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.

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.

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.

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.

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.

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

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

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-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.

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

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.

New technologies for advanced three-dimensional optimum shape design in aeronautics

NASA Astrophysics Data System (ADS)

Dervieux, Alain; Lanteri, Stéphane; Malé, Jean-Michel; Marco, Nathalie; Rostaing-Schmidt, Nicole; Stoufflet, Bruno

1999-05-01

The analysis of complex flows around realistic aircraft geometries is becoming more and more predictive. In order to obtain this result, the complexity of flow analysis codes has been constantly increasing, involving more refined fluid models and sophisticated numerical methods. These codes can only run on top computers, exhausting their memory and CPU capabilities. It is, therefore, difficult to introduce best analysis codes in a shape optimization loop: most previous works in the optimum shape design field used only simplified analysis codes. Moreover, as the most popular optimization methods are the gradient-based ones, the more complex the flow solver, the more difficult it is to compute the sensitivity code. However, emerging technologies are contributing to make such an ambitious project, of including a state-of-the-art flow analysis code into an optimisation loop, feasible. Among those technologies, there are three important issues that this paper wishes to address: shape parametrization, automated differentiation and parallel computing. Shape parametrization allows faster optimization by reducing the number of design variable; in this work, it relies on a hierarchical multilevel approach. The sensitivity code can be obtained using automated differentiation. The automated approach is based on software manipulation tools, which allow the differentiation to be quick and the resulting differentiated code to be rather fast and reliable. In addition, the parallel algorithms implemented in this work allow the resulting optimization software to run on increasingly larger geometries. Copyright

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.

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.

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.

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

Oxalate analysis methodology for decayed wood

Treesearch

Carol A. Clausen; William Kenealy; Patricia K. Lebow

2008-01-01

Oxalate from partially decayed southern pine wood was analyzed by HPLC or colorimetric assay. Oxalate extraction efficiency, assessed by comparing analysis of whole wood cubes with ground wood, showed that both wood geometries could be extracted with comparable efficiency. To differentiate soluble oxalate from total oxalate, three extraction methods were assessed,...

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.

Direct Discrete Method for Neutronic Calculations

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

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for amore » cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)« less

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.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

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

2010-11-01

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

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

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

2010-01-01

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

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.

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.

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.

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.

Recent Advances in the Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1997-01-01

A review of recent progress for the analysis of spiral bevel gears will be described. The foundation of this work relies on the description of the gear geometry of face-milled spiral bevel gears via the approach developed by Litvin. This methodology was extended by combining the basic gear design data with the manufactured surfaces using a differential geometry approach, and provides the data necessary for assembling three-dimensional finite element models. The finite element models have been utilized to conduct thermal and structural analysis of the gear system. Examples of the methods developed for thermal and structural/contact analysis are presented.

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.

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.

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.

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

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.

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.

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.

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.

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.

Modelling crystal growth: Convection in an asymmetrically heated ampoule

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.; Rosenberger, Franz; Pulicani, J. P.; Krukowski, S.; Ouazzani, Jalil

1990-01-01

The objective was to develop and implement a numerical method capable of solving the nonlinear partial differential equations governing heat, mass, and momentum transfer in a 3-D cylindrical geometry in order to examine the character of convection in an asymmetrically heated cylindrical ampoule. The details of the numerical method, including verification tests involving comparison with results obtained from other methods, are presented. The results of the study of 3-D convection in an asymmetrically heated cylinder are described.

Impact of parasitic thermal effects on thermoelectric property measurements by Harman method.

PubMed

Kwon, Beomjin; Baek, Seung-Hyub; Kim, Seong Keun; Kim, Jin-Sang

2014-04-01

Harman method is a rapid and simple technique to measure thermoelectric properties. However, its validity has been often questioned due to the over-simplified assumptions that this method relies on. Here, we quantitatively investigate the influence of the previously ignored parasitic thermal effects on the Harman method and develop a method to determine an intrinsic ZT. We expand the original Harman relation with three extra terms: heat losses via both the lead wires and radiation, and Joule heating within the sample. Based on the expanded Harman relation, we use differential measurement of the sample geometry to measure the intrinsic ZT. To separately evaluate the parasitic terms, the measured ZTs with systematically varied sample geometries and the lead wire types are fitted to the expanded relation. A huge discrepancy (∼28%) of the measured ZTs depending on the measurement configuration is observed. We are able to separately evaluate those parasitic terms. This work will help to evaluate the intrinsic thermoelectric property with Harman method by eliminating ambiguities coming from extrinsic effects.

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.

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…

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

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.

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.

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

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.

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.

Computational Approaches to Image Understanding.

DTIC Science & Technology

1981-10-01

represnting points, edges, surfaces, and volumes to facilitate display. The geometry or perspective and parailcl (or orthographic) projection has...of making the image forming process explicit. This in turn leads to a concern with geometry , such as the properties f the gradient, stereographic, and...dual spaces. Combining geometry and smoothness leads naturally to multi-variate vector analysis, and to differential geometry . For the most part, a

Global differential geometry: An introduction for control engineers

NASA Technical Reports Server (NTRS)

Doolin, B. F.; Martin, C. F.

1982-01-01

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

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

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

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.

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.

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.

Impact of parasitic thermal effects on thermoelectric property measurements by Harman method

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

Kwon, Beomjin, E-mail: bkwon@kist.re.kr; Baek, Seung-Hyub; Keun Kim, Seong

2014-04-15

Harman method is a rapid and simple technique to measure thermoelectric properties. However, its validity has been often questioned due to the over-simplified assumptions that this method relies on. Here, we quantitatively investigate the influence of the previously ignored parasitic thermal effects on the Harman method and develop a method to determine an intrinsic ZT. We expand the original Harman relation with three extra terms: heat losses via both the lead wires and radiation, and Joule heating within the sample. Based on the expanded Harman relation, we use differential measurement of the sample geometry to measure the intrinsic ZT. Tomore » separately evaluate the parasitic terms, the measured ZTs with systematically varied sample geometries and the lead wire types are fitted to the expanded relation. A huge discrepancy (∼28%) of the measured ZTs depending on the measurement configuration is observed. We are able to separately evaluate those parasitic terms. This work will help to evaluate the intrinsic thermoelectric property with Harman method by eliminating ambiguities coming from extrinsic effects.« less

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.

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.

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.

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

Anisotropic scene geometry resampling with occlusion filling for 3DTV applications

NASA Astrophysics Data System (ADS)

Kim, Jangheon; Sikora, Thomas

2006-02-01

Image and video-based rendering technologies are receiving growing attention due to their photo-realistic rendering capability in free-viewpoint. However, two major limitations are ghosting and blurring due to their sampling-based mechanism. The scene geometry which supports to select accurate sampling positions is proposed using global method (i.e. approximate depth plane) and local method (i.e. disparity estimation). This paper focuses on the local method since it can yield more accurate rendering quality without large number of cameras. The local scene geometry has two difficulties which are the geometrical density and the uncovered area including hidden information. They are the serious drawback to reconstruct an arbitrary viewpoint without aliasing artifacts. To solve the problems, we propose anisotropic diffusive resampling method based on tensor theory. Isotropic low-pass filtering accomplishes anti-aliasing in scene geometry and anisotropic diffusion prevents filtering from blurring the visual structures. Apertures in coarse samples are estimated following diffusion on the pre-filtered space, the nonlinear weighting of gradient directions suppresses the amount of diffusion. Aliasing artifacts from low density are efficiently removed by isotropic filtering and the edge blurring can be solved by the anisotropic method at one process. Due to difference size of sampling gap, the resampling condition is defined considering causality between filter-scale and edge. Using partial differential equation (PDE) employing Gaussian scale-space, we iteratively achieve the coarse-to-fine resampling. In a large scale, apertures and uncovered holes can be overcoming because only strong and meaningful boundaries are selected on the resolution. The coarse-level resampling with a large scale is iteratively refined to get detail scene structure. Simulation results show the marked improvements of rendering quality.

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.

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.

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

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.

Shape from sound: toward new tools for quantum gravity.

PubMed

Aasen, David; Bhamre, Tejal; Kempf, Achim

2013-03-22

To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at least in the case of the Euclidean signature, is the discipline of spectral geometry. It aims at describing curved manifolds in terms of the spectra of their canonical differential operators. As an immediate benefit, this would offer a clean gauge-independent identification of the metric's degrees of freedom in terms of invariants that should be ready to quantize. However, spectral geometry is itself hard and has been plagued by ambiguities. Here, we regularize and break up spectral geometry into small, finite-dimensional and therefore manageable steps. We constructively demonstrate that this strategy works at least in two dimensions. We can now calculate the shapes of two-dimensional objects from their vibrational spectra.

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.

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.

Nonconforming mortar element methods: Application to spectral discretizations

NASA Technical Reports Server (NTRS)

Maday, Yvon; Mavriplis, Cathy; Patera, Anthony

1988-01-01

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

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

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

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

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.

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.

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.

Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity

NASA Technical Reports Server (NTRS)

Kolecki, Joseph C.

2005-01-01

Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.

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.

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.

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

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

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

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.

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.

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

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.

Pt thickness dependence of spin Hall effect switching of in-plane magnetized CoFeB free layers studied by differential planar Hall effect

NASA Astrophysics Data System (ADS)

Mihajlović, G.; Mosendz, O.; Wan, L.; Smith, N.; Choi, Y.; Wang, Y.; Katine, J. A.

