Discrete differential geometry: The nonplanar quadrilateral mesh

NASA Astrophysics Data System (ADS)

Twining, Carole J.; Marsland, Stephen

2012-06-01

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

Tropomodulin 1 Constrains Fiber Cell Geometry during Elongation and Maturation in the Lens Cortex

PubMed Central

Nowak, Roberta B.

2012-01-01

Lens fiber cells exhibit a high degree of hexagonal packing geometry, determined partly by tropomodulin 1 (Tmod1), which stabilizes the spectrin-actin network on lens fiber cell membranes. To ascertain whether Tmod1 is required during epithelial cell differentiation to fiber cells or during fiber cell elongation and maturation, the authors quantified the extent of fiber cell disorder in the Tmod1-null lens and determined locations of disorder by confocal microscopy and computational image analysis. First, nearest neighbor analysis of fiber cell geometry in Tmod1-null lenses showed that disorder is confined to focal patches. Second, differentiating epithelial cells at the equator aligned into ordered meridional rows in Tmod1-null lenses, with disordered patches first observed in elongating fiber cells. Third, as fiber cells were displaced inward in Tmod1-null lenses, total disordered area increased due to increased sizes (but not numbers) of individual disordered patches. The authors conclude that Tmod1 is required first to coordinate fiber cell shapes and interactions during tip migration and elongation and second to stabilize ordered fiber cell geometry during maturation in the lens cortex. An unstable spectrin-actin network without Tmod1 may result in imbalanced forces along membranes, leading to fiber cell rearrangements during elongation, followed by propagation of disorder as fiber cells mature. PMID:22473940

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

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.

Development of an Automatic Differentiation Version of the FPX Rotor Code

NASA Technical Reports Server (NTRS)

Hu, Hong

1996-01-01

The ADIFOR2.0 automatic differentiator is applied to the FPX rotor code along with the grid generator GRGN3. The FPX is an eXtended Full-Potential CFD code for rotor calculations. The automatic differentiation version of the code is obtained, which provides both non-geometry and geometry sensitivity derivatives. The sensitivity derivatives via automatic differentiation are presented and compared with divided difference generated derivatives. The study shows that automatic differentiation method gives accurate derivative values in an efficient manner.

Cell-geometry-dependent changes in plasma membrane order direct stem cell signalling and fate

NASA Astrophysics Data System (ADS)

von Erlach, Thomas C.; Bertazzo, Sergio; Wozniak, Michele A.; Horejs, Christine-Maria; Maynard, Stephanie A.; Attwood, Simon; Robinson, Benjamin K.; Autefage, Hélène; Kallepitis, Charalambos; del Río Hernández, Armando; Chen, Christopher S.; Goldoni, Silvia; Stevens, Molly M.

2018-03-01

Cell size and shape affect cellular processes such as cell survival, growth and differentiation1-4, thus establishing cell geometry as a fundamental regulator of cell physiology. The contributions of the cytoskeleton, specifically actomyosin tension, to these effects have been described, but the exact biophysical mechanisms that translate changes in cell geometry to changes in cell behaviour remain mostly unresolved. Using a variety of innovative materials techniques, we demonstrate that the nanostructure and lipid assembly within the cell plasma membrane are regulated by cell geometry in a ligand-independent manner. These biophysical changes trigger signalling events involving the serine/threonine kinase Akt/protein kinase B (PKB) that direct cell-geometry-dependent mesenchymal stem cell differentiation. Our study defines a central regulatory role by plasma membrane ordered lipid raft microdomains in modulating stem cell differentiation with potential translational applications.

Theoretical studies of solar lasers and converters

NASA Technical Reports Server (NTRS)

Heinbockel, John

1988-01-01

The geometry and setup for the n-C3F7I iodine laser are illustrated. The mathematical modeling of this system is described. The chemical kinetics are summarized. A sensitivity analysis was performed on the parameters occurring in the differential equations describing the chemical kinetics.

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.

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

Hermann-Bernoulli-Laplace-Hamilton-Runge-Lenz Vector.

ERIC Educational Resources Information Center

Subramanian, P. R.; And Others

1991-01-01

A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing.

PubMed

Ramme, Austin J; Shivanna, Kiran H; Magnotta, Vincent A; Grosland, Nicole M

2011-10-01

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.

Development of MCAERO wing design panel method with interactive graphics module

NASA Technical Reports Server (NTRS)

Hawk, J. D.; Bristow, D. R.

1984-01-01

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.

Some Problems of Extremes in Geometry and Construction

ERIC Educational Resources Information Center

Yanovsky, Levi

2008-01-01

Two original problems in geometry are presented with solutions utilizing to differential calculus: (a) rectangle inscribed in a sector; (b) point on the ray of the angle. The possibility of applying mathematics in general and differential calculus in particular for solution of practical problems is discussed. (Contains 8 figures.)

Triple differential cross-sections of Ne (2s2) in coplanar to perpendicular plane geometry

NASA Astrophysics Data System (ADS)

Chen, L. Q.; Khajuria, Y.; Chen, X. J.; Xu, K. Z.

2003-10-01

The distorted wave Born approximation (DWBA) with the spin averaged static exchange potential has been used to calculate the triple differential cross-sections (TDCSs) for Ne (2s^2) ionization by electron impact in coplanar to perpendicular plane symmetric geometry at 110.5 eV incident electron energy. The present theoretical results at gun angles Psi = 0^circ (coplanar symmetric geometry) and Psi = 90^circ (perpendicular plane geometry) are in satisfactory agreement with the available experimental data. A deep interference minimum appears in the TDCS in the coplanar symmetric geometry and a strong peak at scattering angle xi = 90^circ caused by the single collision mechanism has been observed in the perpendicular plane geometry. The TDCSs at the gun angles Psi = 30^circ, and Psi = 60^circ are predicted.

DIEGO: detection of differential alternative splicing using Aitchison's geometry.

PubMed

Doose, Gero; Bernhart, Stephan H; Wagener, Rabea; Hoffmann, Steve

2018-03-15

Alternative splicing is a biological process of fundamental importance in most eukaryotes. It plays a pivotal role in cell differentiation and gene regulation and has been associated with a number of different diseases. The widespread availability of RNA-Sequencing capacities allows an ever closer investigation of differentially expressed isoforms. However, most tools for differential alternative splicing (DAS) analysis do not take split reads, i.e. the most direct evidence for a splice event, into account. Here, we present DIEGO, a compositional data analysis method able to detect DAS between two sets of RNA-Seq samples based on split reads. The python tool DIEGO works without isoform annotations and is fast enough to analyze large experiments while being robust and accurate. We provide python and perl parsers for common formats. The software is available at: www.bioinf.uni-leipzig.de/Software/DIEGO. steve@bioinf.uni-leipzig.de. Supplementary data are available at Bioinformatics online.

Modified Beer-Lambert law for blood flow

NASA Astrophysics Data System (ADS)

Baker, Wesley B.; Parthasarathy, Ashwin B.; Busch, David R.; Mesquita, Rickson C.; Greenberg, Joel H.; Yodh, A. G.

2015-03-01

The modified Beer-Lambert law is among the most widely used approaches for analysis of near-infrared spectroscopy (NIRS) reflectance signals for measurements of tissue blood volume and oxygenation. Briefly, the modified Beer-Lambert paradigm is a scheme to derive changes in tissue optical properties based on continuous-wave (CW) diffuse optical intensity measurements. In its simplest form, the scheme relates differential changes in light transmission (in any geometry) to differential changes in tissue absorption. Here we extend this paradigm to the measurement of tissue blood flow by diffuse correlation spectroscopy (DCS). In the new approach, differential changes of the intensity temporal auto-correlation function at a single delay-time are related to differential changes in blood flow. The key theoretical results for measurement of blood flow changes in any tissue geometry are derived, and we demonstrate the new method to monitor cerebral blood flow in a pig under conditions wherein the semi-infinite geometry approximation is fairly good. Specifically, the drug dinitrophenol was injected in the pig to induce a gradual 200% increase in cerebral blood flow, as measured with MRI velocity flow mapping and by DCS. The modified Beer-Lambert law for flow accurately recovered these flow changes using only a single delay-time in the intensity auto-correlation function curve. The scheme offers increased DCS measurement speed of blood flow. Further, the same techniques using the modified Beer-Lambert law to filter out superficial tissue effects in NIRS measurements of deep tissues can be applied to the DCS modified Beer-Lambert law for blood flow monitoring of deep tissues.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2006-10-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2011-03-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

Self-acting geometry for noncontact seals

NASA Technical Reports Server (NTRS)

Allen, G. P.

1981-01-01

Performance ot two self acting seal designs for a liquid oxygen (LOX) turbopump was predicted over ranges of pressure differential and speed. Predictions were compared with test results. Performance of a radial face seal for LOX was predicted up to 448 N/cu cm and 147 m/sec. Performance of a segmented circumferential seal for helium was predicted up to 69 N/cu cm and 189 m/sec. Results confirmed predictions of noncontact operation. Qualitative agreement between test and analysis was found. The LOX face seal evidently operated with mostly liquid in the self acting geometry and mostly gas across the dam.

Thomson's Theorem of Electrostatics: Its Applications and Mathematical Verification

ERIC Educational Resources Information Center

Bakhoum, Ezzat G.

2008-01-01

A 100 years-old formula that was given by J. J. Thomson recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson and later published by Pappas. Unfortunately, Differential Geometry, being a…

Applications of Differential Geometry to Cartography

ERIC Educational Resources Information Center

Benitez, Julio; Thome, Nestor

2004-01-01

This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

Quantum κ-deformed differential geometry and field theory

NASA Astrophysics Data System (ADS)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Bearing diagnostics: A method based on differential geometry

NASA Astrophysics Data System (ADS)

Tian, Ye; Wang, Zili; Lu, Chen; Wang, Zhipeng

2016-12-01

The structures around bearings are complex, and the working environment is variable. These conditions cause the collected vibration signals to become nonlinear, non-stationary, and chaotic characteristics that make noise reduction, feature extraction, fault diagnosis, and health assessment significantly challenging. Thus, a set of differential geometry-based methods with superiorities in nonlinear analysis is presented in this study. For noise reduction, the Local Projection method is modified by both selecting the neighborhood radius based on empirical mode decomposition and determining noise subspace constrained by neighborhood distribution information. For feature extraction, Hessian locally linear embedding is introduced to acquire manifold features from the manifold topological structures, and singular values of eigenmatrices as well as several specific frequency amplitudes in spectrograms are extracted subsequently to reduce the complexity of the manifold features. For fault diagnosis, information geometry-based support vector machine is applied to classify the fault states. For health assessment, the manifold distance is employed to represent the health information; the Gaussian mixture model is utilized to calculate the confidence values, which directly reflect the health status. Case studies on Lorenz signals and vibration datasets of bearings demonstrate the effectiveness of the proposed methods.

Triple differential cross sections for the electron-impact ionization of H{sub 2} molecules for equal and unequal outgoing electron energies

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

Colgan, J.; Al-Hagan, O.; Madison, D. H.

A comprehensive theoretical and experimental investigation of the triple differential cross sections arising from the electron-impact ionization of molecular hydrogen is made, at an incident electron energy of 35.4 eV, for cases where the outgoing electrons have equal and unequal energies, and for a range of experimental geometries. Generally, good agreement is found between two theoretical approaches and experiment, with the best agreement arising for intermediate geometries with large gun angles and for the perpendicular geometry.

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Quadrupole ion traps and trap arrays: geometry, material, scale, performance.

PubMed

Ouyang, Z; Gao, L; Fico, M; Chappell, W J; Noll, R J; Cooks, R G

2007-01-01

Quadrupole ion traps are reviewed, emphasizing recent developments, especially the investigation of new geometries, guided by multiple particle simulations such as the ITSIM program. These geometries include linear ion traps (LITs) and the simplified rectilinear ion trap (RIT). Various methods of fabrication are described, including the use of rapid prototyping apparatus (RPA), in which 3D objects are generated through point-by-point laser polymerization. Fabrication in silicon using multilayer semi-conductor fabrication techniques has been used to construct arrays of micro-traps. The performance of instruments containing individual traps as well as arrays of traps of various sizes and geometries is reviewed. Two types of array are differentiated. In the first type, trap arrays constitute fully multiplexed mass spectrometers in which multiple samples are examined using multiple sources, analyzers and detectors, to achieve high throughput analysis. In the second, an array of individual traps acts collectively as a composite trap to increase trapping capacity and performance for a single sample. Much progress has been made in building miniaturized mass spectrometers; a specific example is a 10 kg hand-held tandem mass spectrometer based on the RIT mass analyzer. The performance of this instrument in air and water analysis, using membrane sampling, is described.

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation.

PubMed

Ingalls, Brian; Mincheva, Maya; Roussel, Marc R

2017-07-01

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.

Geometric Model for a Parametric Study of the Blended-Wing-Body Airplane

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne; Smith, Robert E.; Sadrehaghighi, Ideen; Wiese, Micharl R.

1996-01-01

A parametric model is presented for the blended-wing-body airplane, one concept being proposed for the next generation of large subsonic transports. The model is defined in terms of a small set of parameters which facilitates analysis and optimization during the conceptual design process. The model is generated from a preliminary CAD geometry. From this geometry, airfoil cross sections are cut at selected locations and fitted with analytic curves. The airfoils are then used as boundaries for surfaces defined as the solution of partial differential equations. Both the airfoil curves and the surfaces are generated with free parameters selected to give a good representation of the original geometry. The original surface is compared with the parametric model, and solutions of the Euler equations for compressible flow are computed for both geometries. The parametric model is a good approximation of the CAD model and the computed solutions are qualitatively similar. An optimal NURBS approximation is constructed and can be used by a CAD model for further refinement or modification of the original geometry.

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

Motivated by uncertainty quantification and inference of quantum information systems, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural sample spaces and probability distributions upon these spaces that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation. This project was supported by the Intelligence Advanced Research Projects Activity via Department of Interior National Business Center Contract Number 2012-12050800010.

Moving frames and prolongation algebras

NASA Technical Reports Server (NTRS)

Estabrook, F. B.

1982-01-01

Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

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.

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.

The theory of pseudo-differential operators on the noncommutative n-torus

NASA Astrophysics Data System (ADS)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

Experimental validation on the effect of material geometries and processing methodology of Polyoxymethylene (POM)

NASA Astrophysics Data System (ADS)

Hafizzal, Y.; Nurulhuda, A.; Izman, S.; Khadir, AZA

2017-08-01

POM-copolymer bond breaking leads to change depending with respect to processing methodology and material geometries. This paper present the oversights effect on the material integrity due to different geometries and processing methodology. Thermo-analytical methods with reference were used to examine the degradation of thermomechanical while Thermogravimetric Analysis (TGA) was used to judge the thermal stability of sample from its major decomposition temperature. Differential Scanning Calorimetry (DSC) investigation performed to identify the thermal behaviour and thermal properties of materials. The result shown that plastic gear geometries with injection molding at higher tonnage machine more stable thermally rather than resin geometries. Injection plastic gear geometries at low tonnage machine faced major decomposition temperatures at 313.61°C, 305.76 °C and 307.91 °C while higher tonnage processing method are fully decomposed at 890°C, significantly higher compared to low tonnage condition and resin geometries specimen at 398°C. Chemical composition of plastic gear geometries with injection molding at higher and lower tonnage are compare based on their moisture and Volatile Organic Compound (VOC) content, polymeric material content and the absence of filler. Results of higher moisture and Volatile Organic Compound (VOC) content are report in resin geometries (0.120%) compared to higher tonnage of injection plastic gear geometries which is 1.264%. The higher tonnage of injection plastic gear geometry are less sensitive to thermo-mechanical degradation due to polymer chain length and molecular weight of material properties such as tensile strength, flexural strength, fatigue strength and creep resistance.

Cell-Cell Contact Area Affects Notch Signaling and Notch-Dependent Patterning.

PubMed

Shaya, Oren; Binshtok, Udi; Hersch, Micha; Rivkin, Dmitri; Weinreb, Sheila; Amir-Zilberstein, Liat; Khamaisi, Bassma; Oppenheim, Olya; Desai, Ravi A; Goodyear, Richard J; Richardson, Guy P; Chen, Christopher S; Sprinzak, David

2017-03-13

During development, cells undergo dramatic changes in their morphology. By affecting contact geometry, these morphological changes could influence cellular communication. However, it has remained unclear whether and how signaling depends on contact geometry. This question is particularly relevant for Notch signaling, which coordinates neighboring cell fates through direct cell-cell signaling. Using micropatterning with a receptor trans-endocytosis assay, we show that signaling between pairs of cells correlates with their contact area. This relationship extends across contact diameters ranging from micrometers to tens of micrometers. Mathematical modeling predicts that dependence of signaling on contact area can bias cellular differentiation in Notch-mediated lateral inhibition processes, such that smaller cells are more likely to differentiate into signal-producing cells. Consistent with this prediction, analysis of developing chick inner ear revealed that ligand-producing hair cell precursors have smaller apical footprints than non-hair cells. Together, these results highlight the influence of cell morphology on fate determination processes. Copyright © 2017 Elsevier Inc. All rights reserved.

Cell-cell contact area affects Notch signaling and Notch-dependent patterning

PubMed Central

Shaya, Oren; Binshtok, Udi; Hersch, Micha; Rivkin, Dmitri; Weinreb, Sheila; Amir-Zilberstein, Liat; Khamaisi, Bassma; Oppenheim, Olya; Desai, Ravi A.; Goodyear, Richard J.; Richardson, Guy P.; Chen, Christopher S.; Sprinzak, David

2017-01-01

Summary During development, cells undergo dramatic changes in their morphology. By affecting contact geometry, these morphological changes could influence cellular communication. However, it has remained unclear whether and how signaling depends on contact geometry. This question is particularly relevant for Notch signaling, which coordinates neighboring cell fates through direct cell-cell signaling. Using micropatterning with a receptor trans-endocytosis assay, we show that signaling between pairs of cells correlates with their contact area. This relationship extends across contact diameters ranging from microns to tens of microns. Mathematical modeling predicts that dependence of signaling on contact area can bias cellular differentiation in Notch-mediated lateral inhibition processes, such that smaller cells are more likely to differentiate into signal-producing cells. Consistent with this prediction, analysis of developing chick inner ear revealed that ligand-producing hair cell precursors have smaller apical footprints than non-hair cells. Together, these results highlight the influence of cell morphology on fate determination processes. PMID:28292428

Fractional vector calculus and fluid mechanics

NASA Astrophysics Data System (ADS)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

Azimuthally differential pion femtoscopy relative to the second and third harmonic in Pb-Pb 2.76 TeV collision from ALICE

NASA Astrophysics Data System (ADS)

Saleh, Mohammad; Alice Collaboration

2017-11-01

Azimuthally differential femtoscopic measurements, being sensitive to spatio-temporal characteristics of the source as well as to the collective velocity fields at freeze-out, provide very important information on the nature and dynamics of the system evolution. While the HBT radii modulations relative to the second harmonic event plane reflect mostly the spatial geometry of the source, the third harmonic results are mostly defined by the velocity fields [S. A. Voloshin, J. Phys. G38 (2011) 124097. arXiv:arxiv:arXiv:1106.5830, doi:http://dx.doi.org/10.1088/0954-3899/38/12/124097]. Radii variations with respect to the third harmonic event plane unambiguously signal a collective expansion and anisotropy in the flow fields. Event shape engineering (ESE) is a technique proposed to select events corresponding to a particular shape. Azimuthally differential HBT combined with ESE allows for a detailed analysis of the relation between initial geometry, anisotropic flow and the deformation of source shape. We present azimuthally differential pion femtoscopy with respect to second and third harmonic event planes as a function of the pion transverse momentum for different collision centralities in Pb-Pb collisions at √{sNN} = 2.76 TeV. All these results are compared to existing models. The effects of the selection of the events with high elliptic or triangular flow are also presented.

Calabi's conjecture and some new results in algebraic geometry

PubMed Central

Yau, Shing-Tung

1977-01-01

We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kähler structure on a complex projective space is the standard one. PMID:16592394

Coplanar tail-chase aerial combat as a differential game

NASA Technical Reports Server (NTRS)

Merz, A. W.; Hague, D. S.

1977-01-01

A reduced-order version of the one-on-one aerial combat problem is studied as a pursuit-evasion differential game. The coplanar motion takes place at given speeds and given maximum available turn rates, and is described by three state equations which are equivalent to the range, bearing, and heading of one aircraft relative to the other. The purpose of the study is to determine those relative geometries from which either aircraft can be guaranteed a win, regardless of the maneuver strategies of the other. Termination is specified by the tail-chase geometry, at which time the roles of pursuer and evader are known. The roles are found in general, together with the associated optimal turn maneuvers, by solution of the differential game of kind. For the numerical parameters chosen, neither aircraft can win from the majority of possible initial conditions if the other turns optimally in certain critical geometries.

Directing stem cell fate on hydrogel substrates by controlling cell geometry, matrix mechanics and adhesion ligand composition.

PubMed

Lee, Junmin; Abdeen, Amr A; Zhang, Douglas; Kilian, Kristopher A

2013-11-01

There is a dynamic relationship between physical and biochemical signals presented in the stem cell microenvironment to guide cell fate determination. Model systems that modulate cell geometry, substrate stiffness or matrix composition have proved useful in exploring how these signals influence stem cell fate. However, the interplay between these physical and biochemical cues during differentiation remains unclear. Here, we demonstrate a microengineering strategy to vary single cell geometry and the composition of adhesion ligands - on substrates that approximate the mechanical properties of soft tissues - to study adipogenesis and neurogenesis in adherent mesenchymal stem cells. Cells cultured in small circular islands show elevated expression of adipogenesis markers while cells that spread in anisotropic geometries tend to express elevated neurogenic markers. Arraying different combinations of matrix protein in a myriad of 2D and pseudo-3D geometries reveals optimal microenvironments for controlling the differentiation of stem cells to these "soft" lineages without the use of media supplements. © 2013 Elsevier Ltd. All rights reserved.

Navier-Stokes dynamics on a differential one-form

NASA Astrophysics Data System (ADS)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

Towards the Geometry of Reproducing Kernels

NASA Astrophysics Data System (ADS)

Galé, J. E.

2010-11-01

It is shown here how one is naturally led to consider a category whose objects are reproducing kernels of Hilbert spaces, and how in this way a differential geometry for such kernels may be settled down.

System theory as applied differential geometry. [linear system

NASA Technical Reports Server (NTRS)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Coordination Polymer: Synthesis, Spectral Characterization and Thermal Behaviour of Starch-Urea Based Biodegradable Polymer and Its Polymer Metal Complexes

PubMed Central

Malik, Ashraf; Parveen, Shadma; Ahamad, Tansir; Alshehri, Saad M.; Singh, Prabal Kumar; Nishat, Nahid

2010-01-01

A starch-urea-based biodegradable coordination polymer modified by transition metal Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) was prepared by polycondensation of starch and urea. All the synthesized polymeric compounds were characterized by Fourier transform-infrared spectroscopy (FT-IR), 1H-NMR spectroscopy, 13C-NMR spectroscopy, UV-visible spectra, magnetic moment measurements, differential scanning calorimeter (DSC), and thermogravimetric analysis (TGA). The results of electronic spectra and magnetic moment measurements indicate that Mn(II), Co(II), and Ni(II) complexes show octahedral geometry, while Cu(II) and Zn(II) complexes show square planar and tetrahedral geometry, respectively. The thermogravimetric analysis revealed that all the polymeric metal complexes are more thermally stable than the parental ligand. In addition, biodegradable studies of all the polymeric compounds were also carried out through ASTM standards of biodegradable polymers by CO2 evolution method. PMID:20414461

Differential geometry-based solvation and electrolyte transport models for biomolecular modeling: a review

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

Wei, Guowei; Baker, Nathan A.

2016-11-11

This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has been used to define the surfaces that separate the microscopic (solute) domains for biomolecules from the macroscopic (solvent) domains. In thesemore » approaches, the microscopic domains are modeled with atomistic or quantum mechanical descriptions, while continuum mechanics models (including fluid mechanics, elastic mechanics, and continuum electrostatics) are applied to the macroscopic domains. This multiphysics description is integrated through an energy functional formalism and the resulting Euler-Lagrange equation is employed to derive a variety of governing partial differential equations for different solvation and transport processes; e.g., the Laplace-Beltrami equation for the solvent-solute interface, Poisson or Poisson-Boltzmann equations for electrostatic potentials, the Nernst-Planck equation for ion densities, and the Kohn-Sham equation for solute electron density. Extensive validation of these models has been carried out over hundreds of molecules, including proteins and ion channels, and the experimental data have been compared in terms of solvation energies, voltage-current curves, and density distributions. We also propose a new quantum model for electrolyte transport.« less

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

Computational mechanobiology to study the effect of surface geometry on peri-implant tissue differentiation.

PubMed

Andreykiv, A; van Keulen, F; Prendergast, P J

2008-10-01

The geometry of an implant surface to best promote osseointegration has been the subject of several experimental studies, with porous beads and woven mesh surfaces being among the options available. Furthermore, it is unlikely that one surface geometry is optimal for all loading conditions. In this paper, a computational method is used to simulate tissue differentiation and osseointegration on a smooth surface, a surface covered with sintered beads (this simulated the experiment (Simmons, C., and Pilliar, R., 2000, Biomechanical Study of Early Tissue Formation Around Bone-Interface Implants: The Effects of Implant Surface Geometry," Bone Engineering, J. E. Davies, ed., Emsquared, Chap. A, pp. 369-379) and established that the method gives realistic results) and a surface covered by porous tantalum. The computational method assumes differentiation of mesenchymal stem cells in response to fluid flow and shear strain and models cell migration and proliferation as continuum processes. The results of the simulation show a higher rate of bone ingrowth into the surfaces with porous coatings as compared with the smooth surface. It is also shown that a thicker interface does not increase the chance of fixation failure.

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

Stability analysis of a reinforced carbon carbon shell

NASA Technical Reports Server (NTRS)

Agan, W. E.; Jordan, B. M.

1977-01-01

This paper presents the development of a stability analysis for the nose cap of the NASA Space Shuttle Orbiter. Stability is evaluated by the differential stiffness analysis of the NASTRAN finite-element computer code, addressing those nonstandard characteristics in the nose cap such as nonuniform curvature, asymmetrical and nonuniform loads, support fixity, and various combinations of membrane and bending stresses. A full-sized nose cap, thinner than production, was statically tested and stability analyzed. The failing load level correlated to within 30%. The region and mode of buckling that occurred during test was accurately predicted by analysis. The criterion for predicting instability is based on the behavior of the nonlinear deflections. The deflections are nonlinear elastic in that the stresses are well within the elastic range of the material, but the geometry-load relationship produces nonlinear deflections. The load-deflection relationship is well defined by differential stiffness analysis up to the zero-slope portion of the curve, the point of neutral stability or where the shell 'snaps through' just prior to general instability.

Predicting the bending properties of long bones: Insights from an experimental mouse model.

PubMed

Peacock, Sarah J; Coats, Brittney R; Kirkland, J Kyle; Tanner, Courtney A; Garland, Theodore; Middleton, Kevin M

2018-03-01

Analyses of bone cross-sectional geometry are frequently used by anthropologists and paleontologists to infer the loading histories of past populations. To address some underlying assumptions, we investigated the relative roles of genetics and exercise on bone cross-sectional geometry and bending mechanics in three mouse strains: high bone density (C3H/He), low bone density (C57BL/6), and a high-runner strain homozygous for the Myh4 Minimsc allele (MM). Weanlings of each strain were divided into exercise (wheel) or control (sedentary) treatment groups for a 7-week experimental period. Morphometrics of the femoral mid-diaphysis and mechanical testing were used to assess both theoretical and ex vivo bending mechanics. Across all measured morphological and bending traits, we found relatively small effects of exercise treatment compared to larger and more frequent interstrain differences. In the exercised group, total distance run over the experimental period was not a predictor of any morphological or bending traits. Cross-sectional geometry did not accurately predict bone response to loading. Results from this experimental model do not support hypothesized associations among extreme exercise, cross-sectional geometry, and bending mechanics. Our results suggest that analysis of cross-sectional geometry alone is insufficient to predict loading response, and questions the common assumption that cross-sectional geometry differences are indicative of differential loading history. © 2017 Wiley Periodicals, Inc.

Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry

NASA Technical Reports Server (NTRS)

Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.

2014-01-01

Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.

Surface geometry of protoplanetary disks inferred from near-infrared imaging polarimetry

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

Takami, Michihiro; Hasegawa, Yasuhiro; Gu, Pin-Gao

2014-11-01

We present a new method of analysis for determining the surface geometry of five protoplanetary disks observed with near-infrared imaging polarimetry using Subaru-HiCIAO. Using as inputs the observed distribution of polarized intensity (PI), disk inclination, assumed properties for dust scattering, and other reasonable approximations, we calculate a differential equation to derive the surface geometry. This equation is numerically integrated along the distance from the star at a given position angle. We show that, using these approximations, the local maxima in the PI distribution of spiral arms (SAO 206462, MWC 758) and rings (2MASS J16042165-2130284, PDS 70) are associated with localmore » concave-up structures on the disk surface. We also show that the observed presence of an inner gap in scattered light still allows the possibility of a disk surface that is parallel to the light path from the star, or a disk that is shadowed by structures in the inner radii. Our analysis for rings does not show the presence of a vertical inner wall as often assumed in studies of disks with an inner gap. Finally, we summarize the implications of spiral and ring structures as potential signatures of ongoing planet formation.« less

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

Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games

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

Melikyan, Arik; Bernhard, Pierre

2005-06-15

We investigate a special type of singularity in non-smooth solutions of first-order partial differential equations, with emphasis on Isaacs' equation. This type, called focal manifold, is characterized by the incoming trajectory fields on the two sides and a discontinuous gradient. We provide a complete set of constructive equations under various hypotheses on the singularity, culminating with the case where no a priori hypothesis on its geometry is known, and where the extremal trajectory fields need not be collinear. We show two examples of differential games exhibiting non-collinear fields of extremal trajectories on the focal manifold, one with a transversal approachmore » and one with a tangential approach.« less

Acta Aeronautica et Astronautica Sinica.

DTIC Science & Technology

1981-12-29

34Differential Geometry", People’s Education Publishers, 1964. 16. Xiong Changbing and Ziao Junxiang, "Three Dimensional Stress Analysis For a Shrouded Hollow...0 )0V~~) (.1) ML. RT 1 Mh AJC (5) ?,g v4 T (6) q).Lt il% i T_, k#(L( lqA (16 krol~ ] 1 ) (8) ," 11 - ,i.jt14 r- i PuC,(37)A) (14 P (9) k4m w. *1f ViA

Simplicial lattices in classical and quantum gravity: Mathematical structure and application

NASA Astrophysics Data System (ADS)

Lafave, Norman Joseph

1989-03-01

Geometrodynamics can be understood more clearly in the language of geometry than in the language of differential equations. This is the primary motivation for the development of calculational schemes based on Regge Calculus as an alternative to those schemes based on Ricci Calculus. The mathematics of simplicial lattices were developed to the same level of sophistication as the mathematics of pseudo--Riemannian geometry for continuum manifolds. This involves the definition of the simplicial analogues of several concepts from differential topology and differential geometry-the concept of a point, tangent spaces, forms, tensors, parallel transport, covariant derivatives, connections, and curvature. These simplicial analogues are used to define the Einstein tensor and the extrinsic curvature on a simplicial geometry. This mathematical formalism was applied to the solution of several outstanding problems in the development of a Regge Calculus based computational scheme for general geometrodynamic problems. This scheme is based on a 3 + 1 splitting of spacetime within the Regge Calculus prescription known as Null-Strut Calculus (NSC). NSC describes the foliation of spacetime into spacelike hypersurfaces built of tetrahedra. These hypersurfaces are coupled by light rays (null struts) to past and future momentum-like structures, geometrically dual to the tetrahedral lattice of the hypersurface. Avenues of investigation for NSC in quantum gravity are described.

Anticontrol of chaos in continuous-time systems via time-delay feedback.

PubMed

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

Triple differential cross section measurements for the outer valence molecular orbitals (1t2) of a methane molecule at 250 eV electron impact

NASA Astrophysics Data System (ADS)

Işık, N.; Doğan, M.; Bahçeli, S.

2016-03-01

In this study, detailed experimental research of triple differential cross section (TDCS) measurements is performed to investigate single ionization dynamics for the 1t2 orbital of methane molecule by 250 eV electron impact. In our experiments, the outgoing electrons are simultaneously measured in coincidence in a coplanar asymmetric geometry with the scattering angles of 10° and 20°. Therefore, TDCS measurements are performed for two different values of momentum transfer (K ≈ 0.9 au and 1.5 au). A detailed analysis of the dependence of the TDCS versus the momentum transfer is reported here.

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

NASA Astrophysics Data System (ADS)

Raptis, Ioannis

2007-12-01

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide- cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of ‘poetic language’.

A differential geometry model for the perceived colors space

NASA Astrophysics Data System (ADS)

Provenzi, Edoardo

2016-06-01

The space of perceived colors, before acquiring an industrial interest, has received a systematic theoretical attention from philosophers, physicists and mathematicians. The research about this topic is still active nowadays. In this paper, it will be presented a critical overview of a model based on differential geometry proposed by H. L. Resnikoff in 1974. It will be shown that, while some fundamental and elegant ideas behind this model can be still used as a guiding principle, some other parts of the model must be updated to comply with the modern findings about color perception.

Lectures on Kähler Geometry - Series: London Mathematical Society Student Texts (No. 69)

NASA Astrophysics Data System (ADS)

Moroianu, Andrei

2004-03-01

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory. The first graduate-level text on Kähler geometry, providing a concise introduction for both mathematicians and physicists with a basic knowledge of calculus in several variables and linear algebra Over 130 exercises and worked examples Self-contained and presents varying viewpoints including Riemannian, complex and algebraic

Numerical grid generation techniques. [conference

NASA Technical Reports Server (NTRS)

1980-01-01

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Mega-geomorphology and neotectonics

NASA Technical Reports Server (NTRS)

Lattman, L. H.

1985-01-01

For several decades, subtle neotectonic effects involving several square kilometers have been studied in detail using remote sensing, primarily various types of stereo-aerial photographs at scales of 1:10,000 to 1:80,000. These subtle effects, especially local uplifts associated with growing structures of differential compaction, have been detected by the effect on drainage patterns, changes in hydraulic geometry of individuals channels or groups of channels, tonal halos (soil) and fracture patterns. The studies were extended with the advent of thermal IR imagery particularly in tonal analysis, and SLAR primarily in fracture pattern studies. Lately, quantitative efforts have begun attempting to link measured uplift over known structures with measured changes in hydraulic geometry and alluvial deposition. Thus, efforts are now underway attempting to quantify the relationship between neo- (micro-) tectonic changes and geomorphic parameters of drainage systems.

MO-F-CAMPUS-I-04: Characterization of Fan Beam Coded Aperture Coherent Scatter Spectral Imaging Methods for Differentiation of Normal and Neoplastic Breast Structures

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

Morris, R; Albanese, K; Lakshmanan, M

Purpose: This study intends to characterize the spectral and spatial resolution limits of various fan beam geometries for differentiation of normal and neoplastic breast structures via coded aperture coherent scatter spectral imaging techniques. In previous studies, pencil beam raster scanning methods using coherent scatter computed tomography and selected volume tomography have yielded excellent results for tumor discrimination. However, these methods don’t readily conform to clinical constraints; primarily prolonged scan times and excessive dose to the patient. Here, we refine a fan beam coded aperture coherent scatter imaging system to characterize the tradeoffs between dose, scan time and image quality formore » breast tumor discrimination. Methods: An X-ray tube (125kVp, 400mAs) illuminated the sample with collimated fan beams of varying widths (3mm to 25mm). Scatter data was collected via two linear-array energy-sensitive detectors oriented parallel and perpendicular to the beam plane. An iterative reconstruction algorithm yields images of the sample’s spatial distribution and respective spectral data for each location. To model in-vivo tumor analysis, surgically resected breast tumor samples were used in conjunction with lard, which has a form factor comparable to adipose (fat). Results: Quantitative analysis with current setup geometry indicated optimal performance for beams up to 10mm wide, with wider beams producing poorer spatial resolution. Scan time for a fixed volume was reduced by a factor of 6 when scanned with a 10mm fan beam compared to a 1.5mm pencil beam. Conclusion: The study demonstrates the utility of fan beam coherent scatter spectral imaging for differentiation of normal and neoplastic breast tissues has successfully reduced dose and scan times whilst sufficiently preserving spectral and spatial resolution. Future work to alter the coded aperture and detector geometries could potentially allow the use of even wider fans, thereby making coded aperture coherent scatter imaging a clinically viable method for breast cancer detection. United States Department of Homeland Security; Duke University Medical Center - Department of Radiology; Carl E Ravin Advanced Imaging Laboratories; Duke University Medical Physics Graduate Program.« less

Application of stochastic differential geometry to the term structure of interst rates in developed markets

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

Taranenko, Y.; Barnes, C.

1996-12-31

This paper deals with further developments of the new theory that applies stochastic differential geometry (SDG) to dynamics of interest rates. We examine mathematical constraints on the evolution of interest rate volatilities that arise from stochastic differential calculus under assumptions of an arbitrage free evolution of zero coupon bonds and developed markets (i.e., none of the party/factor can drive the whole market). The resulting new theory incorporates the Heath-Jarrow-Morton (HJM) model of interest rates and provides new equations for volatilities which makes the system of equations for interest rates and volatilities complete and self consistent. It results in much smallermore » amount of volatility data that should be guessed for the SDG model as compared to the HJM model. Limited analysis of the market volatility data suggests that the assumption of the developed market is violated around maturity of two years. Such maturities where the assumptions of the SDG model are violated are suggested to serve as boundaries at which volatilities should be specified independently from the model. Our numerical example with two boundaries (two years and five years) qualitatively resembles the market behavior. Under some conditions solutions of the SDG model become singular that may indicate market crashes. More detail comparison with the data is needed before the theory can be established or refuted.« less

SU-D-BRA-04: Computerized Framework for Marker-Less Localization of Anatomical Feature Points in Range Images Based On Differential Geometry Features for Image-Guided Radiation Therapy

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

Soufi, M; Arimura, H; Toyofuku, F

Purpose: To propose a computerized framework for localization of anatomical feature points on the patient surface in infrared-ray based range images by using differential geometry (curvature) features. Methods: The general concept was to reconstruct the patient surface by using a mathematical modeling technique for the computation of differential geometry features that characterize the local shapes of the patient surfaces. A region of interest (ROI) was firstly extracted based on a template matching technique applied on amplitude (grayscale) images. The extracted ROI was preprocessed for reducing temporal and spatial noises by using Kalman and bilateral filters, respectively. Next, a smooth patientmore » surface was reconstructed by using a non-uniform rational basis spline (NURBS) model. Finally, differential geometry features, i.e. the shape index and curvedness features were computed for localizing the anatomical feature points. The proposed framework was trained for optimizing shape index and curvedness thresholds and tested on range images of an anthropomorphic head phantom. The range images were acquired by an infrared ray-based time-of-flight (TOF) camera. The localization accuracy was evaluated by measuring the mean of minimum Euclidean distances (MMED) between reference (ground truth) points and the feature points localized by the proposed framework. The evaluation was performed for points localized on convex regions (e.g. apex of nose) and concave regions (e.g. nasofacial sulcus). Results: The proposed framework has localized anatomical feature points on convex and concave anatomical landmarks with MMEDs of 1.91±0.50 mm and 3.70±0.92 mm, respectively. A statistically significant difference was obtained between the feature points on the convex and concave regions (P<0.001). Conclusion: Our study has shown the feasibility of differential geometry features for localization of anatomical feature points on the patient surface in range images. The proposed framework might be useful for tasks involving feature-based image registration in range-image guided radiation therapy.« less

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.

Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation

DTIC Science & Technology

1981-01-01

or surfaces. Since the writing of the first memoir on the subject of tensor analysis by Ricci and Levi - Civita [11 in 1901 some very significant...available in the standard texts, such as, Levi - Civita [2], Weatherburn [3), McConnell [41, Eisenhart [51, [6], Tolman [7], Graustein [8], Synge and...Equations (216) have been used in Ref. [29] to compute the coordinates for arbitrary shaped two -dimensional bodies . §7. Miscellaneous Derivations. In this

Exploring volumetrically indexed cups

NASA Astrophysics Data System (ADS)

Jones, Dustin L.

2011-03-01

This article was inspired by a set of 12 cylindrical cups, which are volumetrically indexed; that is to say, the volume of cup n is equal to n times the volume of cup 1. Various sets of volumetrically indexed cylindrical cups are explored. I demonstrate how this children's toy is ripe for mathematical investigation, with connections to geometry, algebra and differential calculus. Students with an understanding of these topics should be able to complete the analysis and related exercises contained herein.

Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS

PubMed Central

Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F.; Becker, James T.; Aizenstein, Howard J.; Lopez, Oscar L.; Tamburo, Robert J.; Toga, Arthur W.; Thompson, Paul M.

2010-01-01

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics - these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. PMID:19900560

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.

Computational algebraic geometry of epidemic models

NASA Astrophysics Data System (ADS)

Rodríguez Vega, Martín.

2014-06-01

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

Solving Partial Differential Equations on Overlapping Grids

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

Henshaw, W D

2008-09-22

We discuss the solution of partial differential equations (PDEs) on overlapping grids. This is a powerful technique for efficiently solving problems in complex, possibly moving, geometry. An overlapping grid consists of a set of structured grids that overlap and cover the computational domain. By allowing the grids to overlap, grids for complex geometries can be more easily constructed. The overlapping grid approach can also be used to remove coordinate singularities by, for example, covering a sphere with two or more patches. We describe the application of the overlapping grid approach to a variety of different problems. These include the solutionmore » of incompressible fluid flows with moving and deforming geometry, the solution of high-speed compressible reactive flow with rigid bodies using adaptive mesh refinement (AMR), and the solution of the time-domain Maxwell's equations of electromagnetism.« less

Noncommutative spherically symmetric spacetimes at semiclassical order

NASA Astrophysics Data System (ADS)

Fritz, Christopher; Majid, Shahn

2017-07-01

Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

Classification of digital affine noncommutative geometries

NASA Astrophysics Data System (ADS)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Interpretation of Quantum Nonlocality by Conformal Quantum Geometrodynamics

NASA Astrophysics Data System (ADS)

De Martini, Francesco; Santamato, Enrico

2014-10-01

The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyl's differential geometry are presented. The theory applied to the case of the relativistic single quantum spin leads a novel and unconventional derivation of Dirac's equation. The further extension of the theory to the case of two spins in EPR entangled state and to the related violation of Bell's inequalities leads, by a non relativistic analysis, to an insightful resolution of the enigma implied by quantum nonlocality.

Landing Gear/Soil Interaction Development of Criteria for Aircraft Operation on Soil During Turning and High Speed Straight Roll

DTIC Science & Technology

1974-01-01

system and does not permit differential thrust during turning. Turning Geometry and Force Analysis An aircraft with a castered -steerable nose wheel ...instantaneous radius of turn S= caster angle of nose wheel The definition of the turning angle and the development of side loads and longitudinal drag...pneumatic trail distance will vary with the turning angle, 0. It is alao possible that for a castered wheel , that the caster axis is displaced from the

Variational submanifolds of Euclidean spaces

NASA Astrophysics Data System (ADS)

Krupka, D.; Urban, Z.; Volná, J.

2018-03-01

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Some applications of mathematics in theoretical physics - A review

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

Bora, Kalpana

2016-06-21

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical toolsmore » are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.« less

Some applications of mathematics in theoretical physics - A review

NASA Astrophysics Data System (ADS)

Bora, Kalpana

2016-06-01

Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

A TENTATIVE GUIDE, DIFFERENTIAL AND INTEGRAL CALCULUS.

ERIC Educational Resources Information Center

BRANT, VINCENT; GERARDI, WILLIAM

THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…

A physically based connection between fractional calculus and fractal geometry

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

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Methods for acquiring data on terrain geomorphology, course geometry and kinematics of competitors' runs in alpine skiing: a historical review.

PubMed

Erdmann, Włodzimierz S; Giovanis, Vassilis; Aschenbrenner, Piotr; Kiriakis, Vaios; Suchanowski, Andrzej

2017-01-01

This paper aims at the description and comparison of methods of topographic analysis of racing courses at all disciplines of alpine skiing sports for the purposes of obtaining: terrain geomorphology (snowless and with snow), course geometry, and competitors' runs. The review presents specific methods and instruments according to the order of their historical appearance as follows: (1) azimuth method with the use of a compass, tape and goniometer instruments; (2) optical method with geodetic theodolite, laser and photocells; (3) triangulation method with the aid of a tape and goniometer; (4) image method with the use of video cameras; (5) differential global positioning system and carrier phase global positioning system methods. Described methods were used at homologation procedure, at training sessions, during competitions of local level and during International Ski Federation World Championships or World Cups. Some methods were used together. In order to provide detailed data on course setting and skiers' running it is recommended to analyse course geometry and kinematics data of competitors' running for all important competitions.

A general multiple-compartment model for the transport of trace elements through animals

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

Assimakopoulos, P.A.; Ioannides, K.G.; Pakou, A.A.

