-aided volumetry. PG phantom volumes by both methods were compared. Using the best volumetric method, volumes of normal PGs and PGs with adenoma were compared. Statistical analysis used the Bland-Altman method, t-statistics, effect size and linear regression analysis. Method comparison between 3D volumetry and geometric volume revealed a lower bias and precision for 3D volumetry. A total of 27 patients exhibited normal PGs (mean age, 42.07 ± 16.17 years), although length, height, width, geometric volume and 3D volumetry were greater in women than in men. A total of 21 patients exhibited adenomas (mean age 39.62 ± 10.79 years), and length, height, width, geometric volume and 3D volumetry were greater in men than in women, with significant volumetric differences. Age did not influence pituitary volumes on linear regression analysis. Results from the present study showed that 3D volumetry was more accurate than the geometric method. In addition, the upper normal limits of PGs overlapped with lower volume limits during early stage microadenomas.

Experimental design and modeling of a microscale differential thermal calorimeter for the purposes of cryopreservation

NASA Astrophysics Data System (ADS)

Armes, James L.

In order to develop successful cryopreservation protocols for various biological materials, it is necessary to determine the thermodynamic properties of nanoliter- scale biological samples: ranging from heat capacity to heat of fusion. Differential thermal analysis is a calorimetric technique which is efficacious at determining these thermodynamic properties and will help lend insight into the formation of intracellular ice which depends heavily on the rate at which the sample is cooled. If too much intracellular ice is formed during the cooling process, the biological material can be destroyed. To investigate the effects of a range of cooling and warming rates on a cell, a control system and data acquisition software has been developed for use with a custom microfabricated differential thermal analyzer (muDTA). Utilizing either an a-priori prediction of the muDTA's thermal response or an integrated software-based PID control system, the program developed allows for precise control over the cooling and warming rate of the muDTA. In order to enhance the accuracy of the a-priori predicted current profile, a 2D numeric model was developed of the muDTA. This model also has allowed for geometric optimization to be performed on the next generation prototype of the muDTA. The muDTA has been shown to accurately measure the freezing point and heat of fusion of deionized water samples, with sample volumes on the order of nanoliters. The heat capacity of dimethyl sulfoxide (DMSO) has also been experimentally determined.

Frequencies and Flutter Speed Estimation for Damaged Aircraft Wing Using Scaled Equivalent Plate Analysis

NASA Technical Reports Server (NTRS)

Krishnamurthy, Thiagarajan

2010-01-01

Equivalent plate analysis is often used to replace the computationally expensive finite element analysis in initial design stages or in conceptual design of aircraft wing structures. The equivalent plate model can also be used to design a wind tunnel model to match the stiffness characteristics of the wing box of a full-scale aircraft wing model while satisfying strength-based requirements An equivalent plate analysis technique is presented to predict the static and dynamic response of an aircraft wing with or without damage. First, a geometric scale factor and a dynamic pressure scale factor are defined to relate the stiffness, load and deformation of the equivalent plate to the aircraft wing. A procedure using an optimization technique is presented to create scaled equivalent plate models from the full scale aircraft wing using geometric and dynamic pressure scale factors. The scaled models are constructed by matching the stiffness of the scaled equivalent plate with the scaled aircraft wing stiffness. It is demonstrated that the scaled equivalent plate model can be used to predict the deformation of the aircraft wing accurately. Once the full equivalent plate geometry is obtained, any other scaled equivalent plate geometry can be obtained using the geometric scale factor. Next, an average frequency scale factor is defined as the average ratio of the frequencies of the aircraft wing to the frequencies of the full-scaled equivalent plate. The average frequency scale factor combined with the geometric scale factor is used to predict the frequency response of the aircraft wing from the scaled equivalent plate analysis. A procedure is outlined to estimate the frequency response and the flutter speed of an aircraft wing from the equivalent plate analysis using the frequency scale factor and geometric scale factor. The equivalent plate analysis is demonstrated using an aircraft wing without damage and another with damage. Both of the problems show that the scaled equivalent plate analysis can be successfully used to predict the frequencies and flutter speed of a typical aircraft wing.

Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

NASA Astrophysics Data System (ADS)

Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea

2017-07-01

This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

Automatic differentiation for Fourier series and the radii polynomial approach

NASA Astrophysics Data System (ADS)

Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian

2016-11-01

In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).

A prospective microstructure imaging study in mixed-martial artists using geometric measures and diffusion tensor imaging: methods and findings

PubMed Central

Mayer, Andrew R.; Ling, Josef M.; Dodd, Andrew B.; Meier, Timothy B.; Hanlon, Faith M.; Klimaj, Stefan D.

2018-01-01

Although diffusion magnetic resonance imaging (dMRI) has been widely used to characterize the effects of repetitive mild traumatic brain injury (rmTBI), to date no studies have investigated how novel geometric models of microstructure relate to more typical diffusion tensor imaging (DTI) sequences. Moreover, few studies have evaluated the sensitivity of different registration pipelines (non-linear, linear and tract-based spatial statistics) for detecting dMRI abnormalities in clinical populations. Results from single-subject analyses in healthy controls (HC) indicated a strong negative relationship between fractional anisotropy (FA) and orientation dispersion index (ODI) in both white and gray matter. Equally important, only moderate relationships existed between all other estimates of free/intracellular water volume fractions and more traditional DTI metrics (FA, mean, axial and radial diffusivity). These findings suggest that geometric measures provide differential information about the cellular microstructure relative to traditional DTI measures. Results also suggest greater sensitivity for non-linear registration pipelines that maximize the anatomical information available in T1-weighted images. Clinically, rmTBI resulted in a pattern of decreased FA and increased ODI, largely overlapping in space, in conjunction with increased intracellular and free water fractions, highlighting the potential role of edema following repeated head trauma. In summary, current results suggest that geometric models of diffusion can provide relatively unique information regarding potential mechanisms of pathology that contribute to long-term neurological damage. PMID:27071950

A prospective microstructure imaging study in mixed-martial artists using geometric measures and diffusion tensor imaging: methods and findings.

PubMed

Mayer, Andrew R; Ling, Josef M; Dodd, Andrew B; Meier, Timothy B; Hanlon, Faith M; Klimaj, Stefan D

2017-06-01

Although diffusion magnetic resonance imaging (dMRI) has been widely used to characterize the effects of repetitive mild traumatic brain injury (rmTBI), to date no studies have investigated how novel geometric models of microstructure relate to more typical diffusion tensor imaging (DTI) sequences. Moreover, few studies have evaluated the sensitivity of different registration pipelines (non-linear, linear and tract-based spatial statistics) for detecting dMRI abnormalities in clinical populations. Results from single-subject analyses in healthy controls (HC) indicated a strong negative relationship between fractional anisotropy (FA) and orientation dispersion index (ODI) in both white and gray matter. Equally important, only moderate relationships existed between all other estimates of free/intracellular water volume fractions and more traditional DTI metrics (FA, mean, axial and radial diffusivity). These findings suggest that geometric measures provide differential information about the cellular microstructure relative to traditional DTI measures. Results also suggest greater sensitivity for non-linear registration pipelines that maximize the anatomical information available in T 1 -weighted images. Clinically, rmTBI resulted in a pattern of decreased FA and increased ODI, largely overlapping in space, in conjunction with increased intracellular and free water fractions, highlighting the potential role of edema following repeated head trauma. In summary, current results suggest that geometric models of diffusion can provide relatively unique information regarding potential mechanisms of pathology that contribute to long-term neurological damage.

Chaotic dynamics of flexible Euler-Bernoulli beams

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

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl; Krysko, A. V., E-mail: anton.krysko@gmail.com; Kutepov, I. E., E-mail: iekutepov@gmail.com

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions ismore » carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.« less

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.

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

PubMed

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

2012-06-01

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

Geometric Bioinspired Networks for Recognition of 2-D and 3-D Low-Level Structures and Transformations.

PubMed

Bayro-Corrochano, Eduardo; Vazquez-Santacruz, Eduardo; Moya-Sanchez, Eduardo; Castillo-Munis, Efrain

2016-10-01

This paper presents the design of radial basis function geometric bioinspired networks and their applications. Until now, the design of neural networks has been inspired by the biological models of neural networks but mostly using vector calculus and linear algebra. However, these designs have never shown the role of geometric computing. The question is how biological neural networks handle complex geometric representations involving Lie group operations like rotations. Even though the actual artificial neural networks are biologically inspired, they are just models which cannot reproduce a plausible biological process. Until now researchers have not shown how, using these models, one can incorporate them into the processing of geometric computing. Here, for the first time in the artificial neural networks domain, we address this issue by designing a kind of geometric RBF using the geometric algebra framework. As a result, using our artificial networks, we show how geometric computing can be carried out by the artificial neural networks. Such geometric neural networks have a great potential in robot vision. This is the most important aspect of this contribution to propose artificial geometric neural networks for challenging tasks in perception and action. In our experimental analysis, we show the applicability of our geometric designs, and present interesting experiments using 2-D data of real images and 3-D screw axis data. In general, our models should be used to process different types of inputs, such as visual cues, touch (texture, elasticity, temperature), taste, and sound. One important task of a perception-action system is to fuse a variety of cues coming from the environment and relate them via a sensor-motor manifold with motor modules to carry out diverse reasoned actions.

Multi-Disciplinary, Multi-Fidelity Discrete Data Transfer Using Degenerate Geometry Forms

NASA Technical Reports Server (NTRS)

Olson, Erik D.

2016-01-01

In a typical multi-fidelity design process, different levels of geometric abstraction are used for different analysis methods, and transitioning from one phase of design to the next often requires a complete re-creation of the geometry. To maintain consistency between lower-order and higher-order analysis results, Vehicle Sketch Pad (OpenVSP) recently introduced the ability to generate and export several degenerate forms of the geometry, representing the type of abstraction required to perform low- to medium-order analysis for a range of aeronautical disciplines. In this research, the functionality of these degenerate models was extended, so that in addition to serving as repositories for the geometric information that is required as input to an analysis, the degenerate models can also store the results of that analysis mapped back onto the geometric nodes. At the same time, the results are also mapped indirectly onto the nodes of lower-order degenerate models using a process called aggregation, and onto higher-order models using a process called disaggregation. The mapped analysis results are available for use by any subsequent analysis in an integrated design and analysis process. A simple multi-fidelity analysis process for a single-aisle subsonic transport aircraft is used as an example case to demonstrate the value of the approach.

Photometric properties of Ceres from telescopic observations using Dawn Framing Camera color filters

NASA Astrophysics Data System (ADS)

Reddy, Vishnu; Li, Jian-Yang; Gary, Bruce L.; Sanchez, Juan A.; Stephens, Robert D.; Megna, Ralph; Coley, Daniel; Nathues, Andreas; Le Corre, Lucille; Hoffmann, Martin

2015-11-01

The dwarf planet Ceres is likely differentiated similar to the terrestrial planets but with a water/ice dominated mantle and an aqueously altered crust. Detailed modeling of Ceres' phase function has never been performed to understand its surface properties. The Dawn spacecraft began orbital science operations at the dwarf planet in April 2015. We observed Ceres with flight spares of the seven Dawn Framing Camera color filters mounted on ground-based telescopes over the course of three years to model its phase function versus wavelength. Our analysis shows that the modeled geometric albedos derived from both the IAU HG model and the Hapke model are consistent with a flat and featureless spectrum of Ceres, although the values are ∼10% higher than previous measurements. Our models also suggest a wavelength dependence of Ceres' phase function. The IAU G-parameter and the Hapke single-particle phase function parameter, g, are both consistent with decreasing (shallower) phase slope with increasing wavelength. Such a wavelength dependence of phase function is consistent with reddening of spectral slope with increasing phase angle, or phase-reddening. This phase reddening is consistent with previous spectra of Ceres obtained at various phase angles archived in the literature, and consistent with the fact that the modeled geometric albedo spectrum of Ceres is the bluest of all spectra because it represents the spectrum at 0° phase angle. Ground-based FC color filter lightcurve data are consistent with HST albedo maps confirming that Ceres' lightcurve is dominated by albedo and not shape. We detected a positive correlation between 1.1-μm absorption band depth and geometric albedo suggesting brighter areas on Ceres have absorption bands that are deeper. We did not see the "extreme" slope values measured by Perna et al. (Perna, D., et al. [2015]. Astron. Astrophys. 575 (L1-6)), which they have attributed to "resurfacing episodes" on Ceres.

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).

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Rotation covariant image processing for biomedical applications.

PubMed

Skibbe, Henrik; Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences.

Expressions Module for the Satellite Orbit Analysis Program

NASA Technical Reports Server (NTRS)

Edmonds, Karina

2008-01-01

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

Dynamic modeling of spacecraft in a collisionless plasma

NASA Technical Reports Server (NTRS)

Katz, I.; Parks, D. E.; Wang, S. S.; Wilson, A.

1977-01-01

A new computational model is described which can simulate the charging of complex geometrical objects in three dimensions. Two sample calculations are presented. In the first problem, the capacitance to infinity of a complex object similar to a satellite with solar array paddles is calculated. The second problem concerns the dynamical charging of a conducting cube partially covered with a thin dielectric film. In this calculation, the photoemission results in differential charging of the object.

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

Differential Drag Analysis to Infer the Geometrical Configuration of a Cubesat

NASA Astrophysics Data System (ADS)

Bussy-Virat, C.; Ridley, A. J.; Cutler, J.; Sharma, S.; Judd, E.

2016-12-01

On May 16th, 2016, the Miniature X-ray Solar Spectrometer (MinXSS) and the CubeSat investigating Atmospheric Density Response to Extreme driving (CADRE) were deployed from the International Space Station. While communication with MinXSS was quickly established, it has been impossible to interact with CADRE thus far. A likely reason could be that its solar panels did not open, preventing the antenna from fully functioning and eliminating communication with the ground stations. An orbit propagator that was developed for mission design and analysis was used to model the trajectories of the satellites. By comparing the drag accelerations on the two CubeSats, we are attempting to infer the number of solar panels that CADRE deployed. Ensemble simulations allow the modeling of uncertainties on its attitude, as it is likely to tumble if no solar panel was deployed. This technique introduces many challenges, as there are many unknowns, including the drag coefficient, the attitude, and the thermospheric density. We present results of this study, as well as these challenges that were encountered.

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.

Probing the links between language and mathematical conceptualisation

NASA Astrophysics Data System (ADS)

Bell, Garry; Woo, Jeong Ho

1998-04-01

Although it is well known that the number-naming grammars of some Asian languages affect the number conceptualisation and operational capacity of the young children who use them, language structure in other fields of the mathematical register appears to have been underemphasised in explanations of the differential mathematical attainment of East Asian and western students. This study probed the conceptual structures which samples of Year 9 students in Korea and Australia had constructed for various geometrical terms. The two samples of students exhibited major differences in definition ranking preferences on angle, and in semantic profiles for parallelogram, triangle, square, circle, cylinder, trapezium and line. It is hypothesised that these differences may be due in part to the noun phrase grammar differences between Korean and English, and to the syntax and semantic transparency of some Korean geometrical names. Results indicated reinforcement for the Vygotskian view that culturally imposed language structures directly influence the cognitive development of the learner.

Geometric correction of synchronous scanned Operational Modular Imaging Spectrometer II hyperspectral remote sensing images using spatial positioning data of an inertial navigation system

NASA Astrophysics Data System (ADS)

Zhou, Xiaohu; Neubauer, Franz; Zhao, Dong; Xu, Shichao

2015-01-01

The high-precision geometric correction of airborne hyperspectral remote sensing image processing was a hard nut to crack, and conventional methods of remote sensing image processing by selecting ground control points to correct the images are not suitable in the correction process of airborne hyperspectral image. The optical scanning system of an inertial measurement unit combined with differential global positioning system (IMU/DGPS) is introduced to correct the synchronous scanned Operational Modular Imaging Spectrometer II (OMIS II) hyperspectral remote sensing images. Posture parameters, which were synchronized with the OMIS II, were first obtained from the IMU/DGPS. Second, coordinate conversion and flight attitude parameters' calculations were conducted. Third, according to the imaging principle of OMIS II, mathematical correction was applied and the corrected image pixels were resampled. Then, better image processing results were achieved.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

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

1982-01-01

An initial value problem for the autonomous system of ordinary differential equations dy/dt = f(y), where y is a vector, is considered. In a number of practical applications the interest lies in obtaining the curve traced by the solution y. These applications include the computation of trajectories in mechanical problems. The term 'trajectory problem' is employed to refer to these cases. Lambert and McLeod (1979) have introduced a method involving local rotation of the axes in the y-plane for the two-dimensional case. The present investigation continues the study of difference schemes specifically derived for trajectory problems. A simple geometrical way of constructing such methods is presented, and the local accuracy of the schemes is investigated. A circularly exact, fixed-step predictor-corrector algorithm is defined, and a variable-step version of a circularly exact algorithm is presented.

Competing spin phases in geometrically frustrated magnetic molecules.

PubMed

Schröder, Christian; Nojiri, Hiroyuki; Schnack, Jürgen; Hage, Peter; Luban, Marshall; Kögerler, Paul

2005-01-14

We identify a class of zero-dimensional classical and quantum Heisenberg spin systems exhibiting anomalous behavior in an external magnetic field B similar to that found for the geometrically frustrated kagome lattice of classical spins. Our calculations for the isotropic Heisenberg model show the emergence of a pronounced minimum in the differential susceptibility dM/dB at B(sat)/3 as the temperature T is raised from 0 K for structures based on corner-sharing triangles, specifically the octahedron, cuboctahedron, and icosidodecahedron. As the first experimental evidence we note that the giant Keplerate magnetic molecule {Mo(72)Fe(30)} (Fe(3+) ions on the 30 vertices of an icosidodecahedron) exhibits this behavior. For low T when B approximately B(sat)/3 two competing families of spin configurations exist of which one behaves magnetically "stiff" leading to a reduction of dM/dB.