2016-11-01

We introduce a differential planar Hall effect method that enables the experimental study of spin orbit torque switching of in-plane magnetized free layers in a simple Hall bar device geometry. Using this method, we study the Pt thickness dependence of switching currents and show that they decrease monotonically down to the minimum experimental thickness of ˜5 nm, while the critical current and power densities are very weakly thickness dependent, exhibiting the minimum values of Jc0 = 1.1 × 108 A/cm2 and ρJc0 2=0.6 ×1012 W/cm 3 at this minimum thickness. Our results suggest that a significant reduction of the critical parameters could be achieved by optimizing the free layer magnetics, which makes this technology a viable candidate for fast, high endurance and low-error rate applications such as cache memories.

Hooked differential mobility spectrometry apparatus and method therefore

DOEpatents

Shvartsburg, Alexandre A [Richland, WA; Tang, Keqi [Richland, WA; Ibrahim, Yehia M [Richland, WA; Smith, Richard D [Richland, WA

2009-02-17

Disclosed are a device and method for improved interfacing of differential mobility spectrometry (DMS) or field asymmetric waveform ion mobility spectrometry (FAIMS) analyzers of substantially planar geometry to subsequent or preceding instrument stages. Interfacing is achieved using curved DMS elements, where a thick ion beam emitted by planar DMS analyzers or injected into them for ion filtering is compressed to the gap median by DMS ion focusing effect in a spatially inhomogeneous electric field. Resulting thinner beams are more effectively transmitted through necessarily constrained conductance limit apertures to subsequent instrument stages operated at a pressure lower than DMS, and/or more effectively injected into planar DMS analyzers. The technology is synergetic with slit apertures, slit aperture/ion funnels, and high-pressure ion funnel interfaces known in the art which allow for increasing cross-sectional area of MS inlets. The invention may be used in integrated analytical platforms, including, e.g., DMS/MS, LC/DMS/MS, and DMS/IMS/MS that could replace and/or enhance current LC/MS methods, e.g., for proteomics research.

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

Hierarchical graph-based segmentation for extracting road networks from high-resolution satellite images

NASA Astrophysics Data System (ADS)

Alshehhi, Rasha; Marpu, Prashanth Reddy

2017-04-01

Extraction of road networks in urban areas from remotely sensed imagery plays an important role in many urban applications (e.g. road navigation, geometric correction of urban remote sensing images, updating geographic information systems, etc.). It is normally difficult to accurately differentiate road from its background due to the complex geometry of the buildings and the acquisition geometry of the sensor. In this paper, we present a new method for extracting roads from high-resolution imagery based on hierarchical graph-based image segmentation. The proposed method consists of: 1. Extracting features (e.g., using Gabor and morphological filtering) to enhance the contrast between road and non-road pixels, 2. Graph-based segmentation consisting of (i) Constructing a graph representation of the image based on initial segmentation and (ii) Hierarchical merging and splitting of image segments based on color and shape features, and 3. Post-processing to remove irregularities in the extracted road segments. Experiments are conducted on three challenging datasets of high-resolution images to demonstrate the proposed method and compare with other similar approaches. The results demonstrate the validity and superior performance of the proposed method for road extraction in urban areas.

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.

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."

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.

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.

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

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

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

Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

NASA Astrophysics Data System (ADS)

Boronin, Ivan; Shevlyakov, Andrey

2018-03-01

Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

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.

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

Automatic anatomical segmentation of the liver by separation planes

NASA Astrophysics Data System (ADS)

Boltcheva, Dobrina; Passat, Nicolas; Agnus, Vincent; Jacob-Da, Marie-Andrée, , Col; Ronse, Christian; Soler, Luc

2006-03-01

Surgical planning in oncological liver surgery is based on the location of the 8 anatomical segments according to Couinaud's definition and tumors inside these structures. The detection of the boundaries between the segments is then the first step of the preoperative planning. The proposed method, devoted to binary images of livers segmented from CT-scans, has been designed to delineate these segments. It automatically detects a set of landmarks using a priori anatomical knowledge and differential geometry criteria. These landmarks are then used to position the Couinaud's segments. Validations performed on 7 clinical cases tend to prove that the method is reliable for most of these separation planes.

Topography printing to locally control wettability.

PubMed

Zheng, Zijian; Azzaroni, Omar; Zhou, Feng; Huck, Wilhelm T S

2006-06-21

This paper reports a new patterning method, which utilizes NaOH to facilitate the irreversible binding between the PDMS stamp and substrates and subsequent cohesive mechanical failure to transfer the PDMS patterns. Our method shows high substrate tolerance and can be used to "print" various PDMS geometries on a wide range of surfaces, including Si100, glass, gold, polymers, and patterned SU8 photoresist. Using this technique, we are able to locally change the wettability of substrate surfaces by printing well-defined PDMS architectures on the patterned SU8 photoresist. It is possible to generate differential wetting and dewetting properties in microchannels and in the PDMS printed area, respectively.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

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.

Simultaneous calibration phantom commission and geometry calibration in cone beam CT

NASA Astrophysics Data System (ADS)

Xu, Yuan; Yang, Shuai; Ma, Jianhui; Li, Bin; Wu, Shuyu; Qi, Hongliang; Zhou, Linghong

2017-09-01

Geometry calibration is a vital step for describing the geometry of a cone beam computed tomography (CBCT) system and is a prerequisite for CBCT reconstruction. In current methods, calibration phantom commission and geometry calibration are divided into two independent tasks. Small errors in ball-bearing (BB) positioning in the phantom-making step will severely degrade the quality of phantom calibration. To solve this problem, we propose an integrated method to simultaneously realize geometry phantom commission and geometry calibration. Instead of assuming the accuracy of the geometry phantom, the integrated method considers BB centers in the phantom as an optimized parameter in the workflow. Specifically, an evaluation phantom and the corresponding evaluation contrast index are used to evaluate geometry artifacts for optimizing the BB coordinates in the geometry phantom. After utilizing particle swarm optimization, the CBCT geometry and BB coordinates in the geometry phantom are calibrated accurately and are then directly used for the next geometry calibration task in other CBCT systems. To evaluate the proposed method, both qualitative and quantitative studies were performed on simulated and realistic CBCT data. The spatial resolution of reconstructed images using dental CBCT can reach up to 15 line pair cm-1. The proposed method is also superior to the Wiesent method in experiments. This paper shows that the proposed method is attractive for simultaneous and accurate geometry phantom commission and geometry calibration.

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

Conceptualizing Vectors in College Geometry: A New Framework for Analysis of Student Approaches and Difficulties

ERIC Educational Resources Information Center

Kwon, Oh Hoon

2012-01-01

This dissertation documents a new way of conceptualizing vectors in college mathematics, especially in geometry. First, I will introduce three problems to show the complexity and subtlety of the construct of vectors with the classical vector representations. These highlight the need for a new framework that: (1) differentiates abstraction from a…

Random-Forest Classification of High-Resolution Remote Sensing Images and Ndsm Over Urban Areas

NASA Astrophysics Data System (ADS)

Sun, X. F.; Lin, X. G.

2017-09-01

As an intermediate step between raw remote sensing data and digital urban maps, remote sensing data classification has been a challenging and long-standing research problem in the community of remote sensing. In this work, an effective classification method is proposed for classifying high-resolution remote sensing data over urban areas. Starting from high resolution multi-spectral images and 3D geometry data, our method proceeds in three main stages: feature extraction, classification, and classified result refinement. First, we extract color, vegetation index and texture features from the multi-spectral image and compute the height, elevation texture and differential morphological profile (DMP) features from the 3D geometry data. Then in the classification stage, multiple random forest (RF) classifiers are trained separately, then combined to form a RF ensemble to estimate each sample's category probabilities. Finally the probabilities along with the feature importance indicator outputted by RF ensemble are used to construct a fully connected conditional random field (FCCRF) graph model, by which the classification results are refined through mean-field based statistical inference. Experiments on the ISPRS Semantic Labeling Contest dataset show that our proposed 3-stage method achieves 86.9% overall accuracy on the test data.

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.

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

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

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.

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.

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

2007-01-01

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

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.

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…

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

ERIC Educational Resources Information Center

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Teachers' Reactions to Pre-Differentiated and Enriched Mathematics Curricula

ERIC Educational Resources Information Center

Rubenstein, Lisa DaVia; Gilson, Cindy M.; Bruce-Davis, Micah N.; Gubbins, E. Jean

2015-01-01

Modern classrooms are often comprised of a heterogeneous student population with varying abilities. To address this variance, third-grade teachers implemented researcher-designed, pre-differentiated, and enriched math curricula in algebra, geometry and measurement, and graphing and data analysis. The goal of the curricula was to provide academic…

Model-based branching point detection in single-cell data by K-branches clustering

PubMed Central

Chlis, Nikolaos K.; Wolf, F. Alexander; Theis, Fabian J.