1991-08-01

Multiple-compartment models employed in the analysis of trace element transport in animals are often based on linear differential equations which relate the rate of change of contaminant (or contaminant concentration) in each compartment to the amount of contaminant (or contaminant concentration) in every other compartment in the system. This has the serious disadvantage of mixing intrinsic physiological properties with the geometry of the animal. The basic equations on which the model presented here is developed are derived from the actual physical process under way and are capable of separating intrinsic physiological properties from geometry. It is thus expected that ratemore » coefficients determined through this model will be applicable to a wider category of physiologically similar animals. A specific application of the model for the study of contamination of sheep--or indeed for any ruminant--is presented, and the temporal evolution of contaminant concentration in the various compartments of the animal is calculated. The application of this model to a system of compartments with changing geometry is also presented.« less

Integrated high-order surface diffraction gratings for diode lasers

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

Zolotarev, V V; Leshko, A Yu; Pikhtin, N A

2015-12-31

High-order surface diffraction gratings acting as a distributed Bragg reflector (DBR) in mesa stripe semiconductor lasers (λ = 1030 nm) have been studied theoretically and experimentally. Higher order interfering radiation modes (IRMs), which propagate off the plane of the waveguide, have been shown to have a crucial effect on the reflection and transmission spectra of the DBR. The decrease in the reflectivity of the DBR in response to the increase in the diffraction efficiency of these modes may reach 80% and more. According to theoretical analysis results, the intensity of the higher order IRMs is determined by the geometry ofmore » the DBR groove profile. Experimental data demonstrate that the noncavity modes are responsible for parasitic light leakage losses in the laser cavity. It has been shown that, in the case of nonoptimal geometry of the grating groove profile, the overall external differential quantum efficiency of the parasitic laser emission may exceed 45%, which is more than half of the laser output power. The optimal geometry of the DBR groove profile is trapezoidal, with the smallest possible lower base. Experimental evidence has been presented that this geometry considerably reduces the power of the higher order IRMs and minimises the parasitic light leakage loss. (lasers)« less

Analytical caustic surfaces

NASA Technical Reports Server (NTRS)

Schmidt, R. F.

1987-01-01

This document discusses the determination of caustic surfaces in terms of rays, reflectors, and wavefronts. Analytical caustics are obtained as a family of lines, a set of points, and several types of equations for geometries encountered in optics and microwave applications. Standard methods of differential geometry are applied under different approaches: directly to reflector surfaces, and alternatively, to wavefronts, to obtain analytical caustics of two sheets or branches. Gauss/Seidel aberrations are introduced into the wavefront approach, forcing the retention of all three coefficients of both the first- and the second-fundamental forms of differential geometry. An existing method for obtaining caustic surfaces through exploitation of the singularities in flux density is examined, and several constant-intensity contour maps are developed using only the intrinsic Gaussian, mean, and normal curvatures of the reflector. Numerous references are provided for extending the material of the present document to the morphologies of caustics and their associated diffraction patterns.

Interpretation of the prominence differential emissions measure for 3 geometries

NASA Technical Reports Server (NTRS)

Schmahl, E. J.; Orrall, F. Q.

1986-01-01

Researchers have used prominence extreme ultraviolet line intensities observed from Skylab to derive the differential emission measure Q(T) in the prominence-corona (PC) interface from 3 x 10,000 to 3 times 1 million K, including the effects of Lyman Continuum absorption. Using lines both shortward and longward of the Lyman limit, researchers have estimated the importance of absorption as function of temperature. The magnitude of the absorption, as well as its rate of increase as a function of temperature, place limits on the thread scales and the character of the interfilar medium. Researchers have calculated models based on three assumed geometries: (1) threads with hot sheaths and cool cores; (2) isothermal threads; and (3) threads with longitudinal temperature gradients along the magnetic field. Comparison of the absorption computed from these models with the observed absorption in prominences shows that none of the geometries is totally satisfactory.

Noncommutative Differential Geometry of Generalized Weyl Algebras

NASA Astrophysics Data System (ADS)

Brzeziński, Tomasz

2016-06-01

Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p;q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p;q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p;q) are constructed, and three-dimensional first-order differential calculi induced by these derivations are described. The associated integrals are computed and it is shown that the dimension of the integral space coincides with the order of the defining polynomial p(z). It is proven that the restriction of these first-order differential calculi to the calculi on B(p;q) is isomorphic to the direct sum of degree 2 and degree -2 components of A(p;q). A Dirac operator for B(p;q) is constructed from a (strong) connection with respect to this differential calculus on the (free) spinor bimodule defined as the direct sum of degree 1 and degree -1 components of A(p;q). The real structure of KO-dimension two for this Dirac operator is also described.

Differential geometry techniques for sets of nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

Distinct endothelial phenotypes evoked by arterial waveforms derived from atherosclerosis-susceptible and -resistant regions of human vasculature

NASA Astrophysics Data System (ADS)

Dai, Guohao; Kaazempur-Mofrad, Mohammad R.; Natarajan, Sripriya; Zhang, Yuzhi; Vaughn, Saran; Blackman, Brett R.; Kamm, Roger D.; García-Cardeña, Guillermo; Gimbrone, Michael A., Jr.

2004-10-01

Atherosclerotic lesion localization to regions of disturbed flow within certain arterial geometries, in humans and experimental animals, suggests an important role for local hemodynamic forces in atherogenesis. To explore how endothelial cells (EC) acquire functional/dysfunctional phenotypes in response to vascular region-specific flow patterns, we have used an in vitro dynamic flow system to accurately reproduce arterial shear stress waveforms on cultured human EC and have examined the effects on EC gene expression by using a high-throughput transcriptional profiling approach. The flow patterns in the carotid artery bifurcations of several normal human subjects were characterized by using 3D flow analysis based on actual vascular geometries and blood flow profiles. Two prototypic arterial waveforms, "athero-prone" and "athero-protective," were defined as representative of the wall shear stresses in two distinct regions of the carotid artery (carotid sinus and distal internal carotid artery) that are typically "susceptible" or "resistant," respectively, to atherosclerotic lesion development. These two waveforms were applied to cultured EC, and cDNA microarrays were used to analyze the differential patterns of EC gene expression. In addition, the differential effects of athero-prone vs. athero-protective waveforms were further characterized on several parameters of EC structure and function, including actin cytoskeletal organization, expression and localization of junctional proteins, activation of the NF-B transcriptional pathway, and expression of proinflammatory cytokines and adhesion molecules. These global gene expression patterns and functional data reveal a distinct phenotypic modulation in response to the wall shear stresses present in atherosclerosis-susceptible vs. atherosclerosis-resistant human arterial geometries.

Triple differential study of ionization of H2 by proton impact for varying electron ejection geometries

NASA Astrophysics Data System (ADS)

Hasan, A.; Sharma, S.; Arthanayaka, T. P.; Lamichhane, B. R.; Remolina, J.; Akula, S.; Madison, D. H.; Schulz, M.

2014-11-01

We have performed a kinematically complete experiment on ionization of H2 by 75 keV proton impact. The triple differential cross sections (TDCS) extracted from the measurement were compared to a molecular 3-body distorted wave (M3DW) calculation for three different electron ejection geometries. Overall, the agreement between experiment and theory is better than in the case of a helium target for the same projectile. Nevertheless, significant quantitative discrepancies remain, which probably result from the capture channel, which may be strongly coupled to the ionization channel. Therefore, improved agreement could be expected from a non-perturbative coupled-channel approach.

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

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

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energymore » for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.« less

Segmentation and Morphometric Analysis of Cells from Fluorescence Microscopy Images of Cytoskeletons

PubMed Central

Ujihara, Yoshihiro; Nakamura, Masanori; Miyazaki, Hiroshi; Wada, Shigeo

2013-01-01

We developed a method to reconstruct cell geometry from confocal fluorescence microscopy images of the cytoskeleton. In the method, region growing was implemented twice. First, it was applied to the extracellular regions to differentiate them from intracellular noncytoskeletal regions, which both appear black in fluorescence microscopy imagery, and then to cell regions for cell identification. Analysis of morphological parameters revealed significant changes in cell shape associated with cytoskeleton disruption, which offered insight into the mechanical role of the cytoskeleton in maintaining cell shape. The proposed segmentation method is promising for investigations on cell morphological changes with respect to internal cytoskeletal structures. PMID:23762186

Segmentation and morphometric analysis of cells from fluorescence microscopy images of cytoskeletons.

PubMed

Ujihara, Yoshihiro; Nakamura, Masanori; Miyazaki, Hiroshi; Wada, Shigeo

2013-01-01

We developed a method to reconstruct cell geometry from confocal fluorescence microscopy images of the cytoskeleton. In the method, region growing was implemented twice. First, it was applied to the extracellular regions to differentiate them from intracellular noncytoskeletal regions, which both appear black in fluorescence microscopy imagery, and then to cell regions for cell identification. Analysis of morphological parameters revealed significant changes in cell shape associated with cytoskeleton disruption, which offered insight into the mechanical role of the cytoskeleton in maintaining cell shape. The proposed segmentation method is promising for investigations on cell morphological changes with respect to internal cytoskeletal structures.

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

PubMed Central

Piao, Daqing; Barbour, Randall L.; Graber, Harry L.; Lee, Daniel C.

2015-01-01

Abstract. This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01  mm−1 and μs′=1.0  mm−1 are on average less than 5% different. The approximation for sphere, generally valid for a diameter ≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation. PMID:26465613

Noncommutative differential geometry related to the Young-Baxter equation

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

Gurevich, D.; Radul, A.; Rubtsov, V.

1995-11-10

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf Z`s considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section.

IUTA: a tool for effectively detecting differential isoform usage from RNA-Seq data.

PubMed

Niu, Liang; Huang, Weichun; Umbach, David M; Li, Leping

2014-10-06

Most genes in mammals generate several transcript isoforms that differ in stability and translational efficiency through alternative splicing. Such alternative splicing can be tissue- and developmental stage-specific, and such specificity is sometimes associated with disease. Thus, detecting differential isoform usage for a gene between tissues or cell lines/types (differences in the fraction of total expression of a gene represented by the expression of each of its isoforms) is potentially important for cell and developmental biology. We present a new method IUTA that is designed to test each gene in the genome for differential isoform usage between two groups of samples. IUTA also estimates isoform usage for each gene in each sample as well as averaged across samples within each group. IUTA is the first method to formulate the testing problem as testing for equal means of two probability distributions under the Aitchison geometry, which is widely recognized as the most appropriate geometry for compositional data (vectors that contain the relative amount of each component comprising the whole). Evaluation using simulated data showed that IUTA was able to provide test results for many more genes than was Cuffdiff2 (version 2.2.0, released in Mar. 2014), and IUTA performed better than Cuffdiff2 for the limited number of genes that Cuffdiff2 did analyze. When applied to actual mouse RNA-Seq datasets from six tissues, IUTA identified 2,073 significant genes with clear patterns of differential isoform usage between a pair of tissues. IUTA is implemented as an R package and is available at http://www.niehs.nih.gov/research/resources/software/biostatistics/iuta/index.cfm. Both simulation and real-data results suggest that IUTA accurately detects differential isoform usage. We believe that our analysis of RNA-seq data from six mouse tissues represents the first comprehensive characterization of isoform usage in these tissues. IUTA will be a valuable resource for those who study the roles of alternative transcripts in cell development and disease.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

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

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.

ERIC Educational Resources Information Center

Scharf, John; And Others

This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…

A spectral element method with adaptive segmentation for accurately simulating extracellular electrical stimulation of neurons.

PubMed

Eiber, Calvin D; Dokos, Socrates; Lovell, Nigel H; Suaning, Gregg J

2017-05-01

The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.

A stage structure pest management model with impulsive state feedback control

NASA Astrophysics Data System (ADS)

Pang, Guoping; Chen, Lansun; Xu, Weijian; Fu, Gang

2015-06-01

A stage structure pest management model with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

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.

The Canyonlands Grabens Revisited, with a New Interpretation of Graben Geometry

NASA Astrophysics Data System (ADS)

Schultz, R. A.; Moore, J. M.

1996-03-01

The relative scale between faults and faulted-layer thickness is critical to the mechanical behavior of faults and fault populations on any planetary body. Due to their fresh, relatively uneroded morphology and simple structural setting, the terrestrial Canyonlands grabens provide a unique opportunity to critically investigate the geometry, growth, interaction, and scaling relationships of normal faults. Symmetrical models have traditionally been used to describe these grabens, but field observations of stratigraphic offsets require asymmetric graben cross-sectional geometry. Topographic profiles reveal differential stratigraphic offsets, graben floor-tilts, and possible roll-over anticlines as well as footwall uplifts. Relationships between the asymmetric graben geometry and brittle-layer thickness are currently being investigated.

Matrix De Rham Complex and Quantum A-infinity algebras

NASA Astrophysics Data System (ADS)

Barannikov, S.

2014-04-01

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A ∞-algebras, introduced in Barannikov (Modular operads and non-commutative Batalin-Vilkovisky geometry. IMRN, vol. 2007, rnm075. Max Planck Institute for Mathematics 2006-48, 2007), is represented via de Rham differential acting on the supermatrix spaces related with Bernstein-Leites simple associative algebras with odd trace q( N), and gl( N| N). I also show that the matrix Lagrangians from Barannikov (Noncommutative Batalin-Vilkovisky geometry and matrix integrals. Isaac Newton Institute for Mathematical Sciences, Cambridge University, 2006) are represented by equivariantly closed differential forms.

Approximated transport-of-intensity equation for coded-aperture x-ray phase-contrast imaging.

PubMed

Das, Mini; Liang, Zhihua

2014-09-15

Transport-of-intensity equations (TIEs) allow better understanding of image formation and assist in simplifying the "phase problem" associated with phase-sensitive x-ray measurements. In this Letter, we present for the first time to our knowledge a simplified form of TIE that models x-ray differential phase-contrast (DPC) imaging with coded-aperture (CA) geometry. The validity of our approximation is demonstrated through comparison with an exact TIE in numerical simulations. The relative contributions of absorption, phase, and differential phase to the acquired phase-sensitive intensity images are made readily apparent with the approximate TIE, which may prove useful for solving the inverse phase-retrieval problem associated with these CA geometry based DPC.

Models for integrated and differential scattering optical properties of encapsulated light absorbing carbon aggregates.

PubMed

Kahnert, Michael; Nousiainen, Timo; Lindqvist, Hannakaisa

2013-04-08

Optical properties of light absorbing carbon (LAC) aggregates encapsulated in a shell of sulfate are computed for realistic model geometries based on field measurements. Computations are performed for wavelengths from the UV-C to the mid-IR. Both climate- and remote sensing-relevant optical properties are considered. The results are compared to commonly used simplified model geometries, none of which gives a realistic representation of the distribution of the LAC mass within the host material and, as a consequence, fail to predict the optical properties accurately. A new core-gray shell model is introduced, which accurately reproduces the size- and wavelength dependence of the integrated and differential optical properties.

Triple differential cross sections of magnesium in doubly symmetric geometry

NASA Astrophysics Data System (ADS)

S, Y. Sun; X, Y. Miao; Xiang-Fu, Jia

2016-01-01

A dynamically screened three-Coulomb-wave (DS3C) method is applied to study the single ionization of magnesium by electron impact. Triple differential cross sections (TDCS) are calculated in doubly symmetric geometry at incident energies of 13.65, 17.65, 22.65, 27.65, 37.65, 47.65, 57.65, and 67.65 eV. Comparisons are made with experimental data and theoretical predictions from a three-Coulomb-wave function (3C) approach and distorted-wave Born approximation (DWBA). The overall agreement between the predictions of the DS3C model and the DWBA approach with the experimental data is satisfactory. Project supported by the National Natural Science Foundation of China (Grant No. 11274215).

Cell growth and differentiation on feeder layers is predicted to be influenced by bioreactor geometry.

PubMed

Peng, C A; Palsson, B Ø

1996-06-05

Tissue function is comprised of a complex interplay between biological and physicochemical rate processes. The design of bioreactors for tissue engineering must account for these processes simultaneously in order to obtain a bioreactor that provides a uniform environment for tissue growth and development. In the present study we consider the effects of fluid flow and mass transfer on the growth of a tissue in a parallel-plate bioreactor configuration. The parenchymal cells grow on a preformed stromal (feeder) layer that secretes a growth factor that stimulates parenchymal stem cell replication and differentiation. The biological dynamics are described by a unilineage model that describes the replication and differentiation of the tissue stem cell. The physicochemical rates are described by the Navier-Stokes and convective-diffusion equations. The model equations are solved by a finite element method. Two dimensionless groups govern the behavior of the solution. One is the Graetz number (Gz) that describes the relative rates of convection and diffusion, and the other a new dimensionless ratio (designated by P) that describes the interplay of the growth factor production, diffusion, and stimulation. Four geometries (slab, gondola, diamond, and radial shapes) for the parallel-plate bioreactor are analyzed. The uniformity of cell growth is measured by a two-dimensional coefficient of variance. The concentration distribution of the stroma-derived growth factor was computed first based on fluid flow and bioreactor geometry. Then the concomitant cell density distribution was obtained by integrating the calculated growth factor concentration with the parenchymal cell growth and unilineage differentiation process. The spatiotemporal cell growth patterns in four different bioreactor configurations were investigated under a variety of combinations of Gz (10(-1), 10(0), and 10(1)) and P(10(-2), 10(-1), 10(0), 10(1), and 10(2)). The results indicate high cell density and uniformity can be achieved for parameter values of P = 0.01, ..., 0.1 and Gz = 0.1, ..., 1.0. Among the four geometries investigated the radial-flow-type bioreactor provides the most uniform environment in which parenchymal cells can grow and differentiate ex vivo due to the absence of walls that are parallel to the flow paths creating slow flowing regions.

Analysis instrument test on mathematical power the material geometry of space flat side for grade 8

NASA Astrophysics Data System (ADS)

Kusmaryono, Imam; Suyitno, Hardi; Dwijanto, Karomah, Nur

2017-08-01

The main problem of research to determine the quality of test items on the material side of flat geometry to assess students' mathematical power. The method used is quantitative descriptive. The subjects were students of class 8 as many as 20 students. The object of research is the quality of test items in terms of the power of mathematics: validity, reliability, level of difficulty and power differentiator. Instrument mathematical power ratings are tested include: written tests and questionnaires about the disposition of mathematical power. Data were obtained from the field, in the form of test data on the material geometry of space flat side and questionnaires. The results of the test instrument to the reliability of the test item is influenced by many factors. Factors affecting the reliability of the instrument is the number of items, homogeneity test questions, the time required, the uniformity of conditions of the test taker, the homogeneity of the group, the variability problem, and motivation of the individual (person taking the test). Overall, the evaluation results of this study stated that the test instrument can be used as a tool to measure students' mathematical power.

Geometry of PDE's. IV

NASA Astrophysics Data System (ADS)

Prástaro, Agostino

2008-02-01

Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.

Assessment of heart rate variability based on mobile device for planning physical activity

NASA Astrophysics Data System (ADS)

Svirin, I. S.; Epishina, E. V.; Voronin, V. V.; Semenishchev, E. A.; Solodova, E. N.; Nabilskaya, N. V.

2015-05-01

In this paper we present a method for the functional analysis of human heart based on electrocardiography (ECG) signals. The approach using the apparatus of analytical and differential geometry and correlation and regression analysis. ECG contains information on the current condition of the cardiovascular system as well as on the pathological changes in the heart. Mathematical processing of the heart rate variability allows to obtain a great set of mathematical and statistical characteristics. These characteristics of the heart rate are used when solving research problems to study physiological changes that determine functional changes of an individual. The proposed method implemented for up-to-date mobile Android and iOS based devices.

Mathematically Gifted in the Heterogeneously Grouped Mathematics Classroom: What Is a Teacher to Do?

ERIC Educational Resources Information Center

Reed, Catherine Finlayson

2004-01-01

Differentiation provides one method by which teachers can provide appropriate challenges at appropriate levels for all learners in a heterogeneously grouped mathematics classroom, where the range of abilities and interests can be wide. This article considers a heterogeneously grouped high school geometry class where differentiation is practiced.…

The monomeric, tetrameric, and fibrillar organization of Fib: the dynamic building block of the bacterial linear motor of Spiroplasma melliferum BC3.

PubMed

Cohen-Krausz, Sara; Cabahug, Pamela C; Trachtenberg, Shlomo

2011-07-08

Spiroplasmas belong to the class Mollicutes, representing the minimal, free-living, and self-replicating forms of life. Spiroplasmas are helical wall-less bacteria and the only ones known to swim by means of a linear motor (rather than the near-universal rotary bacterial motor). The linear motor follows the shortest path along the cell's helical membranal tube. The motor is composed of a flat monolayered ribbon of seven parallel fibrils and is believed to function in controlling cell helicity and motility through dynamic, coordinated, differential length changes in the fibrils. The latter cause local perturbations of helical symmetry, which are essential for net directional displacement in environments with a low Reynolds number. The underlying fibrils' core building block is a circular tetramer of the 59-kDa protein Fib. The fibrils' differential length changes are believed to be driven by molecular switching of Fib, leading consequently to axial ratio and length changes in tetrameric rings. Using cryo electron microscopy, diffractometry, single-particle analysis of isolated ribbons, and sequence analyses of Fib, we determined the overall molecular organization of the Fib monomer, tetramer, fibril, and linear motor of Spiroplasma melliferum BC3 that underlies cell geometry and motility. Fib appears to be a bidomained molecule, of which the N-terminal half is apparently a globular phosphorylase. By a combination of reversible rotation and diagonal shift of Fib monomers, the tetramer adopts either a cross-like nonhanded conformation or a ring-like handed conformation. The sense of Fib rotation may determine the handedness of the linear motor and, eventually, of the cell. A further change in the axial ratio of the ring-like tetramers controls fibril lengths and the consequent helical geometry. Analysis of tetramer quadrants from adjacent fibrils clearly demonstrates local differential fibril lengths. Copyright © 2011 Elsevier Ltd. All rights reserved.

Dynamics and control of state-dependent networks for probing genomic organization

PubMed Central

Rajapakse, Indika; Groudine, Mark; Mesbahi, Mehran

2011-01-01

A state-dependent dynamic network is a collection of elements that interact through a network, whose geometry evolves as the state of the elements changes over time. The genome is an intriguing example of a state-dependent network, where chromosomal geometry directly relates to genomic activity, which in turn strongly correlates with geometry. Here we examine various aspects of a genomic state-dependent dynamic network. In particular, we elaborate on one of the important ramifications of viewing genomic networks as being state-dependent, namely, their controllability during processes of genomic reorganization such as in cell differentiation. PMID:21911407

Geometry and Cloaking Devices

NASA Astrophysics Data System (ADS)

Ochiai, T.; Nacher, J. C.

2011-09-01

Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

Negative tunnel magnetoresistance and differential conductance in transport through double quantum dots

NASA Astrophysics Data System (ADS)

Trocha, Piotr; Weymann, Ireneusz; Barnaś, Józef

2009-10-01

Spin-dependent transport through two coupled single-level quantum dots weakly connected to ferromagnetic leads with collinear magnetizations is considered theoretically. Transport characteristics, including the current, linear and nonlinear conductances, and tunnel magnetoresistance are calculated using the real-time diagrammatic technique in the parallel, serial, and intermediate geometries. The effects due to virtual tunneling processes between the two dots via the leads, associated with off-diagonal coupling matrix elements, are also considered. Negative differential conductance and negative tunnel magnetoresistance have been found in the case of serial and intermediate geometries, while no such behavior has been observed for double quantum dots coupled in parallel. It is also shown that transport characteristics strongly depend on the magnitude of the off-diagonal coupling matrix elements.

Assessment and statistics of surgically induced astigmatism.

PubMed

Naeser, Kristian

2008-05-01

The aim of the thesis was to develop methods for assessment of surgically induced astigmatism (SIA) in individual eyes, and in groups of eyes. The thesis is based on 12 peer-reviewed publications, published over a period of 16 years. In these publications older and contemporary literature was reviewed(1). A new method (the polar system) for analysis of SIA was developed. Multivariate statistical analysis of refractive data was described(2-4). Clinical validation studies were performed. The description of a cylinder surface with polar values and differential geometry was compared. The main results were: refractive data in the form of sphere, cylinder and axis may define an individual patient or data set, but are unsuited for mathematical and statistical analyses(1). The polar value system converts net astigmatisms to orthonormal components in dioptric space. A polar value is the difference in meridional power between two orthogonal meridians(5,6). Any pair of polar values, separated by an arch of 45 degrees, characterizes a net astigmatism completely(7). The two polar values represent the net curvital and net torsional power over the chosen meridian(8). The spherical component is described by the spherical equivalent power. Several clinical studies demonstrated the efficiency of multivariate statistical analysis of refractive data(4,9-11). Polar values and formal differential geometry describe astigmatic surfaces with similar concepts and mathematical functions(8). Other contemporary methods, such as Long's power matrix, Holladay's and Alpins' methods, Zernike(12) and Fourier analyses(8), are correlated to the polar value system. In conclusion, analysis of SIA should be performed with polar values or other contemporary component systems. The study was supported by Statens Sundhedsvidenskabeligt Forskningsråd, Cykelhandler P. Th. Rasmussen og Hustrus Mindelegat, Hotelejer Carl Larsen og Hustru Nicoline Larsens Mindelegat, Landsforeningen til Vaern om Synet, Forskningsinitiativet for Arhus Amt, Alcon Denmark, and Desirée and Niels Ydes Fond.

Simplified analysis and optimization of space base and space shuttle heat rejection systems

NASA Technical Reports Server (NTRS)

Wulff, W.

1972-01-01

A simplified radiator system analysis was performed to predict steady state radiator system performance. The system performance was found to be describable in terms of five non-dimensional system parameters. The governing differential equations are integrated numerically to yield the enthalpy rejection for the coolant fluid. The simplified analysis was extended to produce the derivatives of the coolant exit temperature with respect to the governing system parameters. A procedure was developed to find the optimum set of system parameters which yields the lowest possible coolant exit temperature for either a given projected area or a given total mass. The process can be inverted to yield either the minimum area or the minimum mass, together with the optimum geometry, for a specified heat rejection rate.

The Generation of Three-Dimensional Body-Fitted Coordinate Systems for Viscous Flow Problems.

DTIC Science & Technology

1982-07-01

Geometries," NASA TM X-3206, 1975. iq p] Papers Written Under The Contract 1. "Basic Differential Models For Coordinate Generation ", Z . U. A. Warsi...8217 Ii (C) (4’) p Figure 1. Coordinate Surfaces fr. I • BASIC DIFFERENTIAL MODELS FOR COORDINATE GENERATION Z . U. A. WARSI* Department of Aerospace

Study Paths, Riemann Surfaces, and Strebel Differentials

ERIC Educational Resources Information Center

Buser, Peter; Semmler, Klaus-Dieter

2017-01-01

These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…

Differential porosimetry and permeametry for random porous media.

PubMed

Hilfer, R; Lemmer, A

2015-07-01

Accurate determination of geometrical and physical properties of natural porous materials is notoriously difficult. Continuum multiscale modeling has provided carefully calibrated realistic microstructure models of reservoir rocks with floating point accuracy. Previous measurements using synthetic microcomputed tomography (μ-CT) were based on extrapolation of resolution-dependent properties for discrete digitized approximations of the continuum microstructure. This paper reports continuum measurements of volume and specific surface with full floating point precision. It also corrects an incomplete description of rotations in earlier publications. More importantly, the methods of differential permeametry and differential porosimetry are introduced as precision tools. The continuum microstructure chosen to exemplify the methods is a homogeneous, carefully calibrated and characterized model for Fontainebleau sandstone. The sample has been publicly available since 2010 on the worldwide web as a benchmark for methodical studies of correlated random media. High-precision porosimetry gives the volume and internal surface area of the sample with floating point accuracy. Continuum results with floating point precision are compared to discrete approximations. Differential porosities and differential surface area densities allow geometrical fluctuations to be discriminated from discretization effects and numerical noise. Differential porosimetry and Fourier analysis reveal subtle periodic correlations. The findings uncover small oscillatory correlations with a period of roughly 850μm, thus implying that the sample is not strictly stationary. The correlations are attributed to the deposition algorithm that was used to ensure the grain overlap constraint. Differential permeabilities are introduced and studied. Differential porosities and permeabilities provide scale-dependent information on geometry fluctuations, thereby allowing quantitative error estimates.

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.

Solitary waves in shallow water hydrodynamics and magnetohydrodynamics in rotating spherical coordinates

NASA Astrophysics Data System (ADS)

London, Steven D.

2018-01-01

In a recent paper (London, Geophys. Astrophys. Fluid Dyn. 2017, vol. 111, pp. 115-130, referred to as L1), we considered a perfect electrically conducting rotating fluid in the presence of an ambient toroidal magnetic field, governed by the shallow water magnetohydrodynamic (MHD) equations in a modified equatorial ?-plane approximation. In conjunction with a WKB type approximation, we used a multiple scale asymptotic scheme, previously developed by Boyd (J. Phys. Oceanogr. 1980, vol. 10, pp. 1699-1717) for equatorial solitary hydrodynamic waves, and found solitary MHD waves. In this paper, as in L1, we apply a WKB type approximation in order to extend the results of L1 from the modified ?-plane to the full spherical geometry. We have included differential rotation in the analysis in order to make the results more relevant to the solar case. In addition, we consider the case of hydrodynamic waves on the rotating sphere in the presence of a differential rotation intended to roughly model the varying large scale currents in the oceans and atmosphere. In the hydrodynamic case, we find the usual equatorial solitary waves as found by Boyd, as well as waves in bands away from the equator for sufficiently strong currents. In the MHD case, we find basically the same equatorial waves found in L1. L1 also found non-equatorial modes; no such modes are found in the full spherical geometry.

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.

Silk fibroin scaffolds with inverse opal structure for bone tissue engineering

PubMed Central

Sommer, Marianne R.; Vetsch, Jolanda R.; Leemann, Jessica; Müller, Ralph

2016-01-01

Abstract How scaffold porosity, pore diameter and geometry influence cellular behavior is‐although heavily researched ‐ merely understood, especially in 3D. This is mainly caused by a lack of suitable, reproducible scaffold fabrication methods, with processes such as gas foaming, lyophilization or particulate leaching still being the standard. Here we propose a method to generate highly porous silk fibroin scaffolds with monodisperse spherical pores, namely inverse opals, and study their effect on cell behavior. These silk fibroin inverse opal scaffolds were compared to salt‐leached silk fibroin scaffolds in terms of human mesenchymal stem cell response upon osteogenic differentiation signals. While cell number remained similar on both scaffold types, extracellular matrix mineralization nearly doubled on the newly developed scaffolds, suggesting a positive effect on cell differentiation. By using the very same material with comparable average pore diameters, this increase in mineral content can be attributed to either the differences in pore diameter distribution or the pore geometry. Although the exact mechanisms leading to enhanced mineralization in inverse opals are not yet fully understood, our results indicate that control over pore geometry alone can have a major impact on the bioactivity of a scaffold toward stem cell differentiation into bone tissue. © 2016 The Authors Journal of Biomedical Materials Research Part B: Applied Biomaterials Published by Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 2074–2084, 2017. PMID:27407014

Accurate Modeling of X-ray Extinction by Interstellar Grains

NASA Astrophysics Data System (ADS)

Hoffman, John; Draine, B. T.

2016-02-01

Interstellar abundance determinations from fits to X-ray absorption edges often rely on the incorrect assumption that scattering is insignificant and can be ignored. We show instead that scattering contributes significantly to the attenuation of X-rays for realistic dust grain size distributions and substantially modifies the spectrum near absorption edges of elements present in grains. The dust attenuation modules used in major X-ray spectral fitting programs do not take this into account. We show that the consequences of neglecting scattering on the determination of interstellar elemental abundances are modest; however, scattering (along with uncertainties in the grain size distribution) must be taken into account when near-edge extinction fine structure is used to infer dust mineralogy. We advertise the benefits and accuracy of anomalous diffraction theory for both X-ray halo analysis and near edge absorption studies. We present an open source Fortran suite, General Geometry Anomalous Diffraction Theory (GGADT), that calculates X-ray absorption, scattering, and differential scattering cross sections for grains of arbitrary geometry and composition.

Synthesis, thermogravimetric, spectroscopic and theoretical characterization of copper(II) complex with 4-chloro-2-nitrobenzenosulfonamide

NASA Astrophysics Data System (ADS)

Camí, G.; Chacón Villalba, E.; Di Santi, Y.; Colinas, P.; Estiu, G.; Soria, D. B.

2011-05-01

4-Chloro-2-nitrobenzenesulfonamide (ClNbsa) was purified and characterized. A new copper(II) complex, [Cu(ClNbsa) 2(NH 3) 2], has been prepared using the sulfonamide as ligand. The thermal behavior of both, the ligand and the Cu(II) complex, was investigated by thermogravimetric analyses (TG) and differential thermal analysis (DT), and the electronic characteristics analyzed by UV-VIS, FTIR, Raman and 1H NMR spectroscopies. The experimental IR, Raman and UV-VIS spectra have been assigned on the basis of DFT calculations at the B3LYP level of theory using the standard (6-31 + G ∗∗) basis set. The geometries have been fully optimized in vacuum and in modeled dimethylsulfoxide (DMSO) solvent, using for the latter a continuum solvation model that reproduced the experimental conditions of the UV-VIS spectroscopy. The theoretical results converged to stable conformations for the free sulfonamide and for the complex, suggesting for the latter a distorted square planar geometry in both environments.

Magnetotransport in Artificial Kagome Spin Ice

NASA Astrophysics Data System (ADS)

Chern, Gia-Wei

2017-12-01

Magnetic nanoarrays with special geometries exhibit nontrivial collective behaviors similar to those observed in spin-ice materials. Here, we present a circuit model to describe the complex magnetotransport phenomena in artificial kagome spin ice. In this picture, the system can be viewed as a resistor network driven by voltage sources that are located at vertices of the honeycomb array. The differential voltages across different terminals of these sources are related to the ice rules that govern the local magnetization ordering. The circuit model relates the transverse Hall voltage of kagome ice to the underlying spin correlations. Treating the magnetic nanoarray as metamaterials, we present a mesoscopic constitutive equation relating the Hall resistance to magnetization components of the system. We further show that the Hall signal is significantly enhanced when the kagome ice undergoes a magnetic-charge-ordering transition. Our analysis can be readily generalized to other lattice geometries, providing a quantitative method for the design of magnetoresistance devices based on artificial spin ice.

Non-integumentary melanosomes can bias reconstructions of the colours of fossil vertebrate skin

NASA Astrophysics Data System (ADS)

McNamara, Maria; Kaye, Jonathan; Benton, Mike; Orr, Patrick

2017-04-01

The soft tissues of many fossil vertebrates preserve melanosomes - micron-scale organelles used to inform on original integumentary coloration and the evolution of visual signalling strategies through time. In extant vertebrates, however, melanosomes also occur in internal tissues, and hence melanosomes preserved in fossils may not derive solely from the integument. Here, by analyzing the internal tissues of extant and fossil frogs, we show that non-integumentary melanosomes are extremely abundant; they are usually localised to the torso in fossils but can also occur in the limbs, presumably due to dispersal during decay. Melanosomes from the body outlines of fossils cannot, therefore, reliably inform on integumentary coloration. Crucially, non-integumentary and integumentary melanosomes differ in geometry in both fossil and modern frogs and, in fossils, occur as discrete layers. Analysis of melanosome geometry, distribution and size-specific layering is required to differentiate integumentary from non-integumentary melanosomes and is essential to any attempt to reconstruct the original colours of vertebrate skin.

The method of lines in analyzing solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.

1990-01-01

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

Considerations for using data envelopment analysis for the assessment of radiotherapy treatment plan quality.

PubMed

Simpson, John; Raith, Andrea; Rouse, Paul; Ehrgott, Matthias

2017-10-09

Purpose The operations research method of data envelopment analysis (DEA) shows promise for assessing radiotherapy treatment plan quality. The purpose of this paper is to consider the technical requirements for using DEA for plan assessment. Design/methodology/approach In total, 41 prostate treatment plans were retrospectively analysed using the DEA method. The authors investigate the impact of DEA weight restrictions with reference to the ability to differentiate plan performance at a level of clinical significance. Patient geometry influences plan quality and the authors compare differing approaches for managing patient geometry within the DEA method. Findings The input-oriented DEA method is the method of choice when performing plan analysis using the key undesirable plan metrics as the DEA inputs. When considering multiple inputs, it is necessary to constrain the DEA input weights in order to identify potential plan improvements at a level of clinical significance. All tested approaches for the consideration of patient geometry yielded consistent results. Research limitations/implications This work is based on prostate plans and individual recommendations would therefore need to be validated for other treatment sites. Notwithstanding, the method that requires both optimised DEA weights according to clinical significance and appropriate accounting for patient geometric factors is universally applicable. Practical implications DEA can potentially be used during treatment plan development to guide the planning process or alternatively used retrospectively for treatment plan quality audit. Social implications DEA is independent of the planning system platform and therefore has the potential to be used for multi-institutional quality audit. Originality/value To the authors' knowledge, this is the first published examination of the optimal approach in the use of DEA for radiotherapy treatment plan assessment.

A high-order 3D spectral difference solver for simulating flows about rotating geometries

NASA Astrophysics Data System (ADS)

Zhang, Bin; Liang, Chunlei

2017-11-01

Fluid flows around rotating geometries are ubiquitous. For example, a spinning ping pong ball can quickly change its trajectory in an air flow; a marine propeller can provide enormous amount of thrust to a ship. It has been a long-time challenge to accurately simulate these flows. In this work, we present a high-order and efficient 3D flow solver based on unstructured spectral difference (SD) method and a novel sliding-mesh method. In the SD method, solution and fluxes are reconstructed using tensor products of 1D polynomials and the equations are solved in differential-form, which leads to high-order accuracy and high efficiency. In the sliding-mesh method, a computational domain is decomposed into non-overlapping subdomains. Each subdomain can enclose a geometry and can rotate relative to its neighbor, resulting in nonconforming sliding interfaces. A curved dynamic mortar approach is designed for communication on these interfaces. In this approach, solutions and fluxes are projected from cell faces to mortars to compute common values which are then projected back to ensures continuity and conservation. Through theoretical analysis and numerical tests, it is shown that this solver is conservative, free-stream preservative, and high-order accurate in both space and time.

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Differential Multiscale Modeling of Chemically Complex Materials under Heavy Deformation: Biological, Bioinspired and Synthetic Hierarchical Materials

DTIC Science & Technology

2010-06-01

Buehler, “Meso- Origami : Folding Multilayer Graphene Sheets”, Applied Physics Letters, Vol. 95, paper #: 123121, 2009 D. Sen and M.J. Buehler, “Size and... geometry effects on flow stress in bioinspired de novo metal-matrix nanocomposites”, Advanced Engineering Materials, Vol. 11(10), pp. 774-781, 2009...behavior is recovered. Second, a subset of all geometries shows the inverse banana curve behavior. Interestingly, only 2% of all structures give the

Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings.

PubMed

Ferrero, Alejandro; Rabal, Ana; Campos, Joaquín; Martínez-Verdú, Francisco; Chorro, Elísabet; Perales, Esther; Pons, Alicia; Hernanz, María Luisa

2013-02-01

A reduced set of measurement geometries allows the spectral reflectance of special effect coatings to be predicted for any other geometry. A physical model based on flake-related parameters has been used to determine nonredundant measurement geometries for the complete description of the spectral bidirectional reflectance distribution function (BRDF). The analysis of experimental spectral BRDF was carried out by means of principal component analysis. From this analysis, a set of nine measurement geometries was proposed to characterize special effect coatings. It was shown that, for two different special effect coatings, these geometries provide a good prediction of their complete color shift.

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

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

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE PAGES

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; ...

2017-06-29

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Electrical Spin-Injection into Silicon and Spin FET

DTIC Science & Technology

2010-02-18

differential conductance ( NDC ), which saw the limelight with the realization of the Esaki tunneling diode, had been predicted and observed to occur in a...collector current of a tunneling emitter bipolar transistor, i.e., negative differential transconductance NDTC. Gate controlled NDC had been observed in...measurement and simulation results are relevant as well for other NDC geometries such as FET style tunnel transistors since they offer crucial

Modelisation of the SECMin molten salts environment

NASA Astrophysics Data System (ADS)

Lucas, M.; Slim, C.; Delpech, S.; di Caprio, D.; Stafiej, J.

2014-06-01

We develop a cellular automata modelisation of SECM experiments to study corrosion in molten salt media for generation IV nuclear reactors. The electrodes used in these experiments are cylindrical glass tips with a coaxial metal wire inside. As the result of simulations we obtain the current approach curves of the electrodes with geometries characterized by several values of the ratios of glass to metal area at the tip. We compare these results with predictions of the known analytic expressions, solutions of partial differential equations for flat uniform geometry of the substrate. We present the results for other, more complicated substrate surface geometries e. g. regular saw modulated surface, surface obtained by Eden model process, ...

Differential die-away instrument: Report on comparison of fuel assembly experiments and simulations

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

Goodsell, Alison Victoria; Henzl, Vladimir; Swinhoe, Martyn Thomas

2015-01-14

Experimental results of the assay of mock-up (fresh) fuel with the differential die-away (DDA) instrument were compared to the Monte Carlo N-Particle eXtended (MCNPX) simulation results. Most principal experimental observables, the die-away time and the in tegral of the DDA signal in several time domains, have been found in good agreement with the MCNPX simulation results. The remaining discrepancies between the simulation and experimental results are likely due to small differences between the actual experimental setup and the simulated geometry, including uncertainty in the DT neutron generator yield. Within this report we also present a sensitivity study of the DDAmore » instrument which is a complex and sensitive system and demonstrate to what degree it can be impacted by geometry, material composition, and electronics performance.« less

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters

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

Galitskiy, S. A.; Artemyev, A. N.; Jänkälä, K.

2015-01-21

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li{sub 2−8} are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li{submore » 2} are in a good agreement with the available theoretical data, whereas those computed for Li{sub 3−8} clusters can be considered as theoretical predictions.« less

Silk fibroin scaffolds with inverse opal structure for bone tissue engineering.

PubMed

Sommer, Marianne R; Vetsch, Jolanda R; Leemann, Jessica; Müller, Ralph; Studart, André R; Hofmann, Sandra

2017-10-01

How scaffold porosity, pore diameter and geometry influence cellular behavior is-although heavily researched - merely understood, especially in 3D. This is mainly caused by a lack of suitable, reproducible scaffold fabrication methods, with processes such as gas foaming, lyophilization or particulate leaching still being the standard. Here we propose a method to generate highly porous silk fibroin scaffolds with monodisperse spherical pores, namely inverse opals, and study their effect on cell behavior. These silk fibroin inverse opal scaffolds were compared to salt-leached silk fibroin scaffolds in terms of human mesenchymal stem cell response upon osteogenic differentiation signals. While cell number remained similar on both scaffold types, extracellular matrix mineralization nearly doubled on the newly developed scaffolds, suggesting a positive effect on cell differentiation. By using the very same material with comparable average pore diameters, this increase in mineral content can be attributed to either the differences in pore diameter distribution or the pore geometry. Although the exact mechanisms leading to enhanced mineralization in inverse opals are not yet fully understood, our results indicate that control over pore geometry alone can have a major impact on the bioactivity of a scaffold toward stem cell differentiation into bone tissue. © 2016 The Authors Journal of Biomedical Materials Research Part B: Applied Biomaterials Published by Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 2074-2084, 2017. © 2016 The Authors Journal of Biomedical Materials Research Part B: Applied Biomaterials Published by Wiley Periodicals, Inc.

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.

Numerical Simulation Of Cutting Of Gear Teeth

NASA Technical Reports Server (NTRS)

Oswald, Fred B.; Huston, Ronald L.; Mavriplis, Dimitrios

1994-01-01

Shapes of gear teeth produced by gear cutters of specified shape simulated computationally, according to approach based on principles of differential geometry. Results of computer simulation displayed as computer graphics and/or used in analyses of design, manufacturing, and performance of gears. Applicable to both standard and non-standard gear-tooth forms. Accelerates and facilitates analysis of alternative designs of gears and cutters. Simulation extended to study generation of surfaces other than gears. Applied to cams, bearings, and surfaces of arbitrary rolling elements as well as to gears. Possible to develop analogous procedures for simulating manufacture of skin surfaces like automobile fenders, airfoils, and ship hulls.

Gravitation: Foundations and Frontiers

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2010-01-01

1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

A brief survey of constrained mechanics and variational problems in terms of differential forms

NASA Technical Reports Server (NTRS)

Hermann, Robert

1994-01-01

There has been considerable interest recently in constrained mechanics and variational problems. This is in part due to applied interests (such as 'non-holonomic mechanics in robotics') and in other part due to the fact that several schools of 'pure' mathematics have found that this classical subject is of importance for what they are trying to do. I have made various attempts at developing these subjects since my Lincoln lab days of the late 1950's. In this Chapter, I will sketch a Unified point of view, using Cartan's approach with differential forms. This has the advantage from the C-O-R viewpoint being developed in this Volume that the extension from 'smooth' to 'generalized' data is very systematic and algebraic. (I will only deal with the 'smooth' point of view in this Chapter; I will develop the 'generalized function' material at a later point.) The material presented briefly here about Variational Calculus and Constrained Mechanics can be found in more detail in my books, 'Differential Geometry and the Calculus of Variations', 'Lie Algebras and Quantum Mechanics', and 'Geometry, Physics and Systems'.

Modeling folding related multi-scale deformation of sedimentary rock using ALSM and fracture characterization at Raplee Ridge, UT

NASA Astrophysics Data System (ADS)

Mynatt, I.; Hilley, G. E.; Pollard, D. D.