Geometrothermodynamics for black holes and de Sitter space

NASA Astrophysics Data System (ADS)

Kurihara, Yoshimasa

2018-02-01

A general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald's method using geometrical language, e.g., via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The correspondence between the thermodynamics and general relativity can be seen clearly by comparing the two expressions. This comparison requires a modification of Wald's method. The new method is applied to Schwarzschild, Kerr, and Kerr-Newman black holes and de Sitter space. The results are consistent with previous results obtained using various independent methods. This strongly supports the validity of the area theorem for black holes.

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.

Landmark-based geometric morphometric analysis of wing shape among certain species of Aedes mosquitoes in District Dehradun (Uttarakhand), India.

PubMed

Mondal, Ritwik; Devi, N Pemola; Jauhari, R K

2015-06-01

Insect wing morphology has been used in many studies to describe variations among species and populations using traditional morphometrics, and more recently geometric morphometrics. A landmark-based geometric morphometric analysis of the wings of three species of Aedes (Diptera: Culicidae), viz. Ae. aegypti, Ae. albopictus and Ae. pseudotaeniatus, at District Dehradun was conducted belling on the fact that it can provide insight into the population structure, ecology and taxonomic identification. Adult Aedes mosquito specimens were randomly collected using aerial nets and morphologically examined and identified. The landmarks were identified on the basis of landmark based geometric morphometric analysis thin-plate spline (mainly the software tps-Util 1.28; tps-Dig 1.40; tps-Relw 1.53; and tps-Spline 1.20) and integrated morphometrics programme (mainly twogroup win8 and PCA win8) were utilized. In relative warp (RW) analysis, the first two RW of Ae. aegypti accounted for the highest value (95.82%), followed by Ae. pseudotaeniatus (90.89%), while the lowest (90.12%) being recorded for Ae. albopictus. The bending energies of Ae. aegypti and Ae. pseudotaeniatus were quite identical being 0.1882 and 0.1858 respectively, while Ae. albopictus recorded the highest value of 0.9774. The mean difference values of the distances among Aedes species performing Hotelling's T 2 test were significantly high, predicting major differences among the taxa. In PCA analysis, the horizontal and vertical axis summarized 52.41 and 23.30% of variances respectively. The centroid size exhibited significant differences among populations (non-parametric Kruskal-Wallis test, H = 10.56, p < 0.01). It has been marked out that the geometric morphometrics utilizes powerful and comprehensive statistical procedures to analyze the shape differences of a morphological feature, assuming that the studied mosquitoes may represent different genotypes and probably come from one diverse gene pool.

Design study of the geometry of the blanking tool to predict the burr formation of Zircaloy-4 sheet

NASA Astrophysics Data System (ADS)

Ha, Jisun; Lee, Hyungyil; Kim, Dongchul; Kim, Naksoo

2013-12-01

In this work, we investigated factors that influence burr formation for zircaloy-4 sheet used for spacer grids of nuclear fuel roads. Factors we considered are geometric factors of punch. We changed clearance and velocity in order to consider the failure parameters, and we changed shearing angle and corner radius of L-shaped punch in order to consider geometric factors of punch. First, we carried out blanking test with failure parameter of GTN model using L-shaped punch. The tendency of failure parameters and geometric factors that affect burr formation by analyzing sheared edges is investigated. Consequently, geometric factor's influencing on the burr formation is also high as failure parameters. Then, the sheared edges and burr formation with failure parameters and geometric factors is investigated using FE analysis model. As a result of analyzing sheared edges with the variables, we checked geometric factors more affect burr formation than failure parameters. To check the reliability of the FE model, the blanking force and the sheared edges obtained from experiments are compared with the computations considering heat transfer.

Measure of Backscatter for small particles of atmosphere by lasers

NASA Astrophysics Data System (ADS)

Abud, Mariam M.

2018-05-01

It developed a program for the atmosphere to study the backscattering for contents gas and molecules, aerosol, fog, clouds and rain droplets. By using Rayleigh, Mie and geometric scattering. The aim of research, using different types of lasers from various optical region, is to calculate differential cross scatter section and backscatter of atmosphere component in one layer from height 10-2000m. 180° is backscattering angle using ISA standard sea level condition P=1013.25 (kpa) at t0=15 ° C.and then calculated the density of molecules and water vapor molecules represented D in kg/m3. Results reflected index consist of the large value of the real part and imaginary m=1.463-0.028i.this research diff. scatter cross section of different component of atmosphere layer decreased vs. wavelengths. The purpose of lider research to find backscatter from UV to IR laser within the optical range in the atmosphere and measurement of excitation and analysis of backscatter signals. Recently, the atmosphere of Iraq has become full of dust and pollution, so by knowing the differential cross scatter section and backscatter of atmosphere. Relation between total Rayleigh scatter coefficient & type of particles include fog and clouds, aerosols and water droplets (-0.01, 0.025,- 0.005) m-1/sr-1.

Slackline dynamics and the Helmholtz-Duffing oscillator

NASA Astrophysics Data System (ADS)

Athanasiadis, Panos J.

2018-01-01

Slacklining is a new, rapidly expanding sport, and understanding its physics is paramount for maximizing fun and safety. Yet, compared to other sports, very little has been published so far on slackline dynamics. The equations of motion describing a slackline are fundamentally nonlinear, and assuming linear elasticity, they lead to a form of the Duffing equation. Following this approach, characteristic examples of slackline motion are simulated, including trickline bouncing, leash falls and longline surfing. The time-dependent solutions of the differential equations describing the system are acquired by numerical integration. A simple form of energy dissipation (linear drag) is added in some cases. It is recognized in this study that geometric nonlinearity is a fundamental aspect characterizing the dynamics of slacklines. Sports, and particularly slackline, is an excellent way of engaging young people with physics. A slackline is a simple yet insightful example of a nonlinear oscillator. It is very easy to model in the laboratory, as well as to rig and try on a university campus. For instructive purposes, its behaviour can be explored by numerically integrating the respective equations of motion. A form of the Duffing equation emerges naturally in the analysis and provides a powerful introduction to nonlinear dynamics. The material is suitable for graduate students and undergraduates with a background in classical mechanics and differential equations.

Geometry and the onset of rigidity in a disordered network

NASA Astrophysics Data System (ADS)

Vermeulen, Mathijs F. J.; Bose, Anwesha; Storm, Cornelis; Ellenbroek, Wouter G.

2017-11-01

Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture, the number of nodes and the number of bonds between them, this rigidity transition must have a geometric origin. Naive, degree-of-freedom-based mechanical analyses such as the Maxwell-Calladine count or the pebble game algorithm overlook such geometric rigidity transitions and offer no means of predicting or characterizing them. We apply tools that were developed for the topological analysis of zero modes and states of self-stress on regular lattices to two-dimensional random spring networks and demonstrate that the onset of rigidity, at a finite simple shear strain γ★, coincides with the appearance of a single state of self-stress, accompanied by a single floppy mode. The process conserves the topologically invariant difference between the number of zero modes and the number of states of self-stress but imparts a finite shear modulus to the spring network. Beyond the critical shear, the network acquires a highly anisotropic elastic modulus, resisting further deformation most strongly in the direction of the rigidifying shear. We confirm previously reported critical scaling of the corresponding differential shear modulus. In the subcritical regime, a singular value decomposition of the network's compatibility matrix foreshadows the onset of rigidity by way of a continuously vanishing singular value corresponding to the nascent state of self-stress.

Dentary Morphological Variation in Clevosaurus brasiliensis (Rhynchocephalia, Clevosauridae) from the Upper Triassic of Rio Grande do Sul, Brazil

PubMed Central

Romo de Vivar Martínez, Paula Rosario; Bento Soares, Marina

2015-01-01

Clevosaurus was a cosmopolitan rhynchocephalian genus, known from the Late Triassic to the Early Jurassic. In South America this genus is represented by C. brasiliensis, an important component of the Linha São Luiz taphocoenosis, on the top of the Norian Santa Maria 2 Sequence of Southern Brazil. The best preserved and most abundant bone elements of C. brasiliensis are dentaries, in which variations of shape and size are observed. The aim of this study is to describe and evaluate the variation, using geometric morphometrics methods. Geometric morphometric analysis of 10 specimens highlights variations in relative size of the dentary. Most of the variation observed for PC1 (83.3%) is likely related to ontogeny, and PC2 (10.0%) is likely related to taphonomic signatures. The development patterns observed, such as the growth of the dentary, consists of differential growth in length between the posterior portion of the dentary, that grows at a higher rate, regarding the anterior portion of the element. This allometric growth is similar to what is observed in other rhynchocephalians and is accompanied by the allometric skull growth, similar to the trend exhibited by clevosaurs. The taphocoenosis is bimodal (juveniles and adults) with a bias towards adult preservation. Some diagenetic influence is reflected in deformed skulls and this is observed in the tangent-plot. Finally, a strong correlation was detected between the taphonomic signatures and the PC2, regarding specially disarticulation and degree of fragmentation. PMID:25793754

Quality grading of Atlantic salmon (Salmo salar) by computer vision.

PubMed

Misimi, E; Erikson, U; Skavhaug, A

2008-06-01

In this study, we present a promising method of computer vision-based quality grading of whole Atlantic salmon (Salmo salar). Using computer vision, it was possible to differentiate among different quality grades of Atlantic salmon based on the external geometrical information contained in the fish images. Initially, before the image acquisition, the fish were subjectively graded and labeled into grading classes by a qualified human inspector in the processing plant. Prior to classification, the salmon images were segmented into binary images, and then feature extraction was performed on the geometrical parameters of the fish from the grading classes. The classification algorithm was a threshold-based classifier, which was designed using linear discriminant analysis. The performance of the classifier was tested by using the leave-one-out cross-validation method, and the classification results showed a good agreement between the classification done by human inspectors and by the computer vision. The computer vision-based method classified correctly 90% of the salmon from the data set as compared with the classification by human inspector. Overall, it was shown that computer vision can be used as a powerful tool to grade Atlantic salmon into quality grades in a fast and nondestructive manner by a relatively simple classifier algorithm. The low cost of implementation of today's advanced computer vision solutions makes this method feasible for industrial purposes in fish plants as it can replace manual labor, on which grading tasks still rely.

Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

DOE PAGES

Zhang, Kai; Nusran, N. M.; Slezak, B. R.; ...

2016-05-17

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically bymore » careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (~10) operations. This occurs in spite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. In conclusion, we have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.« less

Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

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

Zhang, Kai; Nusran, N. M.; Slezak, B. R.

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically bymore » careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (~10) operations. This occurs in spite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. In conclusion, we have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.« less

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

USDA-ARS?s Scientific Manuscript database

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

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

ERIC Educational Resources Information Center

Jirotkova, Darina; Littler, Graham

2003-01-01

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

Investigation on the effect of geometrical and geotechnical parameters on elongated offshore piles using fuzzy inference systems

NASA Astrophysics Data System (ADS)

Aminfar, Ali; Mojtahedi, Alireza; Ahmadi, Hamid; Aminfar, Mohammad Hossain

2017-06-01

Among numerous offshore structures used in oil extraction, jacket platforms are still the most favorable ones in shallow waters. In such structures, log piles are used to pin the substructure of the platform to the seabed. The pile's geometrical and geotechnical properties are considered as the main parameters in designing these structures. In this study, ANSYS was used as the FE modeling software to study the geometrical and geotechnical properties of the offshore piles and their effects on supporting jacket platforms. For this purpose, the FE analysis has been done to provide the preliminary data for the fuzzy-logic post-process. The resulting data were implemented to create Fuzzy Inference System (FIS) classifications. The resultant data of the sensitivity analysis suggested that the orientation degree is the main factor in the pile's geometrical behavior because piles which had the optimal operational degree of about 5° are more sustained. Finally, the results showed that the related fuzzified data supported the FE model and provided an insight for extended offshore pile designs.

Modeling and analysis of the chip formation and transient cutting force during elliptical vibration cutting process

NASA Astrophysics Data System (ADS)

Lin, Jieqiong; Guan, Liang; Lu, Mingming; Han, Jinguo; Kan, Yudi

2017-12-01

In traditional diamond cutting, the cutting force is usually large and it will affect tool life and machining quality. Elliptical vibration cutting (EVC) as one of the ultra-precision machining technologies has a lot of advantages, such as reduces cutting force, extend tool life and so on. It's difficult to predict the transient cutting force of EVC due to its unique elliptical motion trajectory. Study on chip formation will helpfully to predict cutting force. The geometric feature of chip has important effects on cutting force, however, few scholars have studied the chip formation. In order to investigate the time-varying cutting force of EVC, the geometric feature model of chip is established based on analysis of chip formation, and the effects of cutting parameters on the geometric feature of chip are analyzed. To predict transient force quickly and effectively, the geometric feature of chip is introduced into the cutting force model. The calculated results show that the error between the predicted cutting force in this paper and that in the literature is less than 2%, which proves its feasibility.

Controlling Cell Function with Geometry

NASA Astrophysics Data System (ADS)

Mrksich, Milan

2012-02-01

This presentation will describe the use of patterned substrates to control cell shape with examples that illustrate the ways in which cell shape can regulate cell function. Most cells are adherent and must attach to and spread on a surface in order to survive, proliferate and function. In tissue, this surface is the extracellular matrix (ECM), an insoluble scaffold formed by the assembly of several large proteins---including fibronectin, the laminins and collagens and others---but in the laboratory, the surface is prepared by adsorbing protein to glass slides. To pattern cells, gold-coated slides are patterned with microcontact printing to create geometric features that promote cell attachment and that are surrounded by inert regions. Cells attach to these substrates and spread to adopt the shape defined by the underlying pattern and remain stable in culture for several days. Examples will be described that used a series of shapes to reveal the relationship between the shape of the cell and the structure of its cytoskeleton. These geometric cues were used to control cell polarity and the tension, or contractility, present in the cytoskeleton. These rules were further used to control the shapes of mesenchymal stem cells and in turn to control the differentiation of these cells into specialized cell types. For example, stem cells that were patterned into a ``star'' shape preferentially differentiated into bone cells whereas those that were patterned into a ``flower'' shape preferred a fat cell fate. These influences of shape on differentiation depend on the mechanical properties of the cytoskeleton. These examples, and others, reveal that shape is an important cue that informs cell function and that can be combined with the more common soluble cues to direct and study cell function.

Differential Geometry Applied To Least-Square Error Surface Approximations

NASA Astrophysics Data System (ADS)

Bolle, Ruud M.; Sabbah, Daniel

1987-08-01

This paper focuses on extraction of the parameters of individual surfaces from noisy depth maps. The basis for this are least-square error polynomial approximations to the range data and the curvature properties that can be computed from these approximations. The curvature properties are derived using the invariants of the Weingarten Map evaluated at the origin of local coordinate systems centered at the range points. The Weingarten Map is a well-known concept in differential geometry; a brief treatment of the differential geometry pertinent to surface curvature is given. We use the curvature properties for extracting certain surface parameters from the curvature properties of the approximations. Then we show that curvature properties alone are not enough to obtain all the parameters of the surfaces; higher order properties (information about change of curvature) are needed to obtain full parametric descriptions. This surface parameter estimation problem arises in the design of a vision system to recognize 3D objects whose surfaces are composed of planar patches and patches of quadrics of revolution. (Quadrics of revolution are quadrics that are surfaces of revolution.) A significant portion of man-made objects can be modeled using these surfaces. The actual process of recognition and parameter extraction is framed as a set of stacked parameter space transforms. The transforms are "stacked" in the sense that any one transform computes only a partial geometric description that forms the input to the next transform. Those who are interested in the organization and control of the recognition and parameter recognition process are referred to [Sabbah86], this paper briefly touches upon the organization, but concentrates mainly on geometrical aspects of the parameter extraction.

The Accuracy Analysis of Lidar-Derived Elevation Data for the Geometric Description of Cross-Sections of a Riverbed

NASA Astrophysics Data System (ADS)

Caroti, G.; Camiciottoli, F.; Piemonte, A.; Redini, M.

2013-01-01

The work stems from a joint study between the Laboratory ASTRO (Department of Civil and Industrial Engineering - University of Pisa), the municipality of Pisa and the province of Arezzo on the advanced analysis and use of digital elevation data. Besides, it is framed in the research carried on by ASTRO about the definition of the priority informative layers for emergency management in the territory, as of PRIN 2008. Specifically, this work is in continuity with other already published results concerning rigorous accuracy checks of LIDAR data and testing of the procedures to transform raw data in formats consistent with CTR and survey data. The analysis of sections of riverbed, derived from interpolation by DTMs featuring different grid density with those detected topographically, is presented. Validation by differential GNSS methodology of the DTMs used showed a good overall quality of the model for open, low-sloping areas. Analysis of the sections, however, has shown that the representation of small or high-sloping (ditches, embankments) morphological elements requires a high point density such as in laser scanner surveys, and a small mesh size of the grid. In addition, the correct representation of riverside structures is often hindered by the presence of thick vegetation and poor raw LIDAR data filtering.