2017-01-01

Abstract Motivation The identification of heterogeneities in cell populations by utilizing single-cell technologies such as single-cell RNA-Seq, enables inference of cellular development and lineage trees. Several methods have been proposed for such inference from high-dimensional single-cell data. They typically assign each cell to a branch in a differentiation trajectory. However, they commonly assume specific geometries such as tree-like developmental hierarchies and lack statistically sound methods to decide on the number of branching events. Results We present K-Branches, a solution to the above problem by locally fitting half-lines to single-cell data, introducing a clustering algorithm similar to K-Means. These halflines are proxies for branches in the differentiation trajectory of cells. We propose a modified version of the GAP statistic for model selection, in order to decide on the number of lines that best describe the data locally. In this manner, we identify the location and number of subgroups of cells that are associated with branching events and full differentiation, respectively. We evaluate the performance of our method on single-cell RNA-Seq data describing the differentiation of myeloid progenitors during hematopoiesis, single-cell qPCR data of mouse blastocyst development, single-cell qPCR data of human myeloid monocytic leukemia and artificial data. Availability and implementation An R implementation of K-Branches is freely available at https://github.com/theislab/kbranches. Contact fabian.theis@helmholtz-muenchen.de Supplementary information Supplementary data are available at Bioinformatics online. PMID:28582478

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.

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern.

PubMed

Nassar, H; Lebée, A; Monasse, L

2017-01-01

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern

NASA Astrophysics Data System (ADS)

Nassar, H.; Lebée, A.; Monasse, L.

2017-01-01

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

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.

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.

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

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.

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

Kinematics of reflections in subsurface offset and angle-domain image gathers

NASA Astrophysics Data System (ADS)

Dafni, Raanan; Symes, William W.

2018-05-01

Seismic migration in the angle-domain generates multiple images of the earth's interior in which reflection takes place at different scattering-angles. Mechanically, the angle-dependent reflection is restricted to happen instantaneously and at a fixed point in space: Incident wave hits a discontinuity in the subsurface media and instantly generates a scattered wave at the same common point of interaction. Alternatively, the angle-domain image may be associated with space-shift (regarded as subsurface offset) extended migration that artificially splits the reflection geometry. Meaning that, incident and scattered waves interact at some offset distance. The geometric differences between the two approaches amount to a contradictory angle-domain behaviour, and unlike kinematic description. We present a phase space depiction of migration methods extended by the peculiar subsurface offset split and stress its profound dissimilarity. In spite of being in radical contradiction with the general physics, the subsurface offset reveals a link to some valuable angle-domain quantities, via post-migration transformations. The angle quantities are indicated by the direction normal to the subsurface offset extended image. They specifically define the local dip and scattering angles if the velocity at the split reflection coordinates is the same for incident and scattered wave pairs. Otherwise, the reflector normal is not a bisector of the opening angle, but of the corresponding slowness vectors. This evidence, together with the distinguished geometry configuration, fundamentally differentiates the angle-domain decomposition based on the subsurface offset split from the conventional decomposition at a common reflection point. An asymptotic simulation of angle-domain moveout curves in layered media exposes the notion of split versus common reflection point geometry. Traveltime inversion methods that involve the subsurface offset extended migration must accommodate the split geometry in the inversion scheme for a robust and successful convergence at the optimal velocity model.

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.

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.

A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

USGS Publications Warehouse

Barall, Michael

2009-01-01

We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

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

Pre-buckling responses of Timoshenko nanobeams based on the integral and differential models of nonlocal elasticity: an isogeometric approach

NASA Astrophysics Data System (ADS)

Norouzzadeh, A.; Ansari, R.; Rouhi, H.

2017-05-01

Differential form of Eringen's nonlocal elasticity theory is widely employed to capture the small-scale effects on the behavior of nanostructures. However, paradoxical results are obtained via the differential nonlocal constitutive relations in some cases such as in the vibration and bending analysis of cantilevers, and recourse must be made to the integral (original) form of Eringen's theory. Motivated by this consideration, a novel nonlocal formulation is developed herein based on the original formulation of Eringen's theory to study the buckling behavior of nanobeams. The governing equations are derived according to the Timoshenko beam theory, and are represented in a suitable vector-matrix form which is applicable to the finite-element analysis. In addition, an isogeometric analysis (IGA) is conducted for the solution of buckling problem. Construction of exact geometry using non-uniform rational B-splines and easy implementation of geometry refinement tools are the main advantages of IGA. A comparison study is performed between the predictions of integral and differential nonlocal models for nanobeams under different kinds of end conditions.

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.

Membrane fouling in a submerged membrane bioreactor: New method and its applications in interfacial interaction quantification.

PubMed

Hong, Huachang; Cai, Xiang; Shen, Liguo; Li, Renjie; Lin, Hongjun

2017-10-01

Quantification of interfacial interactions between two rough surfaces represents one of the most pressing requirements for membrane fouling prediction and control in membrane bioreactors (MBRs). This study firstly constructed regularly rough membrane and particle surfaces by using rigorous mathematical equations. Thereafter, a new method involving surface element integration (SEI) method, differential geometry and composite Simpson's rule was proposed to quantify the interfacial interactions between the two constructed rough surfaces. This new method were then applied to investigate interfacial interactions in a MBR with the data of surface properties of membrane and foulants experimentally measured. The feasibility of the new method was verified. It was found that asperity amplitude and period of the membrane surface exerted profound effects on the total interaction. The new method had broad potential application fields especially including guiding membrane surface design for membrane fouling mitigation. Copyright © 2017 Elsevier Ltd. All rights reserved.

FBP and BPF reconstruction methods for circular X-ray tomography with off-center detector.

PubMed

Schäfer, Dirk; Grass, Michael; van de Haar, Peter

2011-07-01

Circular scanning with an off-center planar detector is an acquisition scheme that allows to save detector area while keeping a large field of view (FOV). Several filtered back-projection (FBP) algorithms have been proposed earlier. The purpose of this work is to present two newly developed back-projection filtration (BPF) variants and evaluate the image quality of these methods compared to the existing state-of-the-art FBP methods. The first new BPF algorithm applies redundancy weighting of overlapping opposite projections before differentiation in a single projection. The second one uses the Katsevich-type differentiation involving two neighboring projections followed by redundancy weighting and back-projection. An averaging scheme is presented to mitigate streak artifacts inherent to circular BPF algorithms along the Hilbert filter lines in the off-center transaxial slices of the reconstructions. The image quality is assessed visually on reconstructed slices of simulated and clinical data. Quantitative evaluation studies are performed with the Forbild head phantom by calculating root-mean-squared-deviations (RMSDs) to the voxelized phantom for different detector overlap settings and by investigating the noise resolution trade-off with a wire phantom in the full detector and off-center scenario. The noise-resolution behavior of all off-center reconstruction methods corresponds to their full detector performance with the best resolution for the FDK based methods with the given imaging geometry. With respect to RMSD and visual inspection, the proposed BPF with Katsevich-type differentiation outperforms all other methods for the smallest chosen detector overlap of about 15 mm. The best FBP method is the algorithm that is also based on the Katsevich-type differentiation and subsequent redundancy weighting. For wider overlap of about 40-50 mm, these two algorithms produce similar results outperforming the other three methods. The clinical case with a detector overlap of about 17 mm confirms these results. The BPF-type reconstructions with Katsevich differentiation are widely independent of the size of the detector overlap and give the best results with respect to RMSD and visual inspection for minimal detector overlap. The increased homogeneity will improve correct assessment of lesions in the entire field of view.

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.

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.

MIB Galerkin method for elliptic interface problems.

PubMed

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

2014-12-15

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

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.

Finsler-Geometric Continuum Dynamics and Shock Compression

DTIC Science & Technology

2018-01-01

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

Transactions of the Army Conference on Applied Mathematics and Computing (8th) Held in Ithaca, New York on 19-22 June 1990

DTIC Science & Technology

1991-02-01

Shamos, M I , "Computational Geometry", Ph.D Thesis , Department of Computer Science, Yale University, New Haven CT, 1978. [53] Steiglitz, K., An...431) whose real and imaginary parts are given by 222 mj cos OmJ + Az -mL cos 2 ML + MS Cos 2MS (432) mj sinO 0M cose OM = L sin aML cos ML + m S sin 9...Aequationes Math. 14, 1976, 271-291. 5. Greenwell, C.E., Finite element methods for partial integro-differential equations, Ph.D. Thesis , University of

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…

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.

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.

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.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

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.

Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures.

PubMed

Souris, Kevin; Lee, John Aldo; Sterpin, Edmond

2016-04-01

Accuracy in proton therapy treatment planning can be improved using Monte Carlo (MC) simulations. However the long computation time of such methods hinders their use in clinical routine. This work aims to develop a fast multipurpose Monte Carlo simulation tool for proton therapy using massively parallel central processing unit (CPU) architectures. A new Monte Carlo, called MCsquare (many-core Monte Carlo), has been designed and optimized for the last generation of Intel Xeon processors and Intel Xeon Phi coprocessors. These massively parallel architectures offer the flexibility and the computational power suitable to MC methods. The class-II condensed history algorithm of MCsquare provides a fast and yet accurate method of simulating heavy charged particles such as protons, deuterons, and alphas inside voxelized geometries. Hard ionizations, with energy losses above a user-specified threshold, are simulated individually while soft events are regrouped in a multiple scattering theory. Elastic and inelastic nuclear interactions are sampled from ICRU 63 differential cross sections, thereby allowing for the computation of prompt gamma emission profiles. MCsquare has been benchmarked with the gate/geant4 Monte Carlo application for homogeneous and heterogeneous geometries. Comparisons with gate/geant4 for various geometries show deviations within 2%-1 mm. In spite of the limited memory bandwidth of the coprocessor simulation time is below 25 s for 10(7) primary 200 MeV protons in average soft tissues using all Xeon Phi and CPU resources embedded in a single desktop unit. MCsquare exploits the flexibility of CPU architectures to provide a multipurpose MC simulation tool. Optimized code enables the use of accurate MC calculation within a reasonable computation time, adequate for clinical practice. MCsquare also simulates prompt gamma emission and can thus be used also for in vivo range verification.