2006-12-01

Understanding and predicting the characteristics of folding induced fracturing is an important and intriguing structural problem. Folded sequences of sedimentary rock at depth are common traps for hydrocarbons and water and fractures can strongly effect (both positively and negatively) this trapping capability. For these reasons fold-fracture relationships are well studied, but due to the complex interactions between the remote tectonic stress, rheologic properties, underlying fault geometry and slip, and pre-existing fractures, fracture characteristics can vary greatly from fold to fold. Additionally, examination of the relationships between fundamental characteristics such as fold geometry and fracture density are difficult even in thoroughly studied producing fields as measurements of fold shape are hampered by the low resolution of seismic surveying and measurements of fractures are limited to sparse well-bore locations. Due to the complexity of the system, the limitations of available data and small number of detailed case studies, prediction of fracture characteristics, e.g. the distribution of fracture density, are often difficult to make for a particular fold. We suggest a combination of mechanical and numerical modeling and analysis combined with detailed field mapping can lead to important insights into fold-fracture relationships. We develop methods to quantify both fold geometry and fracture characteristics, and summarize their relationships for an exhumed analogue reservoir case study. The field area is Raplee Monocline, a Laramide aged, N-S oriented, ~14-km long fold exposed in the Monument Upwarp of south-eastern Utah and part of the larger Colorado Plateau geologic province. The investigation involves three distinct parts: 1) Field based characterization and mapping of the fractures on and near the fold; 2) Development of accurate models of the fold geometry using high resolution data including ~3.5x107 x, y, z topographic points collected using Airborne Laser Swath Mapping (ALSM); and 3) Analysis of the fold shape and fracture patterns using the concepts of differential geometry and fracture mechanics. Field documentation of fracture characteristics enables the classification of distinct pre- and syn- folding fracture sets and the development of conceptual models of multiple stages of fracture evolution. Numerical algorithms, visual methods and field mapping techniques are used to extract the geometry of specific stratigraphic bedding surfaces and interpolate fold geometry between topographic exposures, thereby creating models of the fold geometry at several stratigraphic levels. Geometric characteristics of the fold models, such as magnitudes and directions of maximum and minimum normal curvature and fold limb dip, are compared to the observed fracture characteristics to identify the following relationships: 1) Initiation of folding related fractures at ten degrees of limb dip and increasing fracture density with increasing dip and 2) No correlation between absolute maximum fold curvature and fracture density.

Development of olivine crystallographic preferred orientation in response to strain-induced fabric geometry

NASA Astrophysics Data System (ADS)

Chatzaras, Vasileios; Kruckenberg, Seth C.; Cohen, Shaina M.; Medaris, L. Gordon, Jr.; Withers, Anthony C.; Bagley, Brian

2016-04-01

The effect of finite strain ellipsoid geometry on crystallographic preferred orientation (CPO) is well known for crustal minerals (e.g., quartz, calcite, biotite, and hornblende). In the upper mantle, however, it remains poorly constrained how strain and fabric may affect olivine CPO. We present data from a suite of 40 spinel peridotite xenoliths from Marie Byrd Land (west Antarctica), which support an interpretation that fabric geometry rather than deformation conditions control the development of olivine CPO. We use X-ray computed tomography (XRCT) to quantitatively determine spinel fabric (orientation and geometry). Olivine CPOs, determined by Electron Backscattered Diffraction (EBSD), are plotted with respect to the XRCT-derived spinel foliation and lineation; this approach allows for the accurate, and unbiased, identification of CPO symmetries and types in mantle xenoliths. The combined XRCT and EBSD data show that the xenoliths are characterized by a range of fabric geometries (from oblate to prolate) and olivine CPO patterns; we recognize the A-type, axial-[010], axial-[100], and B-type patterns. The mantle xenoliths equilibrated at temperatures 779-1198 oC, as determined by 2-Px geothermometry. Using a geotherm consistent with the stability of spinel in all xenoliths, the range of equilibration temperatures occurs at depths between 39 and 72 km. Olivine recrystallized grain size piezometry reveals differential stresses ranging 2-60 MPa. Analysis of low-angle misorientation axes show a wide range in the distribution of rotation axes, with dominant {0kl}[100] slip. We use Fourier Transform Infrared (FTIR) spectroscopy to estimate the water content in the xenolith with the B-type CPO pattern. FTIR analysis shows that the equilibrium H concentration in olivine is low (4-13 ppm H2O). Combining these data, we observe that olivine CPO symmetry is controlled neither by the deformation conditions (stress, temperature, pressure, water content) for the range of conditions estimated in the Marie Byrd Land xenoliths, nor by the activation of the slip systems predicted by deformation experiments. Rather, our data show that olivine CPO is controlled by transitions in strain-induced fabric geometry. Microstructures and deformation mechanism maps suggest that deformation is dominated by dislocation-accommodated grain boundary sliding. We propose that slip of olivine glide planes and rotation of olivine grains occur so as to accommodate the imposed material flow, which is guided by the 3D strain-induced fabric geometry. As a result of this process, the axial-[010] and B-type patterns form in relation to oblate fabric ellipsoids, the A-type pattern forms in a range of fabric ellipsoids, and the axial-[100] pattern is associated with prolate fabric ellipsoids. We therefore suggest that the well-known process of strain geometry-induced development of CPO is also applicable to upper mantle rocks.

Experimental and Analytical Determinations of Spiral Bevel Gear-Tooth Bending Stress Compared

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

2000-01-01

Spiral bevel gears are currently used in all main-rotor drive systems for rotorcraft produced in the United States. Applications such as these need spiral bevel gears to turn the corner from the horizontal gas turbine engine to the vertical rotor shaft. These gears must typically operate at extremely high rotational speeds and carry high power levels. With these difficult operating conditions, an improved analytical capability is paramount to increasing aircraft safety and reliability. Also, literature on the analysis and testing of spiral bevel gears has been very sparse in comparison to that for parallel axis gears. This is due to the complex geometry of this type of gear and to the specialized test equipment necessary to test these components. To develop an analytical model of spiral bevel gears, researchers use differential geometry methods to model the manufacturing kinematics. A three-dimensional spiral bevel gear modeling method was developed that uses finite elements for the structural analysis. This method was used to analyze the three-dimensional contact pattern between the test pinion and gear used in the Spiral Bevel Gear Test Facility at the NASA Glenn Research Center at Lewis Field. Results of this analysis are illustrated in the preceding figure. The development of the analytical method was a joint endeavor between NASA Glenn, the U.S. Army Research Laboratory, and the University of North Dakota.

Computerized Modeling and Loaded Tooth Contact Analysis of Hypoid Gears Manufactured by Face Hobbing Process

NASA Astrophysics Data System (ADS)

Nishino, Takayuki

The face hobbing process has been widely applied in automotive industry. But so far few analytical tools have been developed. This makes it difficult for us to optimize gear design. To settle this situation, this study aims at developing a computerized tool to predict the running performances such as loaded tooth contact pattern, static transmission error and so on. First, based upon kinematical analysis of a cutting machine, a mathematical description of tooth surface generation is given. Second, based upon the theory of gearing and differential geometry, conjugate tooth surfaces are studied. Then contact lines are generated. Third, load distribution along contact lines is formulated. Last, the numerical model is validated by measuring loaded transmission error and loaded tooth contact pattern.

The effect of Si nano-columns in 2-D and 3-D on cellular behaviour: nanotopography-induced CaP deposition from differentiating mesenchymal stem cells.

PubMed

Guvendik, S; Trabzon, L; Ramazanoglu, M

2011-10-01

Si nano-columns were deposited in 2-D and 3-D in the form of well-defined geometries by physical vapor deposition. The films were grown by e-beam evaporation with an angle between source and substrate. The Si nano-columns were deposited in the shape of spiral with two different incoming atomic flux angle so that the manipulation of nano-columns in 3-D (out-of-plane) was obtained. The Si nano-columns were also grown as vertical stick with square, triangle and linear cross sections in 2D (in-plane). Rat bone marrow mesenchymal stem cells (MSCs) were cultured on these different Si nanosurfaces. MTS assay was carried out to determine the cell proliferation and viability based on different nanotopographies. For the evaluation of cell distribution and morphology, a SEM (Scanning Electron Microscopy) analysis was performed. Any CaP deposition on Si nanosurfaces was observed using energy dispersive X-Ray spectroscopy in SEM (SEM-EDX). After 4 days of culture, there was a higher value of cell proliferation on square columns and spiral Si nano-columns grown with 85 degrees of incoming atomic flux. The cell attachment and spreading was also affected by the geometry of Si nano-columns. While there were still cells showing round/spherical morphology with minimal spreading on conventional Si surfaces, most of the cells cultured on different Si nanotopographies attached on the surface and displayed flattened morphology, especially on the square columns surface. Moreover, CaP deposition was discovered on square columns and spiral films with 85 degrees substrate angle. So, it can be concluded that there is a clear correlation between cell responses and nano-sized geometry on Si surface and it is possible to induce cellular differentiation and CaP formation in certain geometrical constraints.

Electrodynamics and Spacetime Geometry: Foundations

NASA Astrophysics Data System (ADS)

Cabral, Francisco; Lobo, Francisco S. N.

2017-02-01

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

Positive geometries and canonical forms

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas

2017-11-01

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

A micro-kinematic framework for vorticity analysis in polyphase shear zones using integrated field, microstructural and crystallographic orientation-dispersion methods

NASA Astrophysics Data System (ADS)

Kruckenberg, S. C.; Michels, Z. D.; Parsons, M. M.

2017-12-01

We present results from integrated field, microstructural and textural analysis in the Burlington mylonite zone (BMZ) of eastern Massachusetts to establish a unified micro-kinematic framework for vorticity analysis in polyphase shear zones. Specifically, we define the vorticity-normal surface based on lattice-scale rotation axes calculated from electron backscatter diffraction data using orientation statistics. In doing so, we objectively identify a suitable reference frame for rigid grain methods of vorticity analysis that can be used in concert with textural studies to constrain field- to plate-scale deformation geometries without assumptions that may bias tectonic interpretations, such as relationships between kinematic axes and fabric forming elements or the nature of the deforming zone (e.g., monoclinic vs. triclinic shear zones). Rocks within the BMZ comprise a heterogeneous mix of quartzofeldspathic ± hornblende-bearing mylonitic gneisses and quartzites. Vorticity axes inferred from lattice rotations lie within the plane of mylonitic foliation perpendicular to lineation - a pattern consistent with monoclinic deformation geometries involving simple shear and/or wrench-dominated transpression. The kinematic vorticity number (Wk) is calculated using Rigid Grain Net analysis and ranges from 0.25-0.55, indicating dominant general shear. Using the calculated Wk values and the dominant geographic fabric orientation, we constrain the angle of paleotectonic convergence between the Nashoba and Avalon terranes to 56-75º with the convergence vector trending 142-160° and plunging 3-10°. Application of the quartz recrystallized grain size piezometer suggests differential stresses in the BMZ mylonites ranging from 44 to 92 MPa; quartz CPO patterns are consistent with deformation at greenschist- to amphibolite-facies conditions. We conclude that crustal strain localization in the BMZ involved a combination of pure and simple shear in a sinistral reverse transpressional shear zone formed at or near the brittle-ductile transition under relatively high stress conditions. Moreover, we demonstrate the utility of combined crystallographic and rigid grain methods of vorticity analysis for deducing deformation geometries, kinematics, and tectonic histories in polyphase shear zones.

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

NASA Astrophysics Data System (ADS)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

Sulphur hexaflouride: low energy (e,2e) experiments and molecular three-body distorted wave theory

NASA Astrophysics Data System (ADS)

Nixon, Kate L.; Murray, Andrew J.; Chaluvadi, H.; Ning, C. G.; Colgan, James; Madison, Don H.

2016-10-01

Experimental and theoretical triple differential ionisation cross-sections (TDCSs) are presented for the highest occupied molecular orbital of sulphur hexafluoride. These measurements were performed in the low energy regime, with outgoing electron energies ranging from 5 to 40 eV in a coplanar geometry, and with energies of 10 and 20 eV in a perpendicular geometry. Complementary theoretical predictions of the TDCS were calculated using the molecular three-body distorted wave formalism. Calculations were performed using a proper average over molecular orientations as well as the orientation-averaged molecular orbital approximation. This more sophisticated model was found to be in closer agreement with the experimental data, however neither model accurately predicts the TDCS over all geometries and energies.

Development and design of flexible Fowler flaps for an adaptive wing

NASA Astrophysics Data System (ADS)

Monner, Hans P.; Hanselka, Holger; Breitbach, Elmar J.

1998-06-01

Civil transport airplanes fly with fixed geometry wings optimized only for one design point described by altitude, Mach number and airplane weight. These parameters vary continuously during flight, to which means the wing geometry seldom is optimal. According to aerodynamic investigations a chordwide variation of the wing camber leads to improvements in operational flexibility, buffet boundaries and performance resulting in reduction of fuel consumption. A spanwise differential camber variation allows to gain control over spanwise lift distributions reducing wing root bending moments. This paper describes the design of flexible Fowler flaps for an adaptive wing to be used in civil transport aircraft that allows both a chordwise as well as spanwise differential camber variation during flight. Since both lower and upper skins are flexed by active ribs, the camber variation is achieved with a smooth contour and without any additional gaps.

Theoretical and Experimental Triple Differential Cross Sections for Electron Impact Ionization of SF6

NASA Astrophysics Data System (ADS)

Chaluvadi, Hari; Nixon, Kate; Murray, Andrew; Ning, Chuangang; Colgan, James; Madison, Don

2014-10-01

Experimental and theoretical Triply Differential Cross Sections (TDCS) will be presented for electron-impact ionization of sulfur hexafluoride (SF6) for the molecular orbital 1t1g. M3DW (molecular 3-body distorted wave) results will be compared with experiment for coplanar geometry and for perpendicular plane geometry (a plane which is perpendicular to the incident beam direction). In both cases, the final state electron energies and observation angles are symmetric and the final state electron energies range from 5 eV to 40 eV. It will be shown that there is a large difference between using the OAMO (orientation averaged molecular orbital) approximation and the proper average over all orientations and also that the proper averaged results are in much better agreement with experiment. Work supported by NSF under Grant Number PHY-1068237. Computational work was performed with Institutional resources made available through Los Alamos National Laboratory.

A Method for Thermal Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.; Kicher, Thomas P.

1994-01-01

A modeling method for analyzing the three-dimensional thermal behavior of spiral bevel gears has been developed. The model surfaces are generated through application of differential geometry to the manufacturing process for face-milled spiral bevel gears. Contact on the gear surface is found by combining tooth contact analysis with three-dimensional Hertzian theory. The tooth contact analysis provides the principle curvatures and orientations of the two surfaces. This information is then used directly in the Hertzian analysis to find the contact size and maximum pressure. Heat generation during meshing is determined as a function of the applied load, sliding velocity, and coefficient of friction. Each of these factors change as the point of contact changes during meshing. A nonlinear finite element program was used to conduct the heat transfer analysis. This program permitted the time- and position-varying boundary conditions, found in operation, to be applied to a one-tooth model. An example model and analytical results are presented.

Curvature-Induced Instabilities of Shells

NASA Astrophysics Data System (ADS)

Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark P.; Bade, Abdikhalaq J.; Holmes, Douglas P.

2018-01-01

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

ACCURATE MODELING OF X-RAY EXTINCTION BY INTERSTELLAR GRAINS

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

Hoffman, John; Draine, B. T., E-mail: jah5@astro.princeton.edu, E-mail: draine@astro.princeton.edu

Interstellar abundance determinations from fits to X-ray absorption edges often rely on the incorrect assumption that scattering is insignificant and can be ignored. We show instead that scattering contributes significantly to the attenuation of X-rays for realistic dust grain size distributions and substantially modifies the spectrum near absorption edges of elements present in grains. The dust attenuation modules used in major X-ray spectral fitting programs do not take this into account. We show that the consequences of neglecting scattering on the determination of interstellar elemental abundances are modest; however, scattering (along with uncertainties in the grain size distribution) must bemore » taken into account when near-edge extinction fine structure is used to infer dust mineralogy. We advertise the benefits and accuracy of anomalous diffraction theory for both X-ray halo analysis and near edge absorption studies. We present an open source Fortran suite, General Geometry Anomalous Diffraction Theory (GGADT), that calculates X-ray absorption, scattering, and differential scattering cross sections for grains of arbitrary geometry and composition.« less

The influence of branch order on optimal leaf vein geometries: Murray's law and area preserving branching.

PubMed

Price, Charles A; Knox, Sarah-Jane C; Brodribb, Tim J

2013-01-01

Models that predict the form of hierarchical branching networks typically invoke optimization based on biomechanical similitude, the minimization of impedance to fluid flow, or construction costs. Unfortunately, due to the small size and high number of vein segments found in real biological networks, complete descriptions of networks needed to evaluate such models are rare. To help address this we report results from the analysis of the branching geometry of 349 leaf vein networks comprising over 1.5 million individual vein segments. In addition to measuring the diameters of individual veins before and after vein bifurcations, we also assign vein orders using the Horton-Strahler ordering algorithm adopted from the study of river networks. Our results demonstrate that across all leaves, both radius tapering and the ratio of daughter to parent branch areas for leaf veins are in strong agreement with the expectation from Murray's law. However, as veins become larger, area ratios shift systematically toward values expected under area-preserving branching. Our work supports the idea that leaf vein networks differentiate roles of leaf support and hydraulic supply between hierarchical orders.

Ideal-observer detectability in photon-counting differential phase-contrast imaging using a linear-systems approach

PubMed Central

Fredenberg, Erik; Danielsson, Mats; Stayman, J. Webster; Siewerdsen, Jeffrey H.; Åslund, Magnus

2012-01-01

Purpose: To provide a cascaded-systems framework based on the noise-power spectrum (NPS), modulation transfer function (MTF), and noise-equivalent number of quanta (NEQ) for quantitative evaluation of differential phase-contrast imaging (Talbot interferometry) in relation to conventional absorption contrast under equal-dose, equal-geometry, and, to some extent, equal-photon-economy constraints. The focus is a geometry for photon-counting mammography. Methods: Phase-contrast imaging is a promising technology that may emerge as an alternative or adjunct to conventional absorption contrast. In particular, phase contrast may increase the signal-difference-to-noise ratio compared to absorption contrast because the difference in phase shift between soft-tissue structures is often substantially larger than the absorption difference. We have developed a comprehensive cascaded-systems framework to investigate Talbot interferometry, which is a technique for differential phase-contrast imaging. Analytical expressions for the MTF and NPS were derived to calculate the NEQ and a task-specific ideal-observer detectability index under assumptions of linearity and shift invariance. Talbot interferometry was compared to absorption contrast at equal dose, and using either a plane wave or a spherical wave in a conceivable mammography geometry. The impact of source size and spectrum bandwidth was included in the framework, and the trade-off with photon economy was investigated in some detail. Wave-propagation simulations were used to verify the analytical expressions and to generate example images. Results: Talbot interferometry inherently detects the differential of the phase, which led to a maximum in NEQ at high spatial frequencies, whereas the absorption-contrast NEQ decreased monotonically with frequency. Further, phase contrast detects differences in density rather than atomic number, and the optimal imaging energy was found to be a factor of 1.7 higher than for absorption contrast. Talbot interferometry with a plane wave increased detectability for 0.1-mm tumor and glandular structures by a factor of 3–4 at equal dose, whereas absorption contrast was the preferred method for structures larger than ∼0.5 mm. Microcalcifications are small, but differ from soft tissue in atomic number more than density, which is favored by absorption contrast, and Talbot interferometry was barely beneficial at all within the resolution limit of the system. Further, Talbot interferometry favored detection of “sharp” as opposed to “smooth” structures, and discrimination tasks by about 50% compared to detection tasks. The technique was relatively insensitive to spectrum bandwidth, whereas the projected source size was more important. If equal photon economy was added as a restriction, phase-contrast efficiency was reduced so that the benefit for detection tasks almost vanished compared to absorption contrast, but discrimination tasks were still improved close to a factor of 2 at the resolution limit. Conclusions: Cascaded-systems analysis enables comprehensive and intuitive evaluation of phase-contrast efficiency in relation to absorption contrast under requirements of equal dose, equal geometry, and equal photon economy. The benefit of Talbot interferometry was highly dependent on task, in particular detection versus discrimination tasks, and target size, shape, and material. Requiring equal photon economy weakened the benefit of Talbot interferometry in mammography. PMID:22957600

Differential memory in the earth's magnetotail

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1991-01-01

The process of 'differential memory' in the earth's magnetotail is studied in the framework of the modified Harris magnetotail geometry. It is verified that differential memory can generate non-Maxwellian features in the modified Harris field model. The time scales and the potentially observable distribution functions associated with the process of differential memory are investigated, and it is shown that non-Maxwelllian distributions can evolve as a test particle response to distribution function boundary conditions in a Harris field magnetotail model. The non-Maxwellian features which arise from distribution function mapping have definite time scales associated with them, which are generally shorter than the earthward convection time scale but longer than the typical Alfven crossing time.

Defects in Nonlinear Elastic Crystals: Differential Geometry, Finite Kinematics, and Second-Order Analytical Solutions

DTIC Science & Technology

2015-04-01

of unit length: da = F L a αδ α Ad A , da = F L−1αaδ A α dA . (2.12) The metric tensor associated with the deformed... A spatial density tensor θ and Frank vector ω̂ of the following forms are consistent with geometry of the problem: θ = θzzgz ⊗ gz = ω̂δ(r)gz ⊗ gz = δ...stress depends quadratically on strain, with the elastic potential cubic in strain and including elastic constants of

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

On the computation of steady Hopper flows. II: von Mises materials in various geometries

NASA Astrophysics Data System (ADS)

Gremaud, Pierre A.; Matthews, John V.; O'Malley, Meghan

2004-11-01

Similarity solutions are constructed for the flow of granular materials through hoppers. Unlike previous work, the present approach applies to nonaxisymmetric containers. The model involves ten unknowns (stresses, velocity, and plasticity function) determined by nine nonlinear first order partial differential equations together with a quadratic algebraic constraint (yield condition). A pseudospectral discretization is applied; the resulting problem is solved with a trust region method. The important role of the hopper geometry on the flow is illustrated by several numerical experiments of industrial relevance.

A Mathematics Software Database Update.

ERIC Educational Resources Information Center

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Ground reaction forces and bone parameters in females with tibial stress fracture.

PubMed

Bennell, Kim; Crossley, Kay; Jayarajan, Jyotsna; Walton, Elizabeth; Warden, Stuart; Kiss, Z Stephen; Wrigley, Tim

2004-03-01

Tibial stress fracture is a common overuse running injury that results from the interplay of repetitive mechanical loading and bone strength. This research project aimed to determine whether female runners with a history of tibial stress fracture (TSF) differ in ground reaction force (GRF) parameters during running, regional bone density, and tibial bone geometry from those who have never sustained a stress fracture (NSF). Thirty-six female running athletes (13 TSF; 23 NSF) ranging in age from 18 to 44 yr were recruited for this cross-sectional study. The groups were well matched for demographic, training, and menstrual parameters. A force platform measured selected GRF parameters (peak and time to peak for vertical impact and active forces, and horizontal braking and propulsive forces) during overground running at 4.0 m.s.(-1). Lumbar spine, proximal femur, and distal tibial bone mineral density were assessed by dual energy x-ray absorptiometry. Tibial bone geometry (cross-sectional dimensions and areas, and second moments of area) was calculated from a computerized tomography scan at the junction of the middle and distal thirds. There were no significant differences between the groups for any of the GRF, bone density, or tibial bone geometric parameters (P > 0.05). Both TSF and NSF subjects had bone density levels that were average or above average compared with a young adult reference range. Factor analysis followed by discriminant function analysis did not find any combinations of variables that differentiated between TSF and NSF groups. These findings do not support a role for GRF, bone density, or tibial bone geometry in the development of tibial stress fractures, suggesting that other risk factors were more important in this cohort of female runners.

Radical-Driven Silicon Surface Passivation for Organic-Inorganic Hybrid Photovoltaics

NASA Astrophysics Data System (ADS)

Chandra, Nitish

The advent of metamaterials has increased the complexity of possible light-matter interactions, creating gaps in knowledge and violating various commonly used approximations and rendering some common mathematical frameworks incomplete. Our forward scattering experiments on metallic shells and cavities have created a need for a rigorous geometry-based analysis of scattering problems and more rigorous current distribution descriptions in the volume of the scattering object. In order to build an accurate understanding of these interactions, we have revisited the fundamentals of Maxwell's equations, electromagnetic potentials and boundary conditions to build a bottom-up geometry-based analysis of scattering. Individual structures or meta-atoms can be designed to localize the incident electromagnetic radiation in order to create a change in local constitutive parameters and possible nonlinear responses. Hence, in next generation engineered materials, an accurate determination of current distribution on the surface and in the structure's volume play an important role in describing and designing desired properties. Multipole expansions of the exact current distribution determined using principles of differential geometry provides an elegant way to study these local interactions of meta-atoms. The dynamics of the interactions can be studied using the behavior of the polarization and magnetization densities generated by localized current densities interacting with the electromagnetic potentials associated with the incident waves. The multipole method combined with propagation of electromagnetic potentials can be used to predict a large variety of linear and nonlinear physical phenomena. This has been demonstrated in experiments that enable the analog detection of sources placed at subwavelength separation by using time reversal of observed signals. Time reversal is accomplished by reversing the direction of the magnetic dipole in bianisotropic metasurfaces while simultaneously providing a method to reduce the losses often observed when light interacts with meta-structures.

Computational simulation and aerodynamic sensitivity analysis of film-cooled turbines

NASA Astrophysics Data System (ADS)

Massa, Luca

A computational tool is developed for the time accurate sensitivity analysis of the stage performance of hot gas, unsteady turbine components. An existing turbomachinery internal flow solver is adapted to the high temperature environment typical of the hot section of jet engines. A real gas model and film cooling capabilities are successfully incorporated in the software. The modifications to the existing algorithm are described; both the theoretical model and the numerical implementation are validated. The accuracy of the code in evaluating turbine stage performance is tested using a turbine geometry typical of the last stage of aeronautical jet engines. The results of the performance analysis show that the predictions differ from the experimental data by less than 3%. A reliable grid generator, applicable to the domain discretization of the internal flow field of axial flow turbine is developed. A sensitivity analysis capability is added to the flow solver, by rendering it able to accurately evaluate the derivatives of the time varying output functions. The complex Taylor's series expansion (CTSE) technique is reviewed. Two of them are used to demonstrate the accuracy and time dependency of the differentiation process. The results are compared with finite differences (FD) approximations. The CTSE is more accurate than the FD, but less efficient. A "black box" differentiation of the source code, resulting from the automated application of the CTSE, generates high fidelity sensitivity algorithms, but with low computational efficiency and high memory requirements. New formulations of the CTSE are proposed and applied. Selective differentiation of the method for solving the non-linear implicit residual equation leads to sensitivity algorithms with the same accuracy but improved run time. The time dependent sensitivity derivatives are computed in run times comparable to the ones required by the FD approach.

Registration of cortical surfaces using sulcal landmarks for group analysis of MEG data☆

PubMed Central

Joshi, Anand A.; Shattuck, David W.; Thompson, Paul M.; Leahy, Richard M.

2010-01-01

We present a method to register individual cortical surfaces to a surface-based brain atlas or canonical template using labeled sulcal curves as landmark constraints. To map one cortex smoothly onto another, we minimize a thin-plate spline energy defined on the surface by solving the associated partial differential equations (PDEs). By using covariant derivatives in solving these PDEs, we compute the bending energy with respect to the intrinsic geometry of the 3D surface rather than evaluating it in the flattened metric of the 2D parameter space. This covariant approach greatly reduces the confounding effects of the surface parameterization on the resulting registration. PMID:20824115

Design and Analysis Tools for Supersonic Inlets

NASA Technical Reports Server (NTRS)

Slater, John W.; Folk, Thomas C.

2009-01-01

Computational tools are being developed for the design and analysis of supersonic inlets. The objective is to update existing tools and provide design and low-order aerodynamic analysis capability for advanced inlet concepts. The Inlet Tools effort includes aspects of creating an electronic database of inlet design information, a document describing inlet design and analysis methods, a geometry model for describing the shape of inlets, and computer tools that implement the geometry model and methods. The geometry model has a set of basic inlet shapes that include pitot, two-dimensional, axisymmetric, and stream-traced inlet shapes. The inlet model divides the inlet flow field into parts that facilitate the design and analysis methods. The inlet geometry model constructs the inlet surfaces through the generation and transformation of planar entities based on key inlet design factors. Future efforts will focus on developing the inlet geometry model, the inlet design and analysis methods, a Fortran 95 code to implement the model and methods. Other computational platforms, such as Java, will also be explored.

Investigating the effects of PDC cutters geometry on ROP using the Taguchi technique

NASA Astrophysics Data System (ADS)

Jamaludin, A. A.; Mehat, N. M.; Kamaruddin, S.

2017-10-01

At times, the polycrystalline diamond compact (PDC) bit’s performance dropped and affects the rate of penetration (ROP). The objective of this project is to investigate the effect of PDC cutter geometry and optimize them. An intensive study in cutter geometry would further enhance the ROP performance. The relatively extended analysis was carried out and four significant geometry factors have been identified that directly improved the ROP. Cutter size, back rake angle, side rake angle and chamfer angle are the stated geometry factors. An appropriate optimization technique that effectively controls all influential geometry factors during cutters manufacturing is introduced and adopted in this project. By adopting L9 Taguchi OA, simulation experiment is conducted by using explicit dynamics finite element analysis. Through a structure Taguchi analysis, ANOVA confirms that the most significant geometry to improve ROP is cutter size (99.16% percentage contribution). The optimized cutter is expected to drill with high ROP that can reduce the rig time, which in its turn, may reduce the total drilling cost.

Analysis of Online Composite Mirror Descent Algorithm.

PubMed

Lei, Yunwen; Zhou, Ding-Xuan

2017-03-01

We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: see text] iterates. Our results improve the existing error analysis for the online composite mirror descent algorithm by avoiding averaging and removing boundedness assumptions, and they sharpen the existing convergence rates of the last iterate for online gradient descent without any boundedness assumptions. Our methodology mainly depends on a novel error decomposition in terms of an excess Bregman distance, refined analysis of self-bounding properties of the objective function, and the resulting one-step progress bounds.

Differential morphology and image processing.

PubMed

Maragos, P

1996-01-01

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.

Visualising Three Dimensional Damage and Failure Envelopes: Implications for True Triaxial Deformation

NASA Astrophysics Data System (ADS)

Harland, S. R.; Browning, J.; Healy, D.; Meredith, P. G.; Mitchell, T. M.

2017-12-01

Ultimate failure in brittle rocks is commonly accepted to occur as a coalescence of micro-crack damage into a single failure plane. The geometry and evolution with stress of the cracks (damage) within the medium will play a role in dictating the geometry of the ultimate failure plane. Currently, the majority of experimental studies investigating damage evolution and rock failure use conventional triaxial stress states (σ1 > σ2 = σ3). Results from these tests can easily be represented on a Mohr-Coulomb plot (σn - τ), conveniently allowing the user to determine the geometry of the resultant failure plane. In reality however, stress in the subsurface is generally truly triaxial (σ1 > σ2 > σ3) and in this case, the Mohr-Coulomb failure criterion is inadequate as it incorporates no dependence on the intermediate stress (σ2), which has been shown to play an important role in controlling failure. It has recently been shown that differential stress is the key driver in initiating crack growth, regardless of the mean stress. Polyaxial failure criteria that incorporate the effect of the intermediate stress do exist and include the Modified Lade, Modified Wiebols and Cook, and the Drucker-Prager criteria. However, unlike the Mohr-Coulomb failure criterion, these polyaxial criteria do not offer any prediction of, or insight into, the geometry of the resultant failure plane. An additional downfall of all of the common conventional and polyaxial failure criteria is that they fail to describe the geometry of the damage (i.e. pre-failure microcracking) envelope with progressive stress; it is commonly assumed that the damage envelope is parallel to the ultimate brittle failure envelope. Here we use previously published polyaxial failure data for the Shirahama sandstone and Westerley granite to illustrate that the commonly used Mohr-Coulomb and polyaxial failure criteria do not sufficiently describe or capture failure or damage envelopes under true triaxial stress states. We investigate if and how Mohr-Coulomb type constructions can provide geometrical solutions to truly-triaxial problems. We look to incorporate both the intermediate stress and the differential stress as the controlling parameters in failure and examine the geometry of damage envelopes using damage onset data.

Role of Re-entry Tears on the Dynamics of Type B Dissection Flap.

PubMed

Canchi, Saranya; Guo, Xiaomei; Phillips, Matt; Berwick, Zachary; Kratzberg, Jarin; Krieger, Joshua; Roeder, Blayne; Haulon, Stephan; Chambers, Sean; Kassab, Ghassan S

2018-01-01

Mortality during follow-up after acute Type B aortic dissection is substantial with aortic expansion observed in over 59% of the patients. Lumen pressure differential is considered a prime contributing factor for aortic dilation after propagation. The objective of the study was to evaluate the relationship between changes in vessel geometry with and without lumen pressure differential post propagation in an ex vivo porcine model with comparison with patient clinical data. A pulse duplicator system was utilized to propagate the dissection within descending thoracic porcine aortic vessels for set proximal (%circumference of the entry tear: 40%, axial length: 2 cm) and re-entry (50% of distal vessel circumference) tear geometry. Measurements of lumen pressure differential were made along with quantification of vessel geometry (n = 16). The magnitude of mean lumen pressure difference measured after propagation was low (~ 5 mmHg) with higher pressures measured in false lumen and as anticipated the pressure difference approached zero after the creation of distal re-entry tear. False lumen Dissection Ratio (FDR) defined as arc length of dissected wall divided by arc length of dissection flap, had mean value of 1.59 ± 0.01 at pressure of 120/80 mmHg post propagation with increasing values with increase in pulse pressure that was not rescued with the creation of distal re-entry tear (p < 0.01). An average FDR of 1.87 ± 0.27 was measured in patients with acute Type B dissection. Higher FDR value (FDR = 1 implies zero dissection) in the presence of distal re-entry tear demonstrates an acute change in vessel morphology in response to the dissection independent of local pressure changes challenges the re-apposition of the aortic wall.

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

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.

A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets

DTIC Science & Technology

2014-11-01

linear hybrid systems by linear algebraic methods. In SAS, volume 6337 of LNCS, pages 373–389. Springer, 2010. [19] E. W. Mayr. Membership in polynomial...383–394, 2009. [31] A. Tarski. A decision method for elementary algebra and geometry. Bull. Amer. Math. Soc., 59, 1951. [32] A. Tiwari. Abstractions...A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 November 2014 CMU

Non-smooth saddle-node bifurcations III: Strange attractors in continuous time

NASA Astrophysics Data System (ADS)

Fuhrmann, G.

2016-08-01

Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a non-smooth bifurcation. By a previous result on the occurrence of non-smooth bifurcations in forced discrete time dynamical systems, this yields that within the class of families of quasiperiodically driven differential equations, non-smooth saddle-node bifurcations occur in a set with non-empty C2-interior.

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.

Marginal deformations of heterotic G 2 sigma models

NASA Astrophysics Data System (ADS)

Fiset, Marc-Antoine; Quigley, Callum; Svanes, Eirik Eik

2018-02-01

Recently, the infinitesimal moduli space of heterotic G 2 compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST operator. This BRST operator is nilpotent if and only if the target space geometry satisfies the heterotic supersymmetry conditions. We relate this to the supergravity approach by showing that the corresponding cohomologies are indeed isomorphic. We work at tree-level in α' perturbation theory and study general geometries, in particular with non-vanishing torsion.

Gravitation. [Book on general relativity

NASA Technical Reports Server (NTRS)

Misner, C. W.; Thorne, K. S.; Wheeler, J. A.

1973-01-01

This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.

Stationary black holes and attractor mechanism

NASA Astrophysics Data System (ADS)

Astefanesei, Dumitru; Yavartanoo, Hossein

2008-05-01

We investigate the symmetries of the near horizon geometry of extremal stationary black hole in four-dimensional Einstein gravity coupled to Abelian gauge fields and neutral scalars. Careful consideration of the equations of motion and the boundary conditions at the horizon imply that the near horizon geometry has SO(2,1)×U(1) isometry. This compliments the rotating attractors proposal of hep-th/0606244 that had assumed the presence of this isometry. The extremal solutions are classified into two families differentiated by the presence or absence of an ergo-region. We also comment on the attractor mechanism of both branches.

Radiative Instabilities in Three-Dimensional Astrophysical Masers

NASA Technical Reports Server (NTRS)

Scappaticci, Gerardo A.; Watson, William D.

1995-01-01

Inherent instabilities in the radiative transfer for astrophysical masers have been recognized and calculated in the linear maser idealization in our previous investigations. The same instabilities are now shown to occur in the more realistic, three-dimensional geometries. Fluctuations in the emergent flux result and may be related to the observed fluctuations in the radiative flux from the 1665 MHz OH masers that have been reported to occur on timescales as short as 1000 s. The time-dependent differential equations of radiative transfer are solved numerically for three-dimensional astrophysical masers. Computations are performed for spherical and elongated (rectangular parallelepiped) geometries.

Zero side force volute development

NASA Technical Reports Server (NTRS)

Anderson, P. G.; Franz, R. J.; Farmer, R. C.; Chen, Y. S.

1995-01-01

Collector scrolls on high performance centrifugal pumps are currently designed with methods which are based on very approximate flowfield models. Such design practices result in some volute configurations causing excessive side loads even at design flowrates. The purpose of this study was to develop and verify computational design tools which may be used to optimize volute configurations with respect to avoiding excessive loads on the bearings. The new design methodology consisted of a volute grid generation module and a computational fluid dynamics (CFD) module to describe the volute geometry and predict the radial forces for a given flow condition, respectively. Initially, the CFD module was used to predict the impeller and the volute flowfields simultaneously; however, the required computation time was found to be excessive for parametric design studies. A second computational procedure was developed which utilized an analytical impeller flowfield model and an ordinary differential equation to describe the impeller/volute coupling obtained from the literature, Adkins & Brennen (1988). The second procedure resulted in 20 to 30 fold increase in computational speed for an analysis. The volute design analysis was validated by postulating a volute geometry, constructing a volute to this configuration, and measuring the steady radial forces over a range of flow coefficients. Excellent agreement between model predictions and observed pump operation prove the computational impeller/volute pump model to be a valuable design tool. Further applications are recommended to fully establish the benefits of this new methodology.

SABRINA: an interactive solid geometry modeling program for Monte Carlo

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

West, J.T.

SABRINA is a fully interactive three-dimensional geometry modeling program for MCNP. In SABRINA, a user interactively constructs either body geometry, or surface geometry models, and interactively debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces the effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo Analysis.

A Brief Historical Introduction to Determinants with Applications

ERIC Educational Resources Information Center

Debnath, L.

2013-01-01

This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

Budding Architects: Exploring the Designs of Pyramids and Prisms

ERIC Educational Resources Information Center

Leavy, Aisling; Hourigan, Mairéad

2015-01-01

The context of students as architects is used to examine the similarities and differences between prisms and pyramids. Leavy and Hourigan use the Van Hiele Model as a tool to support teachers to develop expectations for differentiating geometry in the classroom using practical examples.

The Geometrical Nature of the Cosmological Inflation in the Framework of the Weyl-Dirac Conformal Gravity Theory

NASA Astrophysics Data System (ADS)

De Martini, Francesco; Santamato, Enrico

2017-12-01

The nature of the scalar field responsible for the cosmological inflation, the "inflaton", is found to be rooted in the most fundamental concept of the Weyl's differential geometry: the parallel displacement of vectors in curved space-time. The Euler-Lagrange theory based on a scalar-tensor Weyl-Dirac Lagrangian leads straightforwardly to the Einstein equation admitting as a source the characteristic energy-momentum tensor of the inflaton field. Within the dynamics of the inflation, e.g. in the slow roll transition from a "false" toward a "true vacuum", the inflaton's geometry implies a temperature driven symmetry change between a highly symmetrical "Weylan" to a low symmetry "Riemannian" scenario. Since the dynamics of the Weyl curvature scalar, constructed over differentials of the inflaton field, has been found to account for the quantum phenomenology at the microscopic scale, the present work suggests interesting connections between the "micro" and the "macro" aspects of our Universe.

Extended Riemannian geometry II: local heterotic double field theory

NASA Astrophysics Data System (ADS)

Deser, Andreas; Heller, Marc Andre; Sämann, Christian

2018-04-01

We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold that captures heterotic Generalized Geometry which leads to new observations on the generalized metric and its twists. We then give a symplectic pre-N Q-manifold that captures the symmetries and the geometry of local heterotic DFT. We derive a weakened form of the section condition, which arises algebraically from consistency of the symmetry Lie 2-algebra and its action on extended tensors. We also give appropriate notions of twists — which are required for global formulations — and of the torsion and Riemann tensors. Finally, we show how the observed α'-corrections are interpreted naturally in our framework.

Vorticity Dynamics in Single and Multiple Swirling Reacting Jets

NASA Astrophysics Data System (ADS)

Smith, Travis; Aguilar, Michael; Emerson, Benjamin; Noble, David; Lieuwen, Tim

2015-11-01

This presentation describes an analysis of the unsteady flow structures in two multinozzle swirling jet configurations. This work is motivated by the problem of combustion instabilities in premixed flames, a major concern in the development of modern low NOx combustors. The objective is to compare the unsteady flow structures in these two configurations for two separate geometries and determine how certain parameters, primarily distance between jets, influence the flow dynamics. The analysis aims to differentiate between the flow dynamics of single nozzle and triple nozzle configurations. This study looks at how the vorticity in the shear layers of one reacting swirling jet can affect the dynamics of a nearby similar jet. The distance between the swirling jets is found to have an effect on the flow field in determining where swirling jets merge and on the dynamics upstream of the merging location. Graduate Student, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA.

Efficient calculation of higher-order optical waveguide dispersion.

PubMed

Mores, J A; Malheiros-Silveira, G N; Fragnito, H L; Hernández-Figueroa, H E

2010-09-13

An efficient numerical strategy to compute the higher-order dispersion parameters of optical waveguides is presented. For the first time to our knowledge, a systematic study of the errors involved in the higher-order dispersions' numerical calculation process is made, showing that the present strategy can accurately model those parameters. Such strategy combines a full-vectorial finite element modal solver and a proper finite difference differentiation algorithm. Its performance has been carefully assessed through the analysis of several key geometries. In addition, the optimization of those higher-order dispersion parameters can also be carried out by coupling to the present scheme a genetic algorithm, as shown here through the design of a photonic crystal fiber suitable for parametric amplification applications.

Flow study in the cross sectional planes of a turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Abdallah, S.; Tabakoff, W.

1977-01-01

A numerical study of the nonviscous flow characteristics in the cross-sectional planes of a radial inflow turbine scroll is presented. The velocity potential is used in the formulation to determine the flow velocity in these planes resulting from the continuous mass discharge. The effect of the through flow velocity is simulated by a continuous distribution of source/sink in the cross-section. A special iterative procedure is devised to handle the solution of the resulting Poisson's differential equation with Neumann boundary conditions in a domain with generally curved boundaries. The analysis is used to determine the effects of the radius of curvature, the location of the scroll section and its geometry on the flow characteristics in the turbine scroll.

Elastic effects on vibration of bilayer graphene sheets incorporating integrated VdWs interactions

NASA Astrophysics Data System (ADS)

Kamali, Kamran; Nazemnezhad, Reza; Zare, Mojtaba

2018-03-01

The following study addresses the free vibration analysis of a bilayer graphene sheet (BLGS) embedded in an elastic medium in the presence of shear and tensile-compressive effects of van der Waals (vdWs) interactions. To ascertain the contribution of each force, the effects are considered separately and simultaneously. To model the geometry of the BLGS, the sandwich plate theory and the Hamilton’s principle are considered to derive the governing equations of motion. The Harmonic differential quadrature method is applied to solve the coupled equations and obtain the natural frequencies and related mode shapes. The results reveal that the contribution of tensile-compressive modulus of elastic medium is the most in changing the frequency of BLGSs.

Nonlinear analysis of composite thin-walled helicopter blades

NASA Astrophysics Data System (ADS)

Kalfon, J. P.; Rand, O.

Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

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.

Theoretical analysis for the optical deformation of emulsion droplets.

PubMed

Tapp, David; Taylor, Jonathan M; Lubansky, Alex S; Bain, Colin D; Chakrabarti, Buddhapriya

2014-02-24

We propose a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and assuming isotropic surface energy at the oil-water interface, we numerically solve the resulting shape equations to elucidate the three-dimensional droplet geometry. We obtain a plethora of shapes as a function of the number of optical tweezers, their laser powers and positions, surface tension, initial droplet size and geometry. Experimentally, two-dimensional droplet silhouettes have been imaged from above, but their full side-on view has not been observed and reported for current optical configurations. This experimental limitation points to ambiguity in differentiating between droplets having the same two-dimensional projection but with disparate three-dimensional shapes. Our model elucidates and quantifies this difference for the first time. We also provide a dimensionless number that indicates the shape transformation (ellipsoidal to dumbbell) at a value ≈ 1.0, obtained by balancing interfacial tension and laser forces, substantiated using a data collapse.

Theory of Advanced Magnetic Divertors

NASA Astrophysics Data System (ADS)

Kotschenreuther, Michael; Valanju, Prashant; Mahajan, Swadesh; Covele, Brent

2013-10-01

The magnetic field structure in the SOL is the most important determinant of divertor physics. A comprehensive analytical and numerical methodology is developed to investigate SOL magnetic fields in the backdrop of two advanced divertor geometries- the X-divertor (XD) proposed and discussed in 2004, and the snowflake divertor (SFD) of 2007-2010. The analysis shows that XD and SFD represent very distinct and readily distinguishable magnetic geometries, epitomized through a differentiating metric, the Divertor Index (DI). In terms of this simple metric, the XD (DI > 1) and the SFD (DI < 1) fall on opposite sides of the standard divertor SD (DI = 1). Amongst other things, DI signifies the rate of convergence (divergence) of the flux surfaces near the divertor plate; the flux surfaces of SFD are more convergent contracting) than the SD while the XD flux surfaces are less convergent, in fact, divergent (flaring). These different SOL magnetics imply different physics, particularly with respect to detachment dynamics. It is also shown that some experiments on NSTX and DIII-D match both the prescription and the predictions of the 2004 XD paper. Work supported under US-DOE projects DE-FG02-04ER54742 and DE-FG02-04ER54754.