The variants of an LOD of a 3D building model and their influence on spatial analyses

NASA Astrophysics Data System (ADS)

Biljecki, Filip; Ledoux, Hugo; Stoter, Jantien; Vosselman, George

2016-06-01

The level of detail (LOD) of a 3D city model indicates the model's grade and usability. However, there exist multiple valid variants of each LOD. As a consequence, the LOD concept is inconclusive as an instruction for the acquisition of 3D city models. For instance, the top surface of an LOD1 block model may be modelled at the eaves of a building or at its ridge height. Such variants, which we term geometric references, are often overlooked and are usually not documented in the metadata. Furthermore, the influence of a particular geometric reference on the performance of a spatial analysis is not known. In response to this research gap, we investigate a variety of LOD1 and LOD2 geometric references that are commonly employed, and perform numerical experiments to investigate their relative difference when used as input for different spatial analyses. We consider three use cases (estimation of the area of the building envelope, building volume, and shadows cast by buildings), and compute the deviations in a Monte Carlo simulation. The experiments, carried out with procedurally generated models, indicate that two 3D models representing the same building at the same LOD, but modelled according to different geometric references, may yield substantially different results when used in a spatial analysis. The outcome of our experiments also suggests that the geometric reference may have a bigger influence than the LOD, since an LOD1 with a specific geometric reference may yield a more accurate result than when using LOD2 models.

A New Color Image Encryption Scheme Using CML and a Fractional-Order Chaotic System

PubMed Central

Wu, Xiangjun; Li, Yang; Kurths, Jürgen

2015-01-01

The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML) and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks. PMID:25826602

Geometric convex cone volume analysis

NASA Astrophysics Data System (ADS)

Li, Hsiao-Chi; Chang, Chein-I.

2016-05-01

Convexity is a major concept used to design and develop endmember finding algorithms (EFAs). For abundance unconstrained techniques, Pixel Purity Index (PPI) and Automatic Target Generation Process (ATGP) which use Orthogonal Projection (OP) as a criterion, are commonly used method. For abundance partially constrained techniques, Convex Cone Analysis is generally preferred which makes use of convex cones to impose Abundance Non-negativity Constraint (ANC). For abundance fully constrained N-FINDR and Simplex Growing Algorithm (SGA) are most popular methods which use simplex volume as a criterion to impose ANC and Abundance Sum-to-one Constraint (ASC). This paper analyze an issue encountered in volume calculation with a hyperplane introduced to illustrate an idea of bounded convex cone. Geometric Convex Cone Volume Analysis (GCCVA) projects the boundary vectors of a convex cone orthogonally on a hyperplane to reduce the effect of background signatures and a geometric volume approach is applied to address the issue arose from calculating volume and further improve the performance of convex cone-based EFAs.

Theoretical study on the molecular structure and vibrational properties, NBO and HOMO-LUMO analysis of the POX3 (X = F, Cl, Br, I) series of molecules

NASA Astrophysics Data System (ADS)

Galván, Jorge E.; Gil, Diego M.; Lanús, Hernán E.; Altabef, Aida Ben

2015-02-01

The fourth member of the series of compounds of the type POX3 with X = I was synthesized and characterized by infrared spectroscopy. The geometrical parameters and vibrational properties of POX3 (X = F, Cl, Br, I) molecules were investigated theoretically by means DFT and ab initio methods. Available geometrical and vibrational data were used together with theoretical calculations in order to obtain a set of scaled force constants. The observed trends in geometrical parameters are analyzed and compared with those obtained in a previous work for the VOX3 (X = F, Cl, Br, I) series of compounds. NBO analysis was performed in order to know the hyper-conjugative interactions that favor one structure over another. The molecular properties such as ionization potential, electron affinity, electronegativity, chemical potential, chemical hardness, softness and global electrophilicity index have been deduced from HOMO-LUMO analysis.

Statistical Optics

NASA Astrophysics Data System (ADS)

Goodman, Joseph W.

2000-07-01

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

Deformation quantizations with separation of variables on a Kähler manifold

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

1996-10-01

We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifold M such that for each open subset U⊂ M ⋆-multiplication from the left by a holomorphic function and from the right by an antiholomorphic function on U coincides with the pointwise multiplication by these functions. We show that these quantizations are in 1-1 correspondence with the formal deformations of the original Kähler metrics on M.

Computational Fluid Dynamics at ICMA (Institute for Computational Mathematics and Applications)

DTIC Science & Technology

1988-10-18

PERSONAL. AUTHOR(S) Charles A. Hall and Thomas A. Porsching 13a. TYPE OF REPORT 13b. TIME COVERED 114. DATE OF REPORT (YearMOth, De ) 1. PAGE COUNT...of ten ICtA (Institute for Computational Mathe- matics and Applications) personnel, relating to the general area of computational fluid mechanics...questions raised in the previous subsection. Our previous work in this area concentrated on a study of the differential geometric aspects of the prob- lem

Exploration of resistive targets within shallow marine environments using the circular electrical dipole and the differential electrical dipole methods: a time-domain modelling study

NASA Astrophysics Data System (ADS)

Haroon, Amir; Mogilatov, Vladimir; Goldman, Mark; Bergers, Rainer; Tezkan, Bülent

2016-05-01

Two novel transient controlled source electromagnetic methods called circular electrical dipole (CED) and differential electrical dipole (DED) are theoretically analysed for applications in shallow marine environments. 1-D and 3-D time-domain modelling studies are used to investigate the detectability and applicability of the methods when investigating resistive layers/targets representing hydrocarbon-saturated formations. The results are compared to the conventional time-domain horizontal electrical dipole (HED) and vertical electrical dipole (VED) sources. The applied theoretical modelling studies demonstrate that CED and DED have higher signal detectability towards resistive targets compared to TD-CSEM, but demonstrate significantly poorer signal amplitudes. Future CED/DED applications will have to solve this issue prior to measuring. Furthermore, the two novel methods have very similar detectability characteristics towards 3-D resistive targets embedded in marine sediments as VED while being less susceptible towards non-verticality. Due to the complex transmitter design of CED/DED the systems are prone to geometrical errors. Modelling studies show that even small transmitter inaccuracies have strong effects on the signal characteristics of CED making an actual marine application difficult at the present time. In contrast, the DED signal is less affected by geometrical errors in comparison to CED and may therefore be more adequate for marine applications.

From face to interface recognition: a differential geometric approach to distinguish DNA from RNA binding surfaces

PubMed Central

Shazman, Shula; Elber, Gershon; Mandel-Gutfreund, Yael

2011-01-01

Protein nucleic acid interactions play a critical role in all steps of the gene expression pathway. Nucleic acid (NA) binding proteins interact with their partners, DNA or RNA, via distinct regions on their surface that are characterized by an ensemble of chemical, physical and geometrical properties. In this study, we introduce a novel methodology based on differential geometry, commonly used in face recognition, to characterize and predict NA binding surfaces on proteins. Applying the method on experimentally solved three-dimensional structures of proteins we successfully classify double-stranded DNA (dsDNA) from single-stranded RNA (ssRNA) binding proteins, with 83% accuracy. We show that the method is insensitive to conformational changes that occur upon binding and can be applicable for de novo protein-function prediction. Remarkably, when concentrating on the zinc finger motif, we distinguish successfully between RNA and DNA binding interfaces possessing the same binding motif even within the same protein, as demonstrated for the RNA polymerase transcription-factor, TFIIIA. In conclusion, we present a novel methodology to characterize protein surfaces, which can accurately tell apart dsDNA from an ssRNA binding interfaces. The strength of our method in recognizing fine-tuned differences on NA binding interfaces make it applicable for many other molecular recognition problems, with potential implications for drug design. PMID:21693557

Dietary Ecology of Murinae (Muridae, Rodentia): A Geometric Morphometric Approach

PubMed Central

Gómez Cano, Ana Rosa; Hernández Fernández, Manuel; Álvarez-Sierra, M. Ángeles

2013-01-01

Murine rodents represent a highly diverse group, which displays great ecological versatility. In the present paper we analyse the relationship between dental morphology, on one hand, using geometric morphometrics based upon the outline of first upper molar and the dietary preference of extant murine genera, on the other. This ecomorphological study of extant murine rodents demonstrates that dietary groups can be distinguished with the use of a quantitative geometric morphometric approach based on first upper molar outline. A discriminant analysis of the geometric morphometric variables of the first upper molars enables us to infer the dietary preferences of extinct murine genera from the Iberian Peninsula. Most of the extinct genera were omnivore; only Stephanomys showed a pattern of dental morphology alike that of the herbivore genera. PMID:24236090

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.

Development of Multistep and Degenerate Variational Integrators for Applications in Plasma Physics

NASA Astrophysics Data System (ADS)

Ellison, Charles Leland

Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. This dissertation uses a systematic procedure for constructing geometric integrators --- known as variational integration --- to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically multistep methods. Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator assumes coordinates such that one component of the magnetic field is zero; it is shown how to construct such coordinates for nested magnetic surface configurations. Additionally, collisional drag effects are incorporated in the variational guiding center algorithm for the first time, allowing simulation of energetic particle thermalization. Advantages relative to existing canonical-symplectic and non-geometric algorithms are numerically demonstrated. All algorithms have been implemented as part of a modern, parallel, ODE-solving library, suitable for use in high-performance simulations.

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

NASA Astrophysics Data System (ADS)

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

2002-08-01

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

Geometrical analysis of Cys-Cys bridges in proteins and their prediction from incomplete structural information

NASA Technical Reports Server (NTRS)

Goldblum, A.; Rein, R.

1987-01-01

Analysis of C-alpha atom positions from cysteines involved in disulphide bridges in protein crystals shows that their geometric characteristics are unique with respect to other Cys-Cys, non-bridging pairs. They may be used for predicting disulphide connections in incompletely determined protein structures, such as low resolution crystallography or theoretical folding experiments. The basic unit for analysis and prediction is the 3 x 3 distance matrix for Cx positions of residues (i - 1), Cys(i), (i +1) with (j - 1), Cys(j), (j + 1). In each of its columns, row and diagonal vector--outer distances are larger than the central distance. This analysis is compared with some analytical models.

A Geometric Approach to Fair Division

ERIC Educational Resources Information Center

Barbanel, Julius

2010-01-01

We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…

The Changing Expectations for the Reading of Geometric Diagrams

ERIC Educational Resources Information Center

Dietiker, Leslie; Brakoniecki, Aaron; Riling, Meghan

2017-01-01

Students studying geometry at the secondary level are expected to read diagrams in different ways than those in elementary school. In this paper, we present an analysis of the changes in diagrammatic expectations by comparing the geometric diagrams found in Grade 1 U.S. textbooks with those in U.S. high school geometry textbooks. This work…

Understanding Geometric Ideas: Pre-Service Primary Teachers' Knowledge as a Basis for Teaching

ERIC Educational Resources Information Center

Seah, Rebecca

2015-01-01

This paper reports part of an ongoing investigation into aspects of pre-service teachers' geometric knowledge. One hundred and fifty-two Australian pre-service teachers responded to a series of questions that reflect the type of knowledge teachers are expected to know and teach. Analysis of their responses shows that teacher knowledge can be…

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

ERIC Educational Resources Information Center

Chen, Frederick H.

2010-01-01

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

Constructing Knowledge about the Trigonometric Functions and Their Geometric Meaning on the Unit Circle

ERIC Educational Resources Information Center

Altman, Renana; Kidron, Ivy

2016-01-01

Processes of knowledge construction are investigated. A learner is constructing knowledge about the trigonometric functions and their geometric meaning on the unit circle. The analysis is based on the dynamically nested epistemic action model for abstraction in context. Different tasks are offered to the learner. In his effort to perform the…

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.

All-dielectric planar chiral metasurface with gradient geometric phase.

PubMed

Ma, Zhijie; Li, Yi; Li, Yang; Gong, Yandong; Maier, Stefan A; Hong, Minghui

2018-03-05

Planar optical chirality of a metasurface measures its differential response between left and right circularly polarized (CP) lights and governs the asymmetric transmission of CP lights. In 2D ultra-thin plasmonic structures the circular dichroism is limited to 25% in theory and it requires high absorption loss. Here we propose and numerically demonstrate a planar chiral all-dielectric metasurface that exhibits giant circular dichroism and transmission asymmetry over 0.8 for circularly polarized lights with negligible loss, without bringing in bianisotropy or violating reciprocity. The metasurface consists of arrays of high refractive index germanium Z-shape resonators that break the in-plane mirror symmetry and induce cross-polarization conversion. Furthermore, at the transmission peak of one handedness, the transmitted light is efficiently converted into the opposite circular polarization state, with a designated geometric phase depending on the orientation angle of the optical element. In this way, the optical component sets before and after the metasurface to filter the light of certain circular polarization states are not needed and the metasurface can function under any linear polarization, in contrast to the conventional setup for geometry phase based metasurfaces. Anomalous transmission and two-dimensional holography based on the geometric phase chiral metasurface are numerically demonstrate as proofs of concept.

Differences between appetitive and aversive reinforcement on reorientation in a spatial working memory task.

PubMed

Golob, Edward J; Taube, Jeffrey S

2002-10-17

Tasks using appetitive reinforcers show that following disorientation rats use the shape of an arena to reorient, and cannot distinguish two geometrically similar corners to obtain a reward, despite the presence of a prominent visual cue that provides information to differentiate the two corners. Other studies show that disorientation impairs performance on certain appetitive, but not aversive, tasks. This study evaluated whether rats would make similar geometric errors in a working memory task that used aversive reinforcement. We hypothesized that in a task that used aversive reinforcement rats that were initially disoriented would not reorient by arena shape and thus make similar geometric errors. Tests were performed in a rectangular arena having one polarizing cue. In the appetitive condition water consumption was the reward. The aversive condition was a water maze task with reinforcement provided by escape to a hidden platform. In the aversive condition rats returned to the reinforced corner significantly more often than in the dry condition, and did not favor the diagonally opposite corner. Results show that rats can use cues besides arena shape to reorient in an aversive reinforcement condition. These findings may also reflect different strategies, with an escape/homing strategy in the wet condition and a foraging strategy in the dry condition.

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

An algorithm for converting a virtual-bond chain into a complete polypeptide backbone chain

NASA Technical Reports Server (NTRS)

Luo, N.; Shibata, M.; Rein, R.

1991-01-01

A systematic analysis is presented of the algorithm for converting a virtual-bond chain, defined by the coordinates of the alpha-carbons of a given protein, into a complete polypeptide backbone. An alternative algorithm, based upon the same set of geometric parameters used in the Purisima-Scheraga algorithm but with a different "linkage map" of the algorithmic procedures, is proposed. The global virtual-bond chain geometric constraints are more easily separable from the loal peptide geometric and energetic constraints derived from, for example, the Ramachandran criterion, within the framework of this approach.

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

PubMed

Rein, Thomas R; Harvati, Katerina

2014-01-01

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

Apoptosis- and differentiation-inducing activities of jacaric acid, a conjugated linolenic acid isomer, on human eosinophilic leukemia EoL-1 cells.

PubMed

Liu, Wai-Nam; Leung, Kwok-Nam

2014-11-01

Conjugated linolenic acids (CLNAs) are a group of naturally occurring positional and geometrical isomers of the C18 polyunsaturated essential fatty acid, linolenic acid (LNA), with three conjugated double bonds (C18:3). Although previous research has demonstrated the growth-inhibitory effects of CLNA on a wide variety of cancer cell lines in vitro, their action mechanisms and therapeutic potential on human myeloid leukemia cells remain poorly understood. In the present study, we found that jacaric acid (8Z,10E,12Z-octadecatrienoic acid), a CLNA isomer which is present in jacaranda seed oil, inhibited the in vitro growth of human eosinophilic leukemia EoL-1 cells in a time- and concentration-dependent manner. Mechanistic studies showed that jacaric acid triggered cell cycle arrest of EoL-1 cells at the G0/G1 phase and induced apoptosis of the EoL-1 cells, as measured by the Cell Death Detection ELISAPLUS kit, Annexin V assay and JC-1 dye staining. Notably, the jacaric acid-treated EoL-1 cells also underwent differentiation as revealed by morphological and phenotypic analysis. Collectively, our results demonstrated the capability of jacaric acid to inhibit the growth of EoL-1 cells in vitro through triggering cell cycle arrest and by inducing apoptosis and differentiation of the leukemia cells. Therefore, jacaric acid might be developed as a potential candidate for the treatment of certain forms of myeloid leukemia with minimal toxicity and few side effects.

Glioblastoma: does the pre-treatment geometry matter? A postcontrast T1 MRI-based study.

PubMed

Pérez-Beteta, Julián; Martínez-González, Alicia; Molina, David; Amo-Salas, Mariano; Luque, Belén; Arregui, Elena; Calvo, Manuel; Borrás, José M; López, Carlos; Claramonte, Marta; Barcia, Juan A; Iglesias, Lidia; Avecillas, Josué; Albillo, David; Navarro, Miguel; Villanueva, José M; Paniagua, Juan C; Martino, Juan; Velásquez, Carlos; Asenjo, Beatriz; Benavides, Manuel; Herruzo, Ismael; Delgado, María Del Carmen; Del Valle, Ana; Falkov, Anthony; Schucht, Philippe; Arana, Estanislao; Pérez-Romasanta, Luis; Pérez-García, Víctor M

2017-03-01

The potential of a tumour's volumetric measures obtained from pretreatment MRI sequences of glioblastoma (GBM) patients as predictors of clinical outcome has been controversial. Mathematical models of GBM growth have suggested a relation between a tumour's geometry and its aggressiveness. A multicenter retrospective clinical study was designed to study volumetric and geometrical measures on pretreatment postcontrast T1 MRIs of 117 GBM patients. Clinical variables were collected, tumours segmented, and measures computed including: contrast enhancing (CE), necrotic, and total volumes; maximal tumour diameter; equivalent spherical CE width and several geometric measures of the CE "rim". The significance of the measures was studied using proportional hazards analysis and Kaplan-Meier curves. Kaplan-Meier and univariate Cox survival analysis showed that total volume [p = 0.034, Hazard ratio (HR) = 1.574], CE volume (p = 0.017, HR = 1.659), spherical rim width (p = 0.007, HR = 1.749), and geometric heterogeneity (p = 0.015, HR = 1.646) were significant parameters in terms of overall survival (OS). Multivariable Cox analysis for OS provided the later two parameters as age-adjusted predictors of OS (p = 0.043, HR = 1.536 and p = 0.032, HR = 1.570, respectively). Patients with tumours having small geometric heterogeneity and/or spherical rim widths had significantly better prognosis. These novel imaging biomarkers have a strong individual and combined prognostic value for GBM patients. • Three-dimensional segmentation on magnetic resonance images allows the study of geometric measures. • Patients with small width of contrast enhancing areas have better prognosis. • The irregularity of contrast enhancing areas predicts survival in glioblastoma patients.