Kinematic Localization for Global Navigation Satellite Systems: A Kalman Filtering Approach

NASA Astrophysics Data System (ADS)

Tabatabaee, Mohammad Hadi

Use of the Global Positioning System (GNSS) has expanded significantly in the past decade, especially with advances in embedded systems and the emergence of smartphones and the Internet of Things (IoT). The growing demand has stimulated research on development of GNSS techniques and programming tools. The focus of much of the research efforts have been on high-level algorithms and augmentations. This dissertation focuses on the low-level methods at the heart of GNSS systems and proposes a new methods for GNSS positioning problems based on concepts of distance geometry and the use of Kalman filters. The methods presented in this dissertation provide algebraic solutions to problems that have predominantly been solved using iterative methods. The proposed methods are highly efficient, provide accurate estimates, and exhibit a degree of robustness in the presence of unfavorable satellite geometry. The algorithm operates in two stages; an estimation of the receiver clock bias and removal of the bias from the pseudorange observables, followed by the localization of the GNSS receiver. The use of a Kalman filter in between the two stages allows for an improvement of the clock bias estimate with a noticeable impact on the position estimates. The receiver localization step has also been formulated in a linear manner allowing for the direct application of a Kalman filter without any need for linearization. The methodology has also been extended to double differential observables for high accuracy pseudorange and carrier phase position estimates.

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.

Self-similar solutions to isothermal shock problems

NASA Astrophysics Data System (ADS)

Deschner, Stephan C.; Illenseer, Tobias F.; Duschl, Wolfgang J.

We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant initial density is not allowed for isothermal EPs. Reasonable restrictions for this parameter are given. Both, the (genuinely) isothermal implosion as well as the explosion problem are solved for the first time.

Application of the multi-scale finite element method to wave propagation problems in damaged structures

NASA Astrophysics Data System (ADS)

Casadei, F.; Ruzzene, M.

2011-04-01

This work illustrates the possibility to extend the field of application of the Multi-Scale Finite Element Method (MsFEM) to structural mechanics problems that involve localized geometrical discontinuities like cracks or notches. The main idea is to construct finite elements with an arbitrary number of edge nodes that describe the actual geometry of the damage with shape functions that are defined as local solutions of the differential operator of the specific problem according to the MsFEM approach. The small scale information are then brought to the large scale model through the coupling of the global system matrices that are assembled using classical finite element procedures. The efficiency of the method is demonstrated through selected numerical examples that constitute classical problems of great interest to the structural health monitoring community.

FBP and BPF reconstruction methods for circular X-ray tomography with off-center detector

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

Schaefer, Dirk; Grass, Michael; Haar, Peter van de

2011-05-15

Purpose: Circular scanning with an off-center planar detector is an acquisition scheme that allows to save detector area while keeping a large field of view (FOV). Several filtered back-projection (FBP) algorithms have been proposed earlier. The purpose of this work is to present two newly developed back-projection filtration (BPF) variants and evaluate the image quality of these methods compared to the existing state-of-the-art FBP methods. Methods: The first new BPF algorithm applies redundancy weighting of overlapping opposite projections before differentiation in a single projection. The second one uses the Katsevich-type differentiation involving two neighboring projections followed by redundancy weighting andmore » back-projection. An averaging scheme is presented to mitigate streak artifacts inherent to circular BPF algorithms along the Hilbert filter lines in the off-center transaxial slices of the reconstructions. The image quality is assessed visually on reconstructed slices of simulated and clinical data. Quantitative evaluation studies are performed with the Forbild head phantom by calculating root-mean-squared-deviations (RMSDs) to the voxelized phantom for different detector overlap settings and by investigating the noise resolution trade-off with a wire phantom in the full detector and off-center scenario. Results: The noise-resolution behavior of all off-center reconstruction methods corresponds to their full detector performance with the best resolution for the FDK based methods with the given imaging geometry. With respect to RMSD and visual inspection, the proposed BPF with Katsevich-type differentiation outperforms all other methods for the smallest chosen detector overlap of about 15 mm. The best FBP method is the algorithm that is also based on the Katsevich-type differentiation and subsequent redundancy weighting. For wider overlap of about 40-50 mm, these two algorithms produce similar results outperforming the other three methods. The clinical case with a detector overlap of about 17 mm confirms these results. Conclusions: The BPF-type reconstructions with Katsevich differentiation are widely independent of the size of the detector overlap and give the best results with respect to RMSD and visual inspection for minimal detector overlap. The increased homogeneity will improve correct assessment of lesions in the entire field of view.« less

Multigrid Methods for Aerodynamic Problems in Complex Geometries

NASA Technical Reports Server (NTRS)

Caughey, David A.

1995-01-01

Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

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

Comparison of Calibration of Sensors Used for the Quantification of Nuclear Energy Rate Deposition

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

Brun, J.; Reynard-Carette, C.; Tarchalski, M.

This present work deals with a collaborative program called GAMMA-MAJOR 'Development and qualification of a deterministic scheme for the evaluation of GAMMA heating in MTR reactors with exploitation as example MARIA reactor and Jules Horowitz Reactor' between the National Centre for Nuclear Research of Poland, the French Atomic Energy and Alternative Energies Commission and Aix Marseille University. One of main objectives of this program is to optimize the nuclear heating quantification thanks to calculation validated from experimental measurements of radiation energy deposition carried out in irradiation reactors. The quantification of the nuclear heating is a key data especially for themore » thermal, mechanical design and sizing of irradiation experimental devices in specific irradiated conditions and locations. The determination of this data is usually performed by differential calorimeters and gamma thermometers such as used in the experimental multi-sensors device called CARMEN 'Calorimetric en Reacteur et Mesures des Emissions Nucleaires'. In the framework of the GAMMA-MAJOR program a new calorimeter was designed for the nuclear energy deposition quantification. It corresponds to a single-cell calorimeter and it is called KAROLINA. This calorimeter was recently tested during an irradiation campaign inside MARIA reactor in Poland. This new single-cell calorimeter differs from previous CALMOS or CARMEN type differential calorimeters according to three main points: its geometry, its preliminary out-of-pile calibration, and its in-pile measurement method. The differential calorimeter, which is made of two identical cells containing heaters, has a calibration method based on the use of steady thermal states reached by simulating the nuclear energy deposition into the calorimeter sample by Joule effect; whereas the single-cell calorimeter, which has no heater, is calibrated by using the transient thermal response of the sensor (heating and cooling steps). The paper will concern these two kinds of calorimetric sensors. It will focus in particular on studies on their out-of-pile calibrations. Firstly, the characteristics of the sensor designs will be detailed (such as geometry, dimension, material sample, assembly, instrumentation). Then the out-of-pile calibration methods will be described. Furthermore numerical results obtained thanks to 2D axisymmetrical thermal simulations (Finite Element Method, CAST3M) and experimental results will be presented for each sensor. A comparison of the two different thermal sensor behaviours will be realized. To conclude a discussion of the advantages and the drawbacks of each sensor will be performed especially regarding measurement methods. (authors)« less

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

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.

3-D Modeling of Irregular Volcanic Sources Using Sparsity-Promoting Inversions of Geodetic Data and Boundary Element Method

NASA Astrophysics Data System (ADS)

Zhai, Guang; Shirzaei, Manoochehr

2017-12-01

Geodetic observations of surface deformation associated with volcanic activities can be used to constrain volcanic source parameters and their kinematics. Simple analytical models, such as point and spherical sources, are widely used to model deformation data. The inherent nature of oversimplified model geometries makes them unable to explain fine details of surface deformation. Current nonparametric, geometry-free inversion approaches resolve the distributed volume change, assuming it varies smoothly in space, which may detect artificial volume change outside magmatic source regions. To obtain a physically meaningful representation of an irregular volcanic source, we devise a new sparsity-promoting modeling scheme assuming active magma bodies are well-localized melt accumulations, namely, outliers in the background crust. First, surface deformation data are inverted using a hybrid L1- and L2-norm regularization scheme to solve for sparse volume change distributions. Next, a boundary element method is implemented to solve for the displacement discontinuity distribution of the reservoir, which satisfies a uniform pressure boundary condition. The inversion approach is thoroughly validated using benchmark and synthetic tests, of which the results show that source dimension, depth, and shape can be recovered appropriately. We apply this modeling scheme to deformation observed at Kilauea summit for periods of uplift and subsidence leading to and following the 2007 Father's Day event. We find that the magmatic source geometries for these periods are statistically distinct, which may be an indicator that magma is released from isolated compartments due to large differential pressure leading to the rift intrusion.

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

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.

Mathematical modelling of contact of ruled surfaces: theory and practical application

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Niteyskiy, A. S.

2016-04-01

In the theory of ruled surfaces there are well known researches of contact of ruled surfaces along their common generator line (Klein image is often used [1]). In this paper we propose a study of contact of non developable ruled surfaces via the dual vector calculus. The advantages of this method have been demonstrated by E. Study, W. Blaschke and D. N. Zeiliger in differential geometry studies of ruled surfaces in space R3 over the algebra of dual numbers. A practical use of contact is demonstrated by the example modeling of the working surface of the progressive tool for tillage.