Theoretical Analysis for the Optical Shaping of Emulsion Droplets

NASA Astrophysics Data System (ADS)

Tapp, David; Taylor, Jonathan; Lubanksy, Alex; Bain, Colin; Chakrabarti, Buddhapriya

2014-03-01

Motivated by recent experimental observations, I discuss a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and beyond, and assuming isotropic surface energy at the oil-water interface, the resulting shape equations are numerically solved to elucidate the three-dimensional droplet geometry. A plethora of shapes as a function of the number of optical tweezers, their laser powers and positions, surface tension, initial droplet size and geometry are obtained. Experimentally, two-dimensional emulsion droplet silhouettes have been imaged from above, but their full side-on view has not been observed and reported for current optical configurations. This experimental limitation points to ambiguity in differentiating between droplets having the same two-dimensional projection but with disparate three-dimensional shapes. The model I present elucidates and quantifies this difference for the first time. Supported by funding from EPSRC via grant EP/I013377/1.

Ideal-observer analysis of lesion detectability in planar, conventional SPECT, and dedicated SPECT scintimammography using effective multi-dimensional smoothing

NASA Astrophysics Data System (ADS)

La Riviere, P. J.; Pan, X.; Penney, B. C.

1998-06-01

Scintimammography, a nuclear-medicine imaging technique that relies on the preferential uptake of Tc-99m-sestamibi and other radionuclides in breast malignancies, has the potential to provide differentiation of mammographically suspicious lesions, as well as outright detection of malignancies in women with radiographically dense breasts. In this work we use the ideal-observer framework to quantify the detectability of a 1-cm lesion using three different imaging geometries: the planar technique that is the current clinical standard, conventional single-photon emission computed tomography (SPECT), in which the scintillation cameras rotate around the entire torso, and dedicated breast SPECT, in which the cameras rotate around the breast alone. We also introduce an adaptive smoothing technique for the processing of planar images and of sinograms that exploits Fourier transforms to achieve effective multidimensional smoothing at a reasonable computational cost. For the detection of a 1-cm lesion with a clinically typical 6:1 tumor-background ratio, we find ideal-observer signal-to-noise ratios (SNR) that suggest that the dedicated breast SPECT geometry is the most effective of the three, and that the adaptive, two-dimensional smoothing technique should enhance lesion detectability in the tomographic reconstructions.

Design, Generation and Tooth Contact Analysis (TCA) of Asymmetric Face Gear Drive With Modified Geometry

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Fuentes, Alfonso; Hawkins, J. M.; Handschuh, Robert F.

2001-01-01

A new type of face gear drive for application in transmissions, particularly in helicopters, has been developed. The new geometry differs from the existing geometry by application of asymmetric profiles and double-crowned pinion of the face gear mesh. The paper describes the computerized design, simulation of meshing and contact, and stress analysis by finite element method. Special purpose computer codes have been developed to conduct the analysis. The analysis of this new type of face gear is illustrated with a numerical example.

Mesoscopic model for filament orientation in growing actin networks: the role of obstacle geometry

NASA Astrophysics Data System (ADS)

Weichsel, Julian; Schwarz, Ulrich S.

2013-03-01

Propulsion by growing actin networks is a universal mechanism used in many different biological systems, ranging from the sheet-like lamellipodium of crawling animal cells to the actin comet tails induced by certain bacteria and viruses in order to move within their host cells. Although the core molecular machinery for actin network growth is well preserved in all of these cases, the geometry of the propelled obstacle varies considerably. During recent years, filament orientation distribution has emerged as an important observable characterizing the structure and dynamical state of the growing network. Here we derive several continuum equations for the orientation distribution of filaments growing behind stiff obstacles of various shapes and validate the predicted steady state orientation patterns by stochastic computer simulations based on discrete filaments. We use an ordinary differential equation approach to demonstrate that for flat obstacles of finite size, two fundamentally different orientation patterns peaked at either ±35° or +70°/0°/ - 70° exhibit mutually exclusive stability, in agreement with earlier results for flat obstacles of very large lateral extension. We calculate and validate phase diagrams as a function of model parameters and show how this approach can be extended to obstacles with piecewise straight contours. For curved obstacles, we arrive at a partial differential equation in the continuum limit, which again is in good agreement with the computer simulations. In all cases, we can identify the same two fundamentally different orientation patterns, but only within an appropriate reference frame, which is adjusted to the local orientation of the obstacle contour. Our results suggest that two fundamentally different network architectures compete with each other in growing actin networks, irrespective of obstacle geometry, and clarify how simulated and electron tomography data have to be analyzed for non-flat obstacle geometries.

Scale relativity theory and integrative systems biology: 1. Founding principles and scale laws.

PubMed

Auffray, Charles; Nottale, Laurent

2008-05-01

In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, and discuss how scale laws of increasing complexity can be used to model and understand the behaviour of complex biological systems. In scale relativity theory, the geometry of space is considered to be continuous but non-differentiable, therefore fractal (i.e., explicitly scale-dependent). One writes the equations of motion in such a space as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the non-differentiable and fractal geometry. In this first review paper, the scale laws that describe the new dependence on resolutions of physical quantities are obtained as solutions of differential equations acting in the scale space. This leads to several possible levels of description for these laws, from the simplest scale invariant laws to generalized laws with variable fractal dimensions. Initial applications of these laws to the study of species evolution, embryogenesis and cell confinement are discussed.

Conversion of Component-Based Point Definition to VSP Model and Higher Order Meshing

NASA Technical Reports Server (NTRS)

Ordaz, Irian

2011-01-01

Vehicle Sketch Pad (VSP) has become a powerful conceptual and parametric geometry tool with numerous export capabilities for third-party analysis codes as well as robust surface meshing capabilities for computational fluid dynamics (CFD) analysis. However, a capability gap currently exists for reconstructing a fully parametric VSP model of a geometry generated by third-party software. A computer code called GEO2VSP has been developed to close this gap and to allow the integration of VSP into a closed-loop geometry design process with other third-party design tools. Furthermore, the automated CFD surface meshing capability of VSP are demonstrated for component-based point definition geometries in a conceptual analysis and design framework.

Rapid Geometry Creation for Computer-Aided Engineering Parametric Analyses: A Case Study Using ComGeom2 for Launch Abort System Design

NASA Technical Reports Server (NTRS)

Hawke, Veronica; Gage, Peter; Manning, Ted

2007-01-01

ComGeom2, a tool developed to generate Common Geometry representation for multidisciplinary analysis, has been used to create a large set of geometries for use in a design study requiring analysis by two computational codes. This paper describes the process used to generate the large number of configurations and suggests ways to further automate the process and make it more efficient for future studies. The design geometry for this study is the launch abort system of the NASA Crew Launch Vehicle.

Substrate micropatterns produced by polymer demixing regulate focal adhesions, actin anisotropy, and lineage differentiation of stem cells.

PubMed

Vega, Sebastián L; Arvind, Varun; Mishra, Prakhar; Kohn, Joachim; Sanjeeva Murthy, N; Moghe, Prabhas V

2018-06-12

Stem cells are adherent cells whose multipotency and differentiation can be regulated by numerous microenvironmental signals including soluble growth factors and surface topography. This study describes a simple method for creating distinct micropatterns via microphase separation resulting from polymer demixing of poly(desaminotyrosyl-tyrosine carbonate) (PDTEC) and polystyrene (PS). Substrates with co-continuous (ribbons) or discontinuous (islands and pits) PDTEC regions were obtained by varying the ratio of PDTEC and sacrificial PS. Human mesenchymal stem cells (MSCs) cultured on co-continuous PDTEC substrates for 3 days in bipotential adipogenic/osteogenic (AD/OS) induction medium showed no change in cell morphology but exhibited increased anisotropic cytoskeletal organization and larger focal adhesions when compared to MSCs cultured on discontinuous micropatterns. After 14 days in bipotential AD/OS induction medium, MSCs cultured on co-continuous micropatterns exhibited increased expression of osteogenic markers, whereas MSCs on discontinuous PDTEC substrates showed a low expression of adipogenic and osteogenic differentiation markers. Substrates with graded micropatterns were able to reproduce the influence of local underlying topography on MSC differentiation, thus demonstrating their potential for high throughput analysis. This work presents polymer demixing as a simple, non-lithographic technique to produce a wide range of micropatterns on surfaces with complex geometries to influence cellular and tissue regenerative responses. Gaining a better understanding of how engineered microenvironments influence stem cell differentiation is integral to increasing the use of stem cells and materials in a wide range of tissue engineering applications. In this study, we show the range of topography obtained by polymer demixing is sufficient for investigating how surface topography affects stem cell morphology and differentiation. Our findings show that co-continuous topographies favor early (3-day) cytoskeletal anisotropy and focal adhesion maturation as well as long-term (14-day) expression of osteogenic differentiation markers. Taken together, this study presents a simple approach to pattern topographies that induce divergent responses in stem cell morphology and differentiation. Copyright © 2018. Published by Elsevier Ltd.

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.

Differential forms for scientists and engineers

NASA Astrophysics Data System (ADS)

Blair Perot, J.; Zusi, Christopher J.

2014-01-01

This paper is a review of a number of mathematical concepts from differential geometry and exterior calculus that are finding increasing application in the numerical solution of partial differential equations. The objective of the paper is to introduce the scientist/ engineer to some of these ideas via a number of concrete examples in 2, 3, and 4 dimensions. The goal is not to explain these ideas with mathematical precision but to present concrete examples and enable a physical intuition of these concepts for those who are not mathematicians. The objective of this paper is to provide enough context so that scientist/engineers can interpret, implement, and understand other works which use these elegant mathematical concepts.

Optimizing solar-cell grid geometry

NASA Technical Reports Server (NTRS)

Crossley, A. P.

1969-01-01

Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs

NASA Astrophysics Data System (ADS)

Edneral, Victor

2018-02-01

This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form. Example of creating exact first integrals of motion of some planar degenerate system in a closed form is given.

Axisymmetric Liquid Hanging Drops

ERIC Educational Resources Information Center

Meister, Erich C.; Latychevskaia, Tatiana Yu

2006-01-01

The geometry of drops hanging on a circular capillary can be determined by numerically solving a dimensionless differential equation that is independent on any material properties, which enables one to follow the change of the height, surface area, and contact angle of drops hanging on a particular capillary. The results show that the application…

Direct differentiation of the quasi-incompressible fluid formulation of fluid-structure interaction using the PFEM

NASA Astrophysics Data System (ADS)

Zhu, Minjie; Scott, Michael H.

2017-07-01

Accurate and efficient response sensitivities for fluid-structure interaction (FSI) simulations are important for assessing the uncertain response of coastal and off-shore structures to hydrodynamic loading. To compute gradients efficiently via the direct differentiation method (DDM) for the fully incompressible fluid formulation, approximations of the sensitivity equations are necessary, leading to inaccuracies of the computed gradients when the geometry of the fluid mesh changes rapidly between successive time steps or the fluid viscosity is nonzero. To maintain accuracy of the sensitivity computations, a quasi-incompressible fluid is assumed for the response analysis of FSI using the particle finite element method and DDM is applied to this formulation, resulting in linearized equations for the response sensitivity that are consistent with those used to compute the response. Both the response and the response sensitivity can be solved using the same unified fractional step method. FSI simulations show that although the response using the quasi-incompressible and incompressible fluid formulations is similar, only the quasi-incompressible approach gives accurate response sensitivity for viscous, turbulent flows regardless of time step size.

Automated Slicing for a Multi-Axis Metal Deposition System (Preprint)

DTIC Science & Technology

2006-09-01

experimented with different materials like H13 tool steel to build the part. Following the same slicing and scanning toolpath result, there is a geometric...and analysis tool -centroidal axis. Similar to medial axis, it contains geometry and topological information but is significantly computationally...geometry reasoning and analysis tool -centroidal axis. Similar to medial axis, it contains geometry and topological information but is significantly

Nonlinear multimodal model for TLD of irregular tank geometry and small fluid depth

NASA Astrophysics Data System (ADS)

Love, J. S.; Tait, M. J.

2013-11-01

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. TLDs of irregular or complex tank geometry may be required in practice to avoid tank interference with fixed structural or mechanical components. The literature offers few analytical models to predict the response of this type of TLD, particularly when the fluid depth is small. In this paper, a multimodal model is developed utilizing a Boussinesq-type modal theory which is valid for small TLD fluid depths. The Bateman-Luke variational principle is employed to develop a system of coupled nonlinear ordinary differential equations which describe the fluid response when the tank is subjected to base excitation. Energy dissipation is incorporated into the model from the inclusion of damping screens. The fluid model is used to describe the response of a 2D structure-TLD system when the structure is subjected to external loading and the TLD tank geometry is irregular.

Book Review:

NASA Astrophysics Data System (ADS)

Dray, T.

2005-10-01

I have had a love/hate relationship with this book ever since it first came out. On the one hand, this is an excellent introduction for mathematicians to the differential geometry underlying general relativity. On the other hand, this is definitely a book for mathematicians. The book's greatest strength is its clear, precise presentation of the basic ideas in differential geometry, combined with equally clear and precise applications to theoretical physics, notably general relativity. But the book's precision is also its greatest weakness; this is not an easy book to read for non-mathematicians, who may not appreciate the notational complexity, some of which is nonstandard. The present edition is very similar to the original, published in 1992. In addition to minor revisions and clarifications of the material, there is now a brief introduction to fibre bundles, and a (very) brief discussion of the gauge theory description of fundamental particles. The index to the symbols used is also a more complete than in the past, but without the descriptive material present in the previous edition. The bulk of the book consists of a careful introduction to tensors and their properties. Tensors are introduced first as linear maps on vector spaces, and only later generalized to tensor fields on manifolds. The differentiation and integration of differential forms is discussed in detail, including Stokes' theorem, Lie differentiation and Hodge duality, and connections, curvature and torsion. To this point, Wasserman's text can be viewed as an expanded version of Bishop and Goldberg's classic text [1], one major difference being Wasserman's inclusion of the pseudo-Riemannian case from the beginning (in particular, when discussing Hodge duality). Whether one prefers Wasserman's approach to Bishop and Goldberg's is largely a matter of taste: Wasserman's treatment is both more complete and more precise, making it easier to check calculations in detail, but occasionally more difficult to remember what one is calculating. An instructor using this text would be well advised to think carefully about which topics to cover, rather than trying to do everything. The remainder of the book contains applications to mechanics, relativity and gauge theory. In each case, better treatments exist elsewhere. However, each such treatment typically introduces its own notation; it is not without some truth that differential geometry is often described as the study of objects under changes of notation. Having several short treatments of these different topics in one place makes it easy for the instructor to choose those he or she wishes to emphasize, while providing a clear transition to more advanced treatments. The presentation does have some idiosyncrasies. The key concept of a derivation is not clearly defined. Some subtleties are referred to in cryptic comments ('This space is too large') which are never explained. The occasionally nonstandard notation is not always easy to follow, although this is a common criticism of introductory texts in differential geometry, which must balance precision with understanding. And appropriate cross references are not always given in sentences of the form 'Recall that ...', which on occasion contained (correct) results which I did not find obvious, and which I could not quickly find explicitly stated in earlier sections. I also have one minor gripe about the publishing format, namely that the outside margins are too small, at only 1 cm; I found this extremely distracting. But all of these criticisms are minor. Wasserman's book would unquestionably be an excellent introduction to tensor analysis for mathematicians, especially those who are interested in the physics applications. The readers of Classical and Quantum Gravity will want to know whether the book is equally suitable as a text for an introductory course in general relativity. At first glance, this text appears to fill a niche in mathematical sophistication between, say, the undergraduate texts by Schutz [2] or d'Inverno [3], which do not require prior background in differential geometry, and the graduate text by Sachs [4], which does. Nonetheless, the answer, unfortunately, is no. I teach a course in general relativity primarily aimed at advanced undergraduate mathematics majors, which is, however, taken by both undergraduate and graduate students in both mathematics and physics; it is the only course in general relativity taught at my university. Each time I teach the course, I struggle to choose an appropriate text. Wasserman's book has frequently been one of the finalists, but I have never quite been willing to inflict it on my physics students, choosing instead to list it as an optional text. (I have been equally unwilling to inflict Hartle's marvellous book [5] on my mathematics students.) My main objection to this book as a relativity text is not, however, due to concern that the mathematical sophistication is too much for undergraduate physics students. Rather, as a mathematical text in relativity, it does not go far enough. The standard applications are here, but just barely. There is a good discussion of the Schwarzschild solution, including applications to solar system tests and its interpretation as a black hole. However, the Kerr solution is barely mentioned, and the Reissner-Nordström solution is conspicuously absent. Similarly, the cosmological implications of the Friedmann-Robertson-Walker solutions are discussed only briefly. And that's it - no further cosmology, no mention of gravitational waves, etc. Fair enough for a mathematics text in tensor analysis, but not enough to permit this book to be used as a standalone relativity text. This is, ultimately, why I have never used this book as a primary text: I want to spend more time doing relativity and less time proving theorems. For a course for mathematicians (only), however, or as a supplementary text filling in some of the missing mathematical details, this book would be an excellent choice. References [1] Bishop R L and Goldberg S I 1980 Tensor Analysis on Manifolds (New York: Dover) [2] Schutz B F 1985 A First Course in General Relativity (Cambridge: Cambridge University Press) [3] d'Inverno R 1991 Introducing Einstein's Relativity (Oxford: Oxford University Press) [4] Sachs R K 1977 General Relativity for Mathematicians (New York: Springer) [5] Hartle J B 2003 Gravity: An Introduction to Einstein's General Relativity (San Francisco: Addison Wesley)

Origin of the Uinta recess, Sevier fold thrust belt, Utah: influence of basin architecture on fold thrust belt geometry

NASA Astrophysics Data System (ADS)

Paulsen, Timothy; Marshak, Stephen

1999-11-01

Structural trends in the Sevier fold-thrust belt define a pronounced concave-to-the-foreland map-view curve, the Uinta recess, in north-central Utah. This recess separates two convex-to-the-foreland curves, the Provo salient on the south and the Wyoming salient on the north. The two limbs of the recess comprise transverse zones (fault zones at a high-angle to the regional trend of the orogen) that border the flanks of the east-west-trending Uinta/Cottonwood arch. Our structural analysis indicates that the transverse zones formed during the Sevier orogeny, and that they differ markedly from each other in structural style. The Charleston transverse zone (CTZ), on the south side of the arch, initiated as a complex sinistral strike-slip fault system that defines the abrupt northern boundary of the Provo salient. The Mount Raymond transverse zone (MRTZ), on the north side of the arch, represents the region in which the southeast-verging southern limb of the gently curving Wyoming salient was tilted northwards during the Laramide phase of uplift of the Uinta/Cottonwood arch. In effect, the MRTZ represents an oblique cross section through a thrust belt. The contrasting architecture of these transverse zones demonstrates how pre-deformation basin geometry influences the geometry of a fold-thrust belt. Analysis of isopach maps indicates that, at the time the Sevier fold-thrust belt formed, the area just north of the present site of the Uinta/Cottonwood arch was a basement high, with a gently dipping north flank, and a steeply dipping south flank. Thus, predeformational sediment thickened abruptly to the south of the high and thickened gradually to the north of the high. As illustrated by sandbox models, the distance that a fold-thrust belt propagates into the foreland depends on the thickness of the sedimentary layer being deformed, so the shape of the salient mimics the longitudinal cross-sectional shape of the sedimentary basin. Where basins taper gradually along strike, the thrust belt curves gently, but where basins taper abruptly along strike, the thrust belt curves so tightly that it disarticulates and becomes bounded laterally by a strike-slip accommodation zone. The geometry of the Uinta recess provides a field example of this concept. Differential movement of Sevier thrusts led to formation of gradually curving thrusts on the north side of the high, because of the gradual slope of the high's north flank, but led to the along-strike disarticulation of thrusts on the south side of the high, because of the steep slope of the high's south flank. In effect, therefore, thrust belt map-view geometry provides insight into predeformational basin geometry.

Gaussian process regression for geometry optimization

NASA Astrophysics Data System (ADS)

Denzel, Alexander; Kästner, Johannes

2018-03-01

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.

Low energy electron-impact ionization of hydrogen atom for coplanar equal-energy-sharing kinematics in Debye plasmas

NASA Astrophysics Data System (ADS)

Li, Jun; Zhang, Song Bin; Ye, Bang Jiao; Wang, Jian Guo; Janev, R. K.

2016-12-01

Low energy electron-impact ionization of hydrogen atom in Debye plasmas has been investigated by employing the exterior complex scaling method. The interactions between the charged particles in the plasma have been represented by Debye-Hückel potentials. Triple differential cross sections (TDCS) in the coplanar equal-energy-sharing geometry at an incident energy of 15.6 eV for different screening lengths are reported. As the screening strength increases, TDCS change significantly. The evolutions of dominant typical peak structures of the TDCS are studied in detail for different screening lengths and for different coplanar equal-energy-sharing geometries.

Stability and electronic spectra of C76N2 isomers

PubMed Central

Teng, Qi-wen; Wu, Shi

2005-01-01

Study of geometries of 16 possible isomers for C76N2 based on C78(C 2v) by intermediate neglect of differential overlap (INDO) series of methods indicated that the most stable geometry 25,78-C76N2 where two nitrogen atoms substitute two apexes C(25) and C(78) near the shortest X axis and Y axis formed by two hexagons and a pentagon. Electronic structures and spectra of C76N2 were investigated. The reason for the red-shift for absorptions of C76N2 compared with that of C78(C 2v) is discussed. PMID:15909352

SABRINA: an interactive three-dimensional geometry-mnodeling program for MCNP

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

West, J.T. III

SABRINA is a fully interactive three-dimensional geometry-modeling program for MCNP, a Los Alamos Monte Carlo code for neutron and photon transport. In SABRINA, a user constructs either body geometry or surface geometry models and debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo analysis. 2 refs., 33 figs.

Differential rotation in magnetic chemically peculiar stars

NASA Astrophysics Data System (ADS)

Mikulášek, Z.; Krtička, J.; Paunzen, E.; Švanda, M.; Hummerich, S.; Bernhard, K.; Jagelka, M.; Janík, J.; Henry, G. W.; Shultz, M. E.

2018-01-01

Magnetic chemically peculiar (mCP) stars constitute about 10% of upper-main-sequence stars and are characterized by strong magnetic fields and abnormal photospheric abundances of some chemical elements. Most of them exhibit strictly periodic light, magnetic, radio, and spectral variations that can be fully explained by a rigidly rotating main-sequence star with persistent surface structures and a stable global magnetic field. Long-term observations of the phase curves of these variations enable us to investigate possible surface differential rotation with unprecedented accuracy and reliability. The analysis of the phase curves in the best-observed mCP stars indicates that the location and the contrast of photometric and spectroscopic spots as well as the geometry of the magnetic field remain constant for at least many decades. The strict periodicity of mCP variables supports the concept that the outer layers of upper-main-sequence stars do not rotate differentially. However, there is a small, inhomogeneous group consisting of a few mCP stars whose rotation periods vary on timescales of decades. The period oscillations may reflect real changes in the angular velocity of outer layers of the stars which are anchored by their global magnetic fields. In CU Vir, V901 Ori, and perhaps BS Cir, the rotational period variation indicates the presence of vertical differential rotation; however, its exact nature has remained elusive until now. The incidence of mCP stars with variable rotational periods is currently investigated using a sample of fifty newly identified Kepler mCP stars.

Characterization of Relatively Large Track Geometry Variations

DOT National Transportation Integrated Search

1982-03-01

An analysis of existing track geometry data is described from which the signatures of key track geometry variations related to severe track-train dynamic interaction are identified and quantified. Mathematical representations of these signatures are ...

Design and analysis of an intelligent controller for active geometry suspension systems

NASA Astrophysics Data System (ADS)

Goodarzi, Avesta; Oloomi, Ehsan; Esmailzadeh, Ebrahim

2011-02-01

An active geometry suspension (AGS) system is a device to optimise suspension-related factors such as toe angle and roll centre height by controlling vehicle's suspension geometry. The suspension geometry could be changed through control of suspension mounting point's position. In this paper, analysis and control of an AGS system is addressed. First, the effects of suspension geometry change on roll centre height and toe angle are studied. Then, based on an analytical approach, the improvement of the vehicle's stability and handling due to the control of suspension geometry is investigated. In the next section, an eight-degree-of-freedom handling model of a sport utility vehicle equipped with an AGS system is introduced. Finally, a self-tuning proportional-integral controller has been designed, using the fuzzy control theory, to control the actuator that changes the geometry of the suspension system. The simulation results show that an AGS system can improve the handling and stability of the vehicle.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study.

PubMed

MacLean, Adam L; Harrington, Heather A; Stumpf, Michael P H; Byrne, Helen M

2016-01-01

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Analysis of SIR-B radar illumination of geometry for depth of penetration and surface feature and vegetation detection, Nevada and California

NASA Technical Reports Server (NTRS)

Taranik, J. V.; Slemmons, D. B.; Bell, E. J.; Borengasser, M.; Lugaski, T. P.; Vreeland, H.; Vreeland, P.; Kleiner, E.; Peterson, F. F.; Kleiforth, H.

1984-01-01

The measurement capability provided by the Shuttle Imaging Radar (SIR-B) was used to determine: (1) the relationships between radar illumination geometry and depth of penetration in different climatic and physiographic environments in Nevada; and, (2) the relationships between radar illumination geometry and detection and analysis of structural features in different climatic and physiographic environments in Nevada.

Students’ Errors in Geometry Viewed from Spatial Intelligence

NASA Astrophysics Data System (ADS)

Riastuti, N.; Mardiyana, M.; Pramudya, I.

2017-09-01

Geometry is one of the difficult materials because students must have ability to visualize, describe images, draw shapes, and know the kind of shapes. This study aim is to describe student error based on Newmans’ Error Analysis in solving geometry problems viewed from spatial intelligence. This research uses descriptive qualitative method by using purposive sampling technique. The datas in this research are the result of geometri material test and interview by the 8th graders of Junior High School in Indonesia. The results of this study show that in each category of spatial intelligence has a different type of error in solving the problem on the material geometry. Errors are mostly made by students with low spatial intelligence because they have deficiencies in visual abilities. Analysis of student error viewed from spatial intelligence is expected to help students do reflection in solving the problem of geometry.

An Analysis of How and Why High School Geometry Teachers Implement Dynamic Geometry Software Tasks for Student Engagement

ERIC Educational Resources Information Center

Nirode, Wayne

2012-01-01

This study examined teachers' use of student tasks involving dynamic geometry software, in which a figure is constructed then altered while maintaining its constructed properties. Although researchers, professional organizations, and policy makers generally have been proponents of dynamic geometry for instruction, there is little research about…

Transpressional folding and associated cross-fold jointing controlling the geometry of post-orogenic vein-type W-Sn mineralization: examples from Minas da Panasqueira, Portugal

NASA Astrophysics Data System (ADS)

Jacques, Dominique; Vieira, Romeu; Muchez, Philippe; Sintubin, Manuel

2018-02-01

The world-class W-Sn Panasqueira deposit consists of an extensive, subhorizontal vein swarm, peripheral to a late-orogenic greisen cupola. The vein swarm consists of hundreds of co-planar quartz veins that are overlapping and connected laterally over large distances. Various segmentation structures, a local zigzag geometry, and the occurrence of straight propagation paths indicate that they exploited a regional joint system. A detailed orientation analysis of the systematic joints reveals a geometrical relationship with the subvertical F2 fold generation, reflecting late-Variscan transpression. The joints are consistently orthogonal to the steeply plunging S0-S2 intersection lineation, both on the regional and the outcrop scale, and are thus defined as cross-fold or ac-joints. The joint system developed during the waning stages of the Variscan orogeny, when already uplifted to an upper-crustal level. Veining reactivated these cross-fold joints under the conditions of hydraulic overpressures and low differential stress. The consistent subperpendicular orientation of the veins relative to the non-cylindrical F2 hinge lines, also when having an inclined attitude, demonstrates that veining did not occur during far-field horizontal compression. Vein orientation is determined by local stress states variable on a meter-scale but with the minimum principal stress consistently subparallel to fold hinge lines. The conspicuous subhorizontal attitude of the Panasqueira vein swarm is thus dictated by the geometry of late-orogenic folds, which developed synchronous with oroclinal buckling of the Ibero-Armorican arc.

Axial-type olivine crystallographic preferred orientations: The effect of strain geometry on mantle texture

NASA Astrophysics Data System (ADS)

Chatzaras, Vasileios; Kruckenberg, Seth C.; Cohen, Shaina M.; Medaris, L. Gordon; Withers, Anthony C.; Bagley, Brian

2016-07-01

The effect of finite strain geometry on crystallographic preferred orientation (CPO) is poorly constrained in the upper mantle. Specifically, the relationship between shape preferred orientation (SPO) and CPO in mantle rocks remains unclear. We analyzed a suite of 40 spinel peridotite xenoliths from Marie Byrd Land, West Antarctica. X-ray computed tomography allows for quantification of spinel SPO, which ranges from prolate to oblate shape. Electron backscatter diffraction analysis reveals a range of olivine CPO patterns, including A-type, axial-[010], axial-[100], and B-type patterns. Until now, these CPO types were associated with different deformation conditions, deformation mechanisms, or strain magnitudes. Microstructures and deformation mechanism maps suggest that deformation in all studied xenoliths is dominated by dislocation-accommodated grain boundary sliding. For the range of temperatures (780-1200°C), extraction depths (39-72 km), differential stresses (2-60 MPa), and water content (up to 500 H/106Si) of the xenolith suite, variations in olivine CPO do not correlate with changes in deformation conditions. Here we establish for the first time in naturally deformed mantle rocks that finite strain geometry controls the development of axial-type olivine CPOs; axial-[010] and axial-[100] CPOs form in relation to oblate and prolate fabric ellipsoids, respectively. Girdling of olivine crystal axes results from intracrystalline slip with activation of multiple slip systems and grain boundary sliding. Our results demonstrate that mantle deformation may deviate from simple shear. Olivine texture in field studies and seismic anisotropy in geophysical investigations can provide critical constraints for the 3-D strain in the upper mantle.

Aircraft navigation and surveillance analysis for a spherical earth

DOT National Transportation Integrated Search

2014-10-01

This memorandum addresses a fundamental function in surveillance and navigation analysis : quantifying the geometry of two or more locations relative to each other and to a spherical earth. Here, geometry refers to: (a) points (idealized lo...

CAPRI (Computational Analysis PRogramming Interface): A Solid Modeling Based Infra-Structure for Engineering Analysis and Design Simulations

NASA Technical Reports Server (NTRS)

Haimes, Robert; Follen, Gregory J.

1998-01-01

CAPRI is a CAD-vendor neutral application programming interface designed for the construction of analysis and design systems. By allowing access to the geometry from within all modules (grid generators, solvers and post-processors) such tasks as meshing on the actual surfaces, node enrichment by solvers and defining which mesh faces are boundaries (for the solver and visualization system) become simpler. The overall reliance on file 'standards' is minimized. This 'Geometry Centric' approach makes multi-physics (multi-disciplinary) analysis codes much easier to build. By using the shared (coupled) surface as the foundation, CAPRI provides a single call to interpolate grid-node based data from the surface discretization in one volume to another. Finally, design systems are possible where the results can be brought back into the CAD system (and therefore manufactured) because all geometry construction and modification are performed using the CAD system's geometry kernel.

Low-Frequency Microinstabilities in Rotating Tokamak Plasmas.

NASA Astrophysics Data System (ADS)

Artun, Mehmet

1994-01-01

Low-frequency drift-type microinstabilities have often been suggested as the leading candidates to account for the anomalously large transport; observed in tokamak plasmas. The effects of sheared equilibrium flows on this important class of instabilities is systematically investigated in the present thesis. In particular, the analysis is carried out in two parts. In order to gain some insight into the key elements of this problem, the first part deals with the stability properties of the kinetic ion temperature gradient mode under the influence of parallel and perpendicular shear flows in a simplified sheared magnetic slab geometry. The eigenmode analysis is performed using a shooting code for long-wavelength modes (k_|rho _{i} << 1), and an integral eigenmode code for short-wavelength modes (k_ |rho_{i} ~ 1). Numerical results are cross-checked with analytical estimates in the fluid regime. While the differential analysis is mostly limited to ground state modes of the system--due to the requirement that the average perpendicular wavenumber be small--the integral eigenmode code has been used to calculate higher radial eigenmodes with confidence. New features observed through the introduction of shear flows are discussed. In the second part we present the shear flow generalization of the nonlinear electromagnetic gyrokinetic equation for realistic toroidal geometry. In accordance with the most natural choice for such studies, the coordinate frame is chosen to be shifted in velocity space and unchanged in configuration space. The natural equilibrium constraints of the toroidal problem limits the choice of the flow profile to that in which the angular velocity is a function of the flux surface. The general form of the gyrokinetic equation obtained is then used to derive the two-dimensional linear electrostatic eigenmode equation in circular toroidal geometry including trapped particle effects. In addition to magnetic trapping, electrostatic and centrifugal trapping are also found to play an important role here. A modified version of a finite element code is utilized to analyze shear flow effects on the trapped ion mode (TIM) in the long wavelength limit. Numerical results for fully coupled as well as single poloidal harmonic cases are presented. Implications of the results obtained in the present investigation are discussed and suggestions are given for future studies.

Steps Forward and Back in Adult Numeracy Teacher Professional Development: A Reflection on a Teacher Workshop Experience

ERIC Educational Resources Information Center

Saliga, Linda Marie; Daviso, Al; Stuart, Denise; Pachnowski, Lynne

2015-01-01

In this project, a university team of teacher education and mathematics professors conducted eight professional development sessions for General Educational Development (GED) teachers in the area of mathematics teaching. Topics included concretely modeling mathematics concepts in algebra, number sense, geometry, and differentiating instruction in…

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.

Modelling the Landing of a Plane in a Calculus Lab

ERIC Educational Resources Information Center

Morante, Antonio; Vallejo, Jose A.

2012-01-01

We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)

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.

Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric realization |NC|. Equivalence classes of principal bundles with structure group |NC| are shown to be one-to-one with stable equivalence classes of what we call crossed module gerbes bundle gerbes. We can also associate to a crossed module a 2-category C'. Then there are two equivalent ways how to view classifying spaces of NC-bundles and hence of |NC|-bundles and crossed module bundle gerbes. We can either apply the W-construction to NC or take the nerve of the 2-category C'. We discuss the string group and string structures from this point of view. Also a simplicial principal bundle can be equipped with a simplicial connection and a B-field. It is shown how in the case of a simplicial principal NC-bundle these simplicial objects give the bundle gerbe connection and the bundle gerbe B-field.

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.

ISCE: A Modular, Reusable Library for Scalable SAR/InSAR Processing

NASA Astrophysics Data System (ADS)

Agram, P. S.; Lavalle, M.; Gurrola, E. M.; Sacco, G. F.; Rosen, P. A.

2016-12-01

Traditional community SAR/InSAR processing software tools have primarily focused on differential interferometry and Solid Earth applications. The InSAR Scientific Computing Environment (ISCE) was specifically designed to support the Earth Sciences user community as well as large scale operational processing tasks, thanks to its two-layered (Python+C/Fortran) architecture and modular framework. ISCE is freely distributed as a source tarball, allowing advanced users to modify and extend it for their research purposes and developing exploratory applications, while providing a relatively simple user interface for novice users to perform routine data analysis efficiently. Modular design of the ISCE library also enables easier development of applications to address the needs of Ecosystems, Cryosphere and Disaster Response communities in addition to the traditional Solid Earth applications. In this talk, we would like to emphasize the broader purview of the ISCE library and some of its unique features that sets it apart from other freely available community software like GMTSAR and DORIS, including: Support for multiple geometry regimes - Native Doppler (ALOS-1) as well Zero Doppler (ESA missions) systems. Support for data acquired by airborne platforms - e.g, JPL's UAVSAR and AirMOSS, DLR's F-SAR. Radiometric Terrain Correction - Auxiliary output layers from the geometry modules include projection angles, incidence angles, shadow-layover masks. Dense pixel offsets - Parallelized amplitude cross correlation for cryosphere / ionospheric correction applications. Rubber sheeting - Pixel-by-pixel offsets fields for resampling slave imagery for geometric co-registration/ ionospheric corrections. Preliminary Tandem-X processing support - Bistatic geometry modules. Extensibility to support other non-Solid Earth missions - Modules can be directly adopted for use with other SAR missions, e.g., SWOT. Preliminary support for multi-dimensional data products- multi-polarization, multi-frequency, multi-temporal, multi-baseline stacks via the PLANT and GIAnT toolboxes. Rapid prototyping - Geometry manipulation functionality at the python level allows users to prototype and test processing modules at the interpreter level before optimal implementation in C/C++/Fortran.

Comparison of Slab and Cylinder Expansion Test Geometries for PBX 9501

NASA Astrophysics Data System (ADS)

Jackson, Scott; Anderson, Eric; Aslam, Tariq; Whitley, Von

2017-06-01

The slab expansion test or ``sandwich test'' is the two-dimensional analog of the axisymmetric cylinder expansion test. The test consists of a high-aspect-ratio rectangular cuboid of high explosive with the two large sides confined by a thin metal confiner. Analysis of the confiner motion after the passage of the detonation yields the detonation product isentrope, which is a specialized form of the product equation of state. The slab expansion geometry inherently exhibits a lower product expansion rate and lower plastic work on the confiner than the cylinder expansion geometry. The slab geometry does, however, have a shorter test time. We review recent slab and cylinder expansion data with PBX 9501, the associated equation of state analysis, and the advantages of each geometry for different applications.

Mathematical support for automated geometry analysis of lathe machining of oblique peakless round-nose tools

NASA Astrophysics Data System (ADS)

Filippov, A. V.; Tarasov, S. Yu; Podgornyh, O. A.; Shamarin, N. N.; Filippova, E. O.

2017-01-01

Automatization of engineering processes requires developing relevant mathematical support and a computer software. Analysis of metal cutting kinematics and tool geometry is a necessary key task at the preproduction stage. This paper is focused on developing a procedure for determining the geometry of oblique peakless round-nose tool lathe machining with the use of vector/matrix transformations. Such an approach allows integration into modern mathematical software packages in distinction to the traditional analytic description. Such an advantage is very promising for developing automated control of the preproduction process. A kinematic criterion for the applicable tool geometry has been developed from the results of this study. The effect of tool blade inclination and curvature on the geometry-dependent process parameters was evaluated.

Differential geometry based model for eddy current inspection of U-bend sections in steam generator tubes

NASA Astrophysics Data System (ADS)

Mukherjee, Saptarshi; Rosell, Anders; Udpa, Lalita; Udpa, Satish; Tamburrino, Antonello

2017-02-01

The modeling of U-Bend segment in steam generator tubes for predicting eddy current probe signals from cracks, wear and pitting in this region poses challenges and is non-trivial. Meshing the geometry in the cartesian coordinate system might require a large number of elements to model the U-bend region. Also, since the lift-off distance between the probe and tube wall is usually very small, a very fine mesh is required near the probe region to accurately describe the eddy current field. This paper presents a U-bend model using differential geometry principles that exploit the result that Maxwell's equations are covariant with respect to changes of coordinates and independent of metrics. The equations remain unaltered in their form, regardless of the choice of the coordinates system, provided the field quantities are represented in the proper covariant and contravariant form. The complex shapes are mapped into simple straight sections, while small lift-off is mapped to larger values, thus reducing the intrinsic dimension of the mesh and stiffness matrix. In this contribution, the numerical implementation of the above approach will be discussed with regard to field and current distributions within the U-bend tube wall. For the sake of simplicity, a two dimensional test case will be considered. The approach is evaluated in terms of efficiency and accuracy by comparing the results with that obtained using a conventional FE model in cartesian coordinates.

Understanding Gas Phase Modifier Interactions in Rapid Analysis by Differential Mobility-Tandem Mass Spectrometry

NASA Astrophysics Data System (ADS)

Kafle, Amol; Coy, Stephen L.; Wong, Bryan M.; Fornace, Albert J.; Glick, James J.; Vouros, Paul

2014-07-01

A systematic study involving the use and optimization of gas-phase modifiers in quantitative differential mobility-mass spectrometry (DMS-MS) analysis is presented using nucleoside-adduct biomarkers of DNA damage as an important reference point for analysis in complex matrices. Commonly used polar protic and polar aprotic modifiers have been screened for use against two deoxyguanosine adducts of DNA: N-(deoxyguanosin-8-yl)-4-aminobiphenyl (dG-C8-4-ABP) and N-(deoxyguanosin-8-y1)-2-amino-l-methyl-6-phenylimidazo[4,5-b]pyridine (dG-C8-PhIP). Particular attention was paid to compensation voltage (CoV) shifts, peak shapes, and product ion signal intensities while optimizing the DMS-MS conditions. The optimized parameters were then applied to rapid quantitation of the DNA adducts in calf thymus DNA. After a protein precipitation step, adduct levels corresponding to less than one modification in 106 normal DNA bases were detected using the DMS-MS platform. Based on DMS fundamentals and ab initio thermochemical results, we interpret the complexity of DMS modifier responses in terms of thermal activation and the development of solvent shells. At very high bulk gas temperature, modifier dipole moment may be the most important factor in cluster formation and cluster geometry, but at lower temperatures, multi-neutral clusters are important and less predictable. This work provides a useful protocol for targeted DNA adduct quantitation and a basis for future work on DMS modifier effects.

Understanding gas phase modifier interactions in rapid analysis by Differential Mobility-Tandem Mass Spectrometry

PubMed Central

Kafle, Amol; Coy, Stephen L.; Wong, Bryan M.; Fornace, Albert J.; Glick, James J.; Vouros, Paul

2014-01-01

A systematic study involving the use and optimization of gas phase modifiers in quantitative differential mobility- mass spectrometry (DMS-MS) analysis is presented using mucleoside-adduct biomarkers of DNA damage as an important reference point for analysis in complex matrices. Commonly used polar protic and polar aprotic modifiers have been screened for use against two deoxyguanosine adducts of DNA: N-(deoxyguanosin-8-yl)-4-aminobiphenyl (dG-C8-4-ABP) and N-(deoxyguanosin-8-y1)-2-amino-l-methyl-6-phenylimidazo[4,5-b]pyridine (dG-C8-PhIP). Particular attention was paid to compensation voltage (CoV) shifts, peak shapes and product ion signal intensities while optimizing the DMS-MS conditions. The optimized parameters were then applied to rapid quantitation of the DNA adducts in calf thymus DNA. After a protein precipitation step, adduct levels corresponding to less than one modification in 106 normal DNA bases were detected using the DMS-MS platform. Based on DMS fundamentals and ab-initio thermochemical results we interpret the complexity of DMS modifier responses in terms of thermal activation and the development of solvent shells. At very high bulk gas temperature, modifier dipole moment may be the most important factor in cluster formation and cluster geometry in mobility differences, but at lower temperatures multi-neutral clusters are important and less predictable. This work provides a useful protocol for targeted DNA adduct quantitation and a basis for future work on DMS modifier effects. PMID:24452298

The Role of Dynamic Geometry Software in High School Geometry Curricula: An Analysis of Proof Tasks

ERIC Educational Resources Information Center

Oner, Diler

2009-01-01

In this study, I examine the role of dynamic geometry software (DGS) in curricular proof tasks. I investigated seven US high school geometry textbooks that were categorised into three groups: technology-intensive, standards-based, and traditional curricula. I looked at the frequency and purpose of DGS use in these textbooks. In addition, I…

A modular approach to large-scale design optimization of aerospace systems

NASA Astrophysics Data System (ADS)

Hwang, John T.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.

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.

Hover performance tests of full scale variable geometry rotors

NASA Technical Reports Server (NTRS)

Rorke, J. B.

1976-01-01

Full scale whirl tests were conducted to determine the effects of interblade spatial relationships and pitch variations on the hover performance and acoustic signature of a 6-blade main rotor system. The variable geometry rotor (VGR) variations from the conventional baseline were accomplished by: (1) shifting the axial position of alternate blades by one chord-length to form two tip path planes; and (2) varying the relative azimuthal spacing from the upper rotor to the lagging hover rotor in four increments from 25.2 degrees to 62.1 degrees. For each of these four configurations, the differential collective pitch between upper and lower rotors was set at + or - 1 deg, 0 deg and -1 deg. Hover performance data for all configurations were acquired at blade tip Mach numbers of 0.523 and 0.45. Acoustic data were recorded at all test conditions, but analyzed only at 0 deg differential pitch at the higher rotor speed. The VGR configurations tested demonstrated improvements in thrust at constant power as high as 6 percent. Reductions of 3 PNdb in perceived noise level and of 4 db in blade passage frequency noise level were achieved at the higher thrust levels. Consistent correlation exists between performance and acoustic improvements. For any given azimuth spacing, performance was consistently better for the differential pitch condition of + or - 1 degree, i.e. with the upper rotor pitch one degree higher than the lower rotor.

Engine structures analysis software: Component Specific Modeling (COSMO)

NASA Astrophysics Data System (ADS)

McKnight, R. L.; Maffeo, R. J.; Schwartz, S.

1994-08-01

A component specific modeling software program has been developed for propulsion systems. This expert program is capable of formulating the component geometry as finite element meshes for structural analysis which, in the future, can be spun off as NURB geometry for manufacturing. COSMO currently has geometry recipes for combustors, turbine blades, vanes, and disks. Component geometry recipes for nozzles, inlets, frames, shafts, and ducts are being added. COSMO uses component recipes that work through neutral files with the Technology Benefit Estimator (T/BEST) program which provides the necessary base parameters and loadings. This report contains the users manual for combustors, turbine blades, vanes, and disks.

Engine Structures Analysis Software: Component Specific Modeling (COSMO)

NASA Technical Reports Server (NTRS)

Mcknight, R. L.; Maffeo, R. J.; Schwartz, S.

1994-01-01

A component specific modeling software program has been developed for propulsion systems. This expert program is capable of formulating the component geometry as finite element meshes for structural analysis which, in the future, can be spun off as NURB geometry for manufacturing. COSMO currently has geometry recipes for combustors, turbine blades, vanes, and disks. Component geometry recipes for nozzles, inlets, frames, shafts, and ducts are being added. COSMO uses component recipes that work through neutral files with the Technology Benefit Estimator (T/BEST) program which provides the necessary base parameters and loadings. This report contains the users manual for combustors, turbine blades, vanes, and disks.