Engine Structures Modeling Software System (ESMOSS)

NASA Technical Reports Server (NTRS)

1991-01-01

Engine Structures Modeling Software System (ESMOSS) is the development of a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components, and substructures which can be transferred to finite element analysis programs such as NASTRAN. The NASA Lewis Engine Structures Program is concerned with the development of technology for the rational structural design and analysis of advanced gas turbine engines with emphasis on advanced structural analysis, structural dynamics, structural aspects of aeroelasticity, and life prediction. Fundamental and common to all of these developments is the need for geometric and analytical model descriptions at various engine assembly levels which are generated using ESMOSS.

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

Edge Preserved Speckle Noise Reduction Using Integrated Fuzzy Filters

PubMed Central

Dewal, M. L.; Rohit, Manoj Kumar

2014-01-01

Echocardiographic images are inherent with speckle noise which makes visual reading and analysis quite difficult. The multiplicative speckle noise masks finer details, necessary for diagnosis of abnormalities. A novel speckle reduction technique based on integration of geometric, wiener, and fuzzy filters is proposed and analyzed in this paper. The denoising applications of fuzzy filters are studied and analyzed along with 26 denoising techniques. It is observed that geometric filter retains noise and, to address this issue, wiener filter is embedded into the geometric filter during iteration process. The performance of geometric-wiener filter is further enhanced using fuzzy filters and the proposed despeckling techniques are called integrated fuzzy filters. Fuzzy filters based on moving average and median value are employed in the integrated fuzzy filters. The performances of integrated fuzzy filters are tested on echocardiographic images and synthetic images in terms of image quality metrics. It is observed that the performance parameters are highest in case of integrated fuzzy filters in comparison to fuzzy and geometric-fuzzy filters. The clinical validation reveals that the output images obtained using geometric-wiener, integrated fuzzy, nonlocal means, and details preserving anisotropic diffusion filters are acceptable. The necessary finer details are retained in the denoised echocardiographic images. PMID:27437499

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.

Mathematical models of real geometrical factors in restricted blood vessels for the analysis of CAD (coronary artery diseases) using Legendre, Boubaker and Bessel polynomials.

PubMed

Awojoyogbe, O B; Faromika, O P; Dada, M; Boubaker, Karem; Ojambati, O S

2011-12-01

Most cardiovascular emergencies are directly caused by coronary artery disease. Coronary arteries can become clogged or occluded, leading to damage to the heart muscle supplied by the artery. Modem cardiovascular medicine can certainly be improved by meticulous analysis of geometrical factors closely associated with the degenerative disease that results in narrowing of the coronary arteries. There are, however, inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries that are very critical in plaque formation and thickening of the vessel wall. Neither the mathematical models of the blood vessels with arthrosclerosis generated by the heart and blood flow or the NMR/MRI data to construct them are available. In this study, a mathematical formulation for the geometrical factors that are very critical for the understanding of coronary artery disease is presented. Based on the Bloch NMR flow equations, we derive analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in restricted blood vessels. The procedure would apply to the situations in which the geometry of the fatty deposits, (plague) on the interior walls of the coronary arteries is spherical. The boundary conditions are introduced based on Bessel, Boubaker and Legendre polynomials.

CALL FOR PAPERS: Special Issue on `Geometric Numerical Integration of Differential Equations'

NASA Astrophysics Data System (ADS)

Quispel, G. R. W.; McLachlan, R. I.

2005-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Geometric Numerical Integration of Differential Equations'. This issue should be a repository for high quality original work. We are interested in having the topic interpreted broadly, that is, to include contributions dealing with symplectic or multisymplectic integration; volume-preserving integration; symmetry-preserving integration; integrators that preserve first integrals, Lyapunov functions, or dissipation; exponential integrators; integrators for highly oscillatory systems; Lie-group integrators, etc. Papers on geometric integration of both ODEs and PDEs will be considered, as well as application to molecular-scale integration, celestial mechanics, particle accelerators, fluid flows, population models, epidemiological models and/or any other areas of science. We believe that this issue is timely, and hope that it will stimulate further development of this new and exciting field. The Editorial Board has invited G R W Quispel and R I McLachlan to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are the following: • The subject of the paper should relate to geometric numerical integration in the sense described above. • Contributions will be refereed and processed according to the usual procedure of the journal. • Papers should be original; reviews of a work published elsewhere will not be accepted. The guidelines for the preparation of contributions are as follows: • The DEADLINE for submission of contributions is 1 September 2005. This deadline will allow the special issue to appear in late 2005 or early 2006. • There is a strict page limit of 16 printed pages (approximately 9600 words) per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. • Contributions to the special issue should if possible be submitted electronically by web upload at {www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue—Geometric Integration'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the web site for further information on electronic submissions. • Authors unable to submit electronically may send hard copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code on floppy disk if available and quoting `JPhysA Special Issue—Geometric Integration'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue. G R W Quispel and R I McLachlan Guest Editors

Levels of detail analysis of microwave scattering from human head models for brain stroke detection

PubMed Central

2017-01-01

In this paper, we have presented a microwave scattering analysis from multiple human head models. This study incorporates different levels of detail in the human head models and its effect on microwave scattering phenomenon. Two levels of detail are taken into account; (i) Simplified ellipse shaped head model (ii) Anatomically realistic head model, implemented using 2-D geometry. In addition, heterogenic and frequency-dispersive behavior of the brain tissues has also been incorporated in our head models. It is identified during this study that the microwave scattering phenomenon changes significantly once the complexity of head model is increased by incorporating more details using magnetic resonance imaging database. It is also found out that the microwave scattering results match in both types of head model (i.e., geometrically simple and anatomically realistic), once the measurements are made in the structurally simplified regions. However, the results diverge considerably in the complex areas of brain due to the arbitrary shape interface of tissue layers in the anatomically realistic head model. After incorporating various levels of detail, the solution of subject microwave scattering problem and the measurement of transmitted and backscattered signals were obtained using finite element method. Mesh convergence analysis was also performed to achieve error free results with a minimum number of mesh elements and a lesser degree of freedom in the fast computational time. The results were promising and the E-Field values converged for both simple and complex geometrical models. However, the E-Field difference between both types of head model at the same reference point differentiated a lot in terms of magnitude. At complex location, a high difference value of 0.04236 V/m was measured compared to the simple location, where it turned out to be 0.00197 V/m. This study also contributes to provide a comparison analysis between the direct and iterative solvers so as to find out the solution of subject microwave scattering problem in a minimum computational time along with memory resources requirement. It is seen from this study that the microwave imaging may effectively be utilized for the detection, localization and differentiation of different types of brain stroke. The simulation results verified that the microwave imaging can be efficiently exploited to study the significant contrast between electric field values of the normal and abnormal brain tissues for the investigation of brain anomalies. In the end, a specific absorption rate analysis was carried out to compare the ionizing effects of microwave signals to different types of head model using a factor of safety for brain tissues. It is also suggested after careful study of various inversion methods in practice for microwave head imaging, that the contrast source inversion method may be more suitable and computationally efficient for such problems. PMID:29177115

An adaptive maneuvering logic computer program for the simulation of one-to-one air-to-air combat. Volume 2: Program description

NASA Technical Reports Server (NTRS)

Burgin, G. H.; Owens, A. J.

1975-01-01

A detailed description is presented of the computer programs in order to provide an understanding of the mathematical and geometrical relationships as implemented in the programs. The individual sbbroutines and their underlying mathematical relationships are described, and the required input data and the output provided by the program are explained. The relationship of the adaptive maneuvering logic program with the program to drive the differential maneuvering simulator is discussed.

Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold

DTIC Science & Technology

1994-02-15

0. Faugeras. Three dimensional vision, a geometric viewpoint. MIT Press, 1993. [19] 0 . D. Faugeras and S. Maybank . Motion from point mathces...multiplicity of solutions. Int. J. of Computer Vision, 1990. 1201 0.D. Faugeras, Q.T. Luong, and S.J. Maybank . Camera self-calibration: theory and...Kalrnan filter-based algorithms for estimating depth from image sequences. Int. J. of computer vision, 1989. [41] S. Maybank . Theory of

The exponentiated Hencky energy: anisotropic extension and case studies

NASA Astrophysics Data System (ADS)

Schröder, Jörg; von Hoegen, Markus; Neff, Patrizio

2017-10-01

In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \\varvec{F} to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.

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.

Vakonomic Constraints in Higher-Order Classical Field Theory

NASA Astrophysics Data System (ADS)

Campos, Cédric M.

2010-07-01

We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.

Joint Information Theoretic and Differential Geometrical Approach for Robust Automated Target Recognition

DTIC Science & Technology

2012-02-29

surface and Swiss roll) and real-world data sets (UCI Machine Learning Repository [12] and USPS digit handwriting data). In our experiments, we use...less than µn ( say µ = 0.8), we can first use screening technique to select µn candidate nodes, and then apply BIPS on them for further selection and...identified from node j to node i. So we can say the probability for the existence of this connection is approximately 82%. Given the probability matrix

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

PubMed

Zou, Yong; Donner, Reik V; Kurths, Jürgen

2012-03-01

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

Evaluation of Chemical Preparation on Insect Wing Shape for Geometric Morphometrics

PubMed Central

Lorenz, Camila; Suesdek, Lincoln

2013-01-01

Geometric morphometrics is an approach that has been increasingly applied in studies with insects. A limiting factor of this technique is that some mosquitoes have wings with dark spots or many scales, which jeopardizes the visualization of landmarks for morphometric analysis. Recently, in some studies, chemically treatment (staining) of the wings was used to improve the viewing of landmarks. In this study, we evaluated whether this method causes deformation of the wing veins and tested whether it facilitates the visualization of the most problematic landmarks. In addition, we tested whether mechanical removal of the scales was sufficient for this purpose. The results showed that the physical and chemical treatments are equally effective in improving visualization of the landmarks. The chemical method did not cause deformation of the wing. Thus, some of these treatments should be performed before beginning geometric morphometric analysis to avoid erroneous landmark digitizing. PMID:24019438

Research on the effects of geometrical and material uncertainties on the band gap of the undulated beam

NASA Astrophysics Data System (ADS)

Li, Yi; Xu, Yanlong

2017-09-01

Considering uncertain geometrical and material parameters, the lower and upper bounds of the band gap of an undulated beam with periodically arched shape are studied by the Monte Carlo Simulation (MCS) and interval analysis based on the Taylor series. Given the random variations of the overall uncertain variables, scatter plots from the MCS are used to analyze the qualitative sensitivities of the band gap respect to these uncertainties. We find that the influence of uncertainty of the geometrical parameter on the band gap of the undulated beam is stronger than that of the material parameter. And this conclusion is also proved by the interval analysis based on the Taylor series. Our methodology can give a strategy to reduce the errors between the design and practical values of the band gaps by improving the accuracy of the specially selected uncertain design variables of the periodical structures.

gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization

NASA Astrophysics Data System (ADS)

Nguyen, Thang Viet; Patra, Jagdish Chandra; Emmanuel, Sabu

2006-12-01

A new geometric approach for nonlinear independent component analysis (ICA) is presented in this paper. Nonlinear environment is modeled by the popular post nonlinear (PNL) scheme. To eliminate the nonlinearity in the observed signals, a novel linearizing method named as geometric post nonlinear ICA (gpICA) is introduced. Thereafter, a basic linear ICA is applied on these linearized signals to estimate the unknown sources. The proposed method is motivated by the fact that in a multidimensional space, a nonlinear mixture is represented by a nonlinear surface while a linear mixture is represented by a plane, a special form of the surface. Therefore, by geometrically transforming the surface representing a nonlinear mixture into a plane, the mixture can be linearized. Through simulations on different data sets, superior performance of gpICA algorithm has been shown with respect to other algorithms.

Engine structures modeling software system: Computer code. User's manual

NASA Technical Reports Server (NTRS)

1992-01-01

ESMOSS is a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components and substructures which can be transferred to finite element analysis programs such as NASTRAN. The software architecture of ESMOSS is designed in modular form with a central executive module through which the user controls and directs the development of the analytical model. Modules consist of a geometric shape generator, a library of discretization procedures, interfacing modules to join both geometric and discrete models, a deck generator to produce input for NASTRAN and a 'recipe' processor which generates geometric models from parametric definitions. ESMOSS can be executed both in interactive and batch modes. Interactive mode is considered to be the default mode and that mode will be assumed in the discussion in this document unless stated otherwise.

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.

A Hybrid 3D Indoor Space Model

NASA Astrophysics Data System (ADS)

Jamali, Ali; Rahman, Alias Abdul; Boguslawski, Pawel

2016-10-01

GIS integrates spatial information and spatial analysis. An important example of such integration is for emergency response which requires route planning inside and outside of a building. Route planning requires detailed information related to indoor and outdoor environment. Indoor navigation network models including Geometric Network Model (GNM), Navigable Space Model, sub-division model and regular-grid model lack indoor data sources and abstraction methods. In this paper, a hybrid indoor space model is proposed. In the proposed method, 3D modeling of indoor navigation network is based on surveying control points and it is less dependent on the 3D geometrical building model. This research proposes a method of indoor space modeling for the buildings which do not have proper 2D/3D geometrical models or they lack semantic or topological information. The proposed hybrid model consists of topological, geometrical and semantical space.

Geometrical analysis of circular-cut spiral bevel gears

NASA Technical Reports Server (NTRS)

Huston, R. L.

1983-01-01

Geometrical studies of circular cut spiral bevel gears are reported. Tooth profile changes heel to toe are studied in the transverse plane. Pressure angle changes are determined. The radiuses of curvature of the tooth surfaces generated by various cutter profiles are also determined. The consequences of cutter profile changes are explored. Crown gears are emphasized and the implications for conical gears are discussed.

Aeroelasticity of Axially Loaded Aerodynamic Structures for Truss-Braced Wing Aircraft

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Lebofsky, Sonia

2015-01-01

This paper presents an aeroelastic finite-element formulation for axially loaded aerodynamic structures. The presence of axial loading causes the bending and torsional sitffnesses to change. For aircraft with axially loaded structures such as the truss-braced wing aircraft, the aeroelastic behaviors of such structures are nonlinear and depend on the aerodynamic loading exerted on these structures. Under axial strain, a tensile force is created which can influence the stiffness of the overall aircraft structure. This tension stiffening is a geometric nonlinear effect that needs to be captured in aeroelastic analyses to better understand the behaviors of these types of aircraft structures. A frequency analysis of a rotating blade structure is performed to demonstrate the analytical method. A flutter analysis of a truss-braced wing aircraft is performed to analyze the effect of geometric nonlinear effect of tension stiffening on the flutter speed. The results show that the geometric nonlinear tension stiffening effect can have a significant impact on the flutter speed prediction. In general, increased wing loading results in an increase in the flutter speed. The study illustrates the importance of accounting for the geometric nonlinear tension stiffening effect in analyzing the truss-braced wing aircraft.

Iris-based medical analysis by geometric deformation features.

PubMed

Ma, Lin; Zhang, D; Li, Naimin; Cai, Yan; Zuo, Wangmeng; Wang, Kuanguan

2013-01-01

Iris analysis studies the relationship between human health and changes in the anatomy of the iris. Apart from the fact that iris recognition focuses on modeling the overall structure of the iris, iris diagnosis emphasizes the detecting and analyzing of local variations in the characteristics of irises. This paper focuses on studying the geometrical structure changes in irises that are caused by gastrointestinal diseases, and on measuring the observable deformations in the geometrical structures of irises that are related to roundness, diameter and other geometric forms of the pupil and the collarette. Pupil and collarette based features are defined and extracted. A series of experiments are implemented on our experimental pathological iris database, including manual clustering of both normal and pathological iris images, manual classification by non-specialists, manual classification by individuals with a medical background, classification ability verification for the proposed features, and disease recognition by applying the proposed features. The results prove the effectiveness and clinical diagnostic significance of the proposed features and a reliable recognition performance for automatic disease diagnosis. Our research results offer a novel systematic perspective for iridology studies and promote the progress of both theoretical and practical work in iris diagnosis.

Nonlinear effects in the laser-assisted scattering of a positron by a muon

NASA Astrophysics Data System (ADS)

Du, Wen-Yuan; Wang, Bing-Hong; Li, Shu-Min

2018-02-01

The scattering of a positron by a muon in the presence of a linearly polarized laser field is investigated in the first Born approximation. The theoretical results reveal: (1) At large scattering angle, an amount of multiphoton processes take place in the course of scattering. The photon emission processes predominate the photon absorption ones. (2) Some nonlinear phenomena about oscillations, dark angular windows, and asymmetry can be observed in angular distributions. We analyze the cause giving rise to dark windows and geometric asymmetry initially noted in the potential scattering. (3) We also analyze the total differential cross-section, the result shows that the larger the incident energy is, the smaller the total differential cross-section is. The reasons of these new results are analyzed.