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, ...

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

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Sun, Rui

2015-02-01

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

Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures

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

Souris, Kevin, E-mail: kevin.souris@uclouvain.be; Lee, John Aldo; Sterpin, Edmond

2016-04-15

Purpose: Accuracy in proton therapy treatment planning can be improved using Monte Carlo (MC) simulations. However the long computation time of such methods hinders their use in clinical routine. This work aims to develop a fast multipurpose Monte Carlo simulation tool for proton therapy using massively parallel central processing unit (CPU) architectures. Methods: A new Monte Carlo, called MCsquare (many-core Monte Carlo), has been designed and optimized for the last generation of Intel Xeon processors and Intel Xeon Phi coprocessors. These massively parallel architectures offer the flexibility and the computational power suitable to MC methods. The class-II condensed history algorithmmore » of MCsquare provides a fast and yet accurate method of simulating heavy charged particles such as protons, deuterons, and alphas inside voxelized geometries. Hard ionizations, with energy losses above a user-specified threshold, are simulated individually while soft events are regrouped in a multiple scattering theory. Elastic and inelastic nuclear interactions are sampled from ICRU 63 differential cross sections, thereby allowing for the computation of prompt gamma emission profiles. MCsquare has been benchmarked with the GATE/GEANT4 Monte Carlo application for homogeneous and heterogeneous geometries. Results: Comparisons with GATE/GEANT4 for various geometries show deviations within 2%–1 mm. In spite of the limited memory bandwidth of the coprocessor simulation time is below 25 s for 10{sup 7} primary 200 MeV protons in average soft tissues using all Xeon Phi and CPU resources embedded in a single desktop unit. Conclusions: MCsquare exploits the flexibility of CPU architectures to provide a multipurpose MC simulation tool. Optimized code enables the use of accurate MC calculation within a reasonable computation time, adequate for clinical practice. MCsquare also simulates prompt gamma emission and can thus be used also for in vivo range verification.« less

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

DOE PAGES

Xia, Yidong; Luo, Hong; Frisbey, Megan; ...

2014-07-01

A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flowmore » solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.« less

SU-D-BRB-02: Patient-Specific Rectal Toxicity Predictor Based Plan Quality Control for Prostate Stereotactic Body Radiation Therapy (SBRT)

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

Song, T; Zhou, L; Li, Y

2015-06-15

Purpose: To develop a patient-specific rectal toxicity predictor guided plan quality control tool for prostate SBRT plans. Methods: For prostate SBRT cases, four segments of rectal walls including peri-prostatic anterior rectal wall, peri-prostatic lateral rectal walls, peri-prostatic posterior rectal wall and rectum superior to prostate are identified as organs at risk and the circumference of rectal wall receiving more than 39 Gy (CRW39) and 24 Gy (CRW24) are rectal toxicity predictors. In this new geometry-dosimetry model, a patient geometry descriptor, differential circumference of rectal wall (dCRW) is used as model input geometry parameters and plan dosimetric endpoints CRW39 and CRW24more » are output dosimetric parameters. Linear models are built to correlate dCRW to both CRW39 and CRW24 and established with both a linear regression method and a modified bagging ensemble machine learning method. 27 SBRT prostate cases are retrospectively studied from a dose-escalated clinical trial research. 20 prescribed 50 Gy SBRT cases are recruited to train the model and the other rescaled 7 cases are used to evaluated model feasibility and accuracy. Results: Each solved linear coefficient sequence related to CRW39 or CRW24 is a one-dimensional decreasing function of the distance from the PTV boundary, indicating that the different locations of each rectal circumference have different contributions to each particular dosimetric endpoint. The fitting errors for those trained 20 prostate SBRT cases are small with mean values of 2.39%, 2.45% relative to the endpoint values for SBRT rectal toxicity predictor CRW39 and CRW24 respectively. 1 out of 7 evaluation plans is identified as poor quality plan. After re-planning, the CRW39 and CRW24 can be reduced by 3.34% and 3%, without sacrificing PTV coverage. Conclusion: The proposed patient geometry-plan toxicity predictor model for SBRT plans can be successfully applied to plan quality control for prostate SBRT cases.« less

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

Starting geometry creation and design method for freeform optics.

PubMed

Bauer, Aaron; Schiesser, Eric M; Rolland, Jannick P

2018-05-01

We describe a method for designing freeform optics based on the aberration theory of freeform surfaces that guides the development of a taxonomy of starting-point geometries with an emphasis on manufacturability. An unconventional approach to the optimization of these starting designs wherein the rotationally invariant 3rd-order aberrations are left uncorrected prior to unobscuring the system is shown to be effective. The optimal starting-point geometry is created for an F/3, 200 mm aperture-class three-mirror imager and is fully optimized using a novel step-by-step method over a 4 × 4 degree field-of-view to exemplify the design method. We then optimize an alternative starting-point geometry that is common in the literature but was quantified here as a sub-optimal candidate for optimization with freeform surfaces. A comparison of the optimized geometries shows the performance of the optimal geometry is at least 16× better, which underscores the importance of the geometry when designing freeform optics.

Data approximation using a blending type spline construction

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

Dalmo, Rune; Bratlie, Jostein

2014-11-18

Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C{sup k}-smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which aremore » necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences.« less

Design of optimal and ideal 2-D concentrators with the collector immersed in a dielectric tube

NASA Astrophysics Data System (ADS)

Minano, J. C.; Ruiz, J. M.; Luque, A.

1983-12-01

A method is presented for designing ideal and optimal 2-D concentrators when the collector is placed inside a dielectric tube, for the particular case of a bifacial solar collector. The prototype 2-D (cylindrical geometry) concentrator is the compound parabolic concentrator or CPC, and from the beginning of development, it was found by Winston (1978) that filling up the concentrator with a transparent dielectric medium results in a big improvement of the optical properties. The method reported here is based on the extreme ray principle of design and avoids the use of differential equations by means of a proper appliction of Fermat's principle. One advantage of these concentrators is that they allow the size to be small compared with classical CPCs.

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.

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.

Optimization of numerical weather/wave prediction models based on information geometry and computational techniques

NASA Astrophysics Data System (ADS)

Galanis, George; Famelis, Ioannis; Kalogeri, Christina

2014-10-01

The last years a new highly demanding framework has been set for environmental sciences and applied mathematics as a result of the needs posed by issues that are of interest not only of the scientific community but of today's society in general: global warming, renewable resources of energy, natural hazards can be listed among them. Two are the main directions that the research community follows today in order to address the above problems: The utilization of environmental observations obtained from in situ or remote sensing sources and the meteorological-oceanographic simulations based on physical-mathematical models. In particular, trying to reach credible local forecasts the two previous data sources are combined by algorithms that are essentially based on optimization processes. The conventional approaches in this framework usually neglect the topological-geometrical properties of the space of the data under study by adopting least square methods based on classical Euclidean geometry tools. In the present work new optimization techniques are discussed making use of methodologies from a rapidly advancing branch of applied Mathematics, the Information Geometry. The latter prove that the distributions of data sets are elements of non-Euclidean structures in which the underlying geometry may differ significantly from the classical one. Geometrical entities like Riemannian metrics, distances, curvature and affine connections are utilized in order to define the optimum distributions fitting to the environmental data at specific areas and to form differential systems that describes the optimization procedures. The methodology proposed is clarified by an application for wind speed forecasts in the Kefaloniaisland, Greece.

PREFACE: The 7th International Seminar on Geometry, Continua and Microstructures

NASA Astrophysics Data System (ADS)

Burton, David A.

2007-04-01

It gives me great pleasure to present the proceedings of the 7th International Seminar on Geometry, Continua and Microstructures (GCM 7). The conference took place on 25-27 September 2006 at Lancaster University and the local organisers were Robin Tucker, Tim Walton, myself and Jonathan Gratus of the Lancaster University Mathematical Physics Group. Modern field theories of mechanically and electrically responsive continua have a wealth of interesting applications in physics. Such theories provide effective macroscopic models of complex systems, such as living tissue and material with dynamical defects, that capture macroscopic consequences of microscopic phenomena. GCM is an interdisciplinary conference series, initiated by the Eringen medallist Gérard A Maugin, that brings together physicists and applied mathematicians who have interests in continuum mechanics and differential geometry and who aim to develop new and powerful methods for analysing the behaviour of complex mechanical systems. The earlier conferences in the series were held in Paris, Madrid, Mannheim, Turin, Sinaia and Belgrade. This volume addresses a variety of topics including the physics of saturated porous media, the relationship between growth in living tissue and molecular transport, the mechanics of polymer bonds, the macroscopic properties of damaged elastomers, the mechanics of carbon nanotubes, the geometry of balance systems in Continuum Thermodynamics and wave propagation in the material manifold. I would like to warmly thank the rest of the organising committee and the conference participants for making GCM 7 an enjoyable and rewarding occasion. Photographs may be found at http://www.lancs.ac.uk/depts/spc/conf/gcm7/wss/index.htm David A Burton Editor

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'.

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem, the Finsler theory is able to accurately reproduce the vacancy formation energy at a nanoscale resolution, and various solutions describe localized cavitation at the core of the body and/or distributed dilatation and softening associated with amorphization as observed in atomic simulations, with relative stability of solutions depending on the regularization length.