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

Accessible bioprinting: adaptation of a low-cost 3D-printer for precise cell placement and stem cell differentiation.

PubMed

Reid, John A; Mollica, Peter A; Johnson, Garett D; Ogle, Roy C; Bruno, Robert D; Sachs, Patrick C

2016-06-07

The precision and repeatability offered by computer-aided design and computer-numerically controlled techniques in biofabrication processes is quickly becoming an industry standard. However, many hurdles still exist before these techniques can be used in research laboratories for cellular and molecular biology applications. Extrusion-based bioprinting systems have been characterized by high development costs, injector clogging, difficulty achieving small cell number deposits, decreased cell viability, and altered cell function post-printing. To circumvent the high-price barrier to entry of conventional bioprinters, we designed and 3D printed components for the adaptation of an inexpensive 'off-the-shelf' commercially available 3D printer. We also demonstrate via goal based computer simulations that the needle geometries of conventional commercially standardized, 'luer-lock' syringe-needle systems cause many of the issues plaguing conventional bioprinters. To address these performance limitations we optimized flow within several microneedle geometries, which revealed a short tapered injector design with minimal cylindrical needle length was ideal to minimize cell strain and accretion. We then experimentally quantified these geometries using pulled glass microcapillary pipettes and our modified, low-cost 3D printer. This systems performance validated our models exhibiting: reduced clogging, single cell print resolution, and maintenance of cell viability without the use of a sacrificial vehicle. Using this system we show the successful printing of human induced pluripotent stem cells (hiPSCs) into Geltrex and note their retention of a pluripotent state 7 d post printing. We also show embryoid body differentiation of hiPSC by injection into differentiation conducive environments, wherein we observed continuous growth, emergence of various evaginations, and post-printing gene expression indicative of the presence of all three germ layers. These data demonstrate an accessible open-source 3D bioprinter capable of serving the needs of any laboratory interested in 3D cellular interactions and tissue engineering.

A Study of Geometry Content Knowledge of Elementary Preservice Teachers

ERIC Educational Resources Information Center

Aslan-Tutak, Fatma; Adams, Thomasenia Lott

2015-01-01

The purpose of this research is to examine preservice elementary school teachers' geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as…

Reconstruction of normal forms by learning informed observation geometries from data.

PubMed

Yair, Or; Talmon, Ronen; Coifman, Ronald R; Kevrekidis, Ioannis G

2017-09-19

The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an "intrinsic" prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant "normal forms": a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.

Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

NASA Technical Reports Server (NTRS)

Chen, S. C.; Schwab, J. R.

1988-01-01

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.

On the Monge-Ampere equivalent of the sine-Gordon equation

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Nutku, Y.

1994-12-01

Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.

Maximum range of a projectile launched from a height h: a non-calculus treatment

NASA Astrophysics Data System (ADS)

Ganci, S.; Lagomarsino, D.

2014-07-01

The classical example of problem solving, maximizing the range of a projectile launched from height h with velocity v over the ground level, has received various solutions. In some of these, one can find the maximization of the range R by differentiating R as a function of an independent variable or through the implicit differentiation in Cartesian or polar coordinates. In other papers, various elegant non-calculus solutions can be found. In this paper, this problem is revisited on the basis of the elementary analytical geometry and the trigonometry only.

Geometry of the perceptual space

NASA Astrophysics Data System (ADS)

Assadi, Amir H.; Palmer, Stephen; Eghbalnia, Hamid; Carew, John

1999-09-01

The concept of space and geometry varies across the subjects. Following Poincare, we consider the construction of the perceptual space as a continuum equipped with a notion of magnitude. The study of the relationships of objects in the perceptual space gives rise to what we may call perceptual geometry. Computational modeling of objects and investigation of their deeper perceptual geometrical properties (beyond qualitative arguments) require a mathematical representation of the perceptual space. Within the realm of such a mathematical/computational representation, visual perception can be studied as in the well-understood logic-based geometry. This, however, does not mean that one could reduce all problems of visual perception to their geometric counterparts. Rather, visual perception as reported by a human observer, has a subjective factor that could be analytically quantified only through statistical reasoning and in the course of repetitive experiments. Thus, the desire to experimentally verify the statements in perceptual geometry leads to an additional probabilistic structure imposed on the perceptual space, whose amplitudes are measured through intervention by human observers. We propose a model for the perceptual space and the case of perception of textured surfaces as a starting point for object recognition. To rigorously present these ideas and propose computational simulations for testing the theory, we present the model of the perceptual geometry of surfaces through an amplification of theory of Riemannian foliation in differential topology, augmented by statistical learning theory. When we refer to the perceptual geometry of a human observer, the theory takes into account the Bayesian formulation of the prior state of the knowledge of the observer and Hebbian learning. We use a Parallel Distributed Connectionist paradigm for computational modeling and experimental verification of our theory.

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethylcyclopropene II. 3,3-Dimethyl-1,2-bis(trimethylsilyl)cyclopropene

NASA Astrophysics Data System (ADS)

Panchenko, Yu. N.; De Maré, G. R.; Abramenkov, A. V.; Baird, M. S.; Tverezovsky, V. V.; Nizovtsev, A. V.; Bolesov, I. G.

2003-07-01

The IR and Raman spectra of 3,3-dimethyl-1,2-bis(trimethylsilyl)cyclopropene (I) (synthesised using standard procedures) were measured in the liquid phase. Total geometry optimisation was performed at the HF/6-31G* level. The HF/6-31G*//HF/6-31G* quantum mechanical force field (QMFF) was calculated and used to determine the theoretical fundamental vibrational frequencies, their predicted IR intensities, Raman activities, and Raman depolarisation ratios. Using Pulay's scaling method and the theoretical molecular geometry, the QMFF of I was scaled by a set of scaling factors used previously for 3,3-dimethyl-1,2-bis(tert-butyl)cyclopropene (17 scale factors for a 105-dimensional problem). The scaled QMFF obtained was used to solve the vibrational problem. The quantum mechanical values of the Raman activities were converted to differential Raman cross sections. The figures for the experimental and theoretical Raman and IR spectra are presented. Assignments of the experimental vibrational spectra of I are given. They take into account the calculated potential energy distribution and the correlation between the estimations of the experimental IR and Raman intensities and Raman depolarisation ratios and the corresponding theoretical values (including Raman cross sections) calculated using the unscaled QMFF.

Late Oligocene to present contractional structure in and around the Susitna basin, Alaska—Geophysical evidence and geological implications

USGS Publications Warehouse

Saltus, Richard W.; Stanley, Richard G.; Haeussler, Peter J.; Jones, James V.; Potter, Christopher J.; Lewis, Kristen A.

2016-01-01

The Cenozoic Susitna basin lies within an enigmatic lowland surrounded by the Central Alaska Range, Western Alaska Range (including the Tordrillo Mountains), and Talkeetna Mountains in south-central Alaska. Some previous interpretations show normal faults as the defining structures of the basin (e.g., Kirschner, 1994). However, analysis of new and existing geophysical data shows predominantly (Late Oligocene to present) thrust and reverse fault geometries in the region, as previously proposed by Hackett (1978). A key example is the Beluga Mountain fault where a 50-mGal gravity gradient, caused by the density transition from the igneous bedrock of Beluga Mountain to the >4-km-thick Cenozoic sedimentary section of Susitna basin, spans a horizontal distance of ∼40 km and straddles the topographic front. The location and shape of the gravity gradient preclude a normal fault geometry; instead, it is best explained by a southwest-dipping thrust fault, with its leading edge located several kilometers to the northeast of the mountain front, concealed beneath the shallow glacial and fluvial cover deposits. Similar contractional fault relationships are observed for other basin-bounding and regional faults as well. Contractional structures are consistent with a regional shortening strain field inferred from differential offsets on the Denali and Castle Mountain right-lateral strike-slip fault systems.

Project Integration Architecture (PIA) and Computational Analysis Programming Interface (CAPRI) for Accessing Geometry Data from CAD Files

NASA Technical Reports Server (NTRS)

Benyo, Theresa L.

2002-01-01

Integration of a supersonic inlet simulation with a computer aided design (CAD) system is demonstrated. The integration is performed using the Project Integration Architecture (PIA). PIA provides a common environment for wrapping many types of applications. Accessing geometry data from CAD files is accomplished by incorporating appropriate function calls from the Computational Analysis Programming Interface (CAPRI). CAPRI is a CAD vendor neutral programming interface that aids in acquiring geometry data directly from CAD files. The benefits of wrapping a supersonic inlet simulation into PIA using CAPRI are; direct access of geometry data, accurate capture of geometry data, automatic conversion of data units, CAD vendor neutral operation, and on-line interactive history capture. This paper describes the PIA and the CAPRI wrapper and details the supersonic inlet simulation demonstration.

Mission Analysis and Orbit Control of Interferometric Wheel Formation Flying

NASA Astrophysics Data System (ADS)

Fourcade, J.

Flying satellite in formation requires maintaining the specific relative geometry of the spacecraft with high precision. This requirement raises new problem of orbit control. This paper presents the results of the mission analysis of a low Earth observation system, the interferometric wheel, patented by CNES. This wheel is made up of three receiving spacecraft, which follow an emitting Earth observation radar satellite. The first part of this paper presents trades off which were performed to choose orbital elements of the formation flying which fulfils all constraints. The second part presents orbit positioning strategies including reconfiguration of the wheel to change its size. The last part describes the station keeping of the formation. Two kinds of constraints are imposed by the interferometric system : a constraint on the distance between the wheel and the radar satellite, and constraints on the distance between the wheel satellites. The first constraint is fulfilled with a classical chemical station keeping strategy. The second one is fulfilled using pure passive actuators. Due to the high stability of the relative eccentricity of the formation, only the relative semi major axis had to be controlled. Differential drag due to differential attitude motion was used to control relative altitude. An autonomous orbit controller was developed and tested. The final accuracy is a relative station keeping better than few meters for a wheel size of one kilometer.

ACCELERATING FUSION REACTOR NEUTRONICS MODELING BY AUTOMATIC COUPLING OF HYBRID MONTE CARLO/DETERMINISTIC TRANSPORT ON CAD GEOMETRY

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

Biondo, Elliott D; Ibrahim, Ahmad M; Mosher, Scott W

2015-01-01

Detailed radiation transport calculations are necessary for many aspects of the design of fusion energy systems (FES) such as ensuring occupational safety, assessing the activation of system components for waste disposal, and maintaining cryogenic temperatures within superconducting magnets. Hybrid Monte Carlo (MC)/deterministic techniques are necessary for this analysis because FES are large, heavily shielded, and contain streaming paths that can only be resolved with MC. The tremendous complexity of FES necessitates the use of CAD geometry for design and analysis. Previous ITER analysis has required the translation of CAD geometry to MCNP5 form in order to use the AutomateD VAriaNcemore » reducTion Generator (ADVANTG) for hybrid MC/deterministic transport. In this work, ADVANTG was modified to support CAD geometry, allowing hybrid (MC)/deterministic transport to be done automatically and eliminating the need for this translation step. This was done by adding a new ray tracing routine to ADVANTG for CAD geometries using the Direct Accelerated Geometry Monte Carlo (DAGMC) software library. This new capability is demonstrated with a prompt dose rate calculation for an ITER computational benchmark problem using both the Consistent Adjoint Driven Importance Sampling (CADIS) method an the Forward Weighted (FW)-CADIS method. The variance reduction parameters produced by ADVANTG are shown to be the same using CAD geometry and standard MCNP5 geometry. Significant speedups were observed for both neutrons (as high as a factor of 7.1) and photons (as high as a factor of 59.6).« less

Special geometries associated to quaternion-Kähler 8-manifolds

NASA Astrophysics Data System (ADS)

Gambioli, A.; Nagatomo, Y.; Salamon, S.

2015-05-01

We develop a calculus of differential forms on a quaternion-Kähler manifold M4n admitting an isometric circle action. This is used to study three fundamental examples of such actions on the quaternionic projective plane and the construction of G2 and half-flat structures on quotients of M8 and its hypersurfaces.

Navy Prototype Optical Interferometer Imaging of Line Emission Regions of Beta Lyrae Using Differential Phase Referencing

DTIC Science & Technology

2009-02-01

is polarized by a structure perpendicular to this direction. Another result that confirms this geometry is a radio nebula along p.a. 156◦ ± 4...2000) detected a jetlike nebular structure oriented along p.a. = 156◦.5 ± 4◦. This nebula is perpendicular, within uncertainties, to the orbit

Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Cantini, Luigi; Jurčo, Branislav

2005-03-01

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of Yang-Mills theories with 2-form gauge potential.

Examining Gender DIF on a Multiple-Choice Test of Mathematics: A Confirmatory Approach.

ERIC Educational Resources Information Center

Ryan, Katherine E.; Fan, Meichu

1996-01-01

Results for 3,244 female and 3,033 male junior high school students from the Second International Mathematics Study show that applied items in algebra, geometry, and computation were easier for males but arithmetic items were differentially easier for females. Implications of these findings for assessment and instruction are discussed. (SLD)

Roller Coasters without Differential Equations--A Newtonian Approach to Constrained Motion

ERIC Educational Resources Information Center

Muller, Rainer

2010-01-01

Within the context of Newton's equation, we present a simple approach to the constrained motion of a body forced to move along a specified trajectory. Because the formalism uses a local frame of reference, it is simpler than other methods, making more complicated geometries accessible. No Lagrangian multipliers are necessary to determine the…

Techniques of Differentiation and Integration, Mathematics (Experimental): 5297.27.

ERIC Educational Resources Information Center

Forrester, Gary B.

This guidebook on minimum course content was designed for students who have mastered the skills and concepts of analytic geometry. It is a short course in the basic techniques of calculus recommended for the student who has need of these skills in other courses such as beginning physics, economics or statistics. The course does not intend to teach…

Douglas Butler Uses Autograph to Explore the Geometry of Calculus

ERIC Educational Resources Information Center

Butler, Douglas

2012-01-01

In short, this is a "master class". The learning and teaching of mathematics can be revolutionised with the creative use of dynamic software is an oft quoted mantra. Here, this mantra is exemplified through the documented experiences of using Autograph to enliven, to extend, and to foster the understanding of differentiation and integration. The…

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

The Total In-Flight Simulator (TIFS) aerodynamics and systems: Description and analysis. [maneuver control and gust alleviators

NASA Technical Reports Server (NTRS)

Andrisani, D., II; Daughaday, H.; Dittenhauser, J.; Rynaski, E.

1978-01-01

The aerodynamics, control system, instrumentation complement and recording system of the USAF Total In/Flight Simulator (TIFS) airplane are described. A control system that would allow the ailerons to be operated collectively, as well as, differentially to entrance the ability of the vehicle to perform the dual function of maneuver load control and gust alleviation is emphasized. Mathematical prediction of the rigid body and the flexible equations of longitudinal motion using the level 2.01 FLEXSTAB program are included along with a definition of the vehicle geometry, the mass and stiffness distribution, the calculated mode frequencies and mode shapes, and the resulting aerodynamic equations of motion of the flexible vehicle. A complete description of the control and instrumentation system of the aircraft is presented, including analysis, ground test and flight data comparisons of the performance and bandwidth of the aerodynamic surface servos. Proposed modification for improved performance of the servos are also presented.

A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta.

PubMed

Liang, Liang; Liu, Minliang; Martin, Caitlin; Sun, Wei

2018-05-09

Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs. Copyright © 2018 John Wiley & Sons, Ltd.

Injector Element which Maintains a Constant Mean Spray Angle and Optimum Pressure Drop During Throttling by Varying the Geometry of Tangential Inlets

NASA Technical Reports Server (NTRS)

Trinh, Huu P. (Inventor); Myers, William Neill (Inventor)

2014-01-01

A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The tangential inlet area for each throttleable stage is calculated. The correlation between the tangential inlet areas and delta pressure values is used to calculate the spring displacement and variable inlet geometry. An injector designed using the method includes a plurality of geometrically calculated tangential inlets in an injection tube; an injection tube cap with a plurality of inlet slots slidably engages the injection tube. A pressure differential across the injector element causes the cap to slide along the injection tube and variably align the inlet slots with the tangential inlets.

A novel inspection system for cosmetic defects

NASA Astrophysics Data System (ADS)

Hazra, S.; Roy, R.; Williams, D.; Aylmore, R.; Hollingdale, D.

2013-12-01

The appearance of automotive skin panels creates desirability for a product and differentiates it from the competition. Because of the importance of skin panels, considerable care is taken in minimizing defects such as the 'hollow' defect that occur around door-handle depressions. However, the inspection process is manual, subjective and time-consuming. This paper describes the development of an objective and inspection scheme for the 'hollow' defect. In this inspection process, the geometry of a panel is captured using a structured lighting system. The geometry data is subsequently analyzed by a purpose-built wavelet-based algorithm to identify the location of any defects that may be present and to estimate the perceived severity of the defects without user intervention. This paper describes and critically evaluates the behavior of this physically-based algorithm on an ideal and real geometry and compares its result to an actual audit. The results show that the algorithm is capable of objectively locating and classifying 'hollow' defects in actual panels.

Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Christiansen, Ove

2018-06-01

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μEh regime.

Multi-scale characterization of topographic anisotropy

NASA Astrophysics Data System (ADS)

Roy, S. G.; Koons, P. O.; Osti, B.; Upton, P.; Tucker, G. E.

2016-05-01

We present the every-direction variogram analysis (EVA) method for quantifying orientation and scale dependence of topographic anisotropy to aid in differentiation of the fluvial and tectonic contributions to surface evolution. Using multi-directional variogram statistics to track the spatial persistence of elevation values across a landscape, we calculate anisotropy as a multiscale, direction-sensitive variance in elevation between two points on a surface. Tectonically derived topographic anisotropy is associated with the three-dimensional kinematic field, which contributes (1) differential surface displacement and (2) crustal weakening along fault structures, both of which amplify processes of surface erosion. Based on our analysis, tectonic displacements dominate the topographic field at the orogenic scale, while a combination of the local displacement and strength fields are well represented at the ridge and valley scale. Drainage network patterns tend to reflect the geometry of underlying active or inactive tectonic structures due to the rapid erosion of faults and differential uplift associated with fault motion. Regions that have uniform environmental conditions and have been largely devoid of tectonic strain, such as passive coastal margins, have predominantly isotropic topography with typically dendritic drainage network patterns. Isolated features, such as stratovolcanoes, are nearly isotropic at their peaks but exhibit a concentric pattern of anisotropy along their flanks. The methods we provide can be used to successfully infer the settings of past or present tectonic regimes, and can be particularly useful in predicting the location and orientation of structural features that would otherwise be impossible to elude interpretation in the field. Though we limit the scope of this paper to elevation, EVA can be used to quantify the anisotropy of any spatially variable property.

Design of Flight Vehicle Management Systems

NASA Technical Reports Server (NTRS)

Meyer, George; Aiken, Edwin W. (Technical Monitor)

1994-01-01

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possess much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

Nonlinear Control and Discrete Event Systems

NASA Technical Reports Server (NTRS)

Meyer, George; Null, Cynthia H. (Technical Monitor)

1995-01-01

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

A statistical human rib cage geometry model accounting for variations by age, sex, stature and body mass index.

PubMed

Shi, Xiangnan; Cao, Libo; Reed, Matthew P; Rupp, Jonathan D; Hoff, Carrie N; Hu, Jingwen

2014-07-18

In this study, we developed a statistical rib cage geometry model accounting for variations by age, sex, stature and body mass index (BMI). Thorax CT scans were obtained from 89 subjects approximately evenly distributed among 8 age groups and both sexes. Threshold-based CT image segmentation was performed to extract the rib geometries, and a total of 464 landmarks on the left side of each subject׳s ribcage were collected to describe the size and shape of the rib cage as well as the cross-sectional geometry of each rib. Principal component analysis and multivariate regression analysis were conducted to predict rib cage geometry as a function of age, sex, stature, and BMI, all of which showed strong effects on rib cage geometry. Except for BMI, all parameters also showed significant effects on rib cross-sectional area using a linear mixed model. This statistical rib cage geometry model can serve as a geometric basis for developing a parametric human thorax finite element model for quantifying effects from different human attributes on thoracic injury risks. Copyright © 2014 Elsevier Ltd. All rights reserved.

Noninvasive estimation of pharyngeal airway resistance and compliance in children based on volume-gated dynamic MRI and computational fluid dynamics.

PubMed

Persak, Steven C; Sin, Sanghun; McDonough, Joseph M; Arens, Raanan; Wootton, David M

2011-12-01

Computational fluid dynamics (CFD) analysis was used to model the effect of collapsing airway geometry on internal pressure and velocity in the pharyngeal airway of three sedated children with obstructive sleep apnea syndrome (OSAS) and three control subjects. Model geometry was reconstructed from volume-gated magnetic resonance images during normal tidal breathing at 10 increments of tidal volume through the respiratory cycle. Each geometry was meshed with an unstructured grid and solved using a low-Reynolds number k-ω turbulence model driven by flow data averaged over 12 consecutive breathing cycles. Combining gated imaging with CFD modeling created a dynamic three-dimensional view of airway anatomy and mechanics, including the evolution of airway collapse and flow resistance and estimates of the local effective compliance. The upper airways of subjects with OSAS were generally much more compliant during tidal breathing. Compliance curves (pressure vs. cross-section area), derived for different locations along the airway, quantified local differences along the pharynx and between OSAS subjects. In one subject, the distal oropharynx was more compliant than the nasopharynx (1.028 vs. 0.450 mm(2)/Pa) and had a lower theoretical limiting flow rate, confirming the distal oropharynx as the flow-limiting segment of the airway in this subject. Another subject had a more compliant nasopharynx (0.053 mm(2)/Pa) during inspiration and apparent stiffening of the distal oropharynx (C = 0.0058 mm(2)/Pa), and the theoretical limiting flow rate indicated the nasopharynx as the flow-limiting segment. This new method may help to differentiate anatomical and functional factors in airway collapse.

Right Ventricular Strain, Torsion, and Dyssynchrony in Healthy Subjects using 3D Spiral Cine DENSE Magnetic Resonance Imaging

PubMed Central

Suever, Jonathan D; Wehner, Gregory J; Jing, Linyuan; Powell, David K; Hamlet, Sean M; Grabau, Jonathan D; Mojsejenko, Dimitri; Andres, Kristin N; Haggerty, Christopher M; Fornwalt, Brandon K

2017-01-01

Mechanics of the left ventricle (LV) are important indicators of cardiac function. The role of right ventricular (RV) mechanics is largely unknown due to the technical limitations of imaging its thin wall and complex geometry and motion. By combining 3D Displacement Encoding with Stimulated Echoes (DENSE) with a post-processing pipeline that includes a local coordinate system, it is possible to quantify RV strain, torsion, and synchrony. In this study, we sought to characterize RV mechanics in 50 healthy individuals and compare these values to their LV counterparts. For each cardiac frame, 3D displacements were fit to continuous and differentiable radial basis functions, allowing for the computation of the 3D Cartesian Lagrangian strain tensor at any myocardial point. The geometry of the RV was extracted via a surface fit to manually delineated endocardial contours. Throughout the RV, a local coordinate system was used to transform from a Cartesian strain tensor to a polar strain tensor. It was then possible to compute peak RV torsion as well as peak longitudinal and circumferential strain. A comparable analysis was performed for the LV. Dyssynchrony was computed from the standard deviation of regional activation times. Global circumferential strain was comparable between the RV and LV (−18.0% for both) while longitudinal strain was greater in the RV (−18.1% vs. −15.7%). RV torsion was comparable to LV torsion (6.2 vs. 7.1 degrees, respectively). Regional activation times indicated that the RV contracted later but more synchronously than the LV. 3D spiral cine DENSE combined with a post–processing pipeline that includes a local coordinate system can resolve both the complex geometry and 3D motion of the RV. PMID:28055859

Structures in solutions from joint experimental-computational analysis: applications to cyclic molecules and studies of noncovalent interactions.

PubMed

Aliev, Abil E; Mia, Zakirin A; Khaneja, Harmeet S; King, Frank D

2012-01-26

The potential of an approach combining nuclear magnetic resonance (NMR) spectroscopy, molecular dynamics (MD) simulations, and quantum mechanical (QM) calculations for full structural characterizations in solution is assessed using cyclic organic compounds, namely, benzazocinone derivatives 1-3 with fused five- and eight-membered aliphatic rings, camphoric anhydride 4, and bullvalene 5. Various MD simulations were considered, using force field and semiempirical QM treatments, implicit and explicit solvation, and high-temperature MD calculations for selecting plausible molecular geometries for subsequent QM geometry optimizations using mainly B3LYP, M062X, and MP2 methods. The QM-predicted values of NMR parameters were compared to their experimental values for verification of the final structures derived from the MD/QM analysis. From these comparisons, initial estimates of quality thresholds (calculated as rms deviations) were 0.7-0.9 Hz for (3)J(HH) couplings, 0.07-0.11 Å for interproton distances, 0.05-0.08 ppm for (1)H chemical shifts, and 1.0-2.1 ppm for (13)C chemical shifts. The obtained results suggest that the accuracy of the MD analysis in predicting geometries and relative conformational energies is not critical and that the final geometry refinements of the structures selected from the MD simulations using QM methods are sufficient for correcting for the expected inaccuracy of the MD analysis. A unique example of C(sp(3))-H···N(sp(3)) intramolecular noncovalent interaction is also identified using the NMR/MD/QM and the natural bond orbital analyses. As the NMR/MD/QM approach relies on the final QM geometry optimization, comparisons of geometric characteristics predicted by different QM methods and those from X-ray and neutron diffraction measurements were undertaken using rigid and flexible cyclic systems. The joint analysis shows that intermolecular noncovalent interactions present in the solid state alter molecular geometries significantly compared to the geometries of isolated molecules from QM calculations.

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

Axially grooved heat pipe study

NASA Technical Reports Server (NTRS)

1977-01-01

A technology evaluation study on axially grooved heat pipes is presented. The state-of-the-art is reviewed and present and future requirements are identified. Analytical models, the Groove Analysis Program (GAP) and a closed form solution, were developed to facilitate parametric performance evaluations. GAP provides a numerical solution of the differential equations which govern the hydrodynamic flow. The model accounts for liquid recession, liquid/vapor shear interaction, puddle flow as well as laminar and turbulent vapor flow conditions. The closed form solution was developed to reduce computation time and complexity in parametric evaluations. It is applicable to laminar and ideal charge conditions, liquid/vapor shear interaction, and an empirical liquid flow factor which accounts for groove geometry and liquid recession effects. The validity of the closed form solution is verified by comparison with GAP predictions and measured data.

Fractal Geometry Enables Classification of Different Lung Morphologies in a Model of Experimental Asthma

NASA Astrophysics Data System (ADS)

Obert, Martin; Hagner, Stefanie; Krombach, Gabriele A.; Inan, Selcuk; Renz, Harald

2015-06-01

Animal models represent the basis of our current understanding of the pathophysiology of asthma and are of central importance in the preclinical development of drug therapies. The characterization of irregular lung shapes is a major issue in radiological imaging of mice in these models. The aim of this study was to find out whether differences in lung morphology can be described by fractal geometry. Healthy and asthmatic mouse groups, before and after an acute asthma attack induced by methacholine, were studied. In vivo flat-panel-based high-resolution Computed Tomography (CT) was used for mice's thorax imaging. The digital image data of the mice's lungs were segmented from the surrounding tissue. After that, the lungs were divided by image gray-level thresholds into two additional subsets. One subset contained basically the air transporting bronchial system. The other subset corresponds mainly to the blood vessel system. We estimated the fractal dimension of all sets of the different mouse groups using the mass radius relation (mrr). We found that the air transporting subset of the bronchial lung tissue enables a complete and significant differentiation between all four mouse groups (mean D of control mice before methacholine treatment: 2.64 ± 0.06; after treatment: 2.76 ± 0.03; asthma mice before methacholine treatment: 2.37 ± 0.16; after treatment: 2.71 ± 0.03; p < 0.05). We conclude that the concept of fractal geometry allows a well-defined, quantitative numerical and objective differentiation of lung shapes — applicable most likely also in human asthma diagnostics.

Use of Existing CAD Models for Radiation Shielding Analysis

NASA Technical Reports Server (NTRS)

Lee, K. T.; Barzilla, J. E.; Wilson, P.; Davis, A.; Zachman, J.

2015-01-01

The utility of a radiation exposure analysis depends not only on the accuracy of the underlying particle transport code, but also on the accuracy of the geometric representations of both the vehicle used as radiation shielding mass and the phantom representation of the human form. The current NASA/Space Radiation Analysis Group (SRAG) process to determine crew radiation exposure in a vehicle design incorporates both output from an analytic High Z and Energy Particle Transport (HZETRN) code and the properties (i.e., material thicknesses) of a previously processed drawing. This geometry pre-process can be time-consuming, and the results are less accurate than those determined using a Monte Carlo-based particle transport code. The current work aims to improve this process. Although several Monte Carlo programs (FLUKA, Geant4) are readily available, most use an internal geometry engine. The lack of an interface with the standard CAD formats used by the vehicle designers limits the ability of the user to communicate complex geometries. Translation of native CAD drawings into a format readable by these transport programs is time consuming and prone to error. The Direct Accelerated Geometry -United (DAGU) project is intended to provide an interface between the native vehicle or phantom CAD geometry and multiple particle transport codes to minimize problem setup, computing time and analysis error.

Dynamic Geometry Software Improves Mathematical Achievement: Systematic Review and Meta-Analysis

ERIC Educational Resources Information Center

Chan, Kan Kan; Leung, Siu Wai

2014-01-01

Dynamic geometry software (DGS) aims to enhance mathematics education. This systematic review and meta-analysis evaluated the quasi-experimental studies on the effectiveness of DGS-based instruction in improving students' mathematical achievement. Research articles published between 1990 and 2013 were identified from major databases according to a…

Symplectic geometry spectrum regression for prediction of noisy time series

NASA Astrophysics Data System (ADS)

Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie

2016-05-01

We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).

Numerical solutions of atmospheric flow over semielliptical simulated hills

NASA Technical Reports Server (NTRS)

Shieh, C. F.; Frost, W.

1981-01-01

Atmospheric motion over obstacles on plane surfaces to compute simulated wind fields over terrain features was studied. Semielliptical, two dimensional geometry and numerical simulation of flow over rectangular geometries is also discussed. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale were solved by a finite difference technique. The mechanism of flow separation induced by a semiellipse is the same as flow over a gradually sloping surface for which the flow separation is caused by the interaction between the viscous force, the pressure force, and the turbulence level. For flow over bluff bodies, a downstream recirculation bubble is created which increases the aspect ratio and/or the turbulence level results in flow reattachment close behind the obstacle.

Effects of dynamical screening on single ionization of potassium by electron impact in doubly symmetric geometry

NASA Astrophysics Data System (ADS)

Sun, S. Y.; Jia, X. F.; Miao, X. Y.; Zhang, J. F.

2014-03-01

The dynamically screened three-Coulomb-wave (DS3C) method is applied to study the single ionization of potassium by electron impact. Triple differential cross-sections (TDCS) are calculated in doubly symmetric geometry at excess energies of 6, 10, 15, 20, 30, 40, 50 and 60 eV. Comparisons are made with recent experimental data and theoretical predictions from a three-Coulomb-wave (3C) and distorted-wave Born approximation (DWBA). The DS3C method is able to reproduce most of the trend of experimental data and in good agreement with DWBA results. It is shown that the DS3C calculation provides much better shape and relative magnitude agreement with experiment.

Electron impact ionization of metastable 2P-state hydrogen atoms in the coplanar geometry

NASA Astrophysics Data System (ADS)

Dhar, S.; Nahar, N.

Triple differential cross sections (TDCS) for the ionization of metastable 2P-state hydrogen atoms by electrons are calculated for various kinematic conditions in the asymmetric coplanar geometry. In this calculation, the final state is described by a multiple-scattering theory for ionization of hydrogen atoms by electrons. Results show qualitative agreement with the available experimental data and those of other theoretical computational results for ionization of hydrogen atoms from ground state, and our first Born results. There is no available other theoretical results and experimental data for ionization of hydrogen atoms from the 2P state. The present study offers a wide scope for the experimental study for ionization of hydrogen atoms from the metastable 2P state.

Cascading gauge theory on dS4 and String Theory landscape

NASA Astrophysics Data System (ADS)

Buchel, Alex; Galante, Damián A.

2014-06-01

Placing anti-D3 branes at the tip of the conifold in Klebanov-Strassler geometry provides a generic way of constructing meta-stable de Sitter (dS) vacua in String Theory. A local geometry of such vacua exhibit gravitational solutions with a D3 charge measured at the tip opposite to the asymptotic charge. We discuss a restrictive set of such geometries, where anti-D3 branes are smeared at the tip. Such geometries represent holographic dual of cascading gauge theory in dS4 with or without chiral symmetry breaking. We find that in the phase with unbroken chiral symmetry the D3 charge at the tip is always positive. Furthermore, this charge is zero in the phase with spontaneously broken chiral symmetry. We show that the effective potential of the chirally symmetric phase is lower than that in the symmetry broken phase, i.e., there is no spontaneous chiral symmetry breaking for cascading gauge theory in dS4. The positivity of the D3 brane charge in smooth de-Sitter deformed conifold geometries with fluxes presents difficulties in uplifting AdS vacua to dS ones in String Theory via smeared anti-D3 branes. First, turning on fluxes on Calabi-Yau compactifications of type IIB string theory produces highly warped geometry with stabilized complex structure (but not Kähler) moduli of the compactification [3]; Next, including non-perturbative effects (which are under control given the unbroken supersymmetry), one obtains anti-de Sitter (AdS4) vacua with all moduli fixed; Finally, one uses anti-D3 branes of type IIB string theory to uplift AdS4 to de Sitter (dS4) vacua. As the last step of the construction completely breaks supersymmetry, it is much less controlled. In fact, in [4-7] it was argued that putting anti-D3 branes at the tip of the Klebanov-Strassler (KS) [8] geometry (as done in KKLT construction) leads to a naked singularity. Whether or not the resulting singularity is physical is subject to debates. When M4=dS4 and the chiral symmetry is unbroken, the D3 brane charge at the tip of the conifold is always positive, as long as ln H2Λ2/P2g0 ⩾-0.4. When M4=dS4 and the chiral symmetry is broken, the D3 brane charge at the tip of the conifold is always zero; we managed to construct geometries of this type for ln H2Λ2/P2g0⩾-0.03. Comparing effective potential of the gauge theory in broken Veffb and unbroken Veffs phases we establish that in all cases, when we can construct the phase with spontaneously broken chiral symmetry, Veffb>Veffs, when ln H2Λ2/P2g0⩾-0.03, i.e., spontaneous symmetry breaking does not happen for given values of the gauge theory parameters. To put these parameters in perspective, note that the (first-order) confinement/deconfinement and chiral symmetry breaking phase transition in cascading gauge theory plasma occurs at temperature T such that [16] ln Tdeconfinement,χSB2Λ2/P2g0=0.2571(2), and the (first-order) chiral symmetry breaking in cascading gauge theory on S3 occurs for compactification scale μ3≡ℓ3-1 such that [21] ln μ3,χSB2Λ2/P2g0=0.4309(8). When M4=R×S3 and the chiral symmetry is unbroken, the D3 brane charge at the tip of the conifold is negative when ln μ32Λ2/P2g0 μ, and the D3 brane charge at the tip of the conifold in broken phase is zero, the charge in the ground state is in fact zero whenever μ3⩽μ. Furthermore, chirally symmetric states of cascading gauge theory on S3 develop symmetry breaking tachyonic instabilities at μ (below the first order chiral symmetry breaking scale μ) ln μ3,tachyon2Λ2/P2g0=0.3297(3) which is again above μ.Our results represented here, together with those reported in [10], point that the singularity of smeared anti-D3 branes at the tip of the conifold is unphysical: had it been otherwise, we should have been able to implement an infrared cutoff in the geometry with a D3 brane charge measured at the cutoff being negative. The role of the cutoff is played by the temperature (as discussed in [10]), by the compactification scale (when M4=R×S3), or by the Hubble scale (when M4=dS4). Interesting, we find that the D3 brane charge can become negative when the KT throat geometry is S3 deformed; however this occurs in the regime where this phase is unstable both via the first order phase transition and the tachyon condensation to S3 deformed KS throat geometry - the latter geometry has zero D3 brane charge at the tip. All this raises questions about construction of generic de Sitter vacua in String Theory [2].We stress, however, that our analysis does not definitely exclude local non-singular supergravity description of de Sitter vacua in String Theory. The issue stems from the anti-D3 brane “smearing approximation” used. Early discussion of the relevant smearing approximation appeared in [6,9]. There, the authors carefully analyzed non-supersymmetric deformations of KS geometry, invariant under the SU(2)×SU(2) global symmetry of the latter. They further identified a class of perturbations that is being sources by anti-D3 branes, placed at the tip of the conifold, and then computed the leading-order backreaction of those perturbations on KS geometry. Insistence on preserving the SU(2)×SU(2) global symmetry is a smearing approximation - from the brane perspective it implies that anti-D3 branes are uniformly distributed (uniformly smeared) over the transverse compact five-dimensional manifold. Our discussion here shares the same smearing approximation as in [6,9], but extends the analysis to the full (rather than leading-order) backreaction. Smearing approximation is a practical tool enabling the analysis of the complicated cascading geometries involved. However, it must be questioned: it is not clear that non-supersymmetric uniform distribution along T directions of anti-D3 branes is stable against ‘clumping’. While it is highly desirable to lift this approximation, it is very difficult to do this in practice: one is forced to analyze a coupled nonlinear system of partial differential equations, rather than ordinary differential equations. We feel that until fully localized anti-D3 brane analysis in cascading geometries are performed, the singularity question of local supergravity description of de Sitter vacua in String Theory will remain open.

Analysis on singular spaces: Lie manifolds and operator algebras

NASA Astrophysics Data System (ADS)

Nistor, Victor

2016-07-01

We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called ;Lie manifolds; -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

Congruence of Meaning.

ERIC Educational Resources Information Center

Suppes, Patrick

By looking at the history of geometry and the concept of congruence in geometry we can get a new perspective on how to think about the closeness in meaning of two sentences. As in the analysis of congruence in geometry, a definite and concrete set of proposals about congruence of meaning depends essentially on the kind of theoretical framework…

The slab geometry laser. I - Theory

NASA Technical Reports Server (NTRS)

Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.

1984-01-01

Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.

Teachers Modify Geometry Problems: From Proof to Investigation

ERIC Educational Resources Information Center

Leikin, Roza; Grossman, Dorith

2013-01-01

We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

Dynamical Geometry: Analysis of Mistakes in Student Constructions

ERIC Educational Resources Information Center

Vanicek, Jiri

2007-01-01

In the early stages of working with dynamical geometry environments, students make many more mistakes than if they thought out and implemented the same constructions on paper. Most Czech teachers have very little experience of doing geometry using computers. A methodology which could help them to teach students to avoid mistakes dependent on the…

Students' Conceptions of Congruency through the Use of Dynamic Geometry Software

ERIC Educational Resources Information Center

Gonzalez, Gloriana; Herbst, Patricio G.

2009-01-01

This paper describes students' interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK[cent sign] model of conceptions, suggests that incorporating technology in mathematics classrooms…

Measuring striving for understanding and learning value of geometry: a validity study

NASA Astrophysics Data System (ADS)

Ubuz, Behiye; Aydınyer, Yurdagül

2017-11-01

The current study aimed to construct a questionnaire that measures students' personality traits related to striving for understanding and learning value of geometry and then examine its psychometric properties. Through the use of multiple methods on two independent samples of 402 and 521 middle school students, two studies were performed to address this issue to provide support for its validity. In Study 1, exploratory factor analysis indicated the two-factor model. In Study 2, confirmatory factor analysis indicated the better fit of two-factor model compared to one or three-factor model. Convergent and discriminant validity evidence provided insight into the distinctiveness of the two factors. Subgroup validity evidence revealed gender differences for striving for understanding geometry trait favouring girls and grade level differences for learning value of geometry trait favouring the sixth- and seventh-grade students. Predictive validity evidence demonstrated that the striving for understanding geometry trait but not learning value of geometry trait was significantly correlated with prior mathematics achievement. In both studies, each factor and the entire questionnaire showed satisfactory reliability. In conclusion, the questionnaire was psychometrically sound.

Evaluating transition state structures of vanadium-phosphatase protein complexes using shape analysis.

PubMed

Sánchez-Lombardo, Irma; Alvarez, Santiago; McLauchlan, Craig C; Crans, Debbie C

2015-06-01

Shape analysis of coordination complexes is well-suited to evaluate the subtle distortions in the trigonal bipyramidal (TBPY-5) geometry of vanadium coordinated in the active site of phosphatases and characterized by X-ray crystallography. Recent studies using the tau (τ) analysis support the assertion that vanadium is best described as a trigonal bipyramid, because this geometry is the ideal transition state geometry of the phosphate ester substrate hydrolysis (C.C. McLauchlan, B.J. Peters, G.R. Willsky, D.C. Crans, Coord. Chem. Rev. http://dx.doi.org/10.1016/j.ccr.2014.12.012 ; D.C. Crans, M.L. Tarlton, C.C. McLauchlan, Eur. J. Inorg. Chem. 2014, 4450-4468). Here we use continuous shape measures (CShM) analysis to investigate the structural space of the five-coordinate vanadium-phosphatase complexes associated with mechanistic transformations between the tetrahedral geometry and the five-coordinate high energy TBPY-5 geometry was discussed focusing on the protein tyrosine phosphatase 1B (PTP1B) enzyme. No evidence for square pyramidal geometries was observed in any vanadium-protein complexes. The shape analysis positioned the metal ion and the ligands in the active site reflecting the mechanism of the cleavage of the organic phosphate in a phosphatase. We identified the umbrella distortions to be directly on the reaction path between tetrahedral phosphate and the TBPY-5-types of high-energy species. The umbrella distortions of the trigonal bipyramid are therefore identified as being the most relevant types of transition state structures for the phosphoryl group transfer reactions for phosphatases and this may be related to the possibility that vanadium is an inhibitor for enzymes that support both exploded and five-coordinate transition states. Copyright © 2015 Elsevier Inc. All rights reserved.

Integral representations on supermanifolds: super Hodge duals, PCOs and Liouville forms

NASA Astrophysics Data System (ADS)

Castellani, Leonardo; Catenacci, Roberto; Grassi, Pietro Antonio

2017-01-01

We present a few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.

Iterated Hamiltonian type systems and applications

NASA Astrophysics Data System (ADS)

Tiba, Dan

2018-04-01

We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

Assessing non-uniqueness: An algebraic approach

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

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Cell Geometry Guides the Dynamic Targeting of Apoplastic GPI-Linked Lipid Transfer Protein to Cell Wall Elements and Cell Borders in Arabidopsis thaliana

PubMed Central

Wasteneys, Geoffrey

2013-01-01

During cellular morphogenesis, changes in cell shape and cell junction topology are fundamental to normal tissue and organ development. Here we show that apoplastic Glycophosphatidylinositol (GPI)-anchored Lipid Transfer Protein (LTPG) is excluded from cell junctions and flat wall regions, and passively accumulates around their borders in the epidermal cells of Arabidopsis thaliana. Beginning with intense accumulation beneath highly curved cell junction borders, this enrichment is gradually lost as cells become more bulbous during their differentiation. In fully mature epidermal cells, YFP-LTPG often shows a fibrous cellulose microfibril-like pattern within the bulging outer faces. Physical contact between a flat glass surface and bulbous cell surface induces rapid and reversible evacuation from contact sites and accumulation to the curved wall regions surrounding the contact borders. Thus, LTPG distribution is dynamic, responding to changes in cell shape and wall curvature during cell growth and differentiation. We hypothesize that this geometry-based mechanism guides wax-carrying LTPG to functional sites, where it may act to “seal” the vulnerable border surrounding cell-cell junctions and assist in cell wall fortification and cuticular wax deposition. PMID:24260561

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.

BP Piscium: its flaring disc imaged with SPHERE/ZIMPOL★

NASA Astrophysics Data System (ADS)

de Boer, J.; Girard, J. H.; Canovas, H.; Min, M.; Sitko, M.; Ginski, C.; Jeffers, S. V.; Mawet, D.; Milli, J.; Rodenhuis, M.; Snik, F.; Keller, C. U.

2017-03-01

Whether BP Piscium (BP Psc) is either a pre-main sequence T Tauri star at d ≈ 80 pc, or a post-main sequence G giant at d ≈ 300 pc is still not clear. As a first-ascent giant, it is the first to be observed with a molecular and dust disc. Alternatively, BP Psc would be among the nearest T Tauri stars with a protoplanetary disc (PPD). We investigate whether the disc geometry resembles typical PPDs, by comparing polarimetric images with radiative transfer models. Our Very Large Telescope/Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE)/Zurich IMaging Polarimeter (ZIMPOL) observations allow us to perform polarimetric differential imaging, reference star differential imaging, and Richardson-Lucy deconvolution. We present the first visible light polarization and intensity images of the disc of BP Psc. Our deconvolution confirms the disc shape as detected before, mainly showing the southern side of the disc. In polarized intensity the disc is imaged at larger detail and also shows the northern side, giving it the typical shape of high-inclination flared discs. We explain the observed disc features by retrieving the large-scale geometry with MCMAX radiative transfer modelling, which yields a strongly flared model, atypical for discs of T Tauri stars.