Refractive laser beam shaping by means of a functional differential equation based design approach.

PubMed

Duerr, Fabian; Thienpont, Hugo

2014-04-07

Many laser applications require specific irradiance distributions to ensure optimal performance. Geometric optical design methods based on numerical calculation of two plano-aspheric lenses have been thoroughly studied in the past. In this work, we present an alternative new design approach based on functional differential equations that allows direct calculation of the rotational symmetric lens profiles described by two-point Taylor polynomials. The formalism is used to design a Gaussian to flat-top irradiance beam shaping system but also to generate a more complex dark-hollow Gaussian (donut-like) irradiance distribution with zero intensity in the on-axis region. The presented ray tracing results confirm the high accuracy of both calculated solutions and emphasize the potential of this design approach for refractive beam shaping applications.

Cellular and multicellular form and function.

PubMed

Liu, Wendy F; Chen, Christopher S

2007-11-10

Engineering artificial tissue constructs requires the appropriate spatial arrangement of cells within scaffolds. The introduction of microengineering tools to the biological community has provided a valuable set of techniques to manipulate the cellular environment, and to examine how cell structure affects cellular function. Using micropatterning techniques, investigators have found that the geometric presentation of cell-matrix adhesions are important regulators of various cell behaviors including cell growth, proliferation, differentiation, polarity and migration. Furthermore, the presence of neighboring cells in multicellular aggregates has a significant impact on the proliferative and differentiated state of cells. Using microengineering tools, it will now be possible to manipulate the various environmental factors for practical applications such as engineering tissue constructs with greater control over the physical structure and spatial arrangement of cells within their surrounding microenvironment.

Image formation of thick three-dimensional objects in differential-interference-contrast microscopy.

PubMed

Trattner, Sigal; Kashdan, Eugene; Feigin, Micha; Sochen, Nir

2014-05-01

The differential-interference-contrast (DIC) microscope is of widespread use in life sciences as it enables noninvasive visualization of transparent objects. The goal of this work is to model the image formation process of thick three-dimensional objects in DIC microscopy. The model is based on the principles of electromagnetic wave propagation and scattering. It simulates light propagation through the components of the DIC microscope to the image plane using a combined geometrical and physical optics approach and replicates the DIC image of the illuminated object. The model is evaluated by comparing simulated images of three-dimensional spherical objects with the recorded images of polystyrene microspheres. Our computer simulations confirm that the model captures the major DIC image characteristics of the simulated object, and it is sensitive to the defocusing effects.

On the passage of radiation through inhomogeneous, moving media. XI - Nonlinear effects on ray paths in the geometrical optics approximation. [in pulsar magnetospheres

NASA Technical Reports Server (NTRS)

Lee, M. A.; Lerche, I.

1974-01-01

Study illustrating how the presence of a high-intensity pulse of radiation can distort its own passage through a plane differentially shearing medium. It is demonstrated that the distortion is a sensitive function of the precise, and detailed, variation of the medium's refractive index by considering a couple of simple examples which are worked out numerically. In view of the high-intensity pulses observed from pulsars (approximately 10 to the 30th ergs per pulse), it is believed that the present calculations are of more than academic interest in helping unravel the fundamental properties of pulse production in, and propagating through, differentially sheared media - such as pulsars' magnetospheres within the so-called speed-of-light circle.

Physical correction filter for improving the optical quality of an image

NASA Technical Reports Server (NTRS)

Lee, S. Y. (Inventor)

1975-01-01

A family of physical correction filters is described. Each filter is designed to correct image content of a photographed scene of limited resolution and includes a first filter element with a pinhole through which light passes to a differential amplifier. A second filter element through which light passes through one or more openings, whose geometric configuration is a function of the cause of the resolution loss included. The light, passing through the second filter element, is also supplied to the differential amplifier whose output is used to activate an optical display or recorder to reproduce a photograph or display of the scene in the original photograph or display of the scene in the original photograph with resolution which is significantly greater than that characterizing the original photograph.

Continental magnetic anomaly constraints on continental reconstruction

NASA Technical Reports Server (NTRS)

Vonfrese, R. R. B.; Hinze, W. J.; Olivier, R.; Bentley, C. R.

1985-01-01

Crustal magnetic anomalies mapped by the MAGSAT satellite for North and South America, Europe, Africa, India, Australia and Antarctica and adjacent marine areas were adjusted to a common elevation of 400 km and differentially reduced to the radial pole of intensity 60,000 nT. These radially polarized anomalies are normalized for differential inclination, declination and intensity effects of the geomagnetic field, so that in principle they directly reflected the geometric and magnetic polarization attributes of sources which include regional petrologic variations of the crust and upper mantle, and crustal thickness and thermal perturbations. Continental anomalies demonstrate remarkably detailed correlation of regional magnetic sources across rifted margins when plotted on a reconstruction of Pangea. Accordingly, they suggest further fundamental constraints on the geologic evolution of the continents and their reconstructions.

Impact of roadway geometric features on crash severity on rural two-lane highways.

PubMed

Haghighi, Nima; Liu, Xiaoyue Cathy; Zhang, Guohui; Porter, Richard J

2018-02-01

This study examines the impact of a wide range of roadway geometric features on the severity outcomes of crashes occurred on rural two-lane highways. We argue that crash data have a hierarchical structure which needs to be addressed in modeling procedure. Moreover, most of previous studies ignored the impact of geometric features on crash types when developing crash severity models. We hypothesis that geometric features are more likely to determine crash type, and crash type together with other occupant, environmental and vehicle characteristics determine crash severity outcome. This paper presents an application of multilevel models to successfully capture both hierarchical structure of crash data and indirect impact of geometric features on crash severity. Using data collected in Illinois from 2007 to 2009, multilevel ordered logit model is developed to quantify the impact of geometric features and environmental conditions on crash severity outcome. Analysis results revealed that there is a significant variation in severity outcomes of crashes occurred across segments which verifies the presence of hierarchical structure. Lower risk of severe crashes is found to be associated with the presence of 10-ft lane and/or narrow shoulders, lower roadside hazard rate, higher driveway density, longer barrier length, and shorter barrier offset. The developed multilevel model offers greater consistency with data generating mechanism and can be utilized to evaluate safety effects of geometric design improvement projects. Published by Elsevier Ltd.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Analysis of the quench propagation along Nb3Sn Rutherford cables with the THELMA code. Part I: Geometric and thermal models

NASA Astrophysics Data System (ADS)

Manfreda, G.; Bellina, F.

2016-12-01

The paper describes the new lumped thermal model recently implemented in THELMA code for the coupled electromagnetic-thermal analysis of superconducting cables. A new geometrical model is also presented, which describes the Rutherford cables used for the accelerator magnets. A first validation of these models has been given by the analysis of the quench longitudinal propagation velocity in the Nb3Sn prototype coil SMC3, built and tested in the frame of the EUCARD project for the development of high field magnets for LHC machine. This paper shows in detail the models, while their application to the quench propagation analysis is presented in a companion paper.

Airflow and Particle Transport Through Human Airways: A Systematic Review

NASA Astrophysics Data System (ADS)

Kharat, S. B.; Deoghare, A. B.; Pandey, K. M.

2017-08-01

This paper describes review of the relevant literature about two phase analysis of air and particle flow through human airways. An emphasis of the review is placed on elaborating the steps involved in two phase analysis, which are Geometric modelling methods and Mathematical models. The first two parts describes various approaches that are followed for constructing an Airway model upon which analysis are conducted. Broad two categories of geometric modelling viz. Simplified modelling and Accurate modelling using medical scans are discussed briefly. Ease and limitations of simplified models, then examples of CT based models are discussed. In later part of the review different mathematical models implemented by researchers for analysis are briefed. Mathematical models used for Air and Particle phases are elaborated separately.

Scan-To Output Validation: Towards a Standardized Geometric Quality Assessment of Building Information Models Based on Point Clouds

NASA Astrophysics Data System (ADS)

Bonduel, M.; Bassier, M.; Vergauwen, M.; Pauwels, P.; Klein, R.

2017-11-01

The use of Building Information Modeling (BIM) for existing buildings based on point clouds is increasing. Standardized geometric quality assessment of the BIMs is needed to make them more reliable and thus reusable for future users. First, available literature on the subject is studied. Next, an initial proposal for a standardized geometric quality assessment is presented. Finally, this method is tested and evaluated with a case study. The number of specifications on BIM relating to existing buildings is limited. The Levels of Accuracy (LOA) specification of the USIBD provides definitions and suggestions regarding geometric model accuracy, but lacks a standardized assessment method. A deviation analysis is found to be dependent on (1) the used mathematical model, (2) the density of the point clouds and (3) the order of comparison. Results of the analysis can be graphical and numerical. An analysis on macro (building) and micro (BIM object) scale is necessary. On macro scale, the complete model is compared to the original point cloud and vice versa to get an overview of the general model quality. The graphical results show occluded zones and non-modeled objects respectively. Colored point clouds are derived from this analysis and integrated in the BIM. On micro scale, the relevant surface parts are extracted per BIM object and compared to the complete point cloud. Occluded zones are extracted based on a maximum deviation. What remains is classified according to the LOA specification. The numerical results are integrated in the BIM with the use of object parameters.

Geometrically nonlinear analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.

1982-01-01

A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

N-tuple topological/geometric cutoffs for 3D N-linear algebraic molecular codifications: variability, linear independence and QSAR analysis.

PubMed

García-Jacas, C R; Marrero-Ponce, Y; Barigye, S J; Hernández-Ortega, T; Cabrera-Leyva, L; Fernández-Castillo, A

2016-12-01

Novel N-tuple topological/geometric cutoffs to consider specific inter-atomic relations in the QuBiLS-MIDAS framework are introduced in this manuscript. These molecular cutoffs permit the taking into account of relations between more than two atoms by using (dis-)similarity multi-metrics and the concepts related with topological and Euclidean-geometric distances. To this end, the kth two-, three- and four-tuple topological and geometric neighbourhood quotient (NQ) total (or local-fragment) spatial-(dis)similarity matrices are defined, to represent 3D information corresponding to the relations between two, three and four atoms of the molecular structures that satisfy certain cutoff criteria. First, an analysis of a diverse chemical space for the most common values of topological/Euclidean-geometric distances, bond/dihedral angles, triangle/quadrilateral perimeters, triangle area and volume was performed in order to determine the intervals to take into account in the cutoff procedures. A variability analysis based on Shannon's entropy reveals that better distribution patterns are attained with the descriptors based on the cutoffs proposed (QuBiLS-MIDAS NQ-MDs) with regard to the results obtained when all inter-atomic relations are considered (QuBiLS-MIDAS KA-MDs - 'Keep All'). A principal component analysis shows that the novel molecular cutoffs codify chemical information captured by the respective QuBiLS-MIDAS KA-MDs, as well as information not captured by the latter. Lastly, a QSAR study to obtain deeper knowledge of the contribution of the proposed methods was carried out, using four molecular datasets (steroids (STER), angiotensin converting enzyme (ACE), thermolysin inhibitors (THER) and thrombin inhibitors (THR)) widely used as benchmarks in the evaluation of several methodologies. One to four variable QSAR models based on multiple linear regression were developed for each compound dataset following the original division into training and test sets. The results obtained reveal that the novel cutoff procedures yield superior performances relative to those of the QuBiLS-MIDAS KA-MDs in the prediction of the biological activities considered. From the results achieved, it can be suggested that the proposed N-tuple topological/geometric cutoffs constitute a relevant criteria for generating MDs codifying particular atomic relations, ultimately useful in enhancing the modelling capacity of the QuBiLS-MIDAS 3D-MDs.

A nano cold-wire for velocity measurements

NASA Astrophysics Data System (ADS)

Huang, Yi-Chun; Fu, Matthew; Fan, Yuyang; Byers, Clayton; Hultmark, Marcus

2016-11-01

We introduce a novel, strain-based sensor for both gaseous and liquid flows. The sensor consists of a free-standing, electrically conductive, nanoscale ribbon suspended between silicon supports. Due to its size, the nanoribbon deflects in flow under viscously dominated fluid forcing, which induces axial strain and a resistance change in the sensing element. The change in resistance can then be measured by a Wheatstone bridge, resulting in straightforward design and operation of the sensor. Since its operating principle is based on viscous fluid forcing, the sensor has high sensitivity especially in liquid or other highly viscous flows. A simple analytical model to understand the relation between forcing and strain is derived from the geometric and material constraints, and preliminary analysis using a low order model of the dynamic systems suggests that the sensor has a high frequency response. Lastly, a cylindrical structure to house the sensor with an axial and ventral channel to generate a pressure differential is being considered for typical velocimetry applications.

Wavefront-aberration measurement and systematic-error analysis of a high numerical-aperture objective

NASA Astrophysics Data System (ADS)

Liu, Zhixiang; Xing, Tingwen; Jiang, Yadong; Lv, Baobin

2018-02-01

A two-dimensional (2-D) shearing interferometer based on an amplitude chessboard grating was designed to measure the wavefront aberration of a high numerical-aperture (NA) objective. Chessboard gratings offer better diffraction efficiencies and fewer disturbing diffraction orders than traditional cross gratings. The wavefront aberration of the tested objective was retrieved from the shearing interferogram using the Fourier transform and differential Zernike polynomial-fitting methods. Grating manufacturing errors, including the duty-cycle and pattern-deviation errors, were analyzed with the Fourier transform method. Then, according to the relation between the spherical pupil and planar detector coordinates, the influence of the distortion of the pupil coordinates was simulated. Finally, the systematic error attributable to grating alignment errors was deduced through the geometrical ray-tracing method. Experimental results indicate that the measuring repeatability (3σ) of the wavefront aberration of an objective with NA 0.4 was 3.4 mλ. The systematic-error results were consistent with previous analyses. Thus, the correct wavefront aberration can be obtained after calibration.

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

Generalized spherical and simplicial coordinates

NASA Astrophysics Data System (ADS)

Richter, Wolf-Dieter

2007-12-01

Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation cosp([phi])p+sinp([phi])p=1. The p-generalized radius coordinate of a point [xi][set membership, variant]Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.

Final Report: Subcontract B623868 Algebraic Multigrid solvers for coupled PDE systems

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

Brannick, J.

The Pennsylvania State University (“Subcontractor”) continued to work on the design of algebraic multigrid solvers for coupled systems of partial differential equations (PDEs) arising in numerical modeling of various applications, with a main focus on solving the Dirac equation arising in Quantum Chromodynamics (QCD). The goal of the proposed work was to develop combined geometric and algebraic multilevel solvers that are robust and lend themselves to efficient implementation on massively parallel heterogeneous computers for these QCD systems. The research in these areas built on previous works, focusing on the following three topics: (1) the development of parallel full-multigrid (PFMG) andmore » non-Galerkin coarsening techniques in this frame work for solving the Wilson Dirac system; (2) the use of these same Wilson MG solvers for preconditioning the Overlap and Domain Wall formulations of the Dirac equation; and (3) the design and analysis of algebraic coarsening algorithms for coupled PDE systems including Stokes equation, Maxwell equation and linear elasticity.« less

Multiscale deformation of a liquid surface in interaction with a nanoprobe

NASA Astrophysics Data System (ADS)

Ledesma-Alonso, R.; Tordjeman, P.; Legendre, D.

2012-06-01

The interaction between a nanoprobe and a liquid surface is studied. The surface deformation depends on physical and geometric parameters, which are depicted by employing three dimensionless parameters: Bond number Bo, modified Hamaker number Ha, and dimensionless separation distance D*. The evolution of the deformation is described by a strongly nonlinear partial differential equation, which is solved by means of numerical methods. The dynamic analysis of the liquid profile points out the existence of a critical distance Dmin*, below which the irreversible wetting process of the nanoprobe happens. For D*≥Dmin*, the numerical results show the existence of two deformation profiles, one stable and another unstable from the energetic point of view. Different deformation length-scales, characterizing the stable liquid equilibrium interface, define the near- and the far-field deformation zones, where self-similar profiles are found. Finally, our results allow us to provide simple relationships between the parameters, which leads to determine the optimal conditions when performing atomic force microscope measurements over liquids.

Rotation Covariant Image Processing for Biomedical Applications

PubMed Central

Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences. PMID:23710255

A scattering database of marine particles and its application in optical analysis

NASA Astrophysics Data System (ADS)

Xu, G.; Yang, P.; Kattawar, G.; Zhang, X.

2016-12-01

In modeling the scattering properties of marine particles (e.g. phytoplankton), the laboratory studies imply a need to properly account for the influence of particle morphology, in addition to size and composition. In this study, a marine particle scattering database is constructed using a collection of distorted hexahedral shapes. Specifically, the scattering properties of each size bin and refractive index are obtained by the ensemble average associated with distorted hexahedra with randomly tilted facets and selected aspect ratios (from elongated to flattened). The randomness degree in shape-generation process defines the geometric irregularity of the particles in the group. The geometric irregularity and particle aspect ratios constitute a set of "shape factors" to be accounted for (e.g. in best-fit analysis). To cover most of the marine particle size range, we combine the Invariant Imbedding T-matrix (II-TM) method and the Physical-Geometric Optics Hybrid (PGOH) method in the calculations. The simulated optical properties are shown and compared with those obtained from Lorenz-Mie Theory. Using the scattering database, we present a preliminary optical analysis of laboratory-measured optical properties of marine particles.

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.