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

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

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

Exact Solution for Capillary Bridges Properties by Shooting Method

NASA Astrophysics Data System (ADS)

Qiang-Nian, Li; Jia-Qi, Zhang; Feng-Xi, Zhou

2017-04-01

The investigation of liquid bridge force acting between wet particles has great significance in many fields. In this article, the exact solution of capillary force between two unequal-sized spherical particles is investigated. Firstly, The Young-Laplace equation with moving boundary is converted into a set of ordinary differential equations with two fix point boundary using variable substitution technique, in which the gravity effects have been neglected. The geometry of the liquid bridge between two particles is solved by shooting method. After that, the gorge method is applied to calculate the capillary-bridge force that is consists of contributions from the capillary suction and surface tension. Finally, the effect of various parameters including distance between two spheres, radii of spheres, and contact angles on the capillary force are investigated. It is shown that the presented approach is an efficient and accurate algorithm for capillary force between two particles in complex situations.

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.

3D frequency-domain ultrasound waveform tomography breast imaging

NASA Astrophysics Data System (ADS)

Sandhu, Gursharan Yash; West, Erik; Li, Cuiping; Roy, Olivier; Duric, Neb

2017-03-01

Frequency-domain ultrasound waveform tomography is a promising method for the visualization and characterization of breast disease. It has previously been shown to accurately reconstruct the sound speed distributions of breasts of varying densities. The reconstructed images show detailed morphological and quantitative information that can help differentiate different types of breast disease including benign and malignant lesions. The attenuation properties of an ex vivo phantom have also been assessed. However, the reconstruction algorithms assumed a 2D geometry while the actual data acquisition process was not. Although clinically useful sound speed images can be reconstructed assuming this mismatched geometry, artifacts from the reconstruction process exist within the reconstructed images. This is especially true for registration across different modalities and when the 2D assumption is violated. For example, this happens when a patient's breast is rapidly sloping. It is also true for attenuation imaging where energy lost or gained out of the plane gets transformed into artifacts within the image space. In this paper, we will briefly review ultrasound waveform tomography techniques, give motivation for pursuing the 3D method, discuss the 3D reconstruction algorithm, present the results of 3D forward modeling, show the mismatch that is induced by the violation of 3D modeling via numerical simulations, and present a 3D inversion of a numerical phantom.

Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry

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

Huang, Lei; Xue, Junpeng; Gao, Bo

2017-06-14

There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this paper, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish themore » height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. Finally, the new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.« less

The beam stop array method to measure object scatter in digital breast tomosynthesis

NASA Astrophysics Data System (ADS)

Lee, Haeng-hwa; Kim, Ye-seul; Park, Hye-Suk; Kim, Hee-Joung; Choi, Jae-Gu; Choi, Young-Wook

2014-03-01

Scattered radiation is inevitably generated in the object. The distribution of the scattered radiation is influenced by object thickness, filed size, object-to-detector distance, and primary energy. One of the investigations to measure scatter intensities involves measuring the signal detected under the shadow of the lead discs of a beam-stop array (BSA). The measured scatter by BSA includes not only the scattered radiation within the object (object scatter), but also the external scatter source. The components of external scatter source include the X-ray tube, detector, collimator, x-ray filter, and BSA. Excluding background scattered radiation can be applied to different scanner geometry by simple parameter adjustments without prior knowledge of the scanned object. In this study, a method using BSA to differentiate scatter in phantom (object scatter) from external background was used. Furthermore, this method was applied to BSA algorithm to correct the object scatter. In order to confirm background scattered radiation, we obtained the scatter profiles and scatter fraction (SF) profiles in the directions perpendicular to the chest wall edge (CWE) with and without scattering material. The scatter profiles with and without the scattering material were similar in the region between 127 mm and 228 mm from chest wall. This result indicated that the measured scatter by BSA included background scatter. Moreover, the BSA algorithm with the proposed method could correct the object scatter because the total radiation profiles of object scatter correction corresponded to original image in the region between 127 mm and 228 mm from chest wall. As a result, the BSA method to measure object scatter could be used to remove background scatter. This method could apply for different scanner geometry after background scatter correction. In conclusion, the BSA algorithm with the proposed method is effective to correct object scatter.

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

PubMed

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

2011-09-01

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

Japan unified hIgh-resolution relocated catalog for earthquakes (JUICE): Crustal seismicity beneath the Japanese Islands

NASA Astrophysics Data System (ADS)

Yano, Tomoko E.; Takeda, Tetsuya; Matsubara, Makoto; Shiomi, Katsuhiko

2017-04-01

We have generated a high-resolution catalog called the ;Japan Unified hIgh-resolution relocated Catalog for Earthquakes; (JUICE), which can be used to evaluate the geometry and seismogenic depth of active faults in Japan. We relocated > 1.1 million hypocenters from the NIED Hi-net catalog for events which occurred between January 2001 and December 2012, to a depth of 40 km. We apply a relative hypocenter determination method to the data in each grid square, in which entire Japan is divided into 1257 grid squares to parallelize the relocation procedure. We used a double-difference method, incorporating cross-correlating differential times as well as catalog differential times. This allows us to resolve, in detail, a seismicity distribution for the entire Japanese Islands. We estimated location uncertainty by a statistical resampling method, using Jackknife samples, and show that the uncertainty can be within 0.37 km in the horizontal and 0.85 km in the vertical direction with a 90% confidence interval for areas with good station coverage. Our seismogenic depth estimate agrees with the lower limit of the hypocenter distribution for a recent earthquake on the Kamishiro fault (2014, Mj 6.7), which suggests that the new catalog should be useful for estimating the size of future earthquakes for inland active faults.

Ex-situ gas diffusion layer intrusion effect determination of polymer electrolyte membrane fuel cell flow fields

NASA Astrophysics Data System (ADS)

Haase, S.; Rauber, M.

2015-09-01

In automotive PEM fuel cell systems, one of the most important targets is to reduce the parasitic power of balance of plant components, e.g. the air supply. This can be achieved for example by decreasing air stoichiometry. However, this could lead to bad flow sharing in the fuel cell stack. Therefore the fluid distribution in the flow field has to be evaluated, understood and optimized. This work evaluates the effect of GDL intrusion on the pressure drop via ex-situ determination of GDL intrusion using CFD simulation. The intruded GDL geometries, evaluated by an optical microscope with 200 times enlargement, are transferred to pressure drop behaviors by a numerical CFD model. These results are compared to the results of the differential pressure method of mapping the pressure distribution, described in [43]. The intrusion of the GDL leads to homogeneous flow distribution up to clamping pressures of 2.5 MPa. The inhomogeneous intrusion, induced by cracked fibers that extend into the channel, dominates the flow at higher clamping pressures and leads to the exponential increase in pressure drop in the differential pressure method. For clamping pressures used in typical fuel cell applications, the results of both methods show homogeneous flow through the channels.

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

PubMed Central

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

2013-01-01

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

A physics-based solver to optimize the illumination of cylindrical targets in spherically distributed high power laser systems.

PubMed

Gourdain, P-A

2017-05-01

In recent years, our understanding of high energy density plasmas has played an important role in improving inertial fusion confinement and in emerging new fields of physics, such as laboratory astrophysics. Every new idea required developing innovative experimental platforms at high power laser facilities, such as OMEGA or NIF. These facilities, designed to focus all their beams onto spherical targets or hohlraum windows, are now required to shine them on more complex targets. While the pointing on planar geometries is relatively straightforward, it becomes problematic for cylindrical targets or target with more complex geometries. This publication describes how the distribution of laser beams on a cylindrical target can be done simply by using a set of physical laws as a pointing procedure. The advantage of the method is threefold. First, it is straightforward, requiring no mathematical enterprise besides solving ordinary differential equations. Second, it will converge if a local optimum exists. Finally, it is computationally inexpensive. Experimental results show that this approach produces a geometrical beam distribution that yields cylindrically symmetric implosions.

Development of Ultra-High Molecular Weight Polyethylene (UHMWPE) Coating by Cold Spray Technique

NASA Astrophysics Data System (ADS)

Ravi, Kesavan; Ichikawa, Yuji; Deplancke, Tiana; Ogawa, Kazuhiro; Lame, Olivier; Cavaille, Jean-Yves

2015-08-01

Ultra-high molecular weight polyethylene or UHMWPE is an extremely difficult material to coat with, as it is rubbery and chemically very inert. The Cold Spray process appears to be a promising alternative processing technique but polymers are in general difficult to deposit using this method. So, attempts to develop UHMWPE coatings were made using a downstream injection cold spray technique incorporating a few modifications. A conventional cold spray machine yielded only a few deposited particles of UHMWPE on the substrate surface, but with some modifications in the nozzle geometry (especially the length and inner geometry) a thin coating of 45 μm on Al substrate was obtained. Moreover, experiments with the addition of fumed nano-alumina to the feedstock yielded a coating of 1-4 mm thickness on Al and polypropylene substrates. UHMWPE was seen to be melt crystallized during the coating formation, as can be seen from the differential calorimetry curves. Influence of nano-ceramic particles was explained by observing the creation of a bridge bond between UHMWPE particles.