New Techniques in Time-Frequency Analysis: Adaptive Band, Ultra-Wide Band and Multi-Rate Signal Processing

DTIC Science & Technology

2016-03-02

Nyquist tiles and sampling groups in Euclidean geometry, and discussed the extension of these concepts to hyperbolic and spherical geometry and...hyperbolic or spherical spaces. We look to develop a structure for the tiling of frequency spaces in both Euclidean and non-Euclidean domains. In particular...we establish Nyquist tiles and sampling groups in Euclidean geometry, and discuss the extension of these concepts to hyperbolic and spherical geometry

Elastic electron scattering from formamide

NASA Astrophysics Data System (ADS)

Buk, M. V.; Bardela, F. P.; da Silva, L. A.; Iga, I.; Homem, M. G. P.

2018-05-01

Differential cross sections for elastic electron scattering by formamide (NH2CHO) were measured in the 30–800 eV and 10°–120° ranges. The angular distribution of scattered electrons was obtained using a crossed electron beam-molecular beam geometry. The relative flow technique was applied to normalize our data. Integral and momentum-transfer cross sections were derived from the measured differential cross sections. Theoretical results in the framework of the independent-atom model at the static-exchange-polarization plus absorption level of approximation are also given. The present measured and calculated results are compared with those available in the literature showing a generally good agreement.

Time-optimal Aircraft Pursuit-evasion with a Weapon Envelope Constraint

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1990-01-01

The optimal pursuit-evasion problem between two aircraft including a realistic weapon envelope is analyzed using differential game theory. Six order nonlinear point mass vehicle models are employed and the inclusion of an arbitrary weapon envelope geometry is allowed. The performance index is a linear combination of flight time and the square of the vehicle acceleration. Closed form solution to this high-order differential game is then obtained using feedback linearization. The solution is in the form of a feedback guidance law together with a quartic polynomial for time-to-go. Due to its modest computational requirements, this nonlinear guidance law is useful for on-board real-time implementation.

Double ionization of helium by ion impact: second Born order treatment at the fully differential level

NASA Astrophysics Data System (ADS)

López, S. D.; Otranto, S.; Garibotti, C. R.

2015-01-01

In this work, a theoretical study of the double ionization of He by ion impact at the fully differential level is presented. Emphasis is made in the role played by the projectile in the double emission process depending on its charge and the amount of momentum transferred to the target. A Born-CDW model including a second-order term in the projectile charge is introduced and evaluated within an on-shell treatment. We find that emission geometries for which the second-order term dominates lead to asymmetric structures around the momentum transfer direction, a typical characteristic of higher order transitions.

DAB user's guide

NASA Technical Reports Server (NTRS)

Trosin, J.

1985-01-01

Use of the Display AButments (DAB) which plots PAN AIR geometries is presented. The DAB program creates hidden line displays of PAN AIR geometries and labels specified geometry components, such as abutments, networks, and network edges. It is used to alleviate the very time consuming and error prone abutment list checking phase of developing a valid PAN AIR geometry, and therefore represents a valuable tool for debugging complex PAN AIR geometry definitions. DAB is written in FORTRAN 77 and runs on a Digital Equipment Corporation VAX 11/780 under VMS. It utilizes a special color version of the SKETCH hidden line analysis routine.

Synthesis, spectroscopic characterization, electrochemistry and biological evaluation of some metal (II) complexes with ONO donor ligand containing benzo[b]thiophene and coumarin moieties

NASA Astrophysics Data System (ADS)

Mahendra Raj, K.; Mruthyunjayaswamy, B. H. M.

2014-09-01

Schiff base ligand 3-chloro-N‧-((7-hydroxy-4-methyl-2-oxo-2H-chromen-8-yl)methylene)benzo[b]thiophene-2-carbohydrazide and its Cu(II), Co(II), Ni(II) and Zn(II) complexes were synthesized, characterized by elemental analysis and various physico-chemical techniques like, IR, 1H NMR, ESI-mass, UV-Visible, thermogravimetry - differential thermal analysis, magnetic measurements and molar conductance. Spectral analysis indicates octahedral geometry for all the complexes. Cu(II) complex have 1:1 stoichiometry of the type [M(L)(Cl)(H2O)2], whereas Co(II), Ni(II) and Zn(II) complexes have 1:2 stoichiometric ratio of the type [M(L)2]. The bonding sites are the oxygen atom of amide carbonyl, nitrogen of azomethine function and phenolic oxygen of the Schiff base ligand via deprotonation. The thermogravimetry - differential thermal analysis studies gave evidence for the presence of coordinated water molecules in the composition of Cu(II) complex which was further supported by IR measurements. All the complexes were investigated for their electrochemical activity, but only the Cu(II) complex showed the redox property. In order to evaluate the effect of antimicrobial potency of metal ions upon chelation, ligand and its metal complexes along with their respective metal chlorides were screened for their antibacterial and antifungal activities by minimum inhibitory concentration (MIC) method. The results showed that the metal complexes were found to be more active than free ligand. Ligand and its complexes were screened for free radical scavenging activity by DPPH method and DNA cleavage activity using Calf-thymus DNA (Cat. No-105850).

Numerical Analysis Objects

NASA Astrophysics Data System (ADS)

Henderson, Michael

1997-08-01

The Numerical Analysis Objects project (NAO) is a project in the Mathematics Department of IBM's TJ Watson Research Center. While there are plenty of numerical tools available today, it is not an easy task to combine them into a custom application. NAO is directed at the dual problems of building applications from a set of tools, and creating those tools. There are several "reuse" projects, which focus on the problems of identifying and cataloging tools. NAO is directed at the specific context of scientific computing. Because the type of tools is restricted, problems such as tools with incompatible data structures for input and output, and dissimilar interfaces to tools which solve similar problems can be addressed. The approach we've taken is to define interfaces to those objects used in numerical analysis, such as geometries, functions and operators, and to start collecting (and building) a set of tools which use these interfaces. We have written a class library (a set of abstract classes and implementations) in C++ which demonstrates the approach. Besides the classes, the class library includes "stub" routines which allow the library to be used from C or Fortran, and an interface to a Visual Programming Language. The library has been used to build a simulator for petroleum reservoirs, using a set of tools for discretizing nonlinear differential equations that we have written, and includes "wrapped" versions of packages from the Netlib repository. Documentation can be found on the Web at "http://www.research.ibm.com/nao". I will describe the objects and their interfaces, and give examples ranging from mesh generation to solving differential equations.

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.

Optical probe

DOEpatents

Hencken, Kenneth; Flower, William L.

1999-01-01

A compact optical probe is disclosed particularly useful for analysis of emissions in industrial environments. The instant invention provides a geometry for optically-based measurements that allows all optical components (source, detector, rely optics, etc.) to be located in proximity to one another. The geometry of the probe disclosed herein provides a means for making optical measurements in environments where it is difficult and/or expensive to gain access to the vicinity of a flow stream to be measured. Significantly, the lens geometry of the optical probe allows the analysis location within a flow stream being monitored to be moved while maintaining optical alignment of all components even when the optical probe is focused on a plurality of different analysis points within the flow stream.

A Geometry Based Infra-Structure for Computational Analysis and Design

NASA Technical Reports Server (NTRS)

Haimes, Robert

1998-01-01

The computational steps traditionally taken for most engineering analysis suites (computational fluid dynamics (CFD), structural analysis, heat transfer and etc.) are: (1) Surface Generation -- usually by employing a Computer Assisted Design (CAD) system; (2) Grid Generation -- preparing the volume for the simulation; (3) Flow Solver -- producing the results at the specified operational point; (4) Post-processing Visualization -- interactively attempting to understand the results. For structural analysis, integrated systems can be obtained from a number of commercial vendors. These vendors couple directly to a number of CAD systems and are executed from within the CAD Graphical User Interface (GUI). It should be noted that the structural analysis problem is more tractable than CFD; there are fewer mesh topologies used and the grids are not as fine (this problem space does not have the length scaling issues of fluids). For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. In most cases, the output from a CAD system could go to Initial Graphics Exchange Specification (IGES) or Standard Exchange Program (STEP) files. The output from Grid Generators and Solvers do not really have standards though there are a couple of file formats that can be used for a subset of the gridding (i.e. PLOT3D data formats). The user would have to patch up the data or translate from one format to another to move to the next step. Sometimes this could take days. Specifically the problems with this procedure are:(1) File based -- Information flows from one step to the next via data files with formats specified for that procedure. File standards, when they exist, are wholly inadequate. For example, geometry from CAD systems (transmitted via IGES files) is defined as disjoint surfaces and curves (as well as masses of other information of no interest for the Grid Generator). This is particularly onerous for modern CAD systems based on solid modeling. The part was a proper solid and in the translation to IGES has lost this important characteristic. STEP is another standard for CAD data that exists and supports the concept of a solid. The problem with STEP is that a solid modeling geometry kernel is required to query and manipulate the data within this type of file. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. Adroit multi-block methods are not far behind. This means that a million node steady-state solution can be computed on the order of hours (using current high performance computers) starting from this 'good' geometry. Unfortunately, the geometry usually transmitted from the CAD system is not 'good' in the grid generator sense. The grid generator needs smooth closed solid geometry. It can take a week (or more) of interaction with the CAD output (sometimes by hand) before the process can begin. One way Communication. (3) One-way Communication -- All information travels on from one phase to the next. This makes procedures like node adaptation difficult when attempting to add or move nodes that sit on bounding surfaces (when the actual surface data has been lost after the grid generation phase). Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive. There is also no way to easily deal with this system in a modular manner. One can only replace the grid generator, for example, if the software reads and writes the same files. Instead of the serial approach to analysis as described above, CAPRI takes a geometry centric approach. This makes the actual geometry (not a discretized version) accessible to all phases of the analysis. The connection to the geometry is made through an Application Programming Interface (API) and NOT a file system. This API isolates the top-level applications (grid generators, solvers and visualization components) from the geometry engine. Also this allows the replacement of one geometry kernel with another, without effecting these top-level applications. For example, if UniGraphics is used as the CAD package then Parasolid (UG's own geometry engine) can be used for all geometric queries so that no solid geometry information is lost in a translation. This is much better than STEP because when the data is queried, the same software is executed as used in the CAD system. Therefore, one analyzes the exact part that is in the CAD system. CAPRI uses the same idea as the commercial structural analysis codes but does not specify control. Software components of the CAD system are used, but the analysis suite, not the CAD operator, specifies the control of the software session. This also means that the license issues (may be) minimized and individuals need not have to know how to operate a CAD system in order to run the suite.

An approach for management of geometry data

NASA Technical Reports Server (NTRS)

Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

1980-01-01

The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

Main rotor free wake geometry effects on blade air loads and response for helicopters in steady maneuvers. Volume 1: Theoretical formulation and analysis of results

NASA Technical Reports Server (NTRS)

Sadler, S. G.

1972-01-01

A mathematical model and computer program were implemented to study the main rotor free wake geometry effects on helicopter rotor blade air loads and response in steady maneuvers. The theoretical formulation and analysis of results are presented.

Testing for a Signal with Unknown Location and Scale in a Stationary Gaussian Random Field

DTIC Science & Technology

1994-01-07

Secondary 60D05, 52A22. Key words and phrases. Euler characteristic, integral geometry, image analysis , Gaussian fields, volume of tubes. SUMMARY We...words and phrases. Euler characteristic, integral geometry. image analysis . Gaussian fields. volume of tubes. 20. AMST RACT (Coith..o an revmreo ef* It

A network-analysis-based comparative study of the throughput behavior of polymer melts in barrier screw geometries

NASA Astrophysics Data System (ADS)

Aigner, M.; Köpplmayr, T.; Kneidinger, C.; Miethlinger, J.

2014-05-01

Barrier screws are widely used in the plastics industry. Due to the extreme diversity of their geometries, describing the flow behavior is difficult and rarely done in practice. We present a systematic approach based on networks that uses tensor algebra and numerical methods to model and calculate selected barrier screw geometries in terms of pressure, mass flow, and residence time. In addition, we report the results of three-dimensional simulations using the commercially available ANSYS Polyflow software. The major drawbacks of three-dimensional finite-element-method (FEM) simulations are that they require vast computational power and, large quantities of memory, and consume considerable time to create a geometric model created by computer-aided design (CAD) and complete a flow calculation. Consequently, a modified 2.5-dimensional finite volume method, termed network analysis is preferable. The results obtained by network analysis and FEM simulations correlated well. Network analysis provides an efficient alternative to complex FEM software in terms of computing power and memory consumption. Furthermore, typical barrier screw geometries can be parameterized and used for flow calculations without timeconsuming CAD-constructions.

Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo.

PubMed

Scheiding, Sebastian; Yi, Allen Y; Gebhardt, Andreas; Li, Lei; Risse, Stefan; Eberhardt, Ramona; Tünnermann, Andreas

2011-11-21

We report what is to our knowledge the first approach to diamond turn microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo. In recent years ultraprecision machining has been employed to manufacture accurate optical components with 3D structure for beam shaping, imaging and nonimaging applications. As a result, geometries that are difficult or impossible to manufacture using lithographic techniques might be fabricated using small diamond tools with well defined cutting edges. These 3D structures show no rotational symmetry, but rather high frequency asymmetric features thus can be treated as freeform geometries. To transfer the 3D surface data with the high frequency freeform features into a numerical control code for machining, the commonly piecewise differentiable surfaces are represented as a cloud of individual points. Based on this numeric data, the tool radius correction is calculated to account for the cutting-edge geometry. Discontinuities of the cutting tool locations due to abrupt slope changes on the substrate surface are bridged using cubic spline interpolation.When superimposed with the trajectory of the rotationally symmetric substrate the complete microoptical geometry in 3D space is established. Details of the fabrication process and performance evaluation are described. © 2011 Optical Society of America

Errors in the Calculation of 27Al Nuclear Magnetic Resonance Chemical Shifts

PubMed Central

Wang, Xianlong; Wang, Chengfei; Zhao, Hui

2012-01-01

Computational chemistry is an important tool for signal assignment of 27Al nuclear magnetic resonance spectra in order to elucidate the species of aluminum(III) in aqueous solutions. The accuracy of the popular theoretical models for computing the 27Al chemical shifts was evaluated by comparing the calculated and experimental chemical shifts in more than one hundred aluminum(III) complexes. In order to differentiate the error due to the chemical shielding tensor calculation from that due to the inadequacy of the molecular geometry prediction, single-crystal X-ray diffraction determined structures were used to build the isolated molecule models for calculating the chemical shifts. The results were compared with those obtained using the calculated geometries at the B3LYP/6-31G(d) level. The isotropic chemical shielding constants computed at different levels have strong linear correlations even though the absolute values differ in tens of ppm. The root-mean-square difference between the experimental chemical shifts and the calculated values is approximately 5 ppm for the calculations based on the X-ray structures, but more than 10 ppm for the calculations based on the computed geometries. The result indicates that the popular theoretical models are adequate in calculating the chemical shifts while an accurate molecular geometry is more critical. PMID:23203134

A Geometry Based Infra-structure for Computational Analysis and Design

NASA Technical Reports Server (NTRS)

Haimes, Robert

1997-01-01

The computational steps traditionally taken for most engineering analysis (CFD, structural analysis, and etc.) are: Surface Generation - usually by employing a CAD system; Grid Generation - preparing the volume for the simulation; Flow Solver - producing the results at the specified operational point; and Post-processing Visualization - interactively attempting to understand the results For structural analysis, integrated systems can be obtained from a number of commercial vendors. For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. Specifically the problems with this procedure are: (1) File based. Information flows from one step to the next via data files with formats specified for that procedure. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. (3) One-Way communication. All information travels on from one phase to the next. Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive.

Transient potentials in dendritic systems of arbitrary geometry.

PubMed

Butz, E G; Cowan, J D

1974-09-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic "current" inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells.

User's manual for MacPASCO

NASA Technical Reports Server (NTRS)

Lucas, S. H.; Davis, R. C.

1992-01-01

A user's manual is presented for MacPASCO, which is an interactive, graphic, preprocessor for panel design. MacPASCO creates input for PASCO, an existing computer code for structural analysis and sizing of longitudinally stiffened composite panels. MacPASCO provides a graphical user interface which simplifies the specification of panel geometry and reduces user input errors. The user draws the initial structural geometry and reduces user input errors. The user draws the initial structural geometry on the computer screen, then uses a combination of graphic and text inputs to: refine the structural geometry; specify information required for analysis such as panel load and boundary conditions; and define design variables and constraints for minimum mass optimization. Only the use of MacPASCO is described, since the use of PASCO has been documented elsewhere.

Inheritance of silicate differentiation during lunar origin by giant impact

NASA Technical Reports Server (NTRS)

Warren, Paul H.

1992-01-01

It is pointed out that the implication of the popular giant impact model of lunar origin (e.g., Hartmann and Davis, 1975; Cameron and Ward, 1976; Stevenson, 1987) is that any depth-related silicate differentiation within the impactor (and/or the earth) at the time of the impact must be partly inherited by the preferentially peripheral matter that forms the moon. This paper presents calculations of the magnitude of the net differentiation of the protolunar matter for a variety of elements and scenarios, with different assumptions regarding the geometries of the 'sampled' peripheral zones, the relative proportions of the earth-derived to impactor-derived matter in the final moon, and the degree to which the impactor mantle had crystallized prior to the giant impact. It is shown that these differention effects constrain the overall plausibility of the giant impact hypothesis.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

NASA Astrophysics Data System (ADS)

Puķīte, Jānis; Wagner, Thomas

2016-05-01

We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

Statistical assessment of normal mitral annular geometry using automated three-dimensional echocardiographic analysis.

PubMed

Pouch, Alison M; Vergnat, Mathieu; McGarvey, Jeremy R; Ferrari, Giovanni; Jackson, Benjamin M; Sehgal, Chandra M; Yushkevich, Paul A; Gorman, Robert C; Gorman, Joseph H

2014-01-01

The basis of mitral annuloplasty ring design has progressed from qualitative surgical intuition to experimental and theoretical analysis of annular geometry with quantitative imaging techniques. In this work, we present an automated three-dimensional (3D) echocardiographic image analysis method that can be used to statistically assess variability in normal mitral annular geometry to support advancement in annuloplasty ring design. Three-dimensional patient-specific models of the mitral annulus were automatically generated from 3D echocardiographic images acquired from subjects with normal mitral valve structure and function. Geometric annular measurements including annular circumference, annular height, septolateral diameter, intercommissural width, and the annular height to intercommissural width ratio were automatically calculated. A mean 3D annular contour was computed, and principal component analysis was used to evaluate variability in normal annular shape. The following mean ± standard deviations were obtained from 3D echocardiographic image analysis: annular circumference, 107.0 ± 14.6 mm; annular height, 7.6 ± 2.8 mm; septolateral diameter, 28.5 ± 3.7 mm; intercommissural width, 33.0 ± 5.3 mm; and annular height to intercommissural width ratio, 22.7% ± 6.9%. Principal component analysis indicated that shape variability was primarily related to overall annular size, with more subtle variation in the skewness and height of the anterior annular peak, independent of annular diameter. Patient-specific 3D echocardiographic-based modeling of the human mitral valve enables statistical analysis of physiologically normal mitral annular geometry. The tool can potentially lead to the development of a new generation of annuloplasty rings that restore the diseased mitral valve annulus back to a truly normal geometry. Copyright © 2014 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

Parametric Geometry, Structured Grid Generation, and Initial Design Study for REST-Class Hypersonic Inlets

NASA Technical Reports Server (NTRS)

Ferlemann, Paul G.; Gollan, Rowan J.

2010-01-01

Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

PubMed

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

A novel method for automated grid generation of ice shapes for local-flow analysis

NASA Astrophysics Data System (ADS)

Ogretim, Egemen; Huebsch, Wade W.

2004-02-01

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading-edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine-cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness.

Numerical analysis of residual stresses in preforms of stress applying part for PANDA-type polarization maintaining optical fibers in view of technological imperfections of the doped zone geometry

NASA Astrophysics Data System (ADS)

Trufanov, Aleksandr N.; Trufanov, Nikolay A.; Semenov, Nikita V.

2016-09-01

The experimental data analysis of the stress applying rod section geometry for the PANDA-type polarization maintaining optical fiber has been performed. The dependencies of the change in the radial dimensions of the preform and the doping boundary on the angular coordinate have been obtained. The original algorithm of experimental data statistic analysis, which enables determination of the specimens' characteristic form of section, has been described. The influence of actual doped zone geometry on the residual stress fields formed during the stress rod preform fabrication has been investigated. It has been established that the deviation of the boundary between pure silica and the doped zone from the circular shape results in dissymmetry and local concentrations of the residual stress fields along the section, which can cause preforms destruction at high degrees of doping. The observed geometry deviations of up to 10% lead to the increase of the maximum stress intensity value by over 20%.

The trigonal prism in coordination chemistry.

PubMed

Cremades, Eduard; Echeverría, Jorge; Alvarez, Santiago

2010-09-10

Herein we analyze the accessibility of the trigonal-prismatic geometry to metal complexes with different electron configurations, as well as the ability of several hexadentate ligands to favor that coordination polyhedron. Our study combines i) a structural database analysis of the occurrence of the prismatic geometry throughout the transition-metal series, ii) a qualitative molecular orbital analysis of the distortions expected for a trigonal-prismatic geometry, and iii) a computational study of complexes of several transition-metal ions with different hexadentate ligands. Also the tendency of specific electron configurations to present a cis bond-stretch Jahn-Teller distortion is analyzed.

Calabi-Yau structures on categories of matrix factorizations

NASA Astrophysics Data System (ADS)

Shklyarov, Dmytro

2017-09-01

Using tools of complex geometry, we construct explicit proper Calabi-Yau structures, that is, non-degenerate cyclic cocycles on differential graded categories of matrix factorizations of regular functions with isolated critical points. The formulas involve the Kapustin-Li trace and its higher corrections. From the physics perspective, our result yields explicit 'off-shell' models for categories of topological D-branes in B-twisted Landau-Ginzburg models.

Noncommutative complex structures on quantum homogeneous spaces

NASA Astrophysics Data System (ADS)

Ó Buachalla, Réamonn

2016-01-01

A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for quantum homogeneous spaces. A number of basic results are established, producing a simple set of necessary and sufficient conditions for noncommutative complex structures to exist. Throughout, the framework is applied to the quantum projective spaces endowed with the Heckenberger-Kolb calculus.

Beam-smiling in bent-Laue monochromators

NASA Astrophysics Data System (ADS)

Ren, B.; Dilmanian, F. A.; Chapman, L. D.; Wu, X. Y.; Zhong, Z.; Ivanov, I.; Thomlinson, W. C.; Huang, X.

1997-07-01

When a wide fan-shaped x-ray beam is diffracted by a bent crystal in the Laue geometry, the profile of the diffracted beam generally does not appear as a straight line, but as a line with its ends curved up or curved down. This effect, referred to as "beam-smiling", has been a major obstacle in developing bent-Laue crystal monochromators for medical applications of synchrotron x-ray. We modeled a cylindrically bent crystal using the Finite Element Analysis (FEA) method, and we carried out experiments at the National Synchrotron Light Source and Cornell High Energy Synchrotron Source. Our studies show that, while beam-smiling exists in most of the crystal's area because of anticlastic bending effects, there is a region parallel to the bending axis of the crystal where the diffracted beam is "smile-free". By applying asymmetrical bending, this smile-free region can be shifted vertically away from the geometric center of the crystal, as desired. This leads to a novel method of compensating for beam-smiling. We will discuss the method of "differential bending" for smile removal, beam-smiling in the Cauchios and the polychromatic geometry, and the implications of the method on developing single- and double-bent Laue monochromators. The experimental results will be discussed, concentrating on specific beam-smiling observation and removal as applied to the new monochromator of the Multiple Energy Computed Tomography [MECT] project of the Medical Department, Brookhaven National Laboratory.

Synthesis, spectral, DFT modeling, cytotoxicity and microbial studies of novel Zr(IV), Ce(IV) and U(VI) piroxicam complexes

NASA Astrophysics Data System (ADS)

El-Shwiniy, Walaa H.; Zordok, Wael A.

2018-06-01

The Zr(IV), Ce(IV) and U(VI) piroxicam anti-inflammatory drug complexes were prepared and characterized using elemental analyses, conductance, IR, UV-Vis, magnetic moment, IHNMR and thermal analysis. The ratio of metal: Pir is found to be 1:2 in all complexes estimated by using molar ratio method. The conductance data reveal that Zr(IV) and U(VI) chelates are non-electrolytes except Ce(IV) complex is electrolyte. Infrared spectroscopic confirm that the Pir behaves as a bidentate ligand co-ordinated to the metal ions via the oxygen and nitrogen atoms of ν(Cdbnd O)carbonyl and ν(Cdbnd N)pyridyl, respectively. The kinetic parameters of thermogravimetric and its differential, such as activation energy, entropy of activation, enthalpy of activation, and Gibbs free energy evaluated using Coats-Redfern and Horowitz-Metzger equations for Pir and complexes. The geometry of the piroxicam drug in the Free State differs significantly from that in the metal complex. In the time of metal ion-drug bond formation the drug switches-on from the closed structure (equilibrium geometry) to the open one. The antimicrobial tests were assessed towards some types of bacteria and fungi. The in vitro cell cytotoxicity of the complexes in comparison with Pir against colon carcinoma (HCT-116) cell line was measured. Optimized geometrical structure of piroxicam ligand by using DFT calculations.

Transient Potentials in Dendritic Systems of Arbitrary Geometry

PubMed Central

Butz, Edward G.; Cowan, Jack D.

1974-01-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic “current” inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells. PMID:4416699

Aerodynamic Analysis of Simulated Heat Shield Recession for the Orion Command Module

NASA Technical Reports Server (NTRS)

Bibb, Karen L.; Alter, Stephen J.; Mcdaniel, Ryan D.

2008-01-01

The aerodynamic effects of the recession of the ablative thermal protection system for the Orion Command Module of the Crew Exploration Vehicle are important for the vehicle guidance. At the present time, the aerodynamic effects of recession being handled within the Orion aerodynamic database indirectly with an additional safety factor placed on the uncertainty bounds. This study is an initial attempt to quantify the effects for a particular set of recessed geometry shapes, in order to provide more rigorous analysis for managing recession effects within the aerodynamic database. The aerodynamic forces and moments for the baseline and recessed geometries were computed at several trajectory points using multiple CFD codes, both viscous and inviscid. The resulting aerodynamics for the baseline and recessed geometries were compared. The forces (lift, drag) show negligible differences between baseline and recessed geometries. Generally, the moments show a difference between baseline and recessed geometries that correlates with the maximum amount of recession of the geometry. The difference between the pitching moments for the baseline and recessed geometries increases as Mach number decreases (and the recession is greater), and reach a value of -0.0026 for the lowest Mach number. The change in trim angle of attack increases from approx. 0.5deg at M = 28.7 to approx. 1.3deg at M = 6, and is consistent with a previous analysis with a lower fidelity engineering tool. This correlation of the present results with the engineering tool results supports the continued use of the engineering tool for future work. The present analysis suggests there does not need to be an uncertainty due to recession in the Orion aerodynamic database for the force quantities. The magnitude of the change in pitching moment due to recession is large enough to warrant inclusion in the aerodynamic database. An increment in the uncertainty for pitching moment could be calculated from these results and included in the development of the aerodynamic database uncertainty for pitching moment.

Understanding the On-Off Switching Mechanism in Cationic Tetravalent Group-V-Based Fluoride Molecular Sensors Using Orbital Analysis.

PubMed

Usui, Kosuke; Ando, Mikinori; Yokogawa, Daisuke; Irle, Stephan

2015-12-24

The precise control of on-off switching is essential to the design of ideal molecular sensors. To understand the switching mechanism theoretically, we selected as representative example a 9-anthryltriphenylstibonium cation, which was reported as a fluoride ion sensor. In this molecule, the first excited singlet state exhibits two minimum geometries, where one of them is emissive and the other one dark. The excited state at the geometry with bright emission is of π-π* character, whereas it is of π-σ* character at the "dark" geometry. Geometry changes in the excited state were identified by geometry optimization and partial potential energy surface (PES) mapping. We also studied Group V homologues of this molecule. A barrierless relaxation pathway after vertical excitation to the "dark" geometry was found for the Sb-containing compound on the excited-states PES, whereas barriers appear in the case of P and As. Molecular orbital analysis suggests that the σ* orbital of the antimony compound is stabilized along such relaxation and that the excited state changes its nature correspondingly. Our results indicate that the size of the central atom is crucial for the design of fluoride sensors with this ligand framework.

External-Compression Supersonic Inlet Design Code

NASA Technical Reports Server (NTRS)

Slater, John W.

2011-01-01

A computer code named SUPIN has been developed to perform aerodynamic design and analysis of external-compression, supersonic inlets. The baseline set of inlets include axisymmetric pitot, two-dimensional single-duct, axisymmetric outward-turning, and two-dimensional bifurcated-duct inlets. The aerodynamic methods are based on low-fidelity analytical and numerical procedures. The geometric methods are based on planar geometry elements. SUPIN has three modes of operation: 1) generate the inlet geometry from a explicit set of geometry information, 2) size and design the inlet geometry and analyze the aerodynamic performance, and 3) compute the aerodynamic performance of a specified inlet geometry. The aerodynamic performance quantities includes inlet flow rates, total pressure recovery, and drag. The geometry output from SUPIN includes inlet dimensions, cross-sectional areas, coordinates of planar profiles, and surface grids suitable for input to grid generators for analysis by computational fluid dynamics (CFD) methods. The input data file for SUPIN and the output file from SUPIN are text (ASCII) files. The surface grid files are output as formatted Plot3D or stereolithography (STL) files. SUPIN executes in batch mode and is available as a Microsoft Windows executable and Fortran95 source code with a makefile for Linux.

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.

Dirac-Born-Infeld inflation using a one-parameter family of throat geometries

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

Gmeiner, Florian; White, Chris D, E-mail: fgmeiner@nikhef.nl, E-mail: cwhite@nikhef.nl

2008-02-15

We demonstrate the possibility of examining cosmological signatures in the Dirac-Born-Infeld (DBI) inflation setup using the BGMPZ solution, a one-parameter family of geometries for the warped throat which interpolate between the Maldacena-Nunez and Klebanov-Strassler solutions. The warp factor is determined numerically and is subsequently used to calculate cosmological observables, including the scalar and tensor spectral indices, for a sample point in the parameter space. As one moves away from the Klebanov-Strassler (KS) solution for the throat, the warp factor is qualitatively different, which leads to a significant change for the observables, but also generically increases the non-Gaussianity of the models.more » We argue that the different models can potentially be differentiated by current and future experiments.« less

Photon escape probabilities in a semi-infinite plane-parallel medium. [from electron plasma surrounding galactic X-ray sources

NASA Technical Reports Server (NTRS)

Williams, A. C.; Elsner, R. F.; Weisskopf, M. C.; Darbro, W.

1984-01-01

It is shown in this work how to obtain the probabilities of photons escaping from a cold electron plasma environment after having undergone an arbitrary number of scatterings. This is done by retaining the exact differential cross section for Thomson scattering as opposed to using its polarization and angle averaged form. The results are given in the form of recursion relations. The geometry used is the semi-infinite plane-parallel geometry witlh a photon source located on a plane at an arbitrary optical depth below the surface. Analytical expressions are given for the probabilities which are accurate over a wide range of initial optical depth. These results can be used to model compact X-ray galactic sources which are surrounded by an electron-rich plasma.

Two-dimensional radiative transfer. I - Planar geometry. [in stellar atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Auer, L. H.; Mihalas, B. R.

1978-01-01

Differential-equation methods for solving the transfer equation in two-dimensional planar geometries are developed. One method, which uses a Hermitian integration formula on ray segments through grid points, proves to be extremely well suited to velocity-dependent problems. An efficient elimination scheme is developed for which the computing time scales linearly with the number of angles and frequencies; problems with large velocity amplitudes can thus be treated accurately. A very accurate and efficient method for performing a formal solution is also presented. A discussion is given of several examples of periodic media and free-standing slabs, both in static cases and with velocity fields. For the free-standing slabs, two-dimensional transport effects are significant near boundaries, but no important effects were found in any of the periodic cases studied.

Linearized texture of three-dimensional extracellular matrix is mandatory for bladder cancer cell invasion.

PubMed

Alfano, Massimo; Nebuloni, Manuela; Allevi, Raffaele; Zerbi, Pietro; Longhi, Erika; Lucianò, Roberta; Locatelli, Irene; Pecoraro, Angela; Indrieri, Marco; Speziali, Chantal; Doglioni, Claudio; Milani, Paolo; Montorsi, Francesco; Salonia, Andrea

2016-10-25

In the fields of biomaterials and tissue engineering simulating the native microenvironment is of utmost importance. As a major component of the microenvironment, the extracellular matrix (ECM) contributes to tissue homeostasis, whereas modifications of native features are associated with pathological conditions. Furthermore, three-dimensional (3D) geometry is an important feature of synthetic scaffolds favoring cell stemness, maintenance and differentiation. We analyzed the 3D structure, geometrical measurements and anisotropy of the ECM isolated from (i) human bladder mucosa (basal lamina and lamina propria) and muscularis propria; and, (ii) bladder carcinoma (BC). Next, binding and invasion of bladder metastatic cell line was observed on synthetic scaffold recapitulating anisotropy of tumoral ECM, but not on scaffold with disorganized texture typical of non-neoplastic lamina propria. This study provided information regarding the ultrastructure and geometry of healthy human bladder and BC ECMs. Likewise, using synthetic scaffolds we identified linearization of the texture as a mandatory feature for BC cell invasion. Integrating microstructure and geometry with biochemical and mechanical factors could support the development of an innovative synthetic bladder substitute or a tumoral scaffold predictive of chemotherapy outcomes.

Radiative interactions in laminar duct flows

NASA Technical Reports Server (NTRS)

Trivedi, P. A.; Tiwari, S. N.

1990-01-01

Analyses and numerical procedures are presented for infrared radiative energy transfer in gases when other modes of energy transfer occur simultaneously. Two types of geometries are considered, a parallel plate duct and a circular duct. Fully developed laminar incompressible flows of absorbing-emitting species in black surfaced ducts are considered under the conditions of uniform wall heat flux. The participating species considered are OH, CO, CO2, and H2O. Nongray as well as gray formulations are developed for both geometries. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. Tien and Lowder's wide band model correlation was used in nongray formulation. Numerical procedures are presented to solve the integro-differential equations for both geometries. The range of physical variables considered are 300 to 2000 K for temperature, 0.1 to 100.0 atm for pressure, and 0.1 to 100 cm spacings between plates/radius of the tube. An extensive parametric study based on nongray formulation is presented. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows.

Linear information retrieval method in X-ray grating-based phase contrast imaging and its interchangeability with tomographic reconstruction

NASA Astrophysics Data System (ADS)

Wu, Z.; Gao, K.; Wang, Z. L.; Shao, Q. G.; Hu, R. F.; Wei, C. X.; Zan, G. B.; Wali, F.; Luo, R. H.; Zhu, P. P.; Tian, Y. C.

2017-06-01

In X-ray grating-based phase contrast imaging, information retrieval is necessary for quantitative research, especially for phase tomography. However, numerous and repetitive processes have to be performed for tomographic reconstruction. In this paper, we report a novel information retrieval method, which enables retrieving phase and absorption information by means of a linear combination of two mutually conjugate images. Thanks to the distributive law of the multiplication as well as the commutative law and associative law of the addition, the information retrieval can be performed after tomographic reconstruction, thus simplifying the information retrieval procedure dramatically. The theoretical model of this method is established in both parallel beam geometry for Talbot interferometer and fan beam geometry for Talbot-Lau interferometer. Numerical experiments are also performed to confirm the feasibility and validity of the proposed method. In addition, we discuss its possibility in cone beam geometry and its advantages compared with other methods. Moreover, this method can also be employed in other differential phase contrast imaging methods, such as diffraction enhanced imaging, non-interferometric imaging, and edge illumination.

Global geometry of non-planar 3-body motions

NASA Astrophysics Data System (ADS)

Salehani, Mahdi Khajeh

2011-12-01

The aim of this paper is to study the global geometry of non-planar 3-body motions in the realms of equivariant Differential Geometry and Geometric Mechanics. This work was intended as an attempt at bringing together these two areas, in which geometric methods play the major role, in the study of the 3-body problem. It is shown that the Euler equations of a three-body system with non-planar motion introduce non-holonomic constraints into the Lagrangian formulation of mechanics. Applying the method of undetermined Lagrange multipliers to study the dynamics of three-body motions reduced to the level of moduli space {bar{M}} subject to the non-holonomic constraints yields the generalized Euler-Lagrange equations of non-planar three-body motions in {bar{M}} . As an application of the derived dynamical equations in the level of {bar{M}} , we completely settle the question posed by A. Wintner in his book [The analytical foundations of Celestial Mechanics, Sections 394-396, 435 and 436. Princeton University Press (1941)] on classifying the constant inclination solutions of the three-body problem.

Effects of reading picture books on kindergartners' mathematics performance.

PubMed

van den Heuvel-Panhuizen, Marja; Elia, Iliada; Robitzsch, Alexander

2016-02-07

This article describes a field experiment with a pretest-posttest control group design which investigated the potential of reading picture books to children for supporting their mathematical understanding. The study involved 384 children from 18 kindergarten classes in 18 schools in the Netherlands. During three months, the children in the nine experimental classes were read picture books. Data analysis revealed that, when controlled for relevant covariates, the picture book reading programme had a positive effect ( d  = .13) on kindergartners' mathematics performance as measured by a project test containing items on number, measurement and geometry. Compared to the increase from pretest to posttest in the control group, the increase in the experimental group was 22% larger. No significant differential intervention effects were found between subgroups based on kindergarten year, age, home language, socio-economic status and mathematics and language ability, but a significant intervention effect was found for girls and not for boys.

Stochastic models for tumoral growth

NASA Astrophysics Data System (ADS)

Escudero, Carlos

2006-02-01

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.

Effects of reading picture books on kindergartners’ mathematics performance

PubMed Central

van den Heuvel-Panhuizen, Marja; Elia, Iliada; Robitzsch, Alexander

2016-01-01

This article describes a field experiment with a pretest–posttest control group design which investigated the potential of reading picture books to children for supporting their mathematical understanding. The study involved 384 children from 18 kindergarten classes in 18 schools in the Netherlands. During three months, the children in the nine experimental classes were read picture books. Data analysis revealed that, when controlled for relevant covariates, the picture book reading programme had a positive effect (d = .13) on kindergartners’ mathematics performance as measured by a project test containing items on number, measurement and geometry. Compared to the increase from pretest to posttest in the control group, the increase in the experimental group was 22% larger. No significant differential intervention effects were found between subgroups based on kindergarten year, age, home language, socio-economic status and mathematics and language ability, but a significant intervention effect was found for girls and not for boys. PMID:26855457

Strength and viscosity effects on perturbed shock front stability in metals

DOE PAGES

Opie, Saul; Loomis, Eric Nicholas; Peralta, Pedro; ...

2017-05-09

Here, computational modeling and experimental measurements on metal samples subject to a laser-driven, ablative Richtmyer-Meshkov instability showed differences between viscosity and strength effects. In particular, numerical and analytical solutions, coupled with measurements of fed-through perturbations, generated by perturbed shock fronts onto initially flat surfaces, show promise as a validation method for models of deviatoric response in the post shocked material. Analysis shows that measurements of shock perturbation amplitudes at low sample thickness-to-wavelength ratios are not enough to differentiate between strength and viscosity effects, but that surface displacement data of the fed-through fed-thru perturbations appears to resolve the ambiguity. Additionally, analyticalmore » and numerical results show shock front perturbation evolution dependence on initial perturbation amplitude and wavelength is significantly different in viscous and materials with strength, suggesting simple experimental geometry changes should provide data supporting one model or the other.« less

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

Kieselmann, J; Bartzsch, S; Oelfke, U

Purpose: Microbeam Radiation Therapy is a preclinical method in radiation oncology that modulates radiation fields on a micrometre scale. Dose calculation is challenging due to arising dose gradients and therapeutically important dose ranges. Monte Carlo (MC) simulations, often used as gold standard, are computationally expensive and hence too slow for the optimisation of treatment parameters in future clinical applications. On the other hand, conventional kernel based dose calculation leads to inaccurate results close to material interfaces. The purpose of this work is to overcome these inaccuracies while keeping computation times low. Methods: A point kernel superposition algorithm is modified tomore » account for tissue inhomogeneities. Instead of conventional ray tracing approaches, methods from differential geometry are applied and the space around the primary photon interaction is locally warped. The performance of this approach is compared to MC simulations and a simple convolution algorithm (CA) for two different phantoms and photon spectra. Results: While peak doses of all dose calculation methods agreed within less than 4% deviations, the proposed approach surpassed a simple convolution algorithm in accuracy by a factor of up to 3 in the scatter dose. In a treatment geometry similar to possible future clinical situations differences between Monte Carlo and the differential geometry algorithm were less than 3%. At the same time the calculation time did not exceed 15 minutes. Conclusion: With the developed method it was possible to improve the dose calculation based on the CA method with respect to accuracy especially at sharp tissue boundaries. While the calculation is more extensive than for the CA method and depends on field size, the typical calculation time for a 20×20 mm{sup 2} field on a 3.4 GHz and 8 GByte RAM processor remained below 15 minutes. Parallelisation and optimisation of the algorithm could lead to further significant calculation time reductions.« less

Molecular properties of metal difluorides and their interactions with CO2 and H2O molecules: a DFT investigation.

PubMed

Arokiyanathan, Agnes Lincy; Lakshmipathi, Senthilkumar

2017-11-18

A computational study of metal difluorides (MF 2 ; M = Ca to Zn) and their interactions with carbon dioxide and water molecules was performed. The structural parameter values obtained and the results of AIM analysis and energy decomposition analysis indicated that the Ca-F bond is weaker and less ionic than the bonds in the transition metal difluorides. A deformation density plot revealed the stablizing influence of the Jahn-Teller effect in nonlinear MF 2 molecules (e.g., where M= Sc, Ti, Cr). An anaysis of the metal K-edge peaks of the difluorides showed that shifts in the edge energy were due to the combined effects of the ionicity, effective nuclear charge, and the spin state of the metal. The interactions of CO 2 with ScF 2 (Scc3 geometry) and TiF 2 (Tic2 geometry) caused CO 2 to shift from its usual linear geometry to a bent geometry (η 2 (C=O) binding mode), while it retained its linear geometry (η 1 (O) binding mode) when it interacted with the other metal difluorides. Energy decomposition analysis showed that, among the various geometries considered, the Scc3 and Tic2 geometries possessed the highest interaction energies and orbital interaction energies. Heavier transition metal difluorides showed stronger affinities for H 2 O, whereas the lighter transition metal (Sc and Ti) difluorides preferred CO 2 . Overall, the results of this study suggest that fluorides of lighter transition metals with partially filled d orbitals (e.g., Sc and Ti) could be used for CO 2 capture under moist conditions. Graphical abstract Interaction of metal difluorides with carbon dioxide and water.

Analysis of optimisation method for a two-stroke piston ring using the Finite Element Method and the Simulated Annealing Method

NASA Astrophysics Data System (ADS)

Kaliszewski, M.; Mazuro, P.

2016-09-01

Simulated Annealing Method of optimisation for the sealing piston ring geometry is tested. The aim of optimisation is to develop ring geometry which would exert demanded pressure on a cylinder just while being bended to fit the cylinder. Method of FEM analysis of an arbitrary piston ring geometry is applied in an ANSYS software. The demanded pressure function (basing on formulae presented by A. Iskra) as well as objective function are introduced. Geometry definition constructed by polynomials in radial coordinate system is delivered and discussed. Possible application of Simulated Annealing Method in a piston ring optimisation task is proposed and visualised. Difficulties leading to possible lack of convergence of optimisation are presented. An example of an unsuccessful optimisation performed in APDL is discussed. Possible line of further optimisation improvement is proposed.

Lagrangian formulation for penny-shaped and Perkins-Kern geometry models

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

Lee, W.S.

1989-09-01

This paper discusses basic theories for vertical penny-shaped and Perkins-Kern (PK) geometry models developed with a Lagrangian formulation combined with a virtual-work analysis. The Lagrangian formulation yields a pair of nonlinear equations in R/sub f/ or L/sub f/ and b/sub f/, the fracture radius or length and half-width. By introduction of a virtual-work analysis, a simple equation is obtained that can be solved numerically. This equation is written in a form that can be used to determine fracture geometry when the fluid-loss coefficient of the fracturing fluid is known. Also, this equation, coupled with a material-balance equation after shut-in, canmore » be used to analyze pressure-decline data after shut-in to determine the effective fluid-loss coefficient and fracture geometry.« less

Performance Analysis of the Automotive TEG with Respect to the Geometry of the Modules

NASA Astrophysics Data System (ADS)

Yu, C. G.; Zheng, S. J.; Deng, Y. D.; Su, C. Q.; Wang, Y. P.

2017-05-01

Recently there has been increasing interest in applying thermoelectric technology to recover waste heat in automotive exhaust gas. Due to the limited space in the vehicle, it's meaningful to improve the TEG (thermoelectric generator) performance by optimizing the module geometry. This paper analyzes the performance of bismuth telluride modules for two criteria (power density and power output per area), and researches the relationship between the performance and the geometry of the modules. A geometry factor is defined for the thermoelectric element to describe the module geometry, and a mathematical model is set up to study the effects of the module geometry on its performance. It has been found out that the optimal geometry factors for maximum output power, power density and power output per unit area are different, and the value of the optimal geometry factors will be affected by the volume of the thermoelectric material and the thermal input. The results can be referred to as the basis for optimizing the performance of the thermoelectric modules.

Investigation of detection limits for diffuse optical tomography systems: II. Analysis of slab and cup geometry for breast imaging.

PubMed

Ziegler, Ronny; Brendel, Bernhard; Rinneberg, Herbert; Nielsen, Tim

2009-01-21

Using a statistical (chi-square) test on simulated data and a realistic noise model derived from the system's hardware we study the performance of diffuse optical tomography systems for fluorescence imaging. We compare the predicted smallest size of detectable lesions at various positions in slab and cup geometry and model how detection sensitivity depends on breast compression and lesion fluorescence contrast. Our investigation shows that lesion detection is limited by relative noise in slab geometry and by absolute noise in cup geometry.