STUDY OF THE 3D GEOMETRIC STRUCTURE AND TEMPERATURE OF A CORONAL CAVITY USING THE LIMB SYNOPTIC MAP METHOD

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

Karna, N.; Pesnell, W. Dean; Webber, S. A. Hess

2015-09-10

We present the three-dimensional geometric structure and thermal properties of a coronal cavity deduced from limb synoptic maps. The observations are extreme ultraviolet images from the Atmospheric Imager Assembly (AIA) and magnetic images from the Helioseismic Magnetic Imager instruments on board the Solar Dynamics Observatory. We describe a limb synoptic-map method used to effectively identify and measure cavities from annuli of radiance above the solar limb. We find that cavities are best seen in the 211, 193, and 171 Å passbands. The prominence associated with each cavity is best seen in the 304 Å synoptic maps. We also estimate themore » thermal properties of the cavity and surrounding plasma by combining the AIA radiances with a differential emission measure analysis. This paper focuses on one long cavity from a catalog of coronal cavities that we are developing. Cavities in this catalog are designated by a coded name using the Carrington Rotation number and position. Cavity C211347177N was observed during Carrington Rotation 2113 at the northwestern limb of the solar disk with an average latitude of 47° N and a central longitude of 177°. We showed the following. (1) The cavity is a long tube with an elliptical cross-section with ratios of the length to width and the length to height of 11:1 and 7:1, respectively. (2) The cavity is about 1360 Mm long, or 170° in longitude. (3) It is tilted in latitude. (4) And it is slightly hotter than its surroundings.« less

On covariant Poisson brackets in classical field theory

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

Forger, Michael; Salles, Mário O.; Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN

2015-10-15

How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket,more » applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.« less

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.

VARIANCE OF MICROSOMAL PROTEIN AND ...

EPA Pesticide Factsheets

Differences in the pharmacokinetics of xenobiotics among humans makes them differentially susceptible to risk. Differences in enzyme content can mediate pharmacokinetic differences. Microsomal protein is often isolated fromliver to characterize enzyme content and activity, but no measures exist to extrapolate these data to the intact liver. Measures were developed from up to 60 samples of adult human liver to characterize the content of microsomal protein and cytochrome P450 (CYP) enzymes. Statistical evaluations are necessary to estimate values far from the mean value. Adult human liver contains 52.9 - 1.476 mg microsomal protein per g; 2587 - 1.84 pmoles CYP2E1 per g; and 5237 - 2.214 pmols CYP3A per g (geometric mean - geometric standard deviation). These values are useful for identifying and testing susceptibility as a function of enzyme content when used to extrapolate in vitro rates of chemical metabolism for input to physiologically based pharmacokinetic models which can then be exercised to quantify the effect of variance in enzyme expression on risk-relevant pharmacokinetic outcomes.

The Madelung Picture as a Foundation of Geometric Quantum Theory

NASA Astrophysics Data System (ADS)

Reddiger, Maik

2017-10-01

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.

Uncertainty in temperature-based determination of time of death

NASA Astrophysics Data System (ADS)

Weiser, Martin; Erdmann, Bodo; Schenkl, Sebastian; Muggenthaler, Holger; Hubig, Michael; Mall, Gita; Zachow, Stefan

2018-03-01

Temperature-based estimation of time of death (ToD) can be performed either with the help of simple phenomenological models of corpse cooling or with detailed mechanistic (thermodynamic) heat transfer models. The latter are much more complex, but allow a higher accuracy of ToD estimation as in principle all relevant cooling mechanisms can be taken into account. The potentially higher accuracy depends on the accuracy of tissue and environmental parameters as well as on the geometric resolution. We investigate the impact of parameter variations and geometry representation on the estimated ToD. For this, numerical simulation of analytic heat transport models is performed on a highly detailed 3D corpse model, that has been segmented and geometrically reconstructed from a computed tomography (CT) data set, differentiating various organs and tissue types. From that and prior information available on thermal parameters and their variability, we identify the most crucial parameters to measure or estimate, and obtain an a priori uncertainty quantification for the ToD.

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

PubMed

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

1988-01-01

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

Geometric errors in 3D optical metrology systems

NASA Astrophysics Data System (ADS)

Harding, Kevin; Nafis, Chris

2008-08-01

The field of 3D optical metrology has seen significant growth in the commercial market in recent years. The methods of using structured light to obtain 3D range data is well documented in the literature, and continues to be an area of development in universities. However, the step between getting 3D data, and getting geometrically correct 3D data that can be used for metrology is not nearly as well developed. Mechanical metrology systems such as CMMs have long established standard means of verifying the geometric accuracies of their systems. Both local and volumentric measurments are characterized on such system using tooling balls, grid plates, and ball bars. This paper will explore the tools needed to characterize and calibrate an optical metrology system, and discuss the nature of the geometric errors often found in such systems, and suggest what may be a viable standard method of doing characterization of 3D optical systems. Finally, we will present a tradeoff analysis of ways to correct geometric errors in an optical systems considering what can be gained by hardware methods versus software corrections.

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

Exploring students’ adaptive reasoning skills and van Hiele levels of geometric thinking: a case study in geometry

NASA Astrophysics Data System (ADS)

Rizki, H. T. N.; Frentika, D.; Wijaya, A.

2018-03-01

This study aims to explore junior high school students’ adaptive reasoning and the Van Hiele level of geometric thinking. The present study was a quasi-experiment with the non-equivalent control group design. The participants of the study were 34 seventh graders and 35 eighth graders in the experiment classes and 34 seventh graders and 34 eighth graders in the control classes. The students in the experiment classes learned geometry under the circumstances of a Knisley mathematical learning. The data were analyzed quantitatively by using inferential statistics. The results of data analysis show an improvement of adaptive reasoning skills both in the grade seven and grade eight. An improvement was also found for the Van Hiele level of geometric thinking. These results indicate the positive impact of Knisley learning model on students’ adaptive reasoning skills and Van Hiele level of geometric thinking.

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.

Enhanced definition and required examples of common datum imposed by ISO standard

NASA Astrophysics Data System (ADS)

Yan, Yiqing; Bohn, Martin

2017-12-01

According to the ISO Geometrical Product Specifications (GPS), the establishment and definition of common datum for geometrical components are not fully defined. There are two main limitations of this standard. Firstly: the explications of ISO examples of common datums are not matched with their corresponding definitions, and secondly: a full definition of common datum is missing. This paper suggests a new approach for an enhanced definition and concrete examples of common datum and proposes a holistic methodology for establishment of common datum for each geometrical component. This research is based on the analysis of physical behaviour of geometrical components, orientation constraints and invariance classes of datums. This approach fills the definition gaps of common datum based on ISO GPS, thereby eliminating those deficits. As a result, an improved methodology for a fully functional defined definition of common datum was formulated.

Geometrical modelling of textile reinforcements

NASA Technical Reports Server (NTRS)

Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene

1995-01-01

The mechanical properties of textile composites are dictated by the arrangement of yarns contained with the material. Thus to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made form highly flexible yarn systems which experience a certain degree of compressability. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical prediction models are demonstrated. Although more costly than its predecessors, the present analysis is based on the detailed architecture developed by one of the authors and his colleagues and accounts for many of the geometric complexities that other analyses ignore.

Geometry Helps to Compare Persistence Diagrams

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

Kerber, Michael; Morozov, Dmitriy; Nigmetov, Arnur

2015-11-16

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.), and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological datamore » analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.« less

Quality engineering and control semiannual progress report, November--December 1977 and January--April 1978

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

Carpenter, R.L.

1978-10-10

Determination of ppM concentrations of dibutyl phosphate in aqueous solutions of nitric acid or sodium carbonate is possible after an extraction step with carbon tetrachloride. Ester cleavage of the fatty triglyceride constituents is the principal radiolytic reaction in irradiation of a dolphin-head oil base precision watch oil. Use of a special container and a vacuum-brazing furnace permits the high-temperature dynamic determination of volatile surface contamination from samples of large geometric surface areas. Status of the mass spectrometer development project is discussed. A mass spectroscopy method provided rapid, specific, and quantitative results for environmental monitoring of polychlorinated biphenyl compounds. A sequentialmore » procedure for improved separation of actinides in soil samples was developed. Testing of packings in intimate contact with acid was accomplished by differential thermal analysis. Analysis results obtained on the XRD-6 x-ray unit are discussed for Nb in U-Nb alloys and for Cr and Ne in stainless steels. Correlation coefficients of 0.994 or better resulted for the determinations of Cr, Mn, and Ne in the stainless steel standards employed in the statistical evaluation of the Quanta Metrix x-ray unit.« less

Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Wang, Chong; Duan, Wenhui; Glazman, Leonid

2018-01-01

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase (λ ) that is subleading in powers of the field; λ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, λ /π are robustly integer valued, owing to the symmetry of the extremal orbit; i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which λ is a topological invariant, as well as the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalcogenides, 3D Weyl and Dirac metals, and crystalline and Z2 topological insulators. In particular, we point out that a π phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal.

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.

Mapping the Geometric Evolution of Protein Folding Motor.

PubMed

Jerath, Gaurav; Hazam, Prakash Kishore; Shekhar, Shashi; Ramakrishnan, Vibin

2016-01-01

Polypeptide chain has an invariant main-chain and a variant side-chain sequence. How the side-chain sequence determines fold in terms of its chemical constitution has been scrutinized extensively and verified periodically. However, a focussed investigation on the directive effect of side-chain geometry may provide important insights supplementing existing algorithms in mapping the geometrical evolution of protein chains and its structural preferences. Geometrically, folding of protein structure may be envisaged as the evolution of its geometric variables: ϕ, and ψ dihedral angles of polypeptide main-chain directed by χ1, and χ2 of side chain. In this work, protein molecule is metaphorically modelled as a machine with 4 rotors ϕ, ψ, χ1 and χ2, with its evolution to the functional fold is directed by combinations of its rotor directions. We observe that differential rotor motions lead to different secondary structure formations and the combinatorial pattern is unique and consistent for particular secondary structure type. Further, we found that combination of rotor geometries of each amino acid is unique which partly explains how different amino acid sequence combinations have unique structural evolution and functional adaptation. Quantification of these amino acid rotor preferences, resulted in the generation of 3 substitution matrices, which later on plugged in the BLAST tool, for evaluating their efficiency in aligning sequences. We have employed BLOSUM62 and PAM30 as standard for primary evaluation. Generation of substitution matrices is a logical extension of the conceptual framework we attempted to build during the development of this work. Optimization of matrices following the conventional routines and possible application with biologically relevant data sets are beyond the scope of this manuscript, though it is a part of the larger project design.

Convergence analysis of evolutionary algorithms that are based on the paradigm of information geometry.

PubMed

Beyer, Hans-Georg

2014-01-01

The convergence behaviors of so-called natural evolution strategies (NES) and of the information-geometric optimization (IGO) approach are considered. After a review of the NES/IGO ideas, which are based on information geometry, the implications of this philosophy w.r.t. optimization dynamics are investigated considering the optimization performance on the class of positive quadratic objective functions (the ellipsoid model). Exact differential equations describing the approach to the optimizer are derived and solved. It is rigorously shown that the original NES philosophy optimizing the expected value of the objective functions leads to very slow (i.e., sublinear) convergence toward the optimizer. This is the real reason why state of the art implementations of IGO algorithms optimize the expected value of transformed objective functions, for example, by utility functions based on ranking. It is shown that these utility functions are localized fitness functions that change during the IGO flow. The governing differential equations describing this flow are derived. In the case of convergence, the solutions to these equations exhibit an exponentially fast approach to the optimizer (i.e., linear convergence order). Furthermore, it is proven that the IGO philosophy leads to an adaptation of the covariance matrix that equals in the asymptotic limit-up to a scalar factor-the inverse of the Hessian of the objective function considered.

Slip Correction Measurements of Certified PSL Nanoparticles Using a Nanometer Differential Mobility Analyzer (Nano-DMA) for Knudsen Number From 0.5 to 83

PubMed Central

Kim, Jung Hyeun; Mulholland, George W.; Kukuck, Scott R.; Pui, David Y. H.

2005-01-01

The slip correction factor has been investigated at reduced pressures and high Knudsen number using polystyrene latex (PSL) particles. Nano-differential mobility analyzers (NDMA) were used in determining the slip correction factor by measuring the electrical mobility of 100.7 nm, 269 nm, and 19.90 nm particles as a function of pressure. The aerosol was generated via electrospray to avoid multiplets for the 19.90 nm particles and to reduce the contaminant residue on the particle surface. System pressure was varied down to 8.27 kPa, enabling slip correction measurements for Knudsen numbers as large as 83. A condensation particle counter was modified for low pressure application. The slip correction factor obtained for the three particle sizes is fitted well by the equation: C = 1 + Kn (α + β exp(−γ/Kn)), with α = 1.165, β = 0.483, and γ = 0.997. The first quantitative uncertainty analysis for slip correction measurements was carried out. The expanded relative uncertainty (95 % confidence interval) in measuring slip correction factor was about 2 % for the 100.7 nm SRM particles, about 3 % for the 19.90 nm PSL particles, and about 2.5 % for the 269 nm SRM particles. The major sources of uncertainty are the diameter of particles, the geometric constant associated with NDMA, and the voltage. PMID:27308102

Optimal layout design of obstacles for panic evacuation using differential evolution

NASA Astrophysics Data System (ADS)

Zhao, Yongxiang; Li, Meifang; Lu, Xin; Tian, Lijun; Yu, Zhiyong; Huang, Kai; Wang, Yana; Li, Ting

2017-01-01

To improve the pedestrian outflow in panic situations by suitably placing an obstacle in front of the exit, it is vital to understand the physical mechanism behind the evacuation efficiency enhancement. In this paper, a robust differential evolution is firstly employed to optimize the geometrical parameters of different shaped obstacles in order to achieve an optimal evacuation efficiency. Moreover, it is found that all the geometrical parameters of obstacles could markedly influence the evacuation efficiency of pedestrians, and the best way for achieving an optimal pedestrian outflow is to slightly shift the obstacle from the center of the exit which is consistent with findings of extant literature. Most importantly, by analyzing the profiles of density, velocity and specific flow, as well as the spatial distribution of crowd pressure, we have proven that placing an obstacle in panic situations does not reduce or absorb the pressure in the region of exit, on the contrary, promotes the pressure to a much higher level, hence the physical mechanism behind the evacuation efficiency enhancement is not a pressure decrease in the region of exit, but a significant reduction of high density region by effective separation in space which finally causes the increasing of escape speed and evacuation outflow. Finally, it is clearly demonstrated that the panel-like obstacle is considerably more robust and stable than the pillar-like obstacle to guarantee the enhancement of evacuation efficiency under different initial pedestrian distributions, different initial crowd densities as well as different desired velocities.

Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations

NASA Astrophysics Data System (ADS)

Sotoudeh, Zahra

2011-07-01

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

Enhanced cortical thickness measurements for rodent brains via Lagrangian-based RK4 streamline computation

NASA Astrophysics Data System (ADS)

Lee, Joohwi; Kim, Sun Hyung; Oguz, Ipek; Styner, Martin

2016-03-01

The cortical thickness of the mammalian brain is an important morphological characteristic that can be used to investigate and observe the brain's developmental changes that might be caused by biologically toxic substances such as ethanol or cocaine. Although various cortical thickness analysis methods have been proposed that are applicable for human brain and have developed into well-validated open-source software packages, cortical thickness analysis methods for rodent brains have not yet become as robust and accurate as those designed for human brains. Based on a previously proposed cortical thickness measurement pipeline for rodent brain analysis,1 we present an enhanced cortical thickness pipeline in terms of accuracy and anatomical consistency. First, we propose a Lagrangian-based computational approach in the thickness measurement step in order to minimize local truncation error using the fourth-order Runge-Kutta method. Second, by constructing a line object for each streamline of the thickness measurement, we can visualize the way the thickness is measured and achieve sub-voxel accuracy by performing geometric post-processing. Last, with emphasis on the importance of an anatomically consistent partial differential equation (PDE) boundary map, we propose an automatic PDE boundary map generation algorithm that is specific to rodent brain anatomy, which does not require manual labeling. The results show that the proposed cortical thickness pipeline can produce statistically significant regions that are not observed in the previous cortical thickness analysis pipeline.

Morphometric Identification of Queens, Workers and Intermediates in In Vitro Reared Honey Bees (Apis mellifera).

PubMed

De Souza, Daiana A; Wang, Ying; Kaftanoglu, Osman; De Jong, David; Amdam, Gro V; Gonçalves, Lionel S; Francoy, Tiago M

2015-01-01

In vitro rearing is an important and useful tool for honey bee (Apis mellifera L.) studies. However, it often results in intercastes between queens and workers, which are normally are not seen in hive-reared bees, except when larvae older than three days are grafted for queen rearing. Morphological classification (queen versus worker or intercastes) of bees produced by this method can be subjective and generally depends on size differences. Here, we propose an alternative method for caste classification of female honey bees reared in vitro, based on weight at emergence, ovariole number, spermatheca size and size and shape, and features of the head, mandible and basitarsus. Morphological measurements were made with both traditional morphometric and geometric morphometrics techniques. The classifications were performed by principal component analysis, using naturally developed queens and workers as controls. First, the analysis included all the characters. Subsequently, a new analysis was made without the information about ovariole number and spermatheca size. Geometric morphometrics was less dependent on ovariole number and spermatheca information for caste and intercaste identification. This is useful, since acquiring information concerning these reproductive structures requires time-consuming dissection and they are not accessible when abdomens have been removed for molecular assays or in dried specimens. Additionally, geometric morphometrics divided intercastes into more discrete phenotype subsets. We conclude that morphometric geometrics are superior to traditional morphometrics techniques for identification and classification of honey bee castes and intermediates.