Neighborhood Social Inequalities in Road Traffic Injuries: The Influence of Traffic Volume and Road Design

PubMed Central

Gauvin, Lise; Plante, Céline; Fournier, Michel; Morency, Catherine

2012-01-01

Objectives. We examined the extent to which differential traffic volume and road geometry can explain social inequalities in pedestrian, cyclist, and motor vehicle occupant injuries across wealthy and poor urban areas. Methods. We performed a multilevel observational study of all road users injured over 5 years (n = 19 568) at intersections (n = 17 498) in a large urban area (Island of Montreal, Canada). We considered intersection-level (traffic estimates, major roads, number of legs) and area-level (population density, commuting travel modes, household income) characteristics in multilevel Poisson regressions that nested intersections in 506 census tracts. Results. There were significantly more injured pedestrians, cyclists, and motor vehicle occupants at intersections in the poorest than in the richest areas. Controlling for traffic volume, intersection geometry, and pedestrian and cyclist volumes greatly attenuated the event rate ratios between intersections in the poorest and richest areas for injured pedestrians (−70%), cyclists (−44%), and motor vehicle occupants (−44%). Conclusions. Roadway environment can explain a substantial portion of the excess rate of road traffic injuries in the poorest urban areas. PMID:22515869

A physics-based solver to optimize the illumination of cylindrical targets in spherically distributed high power laser systems

NASA Astrophysics Data System (ADS)

Gourdain, P.-A.

2017-05-01

In recent years, our understanding of high energy density plasmas has played an important role in improving inertial fusion confinement and in emerging new fields of physics, such as laboratory astrophysics. Every new idea required developing innovative experimental platforms at high power laser facilities, such as OMEGA or NIF. These facilities, designed to focus all their beams onto spherical targets or hohlraum windows, are now required to shine them on more complex targets. While the pointing on planar geometries is relatively straightforward, it becomes problematic for cylindrical targets or target with more complex geometries. This publication describes how the distribution of laser beams on a cylindrical target can be done simply by using a set of physical laws as a pointing procedure. The advantage of the method is threefold. First, it is straightforward, requiring no mathematical enterprise besides solving ordinary differential equations. Second, it will converge if a local optimum exists. Finally, it is computationally inexpensive. Experimental results show that this approach produces a geometrical beam distribution that yields cylindrically symmetric implosions.

The Van Hiele geometry thinking levels of mild mental retardation students

NASA Astrophysics Data System (ADS)

Shomad, Z. A.; Kusmayadi, T. A.; Riyadi

2017-12-01

This research is to investigate the level of mild mental retardation geometry students thinking. This research focuses on the geometry thinking level based on Van Hiele theory. This study uses qualitative methods with case study strategy. Data obtained from observation and tests result. The subjects are 12 mental retardation students. The result show that ability of mild mental retardation students with each other is different but have same level of level thinking geometry. The geometry thinking level of mental retardation students was identified in level 1 of the Van Hiele theory. Based on the level thinking geometry of mental retardation students simplify geometry thinking teachers in selecting appropriate learning methods, choose the materials in accordance with ability, and can modify the material following the geometry thinking level of mental retardation students.

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.

Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters.

PubMed

Takeuchi, Hiroshi

2018-05-08

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection.

PubMed

Wang, Liansheng; Qin, Jing; Wong, Tien Tsin; Heng, Pheng Ann

2011-10-07

The epicardial potential (EP)-targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a well-known ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But the L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using the L1-norm penalty function, however, may greatly increase computational complexity due to its non-differentiability. We propose an L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1-norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a bound-constrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1-norm regularization methods, especially when the noises are large.

Structure and tectonic evolution of the NE segment of the Polish-Ukrainian Carpathians during the Late Cenozoic: subsurface cross-sections and palinspastic models

NASA Astrophysics Data System (ADS)

Kuśmierek, Jan; Baran, Urszula

2016-08-01

The discrepant arrangement of the Carpathian nappes and syntectonic deposits of the Carpathian Foredeep reveals the oroclinal migration of the subduction direction of the platform margin during the Late Cenozoic. Formation of the nappes was induced by their detachment from disintegrated segments of the European Platform; the segments were shortened as a result of their vertical rotation in zones of compressional sutures. It finds expression in local occurrence of the backward vergence of folding against the generally forward vergence toward the Carpathian Foredeep. The precompressional configuration of sedimentation areas of particular nappes was reconstructed with application of the palinspastic method, on the basis of the hitherto undervalued model which emphasizes the influence of the subduction and differentiated morphology of the platform basement on the tectonic evolution of the fold and thrust belt. Superposition of the palaeogeographic representations and the present geometry of the orogen allows understanding of the impact of the magnitudes of tectonic displacements on the differentiation of the geological structure in the NE segment of the Carpathians. The differentiation has inspired different views of Polish and Ukrainian geologists on structural classification and evolution of the frontal thrusts.

Differential diagnosis of breast cancer using quantitative, label-free and molecular vibrational imaging

PubMed Central

Yang, Yaliang; Li, Fuhai; Gao, Liang; Wang, Zhiyong; Thrall, Michael J.; Shen, Steven S.; Wong, Kelvin K.; Wong, Stephen T. C.

2011-01-01

We present a label-free, chemically-selective, quantitative imaging strategy to identify breast cancer and differentiate its subtypes using coherent anti-Stokes Raman scattering (CARS) microscopy. Human normal breast tissue, benign proliferative, as well as in situ and invasive carcinomas, were imaged ex vivo. Simply by visualizing cellular and tissue features appearing on CARS images, cancerous lesions can be readily separated from normal tissue and benign proliferative lesion. To further distinguish cancer subtypes, quantitative disease-related features, describing the geometry and distribution of cancer cell nuclei, were extracted and applied to a computerized classification system. The results show that in situ carcinoma was successfully distinguished from invasive carcinoma, while invasive ductal carcinoma (IDC) and invasive lobular carcinoma were also distinguished from each other. Furthermore, 80% of intermediate-grade IDC and 85% of high-grade IDC were correctly distinguished from each other. The proposed quantitative CARS imaging method has the potential to enable rapid diagnosis of breast cancer. PMID:21833355

Precision determination of electron scattering angle by differential nuclear recoil energy method

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

Liyanage, N.; Saenboonruang, K.

2015-12-01

The accurate determination of the scattered electron angle is crucial to electron scattering experiments, both with open-geometry large-acceptance spectrometers and ones with dipole-type magnetic spectrometers for electron detection. In particular, for small central-angle experiments using dipole-type magnetic spectrometers, in which surveys are used to measure the spectrometer angle with respect to the primary electron beam, the importance of the scattering angle determination is emphasized. However, given the complexities of large experiments and spectrometers, the accuracy of such surveys is limited and insufficient to meet demands of some experiments. In this article, we present a new technique for determination of themore » electron scattering angle based on an accurate measurement of the primary beam energy and the principle of differential nuclear recoil. This technique was used to determine the scattering angle for several experiments carried out at the Experimental Hall A, Jefferson Lab. Results have shown that the new technique greatly improved the accuracy of the angle determination compared to surveys.« less

Precision Determination of Electron Scattering Angle by Differential Nuclear Recoil Energy Method

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

Liyanage, Nilanga; Saenboonruang, Kiadtisak

2015-09-01

The accurate determination of the scattered electron angle is crucial to electron scattering experiments, both with open-geometry large-acceptance spectrometers and ones with dipole-type magnetic spectrometers for electron detection. In particular, for small central-angle experiments using dipole-type magnetic spectrometers, in which surveys are used to measure the spectrometer angle with respect to the primary electron beam, the importance of the scattering angle determination is emphasized. However, given the complexities of large experiments and spectrometers, the accuracy of such surveys is limited and insufficient to meet demands of some experiments. In this article, we present a new technique for determination of themore » electron scattering angle based on an accurate measurement of the primary beam energy and the principle of differential nuclear recoil. This technique was used to determine the scattering angle for several experiments carried out at the Experimental Hall A, Jefferson Lab. Results have shown that the new technique greatly improved the accuracy of the angle determination compared to surveys.« less

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.

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.

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.

Two-dimensional mesh embedding for Galerkin B-spline methods

NASA Technical Reports Server (NTRS)

Shariff, Karim; Moser, Robert D.

1995-01-01

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

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

Numerical simulation of rough-surface aerodynamics

NASA Astrophysics Data System (ADS)

Chi, Xingkai

Computational fluid dynamics (CFD) simulations of flow over surfaces with roughness in which the details of the surface geometry must be resolved pose major challenges. The objective of this study is to address these challenges through two important engineering problems, where roughness play a critical role---flow over airfoils with accrued ice and flow and heat transfer over turbine blade surfaces roughened by erosion and/or deposition. CFD simulations of iced airfoils face two major challenges. The first is how to generate high-quality single- and multi-block structured grids for highly convoluted convex and concave surface geometries with multiple scales. In this study, two methods were developed for the generation of high-quality grids for such geometries. The method developed for single-block grids involves generating a grid about the clean airfoil, carving out a portion of that grid about the airfoil, replacing that portion with a grid that accounts for the accrued ice geometry, and performing elliptic smoothing. The method developed for multi-block grids involves a transition-layer grid to ensure jaggedness in the ice geometry does not propagate into the domain. It also involves a "thick" wrap-around grid about the ice to ensure grid lines clustered next to solid surfaces do not propagate as streaks of tightly packed grid lines into the domain along block boundaries. For multi-block grids, this study also developed blocking topologies that ensure solutions to multi-block grids converge to steady state as quickly as single-block grids. The second major challenge in CFD simulations of iced airfoils is not knowing when it will predict reliably because of uncertainties in the turbulence modeling. In this study, the effects of turbulence models in predicting lift, drag, and moment coefficients were examined for airfoils with rime ice (i.e., ice with jaggedness only) and with glaze ice (i.e., ice with multiple protruding horns and surface jaggedness) as a function of angle of attack. In this examination, three different CFD codes---WIND, FLUENT, and PowerFLOW were used to examine a variety of turbulence models, including Spalart-Allmaras, RNG k-epsilon, shear-stress transport, v2-f, and differential Reynolds stress with and without non-equilibrium wall functions. The accuracy of the CFD predictions was evaluated by comparing grid-independent solutions with measured experimental data. Results obtained show CFD with WIND and FLUENT to predict the aerodynamics of airfoils with rime ice reliably up to near stall for all turbulence models investigated. (Abstract shortened by UMI.)