Positron collisions with acetylene calculated using the R-matrix with pseudo-states method

NASA Astrophysics Data System (ADS)

Zhang, Rui; Galiatsatos, Pavlos G.; Tennyson, Jonathan

2011-10-01

Eigenphase sums, total cross sections and differential cross sections are calculated for low-energy collisions of positrons with C2H2. The calculations demonstrate that the use of appropriate pseudo-state expansions very significantly improves the representation of this process giving both realistic eigenphases and cross sections. Differential cross sections are strongly forward peaked in agreement with the measurements. These calculations are computationally very demanding; even with improved procedures for matrix diagonalization, fully converged calculations are too expensive with current computer resources. Nonetheless, the calculations show clear evidence for the formation of a virtual state but no indication that acetylene actually binds a positron at its equilibrium geometry.

Quantum dressing orbits on compact groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Šťovíček, Pavel

1993-02-01

The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decompositon in the general case. Quantum dressing orbits are described explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient “coherent states” are introduced and a correspondence between classical and quantum observables is given.

Differentially photo-crosslinked polymers enable self-assembling microfluidics

PubMed Central

Jamal, Mustapha; Zarafshar, Aasiyeh M.; Gracias, David H.

2012-01-01

An important feature of naturally self-assembled systems such as leaves and tissues is that they are curved and have embedded fluidic channels that enable the transport of nutrients to, or removal of waste from, specific three-dimensional (3D) regions. Here, we report the self-assembly of photopatterned polymers, and consequently microfluidic devices, into curved geometries. We discovered that differentially photo-crosslinked SU-8 films spontaneously and reversibly curved upon film de-solvation and re-solvation. Photolithographic patterning of the SU-8 films enabled the self-assembly of cylinders, cubes, and bidirectionally folded sheets. We integrated polydimethylsiloxane (PDMS) microfluidic channels with these SU-8 films to self-assemble curved microfluidic networks. PMID:22068594

IGES transformer and NURBS in grid generation

NASA Technical Reports Server (NTRS)

Yu, Tzu-Yi; Soni, Bharat K.

1993-01-01

In the field of Grid Generation and the CAD/CAM, there are numerous geometry output formats which require the designer to spend a great deal of time manipulating geometrical entities in order to achieve a useful sculptured geometrical description for grid generation. Also in this process, there is a danger of losing fidelity of the geometry under consideration. This stresses the importance of a standard geometry definition for the communication link between varying CAD/CAM and grid system. The IGES (Initial Graphics Exchange Specification) file is a widely used communication between CAD/CAM and the analysis tools. The scientists at NASA Research Centers - including NASA Ames, NASA Langley, NASA Lewis, NASA Marshall - have recognized this importance and, therefore, in 1992 they formed the committee of the 'NASA-IGES' which is the subset of the standard IGES. This committee stresses the importance and encourages the CFD community to use the standard IGES file for the interface between the CAD/CAM and CFD analysis. Also, two of the IGES entities -- the NURBS Curve (Entity 126) and NURBS Surface (Entity 128) -- which have many useful geometric properties -- like the convex hull property, local control property and affine invariance, also widely utilized analytical geometries can be accurately represented using NURBS. This is important in today grid generation tools because of the emphasis of the interactive design. To satisfy the geometry transformation between the CAD/CAM system and Grid Generation field, the CAGI (Computer Aided Geometry Design) developed, which include the Geometry Transformation, Geometry Manipulation and Geometry Generation as well as the user interface. This paper will present the successful development IGES file transformer and application of NURBS definition in the grid generation.

Multilinear Computing and Multilinear Algebraic Geometry

DTIC Science & Technology

2016-08-10

landmark paper titled “Most tensor problems are NP-hard” (see [14] in Section 3) in the Journal of the ACM, the premier journal in Computer Science ...Higher-order cone programming,” Machine Learning Thematic Trimester, International Centre for Mathematics and Computer Science , Toulouse, France...geometry-and-data-analysis • 2014 SIMONS INSTITUTE WORKSHOP: Workshop on Tensors in Computer Science and Geometry, University of California, Berkeley, CA

An Interactive Geometry Program and Its Effect on Elementary Students' Achievement and Understanding of Geometry: A Comparative Study

ERIC Educational Resources Information Center

DeMarinis, Matthew David

2011-01-01

While many studies examining the effectiveness of using dynamic geometry software exist, few studies exist at the elementary school level. An extensive data analysis of student performance on New York State Math Assessments revealed that students in the fifth grade may not have had a clear understanding of interior angles sums of polygons, more…

Rethinking Critical Mathematics: A Comparative Analysis of Critical, Reform, and Traditional Geometry Instructional Texts

ERIC Educational Resources Information Center

Brantlinger, Andrew

2011-01-01

This paper presents findings from a comparative analysis of three similar secondary geometry texts, one critical unit, one standards-based reform unit, and one specialist chapter. I developed the critical unit as I took the tenets of critical mathematics (CM) and substantiated them in printed curricular materials in which to teach as part of a…

BOOK REVIEW Analytical and Numerical Approaches to Mathematical Relativity

NASA Astrophysics Data System (ADS)

Stewart, John M.

2007-08-01

The 319th Wilhelm-and-Else-Heraeus Seminar 'Mathematical Relativity: New Ideas and Developments' took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume, preceded by a foreword by Roger Penrose. The first group consists of four papers on 'differential geometry and differential topology'. Paul Ehrlich opens with a very witty review of global Lorentzian geometry, which caused this reviewer to think more carefully about how he uses the adjective 'generic'. Robert Low addresses the issue of causality with a description of the 'space of null geodesics' and a tentative proposal for a new definition of causal boundary. The underlying review of global Lorentzian geometry is continued by Antonio Masiello, looking at variational approaches (actually valid for more general semi-Riemannian manifolds). This group concludes with a very clear review of pp-wave spacetimes from José Flores and Miguel Sánchez. (This reviewer was delighted to see a reproduction of Roger Penrose's seminal (1965) picture of null geodesics in plane wave spacetimes which attracted him into the subject.) Robert Beig opens the second group 'analytic methods and differential equations' with a brief but careful discussion of symmetric (regular) hyperbolicity for first (second) order systems, respectively, of partial differential equations. His description is peppered with examples, many specific to relativstic continuum mechanics. There follows a succinct review of linear elliptic boundary value problems with applications to general relativity from Sergio Dain. The numerous examples he provides are thought-provoking. The 'standard cosmological model' has been well understood for three quarters of a century. However recent observations suggest that the expansion in our Universe may be accelerating. Alan Rendall provides a careful discussion of the changes, both mathematical and physical, to the standard model which might be needed. This reviewer found the exposition much clearer than much of the phenomenological literature. Finally László Szabados gives a very systematic spacetime discussion of the group theoretical analysis of general relativity by Beig and Ó Murchadha, addressing the Poincaré structure and the centre-of-mass of asymptotically flat spacetimes. The third and final group is entitled 'numerical methods'. Beverly Berger summarizes her 'Living Review' on numerical approaches to spacetime singularities and includes more recent analytical results emphasizing the synergy between mathematical and numerical approaches. For numerical evolutions on a domain of compact spatial support boundary conditions will be needed and, as pointed out by this reviewer, for unconstrained evolutions it is essential that the boundary conditions ensure constraint conservation. This aspect is discussed in a clear elementary way by Simonetta Frittelli and Roberto Gómez. Dave Neilsen, Luis Lehner, Olivier Sarbach and Manuel Tiglio review algorithms adopted recently by the Louisiana group, particularly summation by parts and constraint monitoring with applications to bubble and black hole spacetimes. Finally Maria Babiuc, Béla Szilágyi and Jeffrey Winicour discuss the Pittsburgh group's approach with particular reference to harmonic gauge conditions. It is perhaps unfortunate for the editors of this work that published proceedings of more recent numerical relativity meetings exist already. However, as this reviewer has tried to indicate, this slim (but not inexpensive) volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institution's library purchases a copy!

The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries

NASA Technical Reports Server (NTRS)

Sharobeam, Monir H.

1994-01-01

Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.

Constraining the geometry and kinematics of the quasar broad emission line region using gravitational microlensing. I. Models and simulations

NASA Astrophysics Data System (ADS)

Braibant, L.; Hutsemékers, D.; Sluse, D.; Goosmann, R.

2017-11-01

Recent studies have shown that line profile distortions are commonly observed in gravitationally lensed quasar spectra. Often attributed to microlensing differential magnification, line profile distortions can provide information on the geometry and kinematics of the broad emission line region (BLR) in quasars. We investigate the effect of gravitational microlensing on quasar broad emission line profiles and their underlying continuum, combining the emission from simple representative BLR models with generic microlensing magnification maps. Specifically, we considered Keplerian disk, polar, and equatorial wind BLR models of various sizes. The effect of microlensing has been quantified with four observables: μBLR, the total magnification of the broad emission line; μcont, the magnification of the underlying continuum; as well as red/blue, RBI and wings/core, WCI, indices that characterize the line profile distortions. The simulations showed that distortions of line profiles, such as those recently observed in lensed quasars, can indeed be reproduced and attributed to the differential effect of microlensing on spatially separated regions of the BLR. While the magnification of the emission line μBLR sets an upper limit on the BLR size and, similarly, the magnification of the continuum μcont sets an upper limit on the size of the continuum source, the line profile distortions mainly depend on the BLR geometry and kinematics. We thus built (WCI,RBI) diagrams that can serve as diagnostic diagrams to discriminate between the various BLR models on the basis of quantitative measurements. It appears that a strong microlensing effect puts important constraints on the size of the BLR and on its distance to the high-magnification caustic. In that case, BLR models with different geometries and kinematics are more prone to produce distinctive line profile distortions for a limited number of caustic configurations, which facilitates their discrimination. When the microlensing effect is weak, there is a larger overlap between the characteristics of the line profile distortions produced by the different models, and constraints can only be derived on a statistical basis.

Correction of terrestrial LiDAR intensity channel using Oren-Nayar reflectance model: An application to lithological differentiation

NASA Astrophysics Data System (ADS)

Carrea, Dario; Abellan, Antonio; Humair, Florian; Matasci, Battista; Derron, Marc-Henri; Jaboyedoff, Michel

2016-03-01

Ground-based LiDAR has been traditionally used for surveying purposes via 3D point clouds. In addition to XYZ coordinates, an intensity value is also recorded by LiDAR devices. The intensity of the backscattered signal can be a significant source of information for various applications in geosciences. Previous attempts to account for the scattering of the laser signal are usually modelled using a perfect diffuse reflection. Nevertheless, experience on natural outcrops shows that rock surfaces do not behave as perfect diffuse reflectors. The geometry (or relief) of the scanned surfaces plays a major role in the recorded intensity values. Our study proposes a new terrestrial LiDAR intensity correction, which takes into consideration the range, the incidence angle and the geometry of the scanned surfaces. The proposed correction equation combines the classical radar equation for LiDAR with the bidirectional reflectance distribution function of the Oren-Nayar model. It is based on the idea that the surface geometry can be modelled by a relief of multiple micro-facets. This model is constrained by only one tuning parameter: the standard deviation of the slope angle distribution (σslope) of micro-facets. Firstly, a series of tests have been carried out in laboratory conditions on a 2 m2 board covered by black/white matte paper (perfect diffuse reflector) and scanned at different ranges and incidence angles. Secondly, other tests were carried out on rock blocks of different lithologies and surface conditions. Those tests demonstrated that the non-perfect diffuse reflectance of rock surfaces can be practically handled by the proposed correction method. Finally, the intensity correction method was applied to a real case study, with two scans of the carbonate rock outcrop of the Dents-du-Midi (Swiss Alps), to improve the lithological identification for geological mapping purposes. After correction, the intensity values are proportional to the intrinsic material reflectance and are independent from range, incidence angle and scanned surface geometry. The corrected intensity values significantly improve the material differentiation.

Synthesis and Characterization of Diranitidinecopper(II) Sulfate Dihydrate

NASA Astrophysics Data System (ADS)

Syaima, H.; Rahardjo, S. B.; Zein, I. M.

2018-04-01

The complex of ranitidine with Cu(II) has been synthesized in 1:2-mole ratio of metal to the ligand in water. The forming of the complex was indicated by shifting of maximum wavelength from 816 nm (CuSO4·5H2O) to 626 nm (the complex). Infrared spectra indicated NO2 and NH functional group were coordinated to Cu(II). The percentage of copper in the complex measured by Atomic Absorption Spectroscopy (AAS) analysis was 7.5% indicating that formula of the complex was Cu(ranitidine)2SO4(H2O)n (n=2, 3 or 4). The electrical conductivity of Cu(II) complex in water was 71.0 Scm2mol-1 corresponding to 1:1 electrolytes. Thermogravimetric/Differential Thermal Analysis (TG/DTA) showed the presence of two molecules of H2O in the complex. UV-Vis spectra showed a transition peak on 15974 cm-1 indicating square planar geometry. The complex was paramagnetic with µeff 1.77 BM. The proposed formula of the complex was [Cu(ranitidine)2]SO4·2H2O.

Surface Micromachined Silicon Carbide Accelerometers for Gas Turbine Applications

NASA Technical Reports Server (NTRS)

DeAnna, Russell G.

1998-01-01

A finite-element analysis of possible silicon carbide (SIC) folded-beam, lateral-resonating accelerometers is presented. Results include stiffness coefficients, acceleration sensitivities, resonant frequency versus temperature, and proof-mass displacements due to centripetal acceleration of a blade-mounted sensor. The surface micromachined devices, which are similar to the Analog Devices Inc., (Norwood, MA) air-bag crash detector, are etched from 2-pm thick, 3C-SiC films grown at 1600 K using atmospheric pressure chemical vapor deposition (APCVD). The substrate is a 500 gm-thick, (100) silicon wafer. Polysilicon or silicon dioxide is used as a sacrificial layer. The finite element analysis includes temperature-dependent properties, shape change due to volume expansion, and thermal stress caused by differential thermal expansion of the materials. The finite-element results are compared to experimental results for a SiC device of similar, but not identical, geometry. Along with changes in mechanical design, blade-mounted sensors would require on-chip circuitry to cancel displacements due to centripetal acceleration and improve sensitivity and bandwidth. These findings may result in better accelerometer designs for this application.

Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

DOE PAGES

Zheng, Zhong; Christov, Ivan  C.; Stone, Howard  A.

2014-05-01

We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b)more » a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.« less

The instrumental genesis process in future primary teachers using Dynamic Geometry Software

NASA Astrophysics Data System (ADS)

Ruiz-López, Natalia

2018-05-01

This paper, which describes a study undertaken with pairs of future primary teachers using GeoGebra software to solve geometry problems, includes a brief literature review, the theoretical framework and methodology used. An analysis of the instrumental genesis process for a pair participating in the case study is also provided. This analysis addresses the techniques and types of dragging used, the obstacles to learning encountered, a description of the interaction between the pair and their interaction with the teacher, and the type of language used. Based on this analysis, possibilities and limitations of the instrumental genesis process are identified for the development of geometric competencies such as conjecture creation, property checking and problem researching. It is also suggested that the methodology used in the analysis of the problem solving process may be useful for those teachers and researchers who want to integrate Dynamic Geometry Software (DGS) in their classrooms.

Detecting Shielded Special Nuclear Materials Using Multi-Dimensional Neutron Source and Detector Geometries

NASA Astrophysics Data System (ADS)

Santarius, John; Navarro, Marcos; Michalak, Matthew; Fancher, Aaron; Kulcinski, Gerald; Bonomo, Richard

2016-10-01

A newly initiated research project will be described that investigates methods for detecting shielded special nuclear materials by combining multi-dimensional neutron sources, forward/adjoint calculations modeling neutron and gamma transport, and sparse data analysis of detector signals. The key tasks for this project are: (1) developing a radiation transport capability for use in optimizing adaptive-geometry, inertial-electrostatic confinement (IEC) neutron source/detector configurations for neutron pulses distributed in space and/or phased in time; (2) creating distributed-geometry, gas-target, IEC fusion neutron sources; (3) applying sparse data and noise reduction algorithms, such as principal component analysis (PCA) and wavelet transform analysis, to enhance detection fidelity; and (4) educating graduate and undergraduate students. Funded by DHS DNDO Project 2015-DN-077-ARI095.

Effect of in vitro enzymatic degradation on 3D printed poly(ε-caprolactone) scaffolds: morphological, chemical and mechanical properties.

PubMed

Ferreira, Joana; Gloria, Antonio; Cometa, Stefania; Coelho, Jorge F J; Domingos, Marco

2017-07-27

In recent years, the tissue engineering (TE) field has significantly benefited from advanced techniques such as additive manufacturing (AM), for the design of customized 3D scaffolds with the aim of guided tissue repair. Among the wide range of materials available to biomanufacture 3D scaffolds, poly(ε-caprolactone) (PCL) clearly arises as the synthetic polymer with the greatest potential, due to its unique properties - namely, biocompatibility, biodegradability, thermal and chemical stability and processability. This study aimed for the first time to investigate the effect of pore geometry on the in vitro enzymatic chain cleavage mechanism of PCL scaffolds manufactured by the AM extrusion process. Methods: Morphological properties of 3D printed PCL scaffolds before and after degradation were evaluated using Scanning Electron Microscopy (SEM) and micro-computed tomography (μ-CT). Differential Scanning Calorimetry (DSC) was employed to determine possible variations in the crystallinity of the scaffolds during the degradation period. The molecular weight was assessed using Size Exclusion Chromatography (SEC) while the mechanical properties were investigated under static compression conditions. Morphological results suggested a uniform reduction of filament diameter, while increasing the scaffolds' porosity. DSC analysis revealed and increment in the crystallinity degree while the molecular weight, evaluated through SEC, remained almost constant during the incubation period (25 days). Mechanical analysis highlighted a decrease in the compressive modulus and maximum stress over time, probably related to the significant weight loss of the scaffolds. All of these results suggest that PCL scaffolds undergo enzymatic degradation through a surface erosion mechanism, which leads to significant variations in mechanical, physical and chemical properties, but which has little influence on pore geometry.

Degrees of Freedom: Diversifying Math Requirements for College Readiness and Graduation (Report 1 of a 3-Part Series)

ERIC Educational Resources Information Center

Burdman, Pamela

2015-01-01

Since the mid-20th century, the standard U.S. high school and college math curriculum has been based on two years of algebra and a year of geometry, preparing students to take classes in pre-calculus followed by calculus. Students' math pursuits have been differentiated primarily by how far or how rapidly they proceed along a clearly defined…

Radar Cross Section Prediction for Coated Perfect Conductors with Arbitrary Geometries.

DTIC Science & Technology

1986-01-01

equivalent electric and magnetic surface currents as the desired unknowns. Triangular patch modelling is ap- plied to the boundary surfaces. The method of...matrix inversion for the unknown surface current coefficients. Huygens’ principle is again applied to calculate the scattered electric field produced...differential equations with the equivalent electric and magnetic surface currents as the desired unknowns. Triangular patch modelling is ap- plied to the

Double Alfvén waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Hu, Q.; Dasgupta, B.; Zank, G. P.

2012-02-01

Double Alfvén wave solutions of the magnetohydrodynamic equations in which the physical variables (the gas density ρ, fluid velocity u, gas pressure p, and magnetic field induction B) depend only on two independent wave phases ϕ1(x,t) and ϕ2(x,t) are obtained. The integrals for the double Alfvén wave are the same as for simple waves, namely, the gas pressure, magnetic pressure, and group velocity of the wave are constant. Compatibility conditions on the evolution of the magnetic field B due to changes in ϕ1 and ϕ2, as well as constraints due to Gauss's law ∇ · B = 0 are discussed. The magnetic field lines and hodographs of B in which the tip of the magnetic field B moves on the sphere |B| = B = const. are used to delineate the physical characteristics of the wave. Hamilton's equations for the simple Alfvén wave with wave normal n(ϕ), and with magnetic induction B(ϕ) in which ϕ is the wave phase, are obtained by using the Frenet-Serret equations for curves x=X(ϕ) in differential geometry. The use of differential geometry of 2D surfaces in a 3D Euclidean space to describe double Alfvén waves is briefly discussed.

Free-energy analysis of spin models on hyperbolic lattice geometries.

PubMed

Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej

2016-04-01

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

Stability analysis of an F/A-18 E/F cable mount m odel

NASA Technical Reports Server (NTRS)

Thompson, Nancy; Farmer, Moses

1994-01-01

A full-span F/A-18 E/F cable mounted wind tunnel model is part of a flutter clearance program at the NASA Langley Transonic Dynamics Tunnel. Parametric analysis of this model using GRUMCBL software was conducted to assess stability for wind tunnel tests. Two configurations of the F/A-18 E/F were examined. The parameters examined were pulley-cable friction, mach number, dynamic pressure, cable geometry, center of gravity location, cable tension, snubbing the model, drag, and test medium. For the nominal cable geometry (Cable Geometry 1), Configuration One was unstable for cases with higher pulley-cable friction coefficients. A new cable geometry (Cable Geometry 3) was determined in which Configuration One was stable for all cases evaluated. Configuration Two with the nominal center of gravity position was found to be unstable for cases with higher pulley-cable friction coefficients; however, the model was stable when the center of gravity moved forward 1/2. The model was tested using the cable mount system during the initial wind tunnel entry and was stable as predicted.

An investigation of dynamic-analysis methods for variable-geometry structures

NASA Technical Reports Server (NTRS)

Austin, F.

1980-01-01

Selected space structure configurations were reviewed in order to define dynamic analysis problems associated with variable geometry. The dynamics of a beam being constructed from a flexible base and the relocation of the completed beam by rotating the remote manipulator system about the shoulder joint were selected. Equations of motion were formulated in physical coordinates for both of these problems, and FORTRAN programs were developed to generate solutions by numerically integrating the equations. These solutions served as a standard of comparison to gauge the accuracy of approximate solution techniques that were developed and studied. Good control was achieved in both problems. Unstable control system coupling with the system flexibility did not occur. An approximate method was developed for each problem to enable the analyst to investigate variable geometry effects during a short time span using standard fixed geometry programs such as NASTRAN. The average angle and average length techniques are discussed.

Numerical Modeling of Pulse Detonation Rocket Engine Gasdynamics and Performance

NASA Technical Reports Server (NTRS)

2003-01-01

This paper presents viewgraphs on the numerical modeling of pulse detonation rocket engines (PDRE), with an emphasis on the Gasdynamics and performance analysis of these engines. The topics include: 1) Performance Analysis of PDREs; 2) Simplified PDRE Cycle; 3) Comparison of PDRE and Steady-State Rocket Engines (SSRE) Performance; 4) Numerical Modeling of Quasi 1-D Rocket Flows; 5) Specific PDRE Geometries Studied; 6) Time-Accurate Thrust Calculations; 7) PDRE Performance (Geometries A B C and D); 8) PDRE Blowdown Gasdynamics (Geom. A B C and D); 9) PDRE Geometry Performance Comparison; 10) PDRE Blowdown Time (Geom. A B C and D); 11) Specific SSRE Geometry Studied; 12) Effect of F-R Chemistry on SSRE Performance; 13) PDRE/SSRE Performance Comparison; 14) PDRE Performance Study; 15) Grid Resolution Study; and 16) Effect of F-R Chemistry on SSRE Exit Species Mole Fractions.

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

Object-oriented Persistent Homology

PubMed Central

Wang, Bao; Wei, Guo-Wei

2015-01-01

Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering applications. However, such a success is essentially limited to qualitative data classification and analysis. Indeed, persistent homology has rarely been employed for quantitative modeling and prediction. Additionally, the present persistent homology is a passive tool, rather than a proactive technique, for classification and analysis. In this work, we outline a general protocol to construct object-oriented persistent homology methods. By means of differential geometry theory of surfaces, we construct an objective functional, namely, a surface free energy defined on the data of interest. The minimization of the objective functional leads to a Laplace-Beltrami operator which generates a multiscale representation of the initial data and offers an objective oriented filtration process. The resulting differential geometry based object-oriented persistent homology is able to preserve desirable geometric features in the evolutionary filtration and enhances the corresponding topological persistence. The cubical complex based homology algorithm is employed in the present work to be compatible with the Cartesian representation of the Laplace-Beltrami flow. The proposed Laplace-Beltrami flow based persistent homology method is extensively validated. The consistence between Laplace-Beltrami flow based filtration and Euclidean distance based filtration is confirmed on the Vietoris-Rips complex for a large amount of numerical tests. The convergence and reliability of the present Laplace-Beltrami flow based cubical complex filtration approach are analyzed over various spatial and temporal mesh sizes. The Laplace-Beltrami flow based persistent homology approach is utilized to study the intrinsic topology of proteins and fullerene molecules. Based on a quantitative model which correlates the topological persistence of fullerene central cavity with the total curvature energy of the fullerene structure, the proposed method is used for the prediction of fullerene isomer stability. The efficiency and robustness of the present method are verified by more than 500 fullerene molecules. It is shown that the proposed persistent homology based quantitative model offers good predictions of total curvature energies for ten types of fullerene isomers. The present work offers the first example to design object-oriented persistent homology to enhance or preserve desirable features in the original data during the filtration process and then automatically detect or extract the corresponding topological traits from the data. PMID:26705370

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

Effect of Random Natural Fractures on Hydraulic Fracture Propagation Geometry in Fractured Carbonate Rocks

NASA Astrophysics Data System (ADS)

Liu, Zhiyuan; Wang, Shijie; Zhao, Haiyang; Wang, Lei; Li, Wei; Geng, Yudi; Tao, Shan; Zhang, Guangqing; Chen, Mian

2018-02-01

Natural fractures have a significant influence on the propagation geometry of hydraulic fractures in fractured reservoirs. True triaxial volumetric fracturing experiments, in which random natural fractures are created by placing cement blocks of different dimensions in a cuboid mold and filling the mold with additional cement to create the final test specimen, were used to study the factors that influence the hydraulic fracture propagation geometry. These factors include the presence of natural fractures around the wellbore, the dimension and volumetric density of random natural fractures and the horizontal differential stress. The results show that volumetric fractures preferentially formed when natural fractures occurred around the wellbore, the natural fractures are medium to long and have a volumetric density of 6-9%, and the stress difference is less than 11 MPa. The volumetric fracture geometries are mainly major multi-branch fractures with fracture networks or major multi-branch fractures (2-4 fractures). The angles between the major fractures and the maximum horizontal in situ stress are 30°-45°, and fracture networks are located at the intersections of major multi-branch fractures. Short natural fractures rarely led to the formation of fracture networks. Thus, the interaction between hydraulic fractures and short natural fractures has little engineering significance. The conclusions are important for field applications and for gaining a deeper understanding of the formation process of volumetric fractures.

A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem

PubMed Central

Burian, Agata; Uyttewaal, Magalie

2013-01-01

Cortical microtubules (CMTs) are often aligned in a particular direction in individual cells or even in groups of cells and play a central role in the definition of growth anisotropy. How the CMTs themselves are aligned is not well known, but two hypotheses have been proposed. According to the first hypothesis, CMTs align perpendicular to the maximal growth direction, and, according to the second, CMTs align parallel to the maximal stress direction. Since both hypotheses were formulated on the basis of mainly qualitative assessments, the link between CMT organization, organ geometry, and cell growth is revisited using a quantitative approach. For this purpose, CMT orientation, local curvature, and growth parameters for each cell were measured in the growing shoot apical meristem (SAM) of Arabidopsis thaliana. Using this approach, it has been shown that stable CMTs tend to be perpendicular to the direction of maximal growth in cells at the SAM periphery, but parallel in the cells at the boundary domain. When examining the local curvature of the SAM surface, no strict correlation between curvature and CMT arrangement was found, which implies that SAM geometry, and presumed geometry-derived stress distribution, is not sufficient to prescribe the CMT orientation. However, a better match between stress and CMTs was found when mechanical stress derived from differential growth was also considered. PMID:24153420

A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem.

PubMed

Burian, Agata; Ludynia, Michal; Uyttewaal, Magalie; Traas, Jan; Boudaoud, Arezki; Hamant, Olivier; Kwiatkowska, Dorota

2013-12-01

Cortical microtubules (CMTs) are often aligned in a particular direction in individual cells or even in groups of cells and play a central role in the definition of growth anisotropy. How the CMTs themselves are aligned is not well known, but two hypotheses have been proposed. According to the first hypothesis, CMTs align perpendicular to the maximal growth direction, and, according to the second, CMTs align parallel to the maximal stress direction. Since both hypotheses were formulated on the basis of mainly qualitative assessments, the link between CMT organization, organ geometry, and cell growth is revisited using a quantitative approach. For this purpose, CMT orientation, local curvature, and growth parameters for each cell were measured in the growing shoot apical meristem (SAM) of Arabidopsis thaliana. Using this approach, it has been shown that stable CMTs tend to be perpendicular to the direction of maximal growth in cells at the SAM periphery, but parallel in the cells at the boundary domain. When examining the local curvature of the SAM surface, no strict correlation between curvature and CMT arrangement was found, which implies that SAM geometry, and presumed geometry-derived stress distribution, is not sufficient to prescribe the CMT orientation. However, a better match between stress and CMTs was found when mechanical stress derived from differential growth was also considered.

Integration of design, structural, thermal and optical analysis: And user's guide for structural-to-optical translator (PATCOD)

NASA Technical Reports Server (NTRS)

Amundsen, R. M.; Feldhaus, W. S.; Little, A. D.; Mitchum, M. V.

1995-01-01

Electronic integration of design and analysis processes was achieved and refined at Langley Research Center (LaRC) during the development of an optical bench for a laser-based aerospace experiment. Mechanical design has been integrated with thermal, structural and optical analyses. Electronic import of the model geometry eliminates the repetitive steps of geometry input to develop each analysis model, leading to faster and more accurate analyses. Guidelines for integrated model development are given. This integrated analysis process has been built around software that was already in use by designers and analysis at LaRC. The process as currently implemented used Pro/Engineer for design, Pro/Manufacturing for fabrication, PATRAN for solid modeling, NASTRAN for structural analysis, SINDA-85 and P/Thermal for thermal analysis, and Code V for optical analysis. Currently, the only analysis model to be built manually is the Code V model; all others can be imported for the Pro/E geometry. The translator from PATRAN results to Code V optical analysis (PATCOD) was developed and tested at LaRC. Directions for use of the translator or other models are given.

Preliminary Analysis of an Oscillating Surge Wave Energy Converter with Controlled Geometry: Preprint

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

Tom, Nathan; Lawson, Michael; Yu, Yi-Hsiang

The aim of this paper is to present a novel wave energy converter device concept that is being developed at the National Renewable Energy Laboratory. The proposed concept combines an oscillating surge wave energy converter with active control surfaces. These active control surfaces allow for the device geometry to be altered, which leads to changes in the hydrodynamic properties. The device geometry will be controlled on a sea state time scale and combined with wave-to-wave power-take-off control to maximize power capture, increase capacity factor, and reduce design loads. The paper begins with a traditional linear frequency domain analysis of themore » device performance. Performance sensitivity to foil pitch angle, the number of activated foils, and foil cross section geometry is presented to illustrate the current design decisions; however, it is understood from previous studies that modeling of current oscillating wave energy converter designs requires the consideration of nonlinear hydrodynamics and viscous drag forces. In response, a nonlinear model is presented that highlights the shortcomings of the linear frequency domain analysis and increases the precision in predicted performance.« less

Wind Turbine Blade Design System - Aerodynamic and Structural Analysis

NASA Astrophysics Data System (ADS)

Dey, Soumitr

2011-12-01

The ever increasing need for energy and the depletion of non-renewable energy resources has led to more advancement in the "Green Energy" field, including wind energy. An improvement in performance of a Wind Turbine will enhance its economic viability, which can be achieved by better aerodynamic designs. In the present study, a design system that has been under development for gas turbine turbomachinery has been modified for designing wind turbine blades. This is a very different approach for wind turbine blade design, but will allow it to benefit from the features inherent in the geometry flexibility and broad design space of the presented system. It starts with key overall design parameters and a low-fidelity model that is used to create the initial geometry parameters. The low-fidelity system includes the axisymmetric solver with loss models, T-Axi (Turbomachinery-AXIsymmetric), MISES blade-to-blade solver and 2D wing analysis code XFLR5. The geometry parameters are used to define sections along the span of the blade and connected to the CAD model of the wind turbine blade through CAPRI (Computational Analysis PRogramming Interface), a CAD neutral API that facilitates the use of parametric geometry definition with CAD. Either the sections or the CAD geometry is then available for CFD and Finite Element Analysis. The GE 1.5sle MW wind turbine and NERL NASA Phase VI wind turbine have been used as test cases. Details of the design system application are described, and the resulting wind turbine geometry and conditions are compared to the published results of the GE and NREL wind turbines. A 2D wing analysis code XFLR5, is used for to compare results from 2D analysis to blade-to-blade analysis and the 3D CFD analysis. This kind of comparison concludes that, from hub to 25% of the span blade to blade effects or the cascade effect has to be considered, from 25% to 75%, the blade acts as a 2d wing and from 75% to the tip 3D and tip effects have to be taken into account for design considerations. In addition, the benefits of this approach for wind turbine design and future efforts are discussed.

Contact in an expanding universe: an instructive exercise in dynamic geometry

NASA Astrophysics Data System (ADS)

Zimmerman, Seth

2010-11-01

The particular problem solved in this paper is that of calculating the time required to overtake a distant object receding under cosmic expansion, and the speed at which that object is passed. This is a rarely investigated problem leading to some interesting apparent paradoxes. We employ the problem to promote a deeper understanding of the dynamic geometry behind the expansion of space in three eras, especially for physics undergraduates. We do not utilize the standard cosmological formulae, but deliberately take a simpler approach, comprehensible to any student comfortable with differentials. This should offer an intuitive preparation for later courses in general relativity. The paper can be read straight through, or offered to a class in segments as problems to investigate. The overall intention is to leave students with a more tangible grasp of expanding space.

Analysis of students geometry skills viewed from spatial intelligence

NASA Astrophysics Data System (ADS)

Riastuti, Nova; Mardiyana, Pramudya, Ikrar

2017-12-01

Geometry is one of the difficult materials for students because students must have the ability to visualize, describe the picture, draw a figure, and know the kinds of figures. This study aimisto describe the students geometry skills in resolving geometry problems viewed from spatial intelligence. This research uses a descriptive qualitative method has aim to identify students geometry skills by 6 students in eight grade of Ngawi regency, Indonesia. The subjects were 2 students with high spatial intelligence, 2 students with medium spatial intelligence, and 2 students with low spatial intelligence. Datas were collected based on written test and interview. The result of this research showed that the students geometry skills viewed from spatial intelligence includes. The results of this study indicate that there was a correlation between students' spatial intelligence with geometric skills. Students had different geometric skills in each category of spatial intelligence, although there were similarities in some geometry skill indicators. Students with low spatial intelligence had less geometry skills, thus requiring special attention from teachers. Mathematics teachers are expected to provide more practice questions that reinforce students' geometry skills including visual skills, descriptive skills, drawing skills, logical skills, applied skills.

Sandia Corporation (Albuquerque, NM)

DOEpatents

Ewsuk, Kevin G [Albuquerque, NM; Arguello, Jr., Jose G.

2006-01-31

A method of designing a primary geometry, such as for a forming die, to be used in a powder pressing application by using a combination of axisymmetric geometric shapes, transition radii, and transition spaces to simulate the geometry where the shapes can be selected from a predetermined list or menu of axisymmetric shapes and then developing a finite element mesh to represent the geometry. This mesh, along with material properties of the component to be designed and powder, is input to a standard deformation finite element code to evaluate the deformation characteristics of the component being designed. The user can develop the geometry interactively with a computer interface in minutes and execute a complete analysis of the deformation characteristics of the simulated component geometry.

Surface complexation and precipitate geometry for aqueous Zn(II) sorption on ferrihydrite: II. XANES analysis and simulation

USGS Publications Warehouse

Waychunas, G.A.; Fuller, C.C.; Davis, J.A.; Rehr, J.J.

2003-01-01

X-ray absorption near-edge spectroscopy (XANES) analysis of sorption complexes has the advantages of high sensitivity (10- to 20-fold greater than extended X-ray absorption fine structure [EXAFS] analysis) and relative ease and speed of data collection (because of the short k-space range). It is thus a potentially powerful tool for characterization of environmentally significant surface complexes and precipitates at very low surface coverages. However, quantitative analysis has been limited largely to "fingerprint" comparison with model spectra because of the difficulty of obtaining accurate multiple-scattering amplitudes for small clusters with high confidence. In the present work, calculations of the XANES for 50- to 200-atom clusters of structure from Zn model compounds using the full multiple-scattering code Feff 8.0 accurately replicate experimental spectra and display features characteristic of specific first-neighbor anion coordination geometry and second-neighbor cation geometry and number. Analogous calculations of the XANES for small molecular clusters indicative of precipitation and sorption geometries for aqueous Zn on ferrihydrite, and suggested by EXAFS analysis, are in good agreement with observed spectral trends with sample composition, with Zn-oxygen coordination and with changes in second-neighbor cation coordination as a function of sorption coverage. Empirical analysis of experimental XANES features further verifies the validity of the calculations. The findings agree well with a complete EXAFS analysis previously reported for the same sample set, namely, that octahedrally coordinated aqueous Zn2+ species sorb as a tetrahedral complex on ferrihydrite with varying local geometry depending on sorption density. At significantly higher densities but below those at which Zn hydroxide is expected to precipitate, a mainly octahedral coordinated Zn2+ precipitate is observed. An analysis of the multiple scattering paths contributing to the XANES demonstrates the importance of scattering paths involving the anion sublattice. We also describe the specific advantages of complementary quantitative XANES and EXAFS analysis and estimate limits on the extent of structural information obtainable from XANES analysis. ?? 2003 Elsevier Science Ltd.

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Coulette, David

2016-08-01

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

Modeling of weld bead geometry for rapid manufacturing by robotic GMAW

NASA Astrophysics Data System (ADS)

Yang, Tao; Xiong, Jun; Chen, Hui; Chen, Yong

2015-03-01

Weld-based rapid prototyping (RP) has shown great promises for fabricating 3D complex parts. During the layered deposition of forming metallic parts with robotic gas metal arc welding, the geometry of a single weld bead has an important influence on surface finish quality, layer thickness and dimensional accuracy of the deposited layer. In order to obtain accurate, predictable and controllable bead geometry, it is essential to understand the relationships between the process variables with the bead geometry (bead width, bead height and ratio of bead width to bead height). This paper highlights an experimental study carried out to develop mathematical models to predict deposited bead geometry through the quadratic general rotary unitized design. The adequacy and significance of the models were verified via the analysis of variance. Complicated cause-effect relationships between the process parameters and the bead geometry were revealed. Results show that the developed models can be applied to predict the desired bead geometry with great accuracy in layered deposition with accordance to the slicing process of RP.

3D MR flow analysis in realistic rapid-prototyping model systems of the thoracic aorta: comparison with in vivo data and computational fluid dynamics in identical vessel geometries.

PubMed

Canstein, C; Cachot, P; Faust, A; Stalder, A F; Bock, J; Frydrychowicz, A; Küffer, J; Hennig, J; Markl, M

2008-03-01

The knowledge of local vascular anatomy and function in the human body is of high interest for the diagnosis and treatment of cardiovascular disease. A comprehensive analysis of the hemodynamics in the thoracic aorta is presented based on the integration of flow-sensitive 4D MRI with state-of-the-art rapid prototyping technology and computational fluid dynamics (CFD). Rapid prototyping was used to transform aortic geometries as measured by contrast-enhanced MR angiography into realistic vascular models with large anatomical coverage. Integration into a flow circuit with patient-specific pulsatile in-flow conditions and application of flow-sensitive 4D MRI permitted detailed analysis of local and global 3D flow dynamics in a realistic vascular geometry. Visualization of characteristic 3D flow patterns and quantitative comparisons of the in vitro experiments with in vivo data and CFD simulations in identical vascular geometries were performed to evaluate the accuracy of vascular model systems. The results indicate the potential of such patient-specific model systems for detailed experimental simulation of realistic vascular hemodynamics. Further studies are warranted to examine the influence of refined boundary conditions of the human circulatory system such as fluid-wall interaction and their effect on normal and pathological blood flow characteristics associated with vascular geometry. (c) 2008 Wiley-Liss, Inc.

Theoretical NMR and conformational analysis of solvated oximes for organophosphates-inhibited acetylcholinesterase reactivation

NASA Astrophysics Data System (ADS)

da Silva, Jorge Alberto Valle; Modesto-Costa, Lucas; de Koning, Martijn C.; Borges, Itamar; França, Tanos Celmar Costa

2018-01-01

In this work, quaternary and non-quaternary oximes designed to bind at the peripheral site of acetylcholinesterase previously inhibited by organophosphates were investigated theoretically. Some of those oximes have a large number of degrees of freedom, thus requiring an accurate method to obtain molecular geometries. For this reason, the density functional theory (DFT) was employed to refine their molecular geometries after conformational analysis and to compare their 1H and 13C nuclear magnetic resonance (NMR) theoretical signals in gas-phase and in solvent. A good agreement with experimental data was achieved and the same theoretical approach was employed to obtain the geometries in water environment for further studies.

A Joined-Wing Flight Experiment

DTIC Science & Technology

2008-02-01

and fuselage, reference geometry and ventral fins, reference geometry and winglets and finally reference geometry and main gear strut-fins. He...the addition of winglets or strut fins, unless the center of mass was shifted forward [30]. Throughout his analysis it became clear that VA-1...With the addition of winglets or fins placed over the main wheel struts, 02.0≈Δ βN C . The addition of the winglets or strut fins introduces a spiral

Comparison of calculated and measured model rotor loading and wake geometry

NASA Technical Reports Server (NTRS)

Johnson, W.

1980-01-01

The calculated blade bound circulation and wake geometry are compared with measured results for a model helicopter rotor in hover and forward flight. Hover results are presented for rectangular tip and ogee tip planform blades. The correlation is quite good when the measured wake geometry characteristics are used in the analysis. Available prescribed wake geometry models are found to give fair predictions of the loading, but they do not produce a reasonable prediction of the induced power. Forward flight results are presented for twisted and untwisted blades. Fair correlation between measurements and calculations is found for the bound circulation distribution on the advancing side. The tip vortex geometry in the vicinity of the advancing blade in forward flight was predicted well by the free wake calculation used, although the wake geometry did not have a significant influence on the calculated loading and performance for the cases considered.

Microstructural characterisation of proton irradiated niobium using X-ray diffraction technique

NASA Astrophysics Data System (ADS)

Dutta, Argha; Gayathri, N.; Neogy, S.; Mukherjee, P.

2018-04-01

The microstructural parameters in pure Nb, irradiated with 5 MeV proton beam have been evaluated as a function of dose using X-ray diffraction line profile analysis. In order to assess the microstructural changes in the homogeneous region and in the peak damage region of the damage energy deposition profile, X-ray diffraction patterns have been collected using two different geometries (Bragg-Brentano and parallel beam geometries). Different X-ray line profile analysis like Williamson-Hall (W-H) analysis, modified W-H analysis, double-Voigt analysis, modified Rietveld technique and convolutional multiple whole profile fitting have been employed to extract the microstructural parameters like coherent domain size, microstrain within the domain, dislocation density and arrangement of dislocations. The coherent domain size decreases drastically along with increase in microstrain and dislocation density in the first dose for both the geometries. With increasing dose, a decreasing trend in microstrain associated with decrease in dislocation density is observed for both the geometries. This is attributed to the formation of defect clusters due to irradiation which with increasing dose collapse to dislocation loops to minimise the strain in the matrix. This is corroborated with the observation of black dots and loops in the TEM images. No significant difference is observed in the trend of microstructural parameters between the homogeneous and peak damage region of the damage profile.

Parametric Studies for Scenario Earthquakes: Site Effects and Differential Motion

NASA Astrophysics Data System (ADS)

Panza, G. F.; Panza, G. F.; Romanelli, F.

2001-12-01

In presence of strong lateral heterogeneities, the generation of local surface waves and local resonance can give rise to a complicated pattern in the spatial groundshaking scenario. For any object of the built environment with dimensions greater than the characteristic length of the ground motion, different parts of its foundations can experience severe non-synchronous seismic input. In order to perform an accurate estimate of the site effects, and of differential motion, in realistic geometries, it is necessary to make a parametric study that takes into account the complex combination of the source and propagation parameters. The computation of a wide set of time histories and spectral information, corresponding to possible seismotectonic scenarios for different source and structural models, allows us the construction of damage scenarios that are out of reach of stochastic models. Synthetic signals, to be used as seismic input in a subsequent engineering analysis, e.g. for the design of earthquake-resistant structures or for the estimation of differential motion, can be produced at a very low cost/benefit ratio. We illustrate the work done in the framework of a large international cooperation following the guidelines of the UNESCO IUGS IGCP Project 414 "Realistic Modeling of Seismic Input for Megacities and Large Urban Areas" and show the very recent numerical experiments carried out within the EC project "Advanced methods for assessing the seismic vulnerability of existing motorway bridges" (VAB) to assess the importance of non-synchronous seismic excitation of long structures. >http://www.ictp.trieste.it/www_users/sand/projects.html

Turbomachinery computational fluid dynamics: asymptotes and paradigm shifts.