Morphometric Identification of Queens, Workers and Intermediates in In Vitro Reared Honey Bees (Apis mellifera)

PubMed Central

A. De Souza, Daiana; Wang, Ying; Kaftanoglu, Osman; De Jong, David; V. Amdam, Gro; S. Gonçalves, Lionel; M. Francoy, Tiago

2015-01-01

In vitro rearing is an important and useful tool for honey bee (Apis mellifera L.) studies. However, it often results in intercastes between queens and workers, which are normally are not seen in hive-reared bees, except when larvae older than three days are grafted for queen rearing. Morphological classification (queen versus worker or intercastes) of bees produced by this method can be subjective and generally depends on size differences. Here, we propose an alternative method for caste classification of female honey bees reared in vitro, based on weight at emergence, ovariole number, spermatheca size and size and shape, and features of the head, mandible and basitarsus. Morphological measurements were made with both traditional morphometric and geometric morphometrics techniques. The classifications were performed by principal component analysis, using naturally developed queens and workers as controls. First, the analysis included all the characters. Subsequently, a new analysis was made without the information about ovariole number and spermatheca size. Geometric morphometrics was less dependent on ovariole number and spermatheca information for caste and intercaste identification. This is useful, since acquiring information concerning these reproductive structures requires time-consuming dissection and they are not accessible when abdomens have been removed for molecular assays or in dried specimens. Additionally, geometric morphometrics divided intercastes into more discrete phenotype subsets. We conclude that morphometric geometrics are superior to traditional morphometrics techniques for identification and classification of honey bee castes and intermediates. PMID:25894528

Time-Based Readout of a Silicon Photomultiplier (SiPM) for Time of Flight Positron Emission Tomography (TOF-PET)

NASA Astrophysics Data System (ADS)

Powolny, F.; Auffray, E.; Brunner, S. E.; Garutti, E.; Goettlich, M.; Hillemanns, H.; Jarron, P.; Lecoq, P.; Meyer, T.; Schultz-Coulon, H. C.; Shen, W.; Williams, M. C. S.

2011-06-01

Time of flight (TOF) measurements in positron emission tomography (PET) are very challenging in terms of timing performance, and should ideally achieve less than 100 ps FWHM precision. We present a time-based differential technique to read out silicon photomultipliers (SiPMs) which has less than 20 ps FWHM electronic jitter. The novel readout is a fast front end circuit (NINO) based on a first stage differential current mode amplifier with 20 Ω input resistance. Therefore the amplifier inputs are connected differentially to the SiPM's anode and cathode ports. The leading edge of the output signal provides the time information, while the trailing edge provides the energy information. Based on a Monte Carlo photon-generation model, HSPICE simulations were run with a 3 × 3 mm2 SiPM-model, read out with a differential current amplifier. The results of these simulations are presented here and compared with experimental data obtained with a 3 × 3 × 15 mm3 LSO crystal coupled to a SiPM. The measured time coincidence precision and the limitations in the overall timing accuracy are interpreted using Monte Carlo/SPICE simulation, Poisson statistics, and geometric effects of the crystal.

Using geometric morphometric visualizations of directional selection gradients to investigate morphological differentiation.

PubMed

Weaver, Timothy D; Gunz, Philipp

2018-04-01

Researchers studying extant and extinct taxa are often interested in identifying the evolutionary processes that have lead to the morphological differences among the taxa. Ideally, one could distinguish the influences of neutral evolutionary processes (genetic drift, mutation) from natural selection, and in situations for which selection is implicated, identify the targets of selection. The directional selection gradient is an effective tool for investigating evolutionary process, because it can relate form (size and shape) differences between taxa to the variation and covariation found within taxa. However, although most modern morphometric analyses use the tools of geometric morphometrics (GM) to analyze landmark data, to date, selection gradients have mainly been calculated from linear measurements. To address this methodological gap, here we present a GM approach for visualizing and comparing between-taxon selection gradients with each other, associated difference vectors, and "selection" gradients from neutral simulations. To exemplify our approach, we use a dataset of 347 three-dimensional landmarks and semilandmarks recorded on the crania of 260 primate specimens (112 humans, 67 common chimpanzees, 36 bonobos, 45 gorillas). Results on this example dataset show how incorporating geometric information can provide important insights into the evolution of the human braincase, and serve to demonstrate the utility of our approach for understanding morphological evolution. © 2018 The Author(s). Evolution © 2018 The Society for the Study of Evolution.

Geometric phase effects in ultracold hydrogen exchange reaction

DOE PAGES

Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, Naduvalath

2016-10-14

The role of the geometric phase effect on chemical reaction dynamics is explored by examining the hydrogen exchange process in the fundamental H+HD reaction. Results are presented for vibrationally excited HD molecules in the v = 4 vibrational level and for collision energies ranging from 1 μK to 100 K. It is found that, for collision energies below 3 K, inclusion of the geometric phase leads to dramatic enhancement or suppression of the reaction rates depending on the final quantum state of the HD molecule. The effect was found to be the most prominent for rotationally resolved integral and differential cross sections but it persists to a lesser extent in the vibrationally resolved and total reaction rate coefficients. However, no significant GP effect is present in the reactive channel leading to the D+H 2 product or in the D+H 2more » $$(v=4,j=0)\\,\\to $$ HD+H reaction. A simple interference mechanism involving inelastic (nonreactive) and exchange scattering amplitudes is invoked to account for the observed GP effects. The computed results also reveal a shape resonance in the H+HD reaction near 1 K and the GP effect is found to influence the magnitude of the resonant part of the cross section. In conclusion, experimental detection of the resonance may allow a sensitive probe of the GP effect in the H+HD reaction.« less

The Future Spaceborne Hyperspectral Imager Enmap: its In-Flight Radiometric and Geometric Calibration Concept

NASA Astrophysics Data System (ADS)

Schneider, M.; Müller, R.; Krawzcyk, H.; Bachmann, M.; Storch, T.; Mogulsky, V.; Hofer, S.

2012-07-01

The German Aerospace Center DLR - namely the Earth Observation Center EOC and the German Space Operations Center GSOC - is responsible for the establishment of the ground segment of the future German hyperspectral satellite mission EnMAP (Environmental Mapping and Analysis Program). The Earth Observation Center has long lasting experiences with air- and spaceborne acquisition, processing, and analysis of hyperspectral image data. In the first part of this paper, an overview of the radiometric in-flight calibration concept including dark value measurements, deep space measurements, internal lamps measurements and sun measurements is presented. Complemented by pre-launch calibration and characterization these analyses will deliver a detailed and quantitative assessment of possible changes of spectral and radiometric characteristics of the hyperspectral instrument, e.g. due to degradation of single elements. A geometric accuracy of 100 m, which will be improved to 30 m with respect to a used reference image, if it exists, will be achieved by ground processing. Therfore, and for the required co-registration accuracy between SWIR and VNIR channels, additional to the radiometric calibration, also a geometric calibration is necessary. In the second part of this paper, the concept of the geometric calibration is presented in detail. The geometric processing of EnMAP scenes will be based on laboratory calibration results. During repeated passes over selected calibration areas images will be acquired. The update of geometric camera model parameters will be done by an adjustment using ground control points, which will be extracted by automatic image matching. In the adjustment, the improvements of the attitude angles (boresight angles), the improvements of the interior orientation (view vector) and the improvements of the position data are estimated. In this paper, the improvement of the boresight angles is presented in detail as an example. The other values and combinations follow the same rules. The geometric calibration will mainly be executed during the commissioning phase, later in the mission it is only executed if required, i.e. if the geometric accuracy of the produced images is close to or exceeds the requirements of 100 m or 30 m respectively, whereas the radiometric calibration will be executed periodically during the mission with a higher frequency during commissioning phase.

Spatiotemporal characteristics of gaze of children with autism spectrum disorders while looking at classroom scenes

PubMed Central

Higuchi, Takahiro; Noritake, Atsushi; Yanagimoto, Yoshitoki; Kobayashi, Hodaka; Nakamura, Kae; Kaneko, Kazunari

2017-01-01

Children with autism spectrum disorders (ASD) who have neurodevelopmental impairments in social communication often refuse to go to school because of difficulties in learning in class. The exact cause of maladaptation to school in such children is unknown. We hypothesized that these children have difficulty in paying attention to objects at which teachers are pointing. We performed gaze behavior analysis of children with ASD to understand their difficulties in the classroom. The subjects were 26 children with ASD (19 boys and 7 girls; mean age, 8.6 years) and 27 age-matched children with typical development (TD) (14 boys and 13 girls; mean age, 8.2 years). We measured eye movements of the children while they performed free viewing of two movies depicting actual classes: a Japanese class in which a teacher pointed at cartoon characters and an arithmetic class in which the teacher pointed at geometric figures. In the analysis, we defined the regions of interest (ROIs) as the teacher’s face and finger, the cartoon characters and geometric figures at which the teacher pointed, and the classroom wall that contained no objects. We then compared total gaze time for each ROI between the children with ASD and TD by two-way ANOVA. Children with ASD spent less gaze time on the cartoon characters pointed at by the teacher; they spent more gaze time on the wall in both classroom scenes. We could differentiate children with ASD from those with TD almost perfectly by the proportion of total gaze time that children with ASD spent looking at the wall. These results suggest that children with ASD do not follow the teacher’s instructions in class and persist in gazing at inappropriate visual areas such as walls. Thus, they may have difficulties in understanding content in class, leading to maladaptation to school. PMID:28472111

The evolution of the platyrrhine talus: A comparative analysis of the phenetic affinities of the Miocene platyrrhines with their modern relatives.

PubMed

Püschel, Thomas A; Gladman, Justin T; Bobe, René; Sellers, William I

2017-10-01

Platyrrhines are a diverse group of primates that presently occupy a broad range of tropical-equatorial environments in the Americas. However, most of the fossil platyrrhine species of the early Miocene have been found at middle and high latitudes. Although the fossil record of New World monkeys has improved considerably over the past several years, it is still difficult to trace the origin of major modern clades. One of the most commonly preserved anatomical structures of early platyrrhines is the talus. This work provides an analysis of the phenetic affinities of extant platyrrhine tali and their Miocene counterparts through geometric morphometrics and a series of phylogenetic comparative analyses. Geometric morphometrics was used to quantify talar shape affinities, while locomotor mode percentages (LMPs) were used to test if talar shape is associated with locomotion. Comparative analyses were used to test if there was convergence in talar morphology, as well as different models that could explain the evolution of talar shape and size in platyrrhines. Body mass predictions for the fossil sample were also computed using the available articular surfaces. The results showed that most analyzed fossils exhibit a generalized morphology that is similar to some 'generalist' modern species. It was found that talar shape covaries with LMPs, thus allowing the inference of locomotion from talar morphology. The results further suggest that talar shape diversification can be explained by invoking a model of shifts in adaptive peak to three optima representing a phylogenetic hypothesis in which each platyrrhine family occupied a separate adaptive peak. The analyses indicate that platyrrhine talar centroid size diversification was characterized by an early differentiation related to a multidimensional niche model. Finally, the ancestral platyrrhine condition was reconstructed as a medium-sized, generalized, arboreal, quadruped. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Spatiotemporal characteristics of gaze of children with autism spectrum disorders while looking at classroom scenes.

PubMed

Higuchi, Takahiro; Ishizaki, Yuko; Noritake, Atsushi; Yanagimoto, Yoshitoki; Kobayashi, Hodaka; Nakamura, Kae; Kaneko, Kazunari

2017-01-01

Children with autism spectrum disorders (ASD) who have neurodevelopmental impairments in social communication often refuse to go to school because of difficulties in learning in class. The exact cause of maladaptation to school in such children is unknown. We hypothesized that these children have difficulty in paying attention to objects at which teachers are pointing. We performed gaze behavior analysis of children with ASD to understand their difficulties in the classroom. The subjects were 26 children with ASD (19 boys and 7 girls; mean age, 8.6 years) and 27 age-matched children with typical development (TD) (14 boys and 13 girls; mean age, 8.2 years). We measured eye movements of the children while they performed free viewing of two movies depicting actual classes: a Japanese class in which a teacher pointed at cartoon characters and an arithmetic class in which the teacher pointed at geometric figures. In the analysis, we defined the regions of interest (ROIs) as the teacher's face and finger, the cartoon characters and geometric figures at which the teacher pointed, and the classroom wall that contained no objects. We then compared total gaze time for each ROI between the children with ASD and TD by two-way ANOVA. Children with ASD spent less gaze time on the cartoon characters pointed at by the teacher; they spent more gaze time on the wall in both classroom scenes. We could differentiate children with ASD from those with TD almost perfectly by the proportion of total gaze time that children with ASD spent looking at the wall. These results suggest that children with ASD do not follow the teacher's instructions in class and persist in gazing at inappropriate visual areas such as walls. Thus, they may have difficulties in understanding content in class, leading to maladaptation to school.

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

1977-01-01

The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

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.

Genetic admixture and lineage separation in a southern Andean plant

PubMed Central

Morello, Santiago; Sede, Silvana M.

2016-01-01

Mountain uplifts have generated new ecologic opportunities for plants, and triggered evolutionary processes, favouring an increase on the speciation rate in all continents. Moreover, mountain ranges may act as corridors or barriers for plant lineages and populations. In South America a high rate of diversification has been linked to Andean orogeny during Pliocene/Miocene. More recently, Pleistocene glacial cycles have also shaped species distribution and demography. The endemic genus Escallonia is known to have diversified in the Andes. Species with similar morphology obscure species delimitation and plants with intermediate characters occur naturally. The aim of this study is to characterize genetic variation and structure of two widespread species of Escallonia: E. alpina and E. rubra. We analyzed the genetic variation of populations of the entire distribution range of the species and we also included those with intermediate morphological characters; a total of 94 accessions from 14 populations were used for the Amplified Fragment Length Polymorphism (AFLP) analysis. Plastid DNA sequences (trnS-trnG, 3′trnV-ndhC intergenic spacers and the ndhF gene) from sixteen accessions of Escallonia species were used to construct a Statistical Parsimony network. Additionally, we performed a geometric morphometrics analysis on 88 leaves from 35 individuals of the two E. alpina varieties to further study their differences. Wright’s Fst and analysis of molecular variance tests performed on AFLP data showed a significant level of genetic structure at the species and population levels. Intermediate morphology populations showed a mixed genetic contribution from E. alpina var. alpina and E. rubra both in the Principal Coordinates Analysis (PCoA) and STRUCTURE. On the other hand, E. rubra and the two varieties of E. alpina are well differentiated and assigned to different genetic clusters. Moreover, the Statistical Parsimony network showed a high degree of divergence between the varieties of E. alpina: var. alpina is more closely related to E. rubra and other species than to its own counterpart E. alpina var. carmelitana. Geometric morphometrics analysis (Elliptic Fourier descriptors) revealed significant differences in leaf shape between varieties. We found that diversity in Escallonia species analyzed here is geographically structured and deep divergence between varieties of E. alpina could be associated to ancient evolutionary events like orogeny. Admixture in southern populations could be the result of hybridization at the margins of the parental species’ distribution range. PMID:27179539

Geometric Analysis, Visualization, and Conceptualization of 3D Image Data

Science.gov Websites

collection of geometric primitives (points, lines, polygons, etc.) that accurately represent the shape of the different color. The masks mentioned above are human supplied hints as to where to draw these contour lines ) Acquire information about the inside of an object, and generate a 3D image data set (2) Define the regions

SCATHA-Analysis System

DTIC Science & Technology

1981-01-31

geometric factor. For the low energy FSA detectors, the background counts must be subtracted from the measured (actual) counts before the geometric factor...and high energy) each provide a background measure - ment. The background counts for the low energy ESA (LE ESA) were subtracted from the other four LE...perpendicular to the spacecraft +X reference spin axis and 189.660 around from the +Z axis (with this angle measured from the +Z axis in the direction

Propagation in Striated Media

DTIC Science & Technology

1976-05-01

random walk photon scattering, geometric optics refraction at a thin phase screen, plane wave scattering from a thin screen in the Fraunhofer limit and...significant cases. In the geometric optics regime the distribution of density of allowable multipath rays is gsslanly distributed and the power...3.1 Random Walk Approach to Scattering 10 3.2 Phase Screen Approximation to Strong Scattering 13 3.3 Ray Optics and Stationary Phase Analysis 21 3,3,1

Interplay between Peptide Bond Geometrical Parameters in Nonglobular Structural Contexts

PubMed Central

Esposito, Luciana; De Simone, Alfonso; Vitagliano, Luigi

2013-01-01

Several investigations performed in the last two decades have unveiled that geometrical parameters of protein backbone show a remarkable variability. Although these studies have provided interesting insights into one of the basic aspects of protein structure, they have been conducted on globular and water-soluble proteins. We report here a detailed analysis of backbone geometrical parameters in nonglobular proteins/peptides. We considered membrane proteins and two distinct fibrous systems (amyloid-forming and collagen-like peptides). Present data show that in these systems the local conformation plays a major role in dictating the amplitude of the bond angle N-Cα-C and the propensity of the peptide bond to adopt planar/nonplanar states. Since the trends detected here are in line with the concept of the mutual influence of local geometry and conformation previously established for globular and water-soluble proteins, our analysis demonstrates that the interplay of backbone geometrical parameters is an intrinsic and general property of protein/peptide structures that is preserved also in nonglobular contexts. For amyloid-forming peptides significant distortions of the N-Cα-C bond angle, indicative of sterical hidden strain, may occur in correspondence with side chain interdigitation. The correlation between the dihedral angles Δω/ψ in collagen-like models may have interesting implications for triple helix stability. PMID:24455689

Interplay between peptide bond geometrical parameters in nonglobular structural contexts.