PubMed

Dawes, W N

2007-10-15

This paper reviews the development of computational fluid dynamics (CFD) specifically for turbomachinery simulations and with a particular focus on application to problems with complex geometry. The review is structured by considering this development as a series of paradigm shifts, followed by asymptotes. The original S1-S2 blade-blade-throughflow model is briefly described, followed by the development of two-dimensional then three-dimensional blade-blade analysis. This in turn evolved from inviscid to viscous analysis and then from steady to unsteady flow simulations. This development trajectory led over a surprisingly small number of years to an accepted approach-a 'CFD orthodoxy'. A very important current area of intense interest and activity in turbomachinery simulation is in accounting for real geometry effects, not just in the secondary air and turbine cooling systems but also associated with the primary path. The requirements here are threefold: capturing and representing these geometries in a computer model; making rapid design changes to these complex geometries; and managing the very large associated computational models on PC clusters. Accordingly, the challenges in the application of the current CFD orthodoxy to complex geometries are described in some detail. The main aim of this paper is to argue that the current CFD orthodoxy is on a new asymptote and is not in fact suited for application to complex geometries and that a paradigm shift must be sought. In particular, the new paradigm must be geometry centric and inherently parallel without serial bottlenecks. The main contribution of this paper is to describe such a potential paradigm shift, inspired by the animation industry, based on a fundamental shift in perspective from explicit to implicit geometry and then illustrate this with a number of applications to turbomachinery.

Hybrid finite element method for describing the electrical response of biological cells to applied fields.

PubMed

Ying, Wenjun; Henriquez, Craig S

2007-04-01

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

A reconstruction method for cone-beam differential x-ray phase-contrast computed tomography.

PubMed

Fu, Jian; Velroyen, Astrid; Tan, Renbo; Zhang, Junwei; Chen, Liyuan; Tapfer, Arne; Bech, Martin; Pfeiffer, Franz

2012-09-10

Most existing differential phase-contrast computed tomography (DPC-CT) approaches are based on three kinds of scanning geometries, described by parallel-beam, fan-beam and cone-beam. Due to the potential of compact imaging systems with magnified spatial resolution, cone-beam DPC-CT has attracted significant interest. In this paper, we report a reconstruction method based on a back-projection filtration (BPF) algorithm for cone-beam DPC-CT. Due to the differential nature of phase contrast projections, the algorithm restrains from differentiation of the projection data prior to back-projection, unlike BPF algorithms commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a micro-focus x-ray tube source. Moreover, the numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated cone-beam datasets. We believe that this feature is of particular interest for future medical cone-beam phase-contrast CT imaging applications.

Adaptive Hybrid Picture Coding. Volume 2.

DTIC Science & Technology

1985-02-01

ooo5 V.a Measurement Vector ..eho..............57 V.b Size Variable o .entroi* Vector .......... .- 59 V * c Shape Vector .Ř 0-60o oe 6 I V~d...the Program for the Adaptive Line of Sight Method .i.. 18.. o ... .... .... 1 B Details of the Feature Vector FormationProgram .. o ...oo..-....- .122 C ...shape recognition is analogous to recognition of curves in space. Therefore, well known concepts and theorems from differential geometry can be 34 . o

Comparison of experimental and theoretical triple differential cross sections for the single ionization of C O2 (1 πg ) by electron impact

NASA Astrophysics Data System (ADS)

Ozer, Zehra N.; Ali, Esam; Dogan, Mevlut; Yavuz, Murat; Alwan, Osman; Naja, Adnan; Chuluunbaatar, Ochbadrakh; Joulakian, Boghos B.; Ning, Chuan-Gang; Colgan, James; Madison, Don

2016-06-01

Experimental and theoretical triple differential cross sections for intermediate-energy (250 eV) electron-impact single ionization of the CO2 are presented for three fixed projectile scattering angles. Results are presented for ionization of the outermost 1 πg molecular orbital of C O2 in a coplanar asymmetric geometry. The experimental data are compared to predictions from the three-center Coulomb continuum approximation for triatomic targets, and the molecular three-body distorted wave (M3DW) model. It is observed that while both theories are in reasonable qualitative agreement with experiment, the M3DW is in the best overall agreement with experiment.

In Situ Identification of Nanoparticle Structural Information Using Optical Microscopy.

PubMed

Culver, Kayla S B; Liu, Tingting; Hryn, Alexander J; Fang, Ning; Odom, Teri W

2018-05-11

Diffraction-limited optical microscopy lacks the resolution to characterize directly nanoscale features of single nanoparticles. This paper describes how surprisingly rich structural features of small gold nanostars can be identified using differential interference contrast (DIC) microscopy. First, we established a library of structure-property relationships between nanoparticle shape and DIC optical image and then validated the correlation with electrodynamic simulations and electron microscopy. We found that DIC image patterns of single nanostars could be differentiated between 2D and 3D geometries. Also, DIC images could elucidate the symmetry properties and orientation of nanoparticles. Finally, we demonstrated how this wide-field optical technique can be used for in situ characterization of single nanoparticles rotating at a glass-water interface.

Epidermal differential impedance sensor for conformal skin hydration monitoring.

PubMed

Huang, Xian; Yeo, Woon-Hong; Liu, Yuhao; Rogers, John A

2012-12-01

We present the design and use of an ultrathin, stretchable sensor system capable of conformal lamination onto the skin, for precision measurement and spatial mapping of levels of hydration. This device, which we refer to as a class of 'epidermal electronics' due to its 'skin-like' construction and mode of intimate integration with the body, contains miniaturized arrays of impedance-measurement electrodes arranged in a differential configuration to compensate for common-mode disturbances. Experimental results obtained with different frequencies and sensor geometries demonstrate excellent precision and accuracy, as benchmarked against conventional, commercial devices. The reversible, non-invasive soft contact of this device with the skin makes its operation appealing for applications ranging from skin care, to athletic monitoring to health/wellness assessment.

Differential memory in the trilinear model magnetotail

NASA Technical Reports Server (NTRS)

Chen, James; Mitchell, Horage G.; Palmadesso, Peter J.

1990-01-01

The previously proposed concept of 'differential memory' is quantitatively demonstrated using an idealized analytical model of particle dynamics in the magnetotail geometry. In this model (the 'trilinear' tail model) the magnetotail is divided into three regions. The particle orbits are solved exactly in each region, thus reducing the orbit integration to an analytical mapping. It is shown that the trilinear model reproduces the essential phase space features of the earlier model (Chen and Palmadesso, 1986), possessing well-defined entry and exit regions, and stochastic, integrable (regular), and transient orbits, occupying disjoint phase space regions. Different regions have widely separated characteristic time scales corresponding to different types of particle motion. Using the analytical model, the evolution of single-particle distribution functions is calculated.

A Dose of Reality: Radiation Analysis for Realistic Human Spacecraft

NASA Technical Reports Server (NTRS)

Barzilla, J. E.; Lee, K. T.

2017-01-01

INTRODUCTION As with most computational analyses, a tradeoff exists between problem complexity, resource availability and response accuracy when modeling radiation transport from the source to a detector. The largest amount of analyst time for setting up an analysis is often spent ensuring that any simplifications made have minimal impact on the results. The vehicle shield geometry of interest is typically simplified from the original CAD design in order to reduce computation time, but this simplification requires the analyst to "re-draw" the geometry with a limited set of volumes in order to accommodate a specific radiation transport software package. The resulting low-fidelity geometry model cannot be shared with or compared to other radiation transport software packages, and the process can be error prone with increased model complexity. The work presented here demonstrates the use of the DAGMC (Direct Accelerated Geometry for Monte Carlo) Toolkit from the University of Wisconsin, to model the impacts of several space radiation sources on a CAD drawing of the US Lab module. METHODS The DAGMC toolkit workflow begins with the export of an existing CAD geometry from the native CAD to the ACIS format. The ACIS format file is then cleaned using SpaceClaim to remove small holes and component overlaps. Metadata is then assigned to the cleaned geometry file using CUBIT/Trelis from csimsoft (Registered Trademark). The DAGMC plugin script removes duplicate shared surfaces, facets the geometry to a specified tolerance, and ensures that the faceted geometry is water tight. This step also writes the material and scoring information to a standard input file format that the analyst can alter as desired prior to running the radiation transport program. The scoring results can be transformed, via python script, into a 3D format that is viewable in a standard graphics program. RESULTS The CAD model of the US Lab module of the International Space Station, inclusive of all the racks and components, was simplified to remove holes and volume overlaps. Problematic features within the drawing were also removed or repaired to prevent runtime issues. The cleaned drawing was then run through the DAGMC workflow to prepare for analysis. Pilot tests modeling transport of 1GeV proton and 800MeV/A oxygen sources show that reasonable results are converged upon in an acceptable amount of overall computation time from drawing preparation to data analysis. The FLUKA radiation transport code will next be used to model both a GCR and a trapped radiation source. These results will then be compared with measurements that have been made by the radiation instrumentation deployed inside the US Lab module. DISCUSSION Early analyses have indicated that the DAGMC workflow is a promising toolkit for running vehicle geometries of interest to NASA through multiple radiation transport codes. In addition, recent work has shown that a realistic human phantom, provided via a subcontract with the University of Florida, can be placed inside any vehicle geometry for a combinatorial analysis. This added functionality gives the user the ability to score various parameters at the organ level, and the results can then be used as input for cancer risk models.

Slope Stability Analysis of Waste Dump in Sandstone Open Pit Osielec

NASA Astrophysics Data System (ADS)

Adamczyk, Justyna; Cała, Marek; Flisiak, Jerzy; Kolano, Malwina; Kowalski, Michał

2013-03-01

This paper presents the slope stability analysis for the current as well as projected (final) geometry of waste dump Sandstone Open Pit "Osielec". For the stability analysis six sections were selected. Then, the final geometry of the waste dump was designed and the stability analysis was conducted. On the basis of the analysis results the opportunities to improve the stability of the object were identified. The next issue addressed in the paper was to determine the proportion of the mixture containing mining and processing wastes, for which the waste dump remains stable. Stability calculations were carried out using Janbu method, which belongs to the limit equilibrium methods.

Planar differential mobility spectrometer as a pre-filter for atmospheric pressure ionization mass spectrometry

PubMed Central

Schneider, Bradley B.; Covey, Thomas R.; Coy, Stephen L.; Krylov, Evgeny V.

2010-01-01

Ion filters based on planar DMS can be integrated with the inlet configuration of most mass spectrometers, and are able to enhance the quality of mass analysis and quantitative accuracy by reducing chemical noise, and by pre-separating ions of similar mass. This paper is the first in a series of three papers describing the optimization of DMS / MS instrumentation. In this paper the important physical parameters of a planar DMS-MS interface including analyzer geometry, analyzer coupling to a mass spectrometer, and transport gas flow control are considered. The goal is to optimize ion transmission and transport efficiency, provide optimal and adjustable resolution, and produce stable operation under conditions of high sample contamination. We discuss the principles of DMS separations and highlight the theoretical underpinnings. The main differences between planar and cylindrical geometries are presented, including a discussion of the advantages and disadvantages of RF ion focusing. In addition, we present a description of optimization of the frequency and amplitude of the DMS fields for resolution and ion transmission, and a discussion of the influence and importance of ion residence time in DMS. We have constructed a mass spectrometer interface for planar geometries that takes advantage of atmospheric pressure gas dynamic principles, rather than ion focusing, to minimize ion losses from diffusion in the analyzer and to maximize total ion transport into the mass spectrometer. A variety of experimental results has been obtained that illustrate the performance of this type of interface, including tests of resistance to high contamination levels, and the separation of stereoisomers. In a subsequent publication the control of the chemical interactions that drive the separation process of a DMS / MS system will be considered. In a third publication we describe novel electronics designed to provide the high voltages asymmetric waveform fields (SV) required for these devices as well as the effects of different waveforms. PMID:21278836

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

PubMed

Balzani, Daniel; Deparis, Simone; Fausten, Simon; Forti, Davide; Heinlein, Alexander; Klawonn, Axel; Quarteroni, Alfio; Rheinbach, Oliver; Schröder, Joerg

2016-10-01

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Recent advances in endocrine, metabolic and immune disorders: mesenchymal stem cells (MSCs) and engineered scaffolds.

PubMed

Cantore, Stefania; Crincoli, Vito; Boccaccio, Antonio; Uva, Antonio Emmanuele; Fiorentino, Michele; Monno, Giuseppe; Bollero, Patrizio; Derla, Chiara; Fabiano, Francesca; Ballini, Andrea; Santacroce, Luigi

2018-04-22

New sources of stem cells in adult organisms are constantly emerging. Postnatal Mesenchymal Stem Cells (MSCs), are the most promising support to perform an effective regenerative medicine: such cells have the ability to differentiate into several lineages, such as osteoblasts and chondroblasts, providing novel strategies to improve different complex treatments, during bone regeneration. 3D-printed biomaterials can be designed with geometry aimed to induce stem cells to differentiate towards specific lineage. The interaction between stem cells easy to isolate and engineered 3D-printed scaffolds can translate the tissue bio-engineering into bone regenerative surgery. For those reasons, to better identify the complexity represented by the activities and responses of MSCs requires the advance of new target therapies which are not current in endocrine, metabolic and immune disorders and yet to be developed. This topical review briefly focuses on the new approaches of translational medicine with the use of MSCs and scaffolds engineered with the aid of 3D-printing technology, highlights the osteogenic functions then addressing their applications across the breadth of regenerative medicine. The application of bone constructs consisting of engineered scaffold and MSCs as well as the aspects related to the optimal scaffold geometry that favours the best MSCs differentiation and the improvement of concepts as "sensing surface" were also discussed. Regenerative surgery is largely growing in the field of translational medicine. The use of new sources of MSCs and the improvement of new concepts of bio-engineered scaffolds will certainly be the next step of customized medicine. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Compact multiwire proportional counters for the detection of fission fragments

NASA Astrophysics Data System (ADS)

Jhingan, Akhil; Sugathan, P.; Golda, K. S.; Singh, R. P.; Varughese, T.; Singh, Hardev; Behera, B. R.; Mandal, S. K.

2009-12-01

Two large area multistep position sensitive (two dimensional) multiwire proportional counters have been developed for experiments involving study of fission dynamics using general purpose scattering chamber facility at IUAC. Both detectors have an active area of 20×10 cm2 and provide position signals in horizontal (X) and vertical (Y) planes, timing signal for time of flight measurements and energy signal giving the differential energy loss in the active volume. The design features are optimized for the detection of low energy heavy ions at very low gas pressures. Special care was taken in setting up the readout electronics, constant fraction discriminators for position signals in particular, to get optimum position and timing resolutions along with high count rate handling capability of low energy heavy ions. A custom made charge sensitive preamplifier, having lower gain and shorter decay time, has been developed for extracting the differential energy loss signal. The position and time resolutions of the detectors were determined to be 1.1 mm full width at half maximum (FWHM) and 1.7 ns FWHM, respectively. The detector could handle heavy ion count rates exceeding 20 kHz without any breakdown. Time of flight signal in combination with differential energy loss signal gives a clean separation of fission fragments from projectile and target like particles. The timing and position signals of the detectors are used for fission coincidence measurements and subsequent extraction of their mass, angular, and total kinetic energy distributions. This article describes systematic study of these fission counters in terms of efficiency, time resolution, count rate handling capability, position resolution, and the readout electronics. The detector has been operated with both five electrode geometry and four electrode geometry, and a comparison has been made in their performances.

Teacher's Guide to Secondary Mathematics.

ERIC Educational Resources Information Center

Duval County Schools, Jacksonville, FL.

This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…

Verification of fractional quasilinear renormalization theory using drift-wave turbulence simulations

NASA Astrophysics Data System (ADS)

Newman, D. E.; Sanchez, R.; Carreras, B. A.; van Milligen, B. Ph.

2005-10-01

A very recent renormalization scheme for turbulent transport has been formulated in terms fractional differential operators [1]. In this contribution, we test it against numerous tracer particle transport experiments carried out in simulations of drift-wave turbulence in slab geometry [2]. The simplified geometry allows that simulations be carried out for a sufficiently large number of decorrelation times so that the long-term dynamics captured by these operators can be made apparent. By changing the relative dominance of the polarization and ExB nolinearities artificially, we tune at will the degree of homogeneity and isotropy of the system. Additionally, externally-driven sheared flows can also be considered. This wide spectrum of options creates a superb environment to test the strengths and weaknesses of the fractional renormalization formalism. With it, the potential for application to more realistic geometries such as those in state-of-the-art tokamak turbulence codes will be assessed.References[1] R. S'anchez, B.A. Carreras, D.E. Newman, V. Lynch and B.Ph. van Milligen, submitted (2005) [2] D.E. Newman, P.W. Terry, P.H. Diamond and Y. Liang, Phys. Fluids B 5, 1140 (1993)

Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy

NASA Astrophysics Data System (ADS)

Hasebe, Kazuki

2017-07-01

We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.

A COMPUTATIONAL ANALYSIS OF BONE FORMATION IN THE CRANIAL VAULT USING A COUPLED REACTION-DIFFUSION-STRAIN MODEL

PubMed Central

LEE, CHANYOUNG; RICHTSMEIER, JOAN T.; KRAFT, REUBEN H.

2017-01-01

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing’s reaction-diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction-diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-diffusion model with structural mechanics. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provide precise three dimensional (3D) measures of murine cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures. PMID:29225392

Greater association of peak neuromuscular performance with cortical bone geometry, bone mass and bone strength than bone density: A study in 417 older women.

PubMed

Belavý, Daniel L; Armbrecht, Gabriele; Blenk, Tilo; Bock, Oliver; Börst, Hendrikje; Kocakaya, Emine; Luhn, Franziska; Rantalainen, Timo; Rawer, Rainer; Tomasius, Frederike; Willnecker, Johannes; Felsenberg, Dieter

2016-02-01

We evaluated which aspects of neuromuscular performance are associated with bone mass, density, strength and geometry. 417 women aged 60-94years were examined. Countermovement jump, sit-to-stand test, grip strength, forearm and calf muscle cross-sectional area, areal bone mineral content and density (aBMC and aBMD) at the hip and lumbar spine via dual X-ray absorptiometry, and measures of volumetric vBMC and vBMD, bone geometry and section modulus at 4% and 66% of radius length and 4%, 38% and 66% of tibia length via peripheral quantitative computed tomography were performed. The first principal component of the neuromuscular variables was calculated to generate a summary neuromuscular variable. Percentage of total variance in bone parameters explained by the neuromuscular parameters was calculated. Step-wise regression was also performed. At all pQCT bone sites (radius, ulna, tibia, fibula), a greater percentage of total variance in measures of bone mass, cortical geometry and/or bone strength was explained by peak neuromuscular performance than for vBMD. Sit-to-stand performance did not relate strongly to bone parameters. No obvious differential in the explanatory power of neuromuscular performance was seen for DXA aBMC versus aBMD. In step-wise regression, bone mass, cortical morphology, and/or strength remained significant in relation to the first principal component of the neuromuscular variables. In no case was vBMD positively related to neuromuscular performance in the final step-wise regression models. Peak neuromuscular performance has a stronger relationship with leg and forearm bone mass and cortical geometry as well as proximal forearm section modulus than with vBMD. Copyright © 2015 Elsevier Inc. All rights reserved.

Development and evaluation of thermal model reduction algorithms for spacecraft

NASA Astrophysics Data System (ADS)

Deiml, Michael; Suderland, Martin; Reiss, Philipp; Czupalla, Markus

2015-05-01

This paper is concerned with the topic of the reduction of thermal models of spacecraft. The work presented here has been conducted in cooperation with the company OHB AG, formerly Kayser-Threde GmbH, and the Institute of Astronautics at Technische Universität München with the goal to shorten and automatize the time-consuming and manual process of thermal model reduction. The reduction of thermal models can be divided into the simplification of the geometry model for calculation of external heat flows and radiative couplings and into the reduction of the underlying mathematical model. For simplification a method has been developed which approximates the reduced geometry model with the help of an optimization algorithm. Different linear and nonlinear model reduction techniques have been evaluated for their applicability in reduction of the mathematical model. Thereby the compatibility with the thermal analysis tool ESATAN-TMS is of major concern, which restricts the useful application of these methods. Additional model reduction methods have been developed, which account to these constraints. The Matrix Reduction method allows the approximation of the differential equation to reference values exactly expect for numerical errors. The summation method enables a useful, applicable reduction of thermal models that can be used in industry. In this work a framework for model reduction of thermal models has been created, which can be used together with a newly developed graphical user interface for the reduction of thermal models in industry.

Applying Turbulence Models to Hydroturbine Flows: A Sensitivity Analysis Using the GAMM Francis Turbine

NASA Astrophysics Data System (ADS)

Lewis, Bryan; Cimbala, John; Wouden, Alex

2011-11-01

Turbulence models are generally developed to study common academic geometries, such as flat plates and channels. Creating quality computational grids for such geometries is trivial, and allows stringent requirements to be met for boundary layer grid refinement. However, engineering applications, such as flow through hydroturbines, require the analysis of complex, highly curved geometries. To produce body-fitted grids for such geometries, the mesh quality requirements must be relaxed. Relaxing these requirements, along with the complexity of rotating flows, forces turbulence models to be employed beyond their developed scope. This study explores the solution sensitivity to boundary layer grid quality for various turbulence models and boundary conditions currently implemented in OpenFOAM. The following models are resented: k-omega, k-omega SST, k-epsilon, realizable k-epsilon, and RNG k-epsilon. Standard wall functions, adaptive wall functions, and sub-grid integration are compared using various grid refinements. The chosen geometry is the GAMM Francis Turbine because experimental data and comparison computational results are available for this turbine. This research was supported by a grant from the DoE and a National Defense Science and Engineering Graduate Fellowship.

The ``cinquefoil" resistive/Hall measurement geometry

NASA Astrophysics Data System (ADS)

Koon, Daniel W.

2000-03-01

This talk begins by analyzing the charge transport weighting functions -- the sensitivity of resistive and Hall measurements to local macroscopic inhomogeneities -- of bridge-shaped transport specimens. As expected, such measurements sample only that region of the specimen between the central voltage electrodes, in the limit of narrow current channels connected by even narrower arms to the voltage electrodes. The bridge geometry has a few advantages over the van der Pauw cloverleaf geometry -- including ease in zeroing out the null-field Hall voltage -- but also some disadvantages. The talk concludes with an analysis of a hybrid geometry, the “cinquefoil” or five-leafed clover, which combines the best features of both.

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

Midulla, Marco, E-mail: marco.midulla@chru-lille.fr; Moreno, Ramiro, E-mail: ramoroa@gmail.com; Negre-Salvayre, Anne, E-mail: anne.negre-salvayre@inserm.fr

PurposeAlthough the widespread acceptance of thoracic endovascular aortic repair (TEVAR) as a first-line treatment option for a multitude of thoracic aortic diseases, little is known about the consequences of the device implantation on the native aortic anatomy. We propose a comparative analysis of the pre- and postoperative geometry on a clinical series of patients and discuss the potential clinical implicationsMethodsCT pre- and postoperative acquisitions of 30 consecutive patients treated by TEVAR for different pathologies (20 thoracic aortic aneurysms, 6 false aneurysms, 3 penetrating ulcers, 1 traumatic rupture) were used to model the vascular geometry. Pre- and postoperative geometries were comparedmore » for each patient by pairing and matching the 3D models. An implantation site was identified, and focal differences were detected and described.ResultsSegmentation of the data sets was successfully performed for all 30 subjects. Geometry differences between the pre- and postoperative meshes were depicted in 23 patients (76 %). Modifications at the upper implantation site were detected in 14 patients (47 %), and among them, the implantation site involved the arch (Z0–3) in 11 (78 %).ConclusionModeling the vascular geometry on the basis of imaging data offers an effective tool to perform patient-specific analysis of the vascular geometry before and after the treatment. Future studies will evaluate the consequences of these changes on the aortic function.« less

Thermal analysis of combinatorial solid geometry models using SINDA

NASA Technical Reports Server (NTRS)

Gerencser, Diane; Radke, George; Introne, Rob; Klosterman, John; Miklosovic, Dave

1993-01-01

Algorithms have been developed using Monte Carlo techniques to determine the thermal network parameters necessary to perform a finite difference analysis on Combinatorial Solid Geometry (CSG) models. Orbital and laser fluxes as well as internal heat generation are modeled to facilitate satellite modeling. The results of the thermal calculations are used to model the infrared (IR) images of targets and assess target vulnerability. Sample analyses and validation are presented which demonstrate code products.

The Analysis of Leaf Shape Using Fractal Geometry.

ERIC Educational Resources Information Center

Hartvigsen, Gregg

2000-01-01

Describes ways to examine leaf structure and shape using fractal geometry. Students can test hypotheses using the leaves of replicated plants to look for non-linear trends in leaf shape along the stems of plants, across species, and under different environmental growth conditions. (SAH)

SMITHERS: An object-oriented modular mapping methodology for MCNP-based neutronic–thermal hydraulic multiphysics

DOE PAGES

Richard, Joshua; Galloway, Jack; Fensin, Michael; ...

2015-04-04

A novel object-oriented modular mapping methodology for externally coupled neutronics–thermal hydraulics multiphysics simulations was developed. The Simulator using MCNP with Integrated Thermal-Hydraulics for Exploratory Reactor Studies (SMITHERS) code performs on-the-fly mapping of material-wise power distribution tallies implemented by MCNP-based neutron transport/depletion solvers for use in estimating coolant temperature and density distributions with a separate thermal-hydraulic solver. The key development of SMITHERS is that it reconstructs the hierarchical geometry structure of the material-wise power generation tallies from the depletion solver automatically, with only a modicum of additional information required from the user. In addition, it performs the basis mapping from themore » combinatorial geometry of the depletion solver to the required geometry of the thermal-hydraulic solver in a generalizable manner, such that it can transparently accommodate varying levels of thermal-hydraulic solver geometric fidelity, from the nodal geometry of multi-channel analysis solvers to the pin-cell level of discretization for sub-channel analysis solvers.« less

Computer-aided evaluation of the railway track geometry on the basis of satellite measurements

NASA Astrophysics Data System (ADS)

Specht, Cezary; Koc, Władysław; Chrostowski, Piotr

2016-05-01

In recent years, all over the world there has been a period of intensive development of GNSS (Global Navigation Satellite Systems) measurement techniques and their extension for the purpose of their applications in the field of surveying and navigation. Moreover, in many countries a rising trend in the development of rail transportation systems has been noticed. In this paper, a method of railway track geometry assessment based on mobile satellite measurements is presented. The paper shows the implementation effects of satellite surveying railway geometry. The investigation process described in the paper is divided on two phases. The first phase is the GNSS mobile surveying and the analysis obtained data. The second phase is the analysis of the track geometry using the flat coordinates from the surveying. The visualization of the measured route, separation and quality assessment of the uniform geometric elements (straight sections, arcs), identification of the track polygon (main directions and intersection angles) are discussed and illustrated by the calculation example within the article.

Using a commercial CAD system for simultaneous input to theoretical aerodynamic programs and wind-tunnel model construction

NASA Technical Reports Server (NTRS)

Enomoto, F.; Keller, P.

1984-01-01

The Computer Aided Design (CAD) system's common geometry database was used to generate input for theoretical programs and numerically controlled (NC) tool paths for wind tunnel part fabrication. This eliminates the duplication of work in generating separate geometry databases for each type of analysis. Another advantage is that it reduces the uncertainty due to geometric differences when comparing theoretical aerodynamic data with wind tunnel data. The system was adapted to aerodynamic research by developing programs written in Design Analysis Language (DAL). These programs reduced the amount of time required to construct complex geometries and to generate input for theoretical programs. Certain shortcomings of the Design, Drafting, and Manufacturing (DDM) software limited the effectiveness of these programs and some of the Calma NC software. The complexity of aircraft configurations suggests that more types of surface and curve geometry should be added to the system. Some of these shortcomings may be eliminated as improved versions of DDM are made available.

Static Aeroelastic Analysis with an Inviscid Cartesian Method

NASA Technical Reports Server (NTRS)

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.

2014-01-01

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Bio-inspired self-shaping ceramics

PubMed Central

Bargardi, Fabio L.; Le Ferrand, Hortense; Libanori, Rafael; Studart, André R.

2016-01-01

Shaping ceramics into complex and intricate geometries using cost-effective processes is desirable in many applications but still remains an open challenge. Inspired by plant seed dispersal units that self-fold on differential swelling, we demonstrate that self-shaping can be implemented in ceramics by programming the material's microstructure to undergo local anisotropic shrinkage during heat treatment. Such microstructural design is achieved by magnetically aligning functionalized ceramic platelets in a liquid ceramic suspension, subsequently consolidated through an established enzyme-catalysed reaction. By fabricating alumina compacts exhibiting bio-inspired bilayer architectures, we achieve deliberate control over shape change during the sintering step. Bending, twisting or combinations of these two basic movements can be successfully programmed to obtain a myriad of complex shapes. The simplicity and the universality of such a bottom-up shaping method makes it attractive for applications that would benefit from low-waste ceramic fabrication, temperature-resistant interlocking structures or unusual geometries not accessible using conventional top–down manufacturing. PMID:28008930

Laser-induced free-free transitions in elastic electron scattering from CO2

NASA Astrophysics Data System (ADS)

Musa, Mohamed; MacDonald, Amy; Tidswell, Lisa; Holmes, Jim; St. Francis Xavier Laser Scattering Lab Team

2011-03-01

This report presents measurements of laser-induced free-free transitions of electrons scattered from CO2 molecules in the ground electronic state at incident electron energies of 3.8 and 5.8 eV under pulsed CO2 laser field. The differential cross section of free-free transitions involving absorption and emission of up to two photons were measured at various scattering angles with the polarization of the laser either parallel with or perpendicular to the the momentum change vector of the scattered electrons. The results of the parallel geometry are found to be in qualitative agreement with the predictions of the Kroll-Watson approximation within the experimental uncertainty whereas those of the perpendicular geometry show marked discrepancy with the Kroll-Watson predictions. This work was supported by the Natural Sciences and Engineering Research Council of Canada and the St. Francis Xavier University Council for Research.

Bio-inspired self-shaping ceramics

NASA Astrophysics Data System (ADS)

Bargardi, Fabio L.; Le Ferrand, Hortense; Libanori, Rafael; Studart, André R.

2016-12-01

Shaping ceramics into complex and intricate geometries using cost-effective processes is desirable in many applications but still remains an open challenge. Inspired by plant seed dispersal units that self-fold on differential swelling, we demonstrate that self-shaping can be implemented in ceramics by programming the material's microstructure to undergo local anisotropic shrinkage during heat treatment. Such microstructural design is achieved by magnetically aligning functionalized ceramic platelets in a liquid ceramic suspension, subsequently consolidated through an established enzyme-catalysed reaction. By fabricating alumina compacts exhibiting bio-inspired bilayer architectures, we achieve deliberate control over shape change during the sintering step. Bending, twisting or combinations of these two basic movements can be successfully programmed to obtain a myriad of complex shapes. The simplicity and the universality of such a bottom-up shaping method makes it attractive for applications that would benefit from low-waste ceramic fabrication, temperature-resistant interlocking structures or unusual geometries not accessible using conventional top-down manufacturing.

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.

Ultrastable gold substrates: Properties of a support for high-resolution electron cryomicroscopy of biological specimens

PubMed Central

Russo, Christopher J.; Passmore, Lori A.

2016-01-01

Electron cryomicroscopy (cryo-EM) allows structure determination of a wide range of biological molecules and specimens. All-gold supports improve cryo-EM images by reducing radiation-induced motion and image blurring. Here we compare the mechanical and electrical properties of all-gold supports to amorphous carbon foils. Gold supports are more conductive, and have suspended foils that are not compressed by differential contraction when cooled to liquid nitrogen temperatures. These measurements show how the choice of support material and geometry can reduce specimen movement by more than an order of magnitude during low-dose imaging. We provide methods for fabrication of all-gold supports and preparation of vitrified specimens. We also analyse illumination geometry for optimal collection of high resolution, low-dose data. Together, the support structures and methods herein can improve the resolution and quality of images from any electron cryomicroscope. PMID:26592474

A differential game solution to the Coplanar tail-chase aerial combat problem

NASA Technical Reports Server (NTRS)

Merz, A. W.; Hague, D. S.

1976-01-01

Numerical results obtained in a simplified version of the one on one aerial combat problem are presented. The primary aim of the data is to specify the roles of pursuer and evader as functions of the relative geometry and of the significant physical parameters of the problem. Numerical results are given in a case in which the slower aircraft is more maneuverable than the faster aircraft. A third order dynamic model of the relative motion is described, for which the state variables are relative range, bearing, and heading. The ranges at termination are arbitary in the present version of the problem, so the weapon systems of both aircraft can be visualized as forward firing high velocity weapons, which must be aimed at the tail pipe of the evader. It was found that, for the great majority of the ralative geometries, each aircraft can evade the weapon system of the other.

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.

Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

PubMed

Berenstein, David; Miller, Alexandra

2017-06-30

In the context of Lin-Lunin-Maldacena geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

User's guide for a computer program for calculating the zero-lift wave drag of complex aircraft configurations

NASA Technical Reports Server (NTRS)

Craidon, C. B.

1983-01-01

A computer program was developed to extend the geometry input capabilities of previous versions of a supersonic zero lift wave drag computer program. The arbitrary geometry input description is flexible enough to describe almost any complex aircraft concept, so that highly accurate wave drag analysis can now be performed because complex geometries can be represented accurately and do not have to be modified to meet the requirements of a restricted input format.

Three-dimensional spatially curved local Bessel beams generated by metasurface

NASA Astrophysics Data System (ADS)

Liu, Dawei; Wu, Jiawen; Cheng, Bo; Li, Hongliang

2018-03-01

We propose a reflective metasurface based on an artificial admittance modulation surface to generate three-dimensional spatially curved beams. The phase acquisition utilized to modulate this sinusoidally varying surface admittance combines the enveloping theory of differential geometry and the method for producing two-dimensional Bessel beams. The metasurface is fabricated, and the comparison between the full-wave simulations and experimental results demonstrates good performance of three-dimensional spatially curved beams generated by the metasurface.

Solving Variational Problems and Partial Differential Equations Mapping into General Target Manifolds

DTIC Science & Technology

2002-01-01

1998. [36] T. Sakai, Riemannian Geometry, AMS Translations of Mathematical Monographs, vol 149. [37] N. Sochen, R . Kimmel, and R , Malladi , “A general...matical Physics 107, pp. 649-705, 1986. [5] V. Caselles, R . Kimmel, G. Sapiro, and C. Sbert, “Minimal surfaces based object segmentation,” IEEE- PAMI...June 2000 [9] R . Cohen, R . M. Hardt, D. Kinderlehrer, S. Y. Lin, and M. Luskin, “Minimum energy configurations for liquid crystals: Computational

Generalized Cartan Calculus in general dimension

DOE PAGES

Wang, Yi -Nan

2015-07-22

We develop the generalized Cartan Calculus for the groups G = SL(2,R) × R +, SL(5,R) and SO(5,5). They are the underlying algebraic structures of d=9,7,6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincar\\'e lemmas in this new differential geometry is also discussed. Lastly, we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Study of Antenna Radome Problems

DTIC Science & Technology

1981-04-01

115 DISTRIBUTION LIST .... ......................... 117 4 - #iE MU aM . a--. LIST 01 FICURZS Figure Page 1. Antenna A end radoe E...coetficiente at points 1 and 2 (Figure 26a) T -T n1E + (1/0) (5.18) In a sitmitar manner, we can calculate the field on the multiply refracted rays (t. twice...34 Differential geometry for GTD applications," ElectromagneticsLaboratory Report 77-21, University of Illinois, Urbana, IL, 1977. (lij F. W. Sears, M. W

Statistical and Variational Methods for Problems in Visual Control

DTIC Science & Technology

2009-03-02

plane curves to round points," /. Differential Geometry 26 (1987), pp. 285-314. 12 [7] S. Haker , G. Sapiro, and A. Tannenbaum, "Knowledge-based...segmentation of SAR data with learned priors," IEEE Trans. Image Processing, vol. 9, pp. 298-302, 2000. [8] S. Haker , L. Zhu, S. Angenent, and A...Tannenbaum, "Optimal mass transport for registration and warping" Int. Journal Computer Vision, vol. 60, pp. 225-240, 2004. [9] S. Haker , G. Sapiro, A

Chemistry and Physics of Analyte Identification in Integrated Nanosensors

DTIC Science & Technology

2009-02-05

points," / Differential Geometry 26 (1987), pp. 285-314. 12 [7] S. Haker , G. Sapiro, and A. Tannenbaum, "Knowledge-based segmentation of SAR data with...learned priors," IEEE Trans. Image Processing, vol. 9, pp. 298-302, 2000. [8] S. Haker , L. Zhu, S. Angenent, and A. Tannenbaum, "Optimal mass...transport for registration and warping" Int. Journal Computer Vision, vol. 60, pp. 225-240, 2004. [9] S. Haker , G. Sapiro, A. Tannenbaum, and D. Washburn

Nonexistence of degenerate horizons in static vacua and black hole uniqueness

NASA Astrophysics Data System (ADS)

Khuri, Marcus; Woolgar, Eric

2018-02-01

We show that in any spacetime dimension D ≥ 4, degenerate components of the event horizon do not exist in static vacuum configurations with positive cosmological constant. We also show that without a cosmological constant asymptotically flat solutions cannot possess a degenerate horizon component. Several independent proofs are presented. One proof follows easily from differential geometry in the near-horizon limit, while others use Bakry-Émery-Ricci bounds for static Einstein manifolds.

Conformal Geometry, Hotine’s Conjecture, and Differential Geodesy.

DTIC Science & Technology

1987-07-27

ellipsoid (Stokes Theorem). Rayleigh and Poincare extensively studied tides. Starting around 1900 the close connection between geodesy and mathematics...locally conformal maps on neighborhoods of M ,.’ P -a ,r r’ " % "% J and M’ For example, consider the 2-sphere S and the plane E It 2 2 is well...coordinates where the coordinate surfaces are respectively planes ; planes and cylinders; and planes , spheres, - and cones. we give one less trivial example

Fluid manifold design for a solar energy storage tank

NASA Technical Reports Server (NTRS)

Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.

1975-01-01

A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

Railway track geometry degradation due to differential settlement of ballast/subgrade - Numerical prediction by an iterative procedure

NASA Astrophysics Data System (ADS)

Nielsen, Jens C. O.; Li, Xin

2018-01-01

An iterative procedure for numerical prediction of long-term degradation of railway track geometry (longitudinal level) due to accumulated differential settlement of ballast/subgrade is presented. The procedure is based on a time-domain model of dynamic vehicle-track interaction to calculate the contact loads between sleepers and ballast in the short-term, which are then used in an empirical model to determine the settlement of ballast/subgrade below each sleeper in the long-term. The number of load cycles (wheel passages) accounted for in each iteration step is determined by an adaptive step length given by a maximum settlement increment. To reduce the computational effort for the simulations of dynamic vehicle-track interaction, complex-valued modal synthesis with a truncated modal set is applied for the linear subset of the discretely supported track model with non-proportional spatial distribution of viscous damping. Gravity loads and state-dependent vehicle, track and wheel-rail contact conditions are accounted for as external loads on the modal model, including situations involving loss of (and recovered) wheel-rail contact, impact between hanging sleeper and ballast, and/or a prescribed variation of non-linear track support stiffness properties along the track model. The procedure is demonstrated by calculating the degradation of longitudinal level over time as initiated by a prescribed initial local rail irregularity (dipped welded rail joint).

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Definition and verification of a complex aircraft for aerodynamic calculations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1986-01-01

Techniques are reviewed which are of value in CAD/CAM CFD studies of the geometries of new fighter aircraft. In order to refine the computations of the flows to take advantage of the computing power available from supercomputers, it is often necessary to interpolate the geometry of the mesh selected for the numerical analysis of the aircraft shape. Interpolating the geometry permits a higher level of detail in calculations of the flow past specific regions of a design. A microprocessor-based mathematics engine is described for fast image manipulation and rotation to verify that the interpolated geometry will correspond to the design geometry in order to ensure that the flow calculations will remain valid through the interpolation. Applications of the image manipulation system to verify geometrical representations with wire-frame and shaded-surface images are described.

Direct Hydrogel Encapsulation of Pluripotent Stem Cells Enables Ontomimetic Differentiation and Growth of Engineered Human Heart Tissues

PubMed Central

Kerscher, Petra; Turnbull, Irene C; Hodge, Alexander J; Kim, Joonyul; Seliktar, Dror; Easley, Christopher J; Costa, Kevin D; Lipke, Elizabeth A

2016-01-01

Human engineered heart tissues have potential to revolutionize cardiac development research, drug-testing, and treatment of heart disease; however, implementation is limited by the need to use pre-differentiated cardiomyocytes (CMs). Here we show that by providing a 3D poly(ethylene glycol)-fibrinogen hydrogel microenvironment, we can directly differentiate human pluripotent stem cells (hPSCs) into contracting heart tissues. Our straight-forward, ontomimetic approach, imitating the process of development, requires only a single cell-handling step, provides reproducible results for a range of tested geometries and size scales, and overcomes inherent limitations in cell maintenance and maturation, while achieving high yields of CMs with developmentally appropriate temporal changes in gene expression. Here we demonstrate that hPSCs encapsulated within this biomimetic 3D hydrogel microenvironment develop into functional cardiac tissues composed of self-aligned CMs with evidence of ultrastructural maturation, mimicking heart development, and enabling investigation of disease mechanisms and screening of compounds on developing human heart tissue. PMID:26826618

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.

Probabilistic structural analysis methods and applications

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Wu, Y.-T.; Dias, B.; Rajagopal, K. R.

1988-01-01

An advanced algorithm for simulating the probabilistic distribution of structural responses due to statistical uncertainties in loads, geometry, material properties, and boundary conditions is reported. The method effectively combines an advanced algorithm for calculating probability levels for multivariate problems (fast probability integration) together with a general-purpose finite-element code for stress, vibration, and buckling analysis. Application is made to a space propulsion system turbine blade for which the geometry and material properties are treated as random variables.

Combination of ray-tracing and the method of moments for electromagnetic radiation analysis using reduced meshes

NASA Astrophysics Data System (ADS)

Delgado, Carlos; Cátedra, Manuel Felipe

2018-05-01

This work presents a technique that allows a very noticeable relaxation of the computational requirements for full-wave electromagnetic simulations based on the Method of Moments. A ray-tracing analysis of the geometry is performed in order to extract the critical points with significant contributions. These points are then used to generate a reduced mesh, considering the regions of the geometry that surround each critical point and taking into account the electrical path followed from the source. The electromagnetic analysis of the reduced mesh produces very accurate results, requiring a fraction of the resources that the conventional analysis would utilize.

Enabling Rapid and Robust Structural Analysis During Conceptual Design

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Padula, Sharon L.; Li, Wu

2015-01-01

This paper describes a multi-year effort to add a structural analysis subprocess to a supersonic aircraft conceptual design process. The desired capabilities include parametric geometry, automatic finite element mesh generation, static and aeroelastic analysis, and structural sizing. The paper discusses implementation details of the new subprocess, captures lessons learned, and suggests future improvements. The subprocess quickly compares concepts and robustly handles large changes in wing or fuselage geometry. The subprocess can rank concepts with regard to their structural feasibility and can identify promising regions of the design space. The automated structural analysis subprocess is deemed robust and rapid enough to be included in multidisciplinary conceptual design and optimization studies.

Solar Proton Transport Within an ICRU Sphere Surrounded by a Complex Shield: Ray-trace Geometry

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

2015-01-01

A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z is less than or equal to 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.

Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry.

PubMed

Slaba, Tony C; Wilson, John W; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A

2016-06-01

A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency. Published by Elsevier Ltd.

Forward Propagation Analysis for determining the 16O(n,α)13C Reaction Cross Section at LANSCE

NASA Astrophysics Data System (ADS)

Purcell, Zachary; Lee, Hye Young; Davison, Jacob

2017-09-01

Oxygen is present in many materials and the uncertainties in its nuclear data can have a significant impact on applications. In particular, neutron-absorption reactions reduceavailable neutrons in applications. Thus,high precision in knowledge of this reaction cross sectionis required. To decreasethe systematic uncertainty, we developed a framework that uses Forward Propagation Analysis (FPA) for determining the 16O(n,α)13C reaction cross section from data measured at LANSCE. The Low Energy NZ (LENZ) instrument was used to detectreaction alphas on the Ta2 O5 solid target with silicon strip detectors. The FPA was performed in GEANT4. The geometry, efficiency, and resolution functions of LENZ werevalidated by comparing with the alpha emitting Th-229 source measurement. To reproduce experimental yields in silicon strip detectors, the energy dependent neutron beam flux distribution, the 16O(n,a) reaction differential cross sections, and the 2-body kinematics calculations were implemented in the simulation. We present results from the FPA on LENZ data anddiscuss the improved data analysis [LA-UR-17-26436]. This work has benefited from the use of the Los Alamos Neutron Science Center, is funded by the US Department of Energy and operated by Los Alamos National Security, LLC under Contract DE-AC52-06NA25396.

Features and applications of the Groove Analysis Program (GAP)

NASA Technical Reports Server (NTRS)

Ku, Jentung; Nguyen, Tu M.; Brennan, Patrick J.

1995-01-01

An IBM Personal Computer (PC) version of the Groove Analysis program (GAP) was developed to predict the steady state heat transport capability of an axially grooved heat pipe for a specified groove geometry and working fluid. In the model, the capillary limit is determined by the numerical solution of the differential equation for momentum conservation with the appropriate boundary conditions. This governing equation accounts for the hydrodynamic losses due to friction in liquid and vapor flows and due to liquid/vapor shear interaction. Back-pumping in both 0-g and 1-g is accounted for in the boundary condition at the condenser end. Slug formation in 0-g and puddle flow in 1-g are also considered in the model. At the user's discretion, the code will perform the analysis for various fluid inventories (undercharge, nominal charge, overcharge, or a fixed fluid charge) and heat pipe elevations. GAP will also calculate the minimum required heat pipe wall thickness for pressure containment at design temperatures that are greater than or lower than the critical temperature of the working fluid. This paper discusses the theory behind the development of the GAP model. It also presents the many useful and powerful capabilities of the model. Furthermore, a correlation of flight test performance data and the predictions using GAP are presented and discussed.

Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry

NASA Technical Reports Server (NTRS)

Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.

2015-01-01

The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.