PubMed

Esposito, Luciana; Balasco, Nicole; De Simone, Alfonso; Berisio, Rita; Vitagliano, Luigi

2013-01-01

Several investigations performed in the last two decades have unveiled that geometrical parameters of protein backbone show a remarkable variability. Although these studies have provided interesting insights into one of the basic aspects of protein structure, they have been conducted on globular and water-soluble proteins. We report here a detailed analysis of backbone geometrical parameters in nonglobular proteins/peptides. We considered membrane proteins and two distinct fibrous systems (amyloid-forming and collagen-like peptides). Present data show that in these systems the local conformation plays a major role in dictating the amplitude of the bond angle N-C(α)-C and the propensity of the peptide bond to adopt planar/nonplanar states. Since the trends detected here are in line with the concept of the mutual influence of local geometry and conformation previously established for globular and water-soluble proteins, our analysis demonstrates that the interplay of backbone geometrical parameters is an intrinsic and general property of protein/peptide structures that is preserved also in nonglobular contexts. For amyloid-forming peptides significant distortions of the N-C(α)-C bond angle, indicative of sterical hidden strain, may occur in correspondence with side chain interdigitation. The correlation between the dihedral angles Δω/ψ in collagen-like models may have interesting implications for triple helix stability.

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.

Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector

NASA Technical Reports Server (NTRS)

Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)

2001-01-01

Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.

The Legendre transform in geometric calculus

NASA Astrophysics Data System (ADS)

McClellan, Gene E.

2013-10-01

This paper explores the extension of the Legendre transform from scalar calculus to geometric calculus. In physics, the Legendre transform provides a change of variables to express equations of motion or other physical relationships in terms of the most convenient dynamical quantities for a given experimental or theoretical analysis. In classical mechanics and in field theory, the Legendre transform generates the Hamiltonian function of a system from the Lagrangian function or vice versa. In thermodynamics, the Legendre transform allows thermodynamic relationships to be written in terms of alternative sets of independent variables. In this paper, we review the properties of the Legendre transform in scalar calculus and show how an analogous transformation with similar properties may be constructed in geometric calculus.

Aerodynamic shape optimization of a HSCT type configuration with improved surface definition

NASA Technical Reports Server (NTRS)

Thomas, Almuttil M.; Tiwari, Surendra N.

1994-01-01

Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process.

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.

High-contrast differentiation resolution 3D imaging of rodent brain by X-ray computed microtomography

NASA Astrophysics Data System (ADS)

Zikmund, T.; Novotná, M.; Kavková, M.; Tesařová, M.; Kaucká, M.; Szarowská, B.; Adameyko, I.; Hrubá, E.; Buchtová, M.; Dražanová, E.; Starčuk, Z.; Kaiser, J.

2018-02-01

The biomedically focused brain research is largely performed on laboratory mice considering a high homology between the human and mouse genomes. A brain has an intricate and highly complex geometrical structure that is hard to display and analyse using only 2D methods. Applying some fast and efficient methods of brain visualization in 3D will be crucial for the neurobiology in the future. A post-mortem analysis of experimental animals' brains usually involves techniques such as magnetic resonance and computed tomography. These techniques are employed to visualize abnormalities in the brains' morphology or reparation processes. The X-ray computed microtomography (micro CT) plays an important role in the 3D imaging of internal structures of a large variety of soft and hard tissues. This non-destructive technique is applied in biological studies because the lab-based CT devices enable to obtain a several-micrometer resolution. However, this technique is always used along with some visualization methods, which are based on the tissue staining and thus differentiate soft tissues in biological samples. Here, a modified chemical contrasting protocol of tissues for a micro CT usage is introduced as the best tool for ex vivo 3D imaging of a post-mortem mouse brain. This way, the micro CT provides a high spatial resolution of the brain microscopic anatomy together with a high tissue differentiation contrast enabling to identify more anatomical details in the brain. As the micro CT allows a consequent reconstruction of the brain structures into a coherent 3D model, some small morphological changes can be given into context of their mutual spatial relationships.

Manipulatives and problem situations as escalators for students' geometric understanding: a semiotic analysis

NASA Astrophysics Data System (ADS)

Daher, Wajeeh M.

2014-04-01

Mathematical learning and teaching are increasingly seen as a multimodal experience involved in cultural and social semiotic registers and means, and as such social-cultural semiotic analysis is expected to shed light on learning and teaching processes occurring in the mathematics classroom. In this research, three social-cultural semiotic frameworks were utilised to analyse elementary school students' learning of a geometric relation: the semiotic bundle, the space of action, production and communication and the theoretical framework of attention, awareness and objectification. Educational mathematical situations are described, in addition to semiotic sets, registers and means emerging in the different mathematical situations and that are relevant to the three social-cultural semiotic frameworks which the current research utilizes. Further, the students, as a consequence of (1) their multimodal experience, (2) their connecting between the different mathematical situations and semiotic registers, and (3) the teacher's questions and tasks, could objectify the geometric relation between the lengths of the triangle's edges.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference

NASA Astrophysics Data System (ADS)

Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.

2016-09-01

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference.

PubMed

Samlan, C T; Naik, Dinesh N; Viswanathan, Nirmal K

2016-09-14

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

Design optimization of hydraulic turbine draft tube based on CFD and DOE method

NASA Astrophysics Data System (ADS)

Nam, Mun chol; Dechun, Ba; Xiangji, Yue; Mingri, Jin

2018-03-01

In order to improve performance of the hydraulic turbine draft tube in its design process, the optimization for draft tube is performed based on multi-disciplinary collaborative design optimization platform by combining the computation fluid dynamic (CFD) and the design of experiment (DOE) in this paper. The geometrical design variables are considered as the median section in the draft tube and the cross section in its exit diffuser and objective function is to maximize the pressure recovery factor (Cp). Sample matrixes required for the shape optimization of the draft tube are generated by optimal Latin hypercube (OLH) method of the DOE technique and their performances are evaluated through computational fluid dynamic (CFD) numerical simulation. Subsequently the main effect analysis and the sensitivity analysis of the geometrical parameters of the draft tube are accomplished. Then, the design optimization of the geometrical design variables is determined using the response surface method. The optimization result of the draft tube shows a marked performance improvement over the original.

Polychromatic Microdiffraction Analysis of Defect Self-Organization in Shock Deformed Single Crystals

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

Barabash, Rozaliya; Ice, Gene E; Liu, Wenjun

A spatially resolved X-ray diffraction method - with a submicron 3D resolution together with SEM and OIM analysis are applied to understand the arrangements of voids, geometrically necessary dislocations and strain gradient distributions in samples of Al (1 2 3) and Cu (0 0 1) single crystals shocked to incipient spallation fracture. We describe how geometrically necessary dislocations and the effective strain gradient alter white beam Laue patterns of the shocked materials. Several distinct structural zones are observed at different depths under the impact surface. The density of geometrically necessary dislocations (GNDs) is extremely high near the impact and backmore » surface of the shock recovered crystals. The spall region is characterized by a large density of mesoscale voids and GNDs. The spall region is separated from the impact and back surfaces by compressed regions with high total dislocation density but lower GNDs density. Self-organization of shear bands is observed in the shock recovered Cu single crystal.« less

A geometric measure of dark energy with pairs of galaxies.

PubMed

Marinoni, Christian; Buzzi, Adeline

2010-11-25

Observations indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance (Ω(X)) and equation of state (W(X)) of dark energy. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at Ω(k)≡0 and the dark energy equation-of-state parameter at W(X)≡-1, and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and -0.85>W(X)>-1.12 and 0.60<Ω(X)<0.80.

Quickbird Geometry Report for Summer 2003

NASA Technical Reports Server (NTRS)

Darbha, Ravikanth; Helder, Dennis; Choi, Taeyoung

2005-01-01

Digital Globe provides for general use 2.4 m multi-spectral and 0.7 m panchromatic imagery acquired by the Quickbird satellite. This geometrically corrected imagery was obtained as standard and orthorectified products; the difference between the two products is primarily in the degree of geometric accuracy that Digital Globe claims. For both products, every image pixel contains estimated sets of Northing/Easting and lat/long coordinates accessible through an image display application such as ENVI. Ground processing was performed by Digital Globe using the ADP 2.1 version of their system. Analysis conducted at South Dakota State University attempted to verify the geometric accuracy of standard and orthorectified Quickbird imagery to determine if specifications for the NASA Science Data Purchase (SDP) were met. These specifications are in Table 1 of Appendix 1. In this analysis, we had approximately 90 Ground Control Points (varies depending on scene size on each date), uniformly distributed over the Brookings, SD, area, from 4 Quickbird scenes acquired August 23, September 15, and October 21 of 2003.

Intervertebral disc biomechanical analysis using the finite element modeling based on medical images.

PubMed

Li, Haiyun; Wang, Zheng

2006-01-01

In this paper, a 3D geometric model of the intervertebral and lumbar disks has been presented, which integrated the spine CT and MRI data-based anatomical structure. Based on the geometric model, a 3D finite element model of an L1-L2 segment was created. Loads, which simulate the pressure from above were applied to the FEM, while a boundary condition describing the relative L1-L2 displacement is imposed on the FEM to account for 3D physiological states. The simulation calculation illustrates the stress and strain distribution and deformation of the spine. The method has two characteristics compared to previous studies: first, the finite element model of the lumbar are based on the data directly derived from medical images such as CTs and MRIs. Second, the result of analysis will be more accurate than using the data of geometric parameters. The FEM provides a promising tool in clinical diagnosis and for optimizing individual therapy in the intervertebral disc herniation.

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Geometric morphometrics in primatology: craniofacial variation in Homo sapiens and Pan troglodytes.

PubMed

Lynch, J M; Wood, C G; Luboga, S A

1996-01-01

Traditionally, morphometric studies have relied on statistical analysis of distances, angles or ratios to investigate morphometric variation among taxa. Recently, geometric techniques have been developed for the direct analysis of landmark data. In this paper, we offer a summary (with examples) of three of these newer techniques, namely shape coordinate, thin-plate spline and relative warp analyses. Shape coordinate analysis detected significant craniofacial variation between 4 modern human populations, with African and Australian Aboriginal specimens being relatively prognathous compared with their Eurasian counterparts. In addition, the Australian specimens exhibited greater basicranial flexion than all other samples. The observed relationships between size and craniofacial shape were weak. The decomposition of shape variation into affine and non-affine components is illustrated via a thin-plate spline analysis of Homo and Pan cranial landmarks. We note differences between Homo and Pan in the degree of prognathism and basicranial flexion and the position and orientation of the foramen magnum. We compare these results with previous studies of these features in higher primates and discuss the utility of geometric morphometrics as a tool in primatology and physical anthropology. We conclude that many studies of morphological variation, both within and between taxa, would benefit from the graphical nature of these techniques.

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.

Georeferencing CAMS data: Polynomial rectification and beyond

NASA Astrophysics Data System (ADS)

Yang, Xinghe

The Calibrated Airborne Multispectral Scanner (CAMS) is a sensor used in the commercial remote sensing program at NASA Stennis Space Center. In geographic applications of the CAMS data, accurate geometric rectification is essential for the analysis of the remotely sensed data and for the integration of the data into Geographic Information Systems (GIS). The commonly used rectification techniques such as the polynomial transformation and ortho rectification have been very successful in the field of remote sensing and GIS for most remote sensing data such as Landsat imagery, SPOT imagery and aerial photos. However, due to the geometric nature of the airborne line scanner which has high spatial frequency distortions, the polynomial model and the ortho rectification technique in current commercial software packages such as Erdas Imagine are not adequate for obtaining sufficient geometric accuracy. In this research, the geometric nature, especially the major distortions, of the CAMS data has been described. An analytical step-by-step geometric preprocessing has been utilized to deal with the potential high frequency distortions of the CAMS data. A generic sensor-independent photogrammetric model has been developed for the ortho-rectification of the CAMS data. Three generalized kernel classes and directional elliptical basis have been formulated into a rectification model of summation of multisurface functions, which is a significant extension to the traditional radial basis functions. The preprocessing mechanism has been fully incorporated into the polynomial, the triangle-based finite element analysis as well as the summation of multisurface functions. While the multisurface functions and the finite element analysis have the characteristics of localization, piecewise logic has been applied to the polynomial and photogrammetric methods, which can produce significant accuracy improvement over the global approach. A software module has been implemented with full integration of data preprocessing and rectification techniques under Erdas Imagine development environment. The final root mean square (RMS) errors for the test CAMS data are about two pixels which are compatible with the random RMS errors existed in the reference map coordinates.

Geometry of the submanifolds of SEXn. II. The generalized fundamental equations for the hypersubmanifold of SEXn

NASA Astrophysics Data System (ADS)

Chung, Kyung Tae; Lee, Jong Woo

1989-08-01

A connection which is both Einstein and semisymmetric is called an SE connection, and a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by g λμ through an SE connection is called an n-dimensional SE manifold and denoted by SEXn. This paper is a direct continuation of earlier work. In this paper, we derive the generalized fundamental equations for the hypersubmanifold of SEXn, including generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations.

Differential Global Positioning System (DGPS) for Flight Testing (Global Positioning System Differentiel (DGPS) pour les Essais en vol)

DTIC Science & Technology

2008-10-01

pseudorange measurement, ρi p denotes the geometric distance between the stations and satellite, dti denotes the receiver’s clock offsets, di p, denotes the...the DGPS data quality. For this purpose a number of over-sea flight legs were included in the trials. The ASHTECH DGPS altitude data output was both...12 where a short leg of a flight trial is represented (the full horizontal track is shown in Figure C-13). Figure C-12: Latitude Error (TANS – 3

Towards an exact relativistic theory of Earth's geoid undulation

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.

2015-08-01

The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.

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.

The Local Geometry of Multiattribute Tradeoff Preferences

PubMed Central

McGeachie, Michael; Doyle, Jon

2011-01-01

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

[Finite element stress analysis of all-ceramic continuous crowns of the lower anterior teeth in differential shoulder thickness].

PubMed

Ouyang, Shao-bo; Wang, Jun; Zhang, Hong-bin; Liao, Lan; Zhu, Hong-shui

2014-04-01

To investigate the stress distributions under load in 3 types of all-ceramic continuous crowns of the lower anterior teeth with differential shoulder thickness. Cone-beam CT (CBCT) was used to scan the in vitro mandibular central incisors, and achieve three-dimensional finite element model of all-ceramic continuous crowns with different shoulder width by using Mimics, Abaqus software. Different load conditions were simulated based on this model to study the effect of shoulder width variation on finite element analysis of 3 kinds of different all-ceramic materials of incisors fixed continuous crowns of the mandibular. Using CBCT, Mimics10.01 software and Abaqus 6.11 software, three-dimensional finite element model of all-ceramic continuous crowns of the mandibular incisor, abutment, periodontal ligament and alveolar bone was established. Different ceramic materials and various shoulder width had minor no impact on the equivalent stress peak of periodontal membrane, as well as alveolar bone. With the same shoulder width and large area of vertical loading of 120 N, the tensile stress was the largest in In-Ceram Alumina, followed by In-Ceram Zirconia and the minimum was IPS.Empress II. Under large area loading of 120 N 45° labially, when the material was IPS.Empress II, with the shoulder width increased, the porcelain plate edge of the maximum tensile stress value increased, while the other 2 materials had no obvious change. Finite element model has good geometric similarity. In the setting range of this study, when the elastic modulus of ceramic materials is bigger, the tensile stress of the continuous crown is larger. Supported by Research Project of Department of Education, Jiangxi Province (GJJ09130).

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

NASA Astrophysics Data System (ADS)

Dimitriou, Ioannis

2017-11-01

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

The vehicle design evaluation program - A computer-aided design procedure for transport aircraft

NASA Technical Reports Server (NTRS)

Oman, B. H.; Kruse, G. S.; Schrader, O. E.

1977-01-01

The vehicle design evaluation program is described. This program is a computer-aided design procedure that provides a vehicle synthesis capability for vehicle sizing, external load analysis, structural analysis, and cost evaluation. The vehicle sizing subprogram provides geometry, weight, and balance data for aircraft using JP, hydrogen, or methane fuels. The structural synthesis subprogram uses a multistation analysis for aerodynamic surfaces and fuselages to develop theoretical weights and geometric dimensions. The parts definition subprogram uses the geometric data from the structural analysis and develops the predicted fabrication dimensions, parts material raw stock buy requirements, and predicted actual weights. The cost analysis subprogram uses detail part data in conjunction with standard hours, realization factors, labor rates, and material data to develop the manufacturing costs. The program is used to evaluate overall design effects on subsonic commercial type aircraft due to parameter variations.

Analysis of lead twist in modern high-performance grinding methods

NASA Astrophysics Data System (ADS)

Kundrák, J.; Gyáni, K.; Felhő, C.; Markopoulos, AP; Deszpoth, I.

2016-11-01

According to quality requirements of road vehicles shafts, which bear dynamic seals, twisted-pattern micro-geometrical topography is not allowed. It is a question whether newer modern grinding methods - such as quick-point grinding and peel grinding - could provide twist- free topography. According to industrial experience, twist-free surfaces can be made, however with certain settings, same twist occurs. In this paper it is proved by detailed chip-geometrical analysis that the topography generated by the new procedures is theoretically twist-patterned because of the feeding motion of the CBN tool. The presented investigation was carried out by a single-grain wheel model and computer simulation.