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)

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

Sprays and Cartan projective connections

NASA Astrophysics Data System (ADS)

Saunders, D. J.

2004-10-01

Around 80 years ago, several authors (for instance H. Weyl, T.Y. Thomas, J. Douglas and J.H.C. Whitehead) studied the projective geometry of paths, using the methods of tensor calculus. The principal object of study was a spray, namely a homogeneous second-order differential equation, or more generally a projective equivalence class of sprays. At around the same time, E. Cartan studied the same topic from a different point of view, by imagining a projective space attached to a manifold, or, more generally, attached to a `manifold of elements'; the infinitesimal `glue' may be interpreted in modern language as a Cartan projective connection on a principal bundle. This paper describes the geometrical relationship between these two points of view.

Study of picrate salts with amines

NASA Astrophysics Data System (ADS)

Goel, Nidhi; Singh, Udai P.; Singh, Gurdip; Srivastava, Pratibha

2013-03-01

The reaction of picric acid (2,4,6-trinitrophenol) with amines [urea, cyclohexane-1,2-diamine, 1H-1,2,4-triazole-3,5-diamine, 6-phenyl-1,3.5-triazine-2,4-diamine] yielded the corresponding picrate salts 1-4. Theoretical studies reveal that the hydrogen-bond interaction energy decreases on increasing the steric hindrance in amines. The solid state structure of compounds 1-4 was measured by X-ray techniques and compared to the gas phase optimized geometries (DFT/B3LYP). Thermal stability of these salts has been studied by means of thermogravimetric-differential scanning calorimetry (TG-DSC) while kinetic parameters have been evaluated using models fitting and isoconversional methods. Thermolytic pathways have also been suggested.

Topography Modeling in Atmospheric Flows Using the Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Ackerman, A. S.; Senocak, I.; Mansour, N. N.; Stevens, D. E.

2004-01-01

Numerical simulation of flow over complex geometry needs accurate and efficient computational methods. Different techniques are available to handle complex geometry. The unstructured grid and multi-block body-fitted grid techniques have been widely adopted for complex geometry in engineering applications. In atmospheric applications, terrain fitted single grid techniques have found common use. Although these are very effective techniques, their implementation, coupling with the flow algorithm, and efficient parallelization of the complete method are more involved than a Cartesian grid method. The grid generation can be tedious and one needs to pay special attention in numerics to handle skewed cells for conservation purposes. Researchers have long sought for alternative methods to ease the effort involved in simulating flow over complex geometry.

Use of CAD Geometry in MDO

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

1996-01-01

The purpose of this paper is to discuss the use of Computer-Aided Design (CAD) geometry in a Multi-Disciplinary Design Optimization (MDO) environment. Two techniques are presented to facilitate the use of CAD geometry by different disciplines, such as Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM). One method is to transfer the load from a CFD grid to a CSM grid. The second method is to update the CAD geometry for CSM deflection.

Combinatorial Formulas for Characteristic Classes, and Localization of Secondary Topological Invariants.

NASA Astrophysics Data System (ADS)

Smirnov, Mikhail

1995-01-01

The problems solved in this thesis originated from combinatorial formulas for characteristic classes. This thesis deals with Chern-Simons classes, their generalizations and related algebraic and analytic problems. (1) In this thesis, I describe a new class of algebras whose elements contain Chern and generalized Chern -Simons classes. There is a Poisson bracket in these algebras, similar to the bracket in Kontsevich's noncommutative symplectic geometry (Kon). I prove that the Poisson bracket gives rise to a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. This is a new result. I describe algebraic analogs of the dilogarithm and higher polylogarithms in the algebra corresponding to Chern-Simons classes. (2) I study the properties of this bracket. It is possible to write the exterior differential and other operations in the algebra using this bracket. The bracket of any two Chern classes is zero and the bracket of a Chern class and a Chern-Simons class is d-closed. The construction developed here easily gives explicit formulas for known secondary classes and makes it possible to construct new ones. (3) I develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action (see theorem 3 page xi). (4) It is possible give new explicit formulas for cocycles on a gauge group of a bundle and for the corresponding cocycles on the Lie algebra of the gauge group. I use formulas for secondary characteristic classes and an algebraic approach developed in chapter 1. I also use the work of Faddeev, Reiman and Semyonov-Tian-Shanskii (FRS) on cocycles as quantum anomalies. (5) I apply the methods of differential geometry of formal power series to construct universal characteristic and secondary characteristic classes. Given a pair of gauge equivalent connections using local formulas I obtain dilogarithmic and trilogarithmic analogs of Chern-Simons classes.

Efficient discretization in finite difference method

NASA Astrophysics Data System (ADS)

Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris

2015-04-01

Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.

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.

Turbine blade profile design method based on Bezier curves

NASA Astrophysics Data System (ADS)

Alexeev, R. A.; Tishchenko, V. A.; Gribin, V. G.; Gavrilov, I. Yu.

2017-11-01

In this paper, the technique of two-dimensional parametric blade profile design is presented. Bezier curves are used to create the profile geometry. The main feature of the proposed method is an adaptive approach of curve fitting to given geometric conditions. Calculation of the profile shape is produced by multi-dimensional minimization method with a number of restrictions imposed on the blade geometry.The proposed method has been used to describe parametric geometry of known blade profile. Then the baseline geometry was modified by varying some parameters of the blade. The numerical calculation of obtained designs has been carried out. The results of calculations have shown the efficiency of chosen approach.

Development and Application of Compatible Discretizations of Maxwell's Equations

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

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

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.

3DHZETRN: Inhomogeneous Geometry Issues

NASA Technical Reports Server (NTRS)

Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.

2017-01-01

Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.

Planar quadrature RF transceiver design using common-mode differential-mode (CMDM) transmission line method for 7T MR imaging.

PubMed

Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B; Zhang, Xiaoliang

2013-01-01

The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.

PubMed

Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W

2009-03-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

A Diffusion Tensor Imaging Tractography Algorithm Based on Navier-Stokes Fluid Mechanics

PubMed Central

Hageman, Nathan S.; Toga, Arthur W.; Narr, Katherine; Shattuck, David W.

2009-01-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color (DEC) images of the DTI dataset. PMID:19244007

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.

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.

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.

Non-metallocene organometallic complexes and related methods and systems

DOEpatents

Agapie, Theodor; Golisz, Suzanne Rose; Tofan, Daniel; Bercaw, John E.

2010-12-07

A non-metallocene organometallic complex comprising a tridentate ligand and a metal bonded to a tridentate ligand, wherein two substituted aryl groups in the tridentate ligand are connected to a cyclic group at the ortho position via semi-rigid ring-ring linkages, and selected so to provide the resulting non-metallocene organometallic complex with a C.sub.S geometry, a C.sub.1 geometry, a C.sub.2 geometry or a C.sub.2v geometry. Method for performing olefin polymerization with a non-metallocene organometallic complex as a catalyst, related catalytic systems, tridentate ligand and method for providing a non-metallocene organometallic complex.

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.

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.

Computation of molecular vibrational frequencies using anomalous harmoniclike potentials.

PubMed

Li, Xiangzhu; Paldus, Josef

2009-07-28

The instabilities of Hartree-Fock (HF) solutions at or near the equilibrium geometry of symmetric molecular species imply the existence of broken-symmetry solutions having a lower energy than the corresponding symmetry-adapted ones. Moreover, the distortion of the nuclear framework along the normal modes that are implied by such broken-symmetry solutions results in an anomalous or even singular behavior in the corresponding cuts of the potential energy surface (PES). Using such HF solutions as a reference, these anomalies propagate to a post-HF level and make it impossible to determine reliable harmonic or fundamental vibrational frequencies for such modes by relying on either numerical or analytical differentiation of the PES, requiring instead a numerical integration of the Schrodinger equation for the nuclear motion. This, in turn, requires a detailed knowledge on the PES in a wide range of geometries, necessitating a computation of the potential energy function in a large number of points. We present an alternative approach to this problem, referred to as the integral averaging method (IAM), which facilitates this task by significantly reducing the number of geometries for which one has to compute the potential energy while yielding results of practically the same accuracy as the solution of the Schrodinger equation. The IAM is applied to several ABA-type triatomics and to the allyl radical, whose asymmetric stretching mode potential suffers from an anomalous behavior due to the spin-preserving instabilities in restricted open-shell HF solutions.

Methods of treating complex space vehicle geometry for charged particle radiation transport

NASA Technical Reports Server (NTRS)

Hill, C. W.

1973-01-01

Current methods of treating complex geometry models for space radiation transport calculations are reviewed. The geometric techniques used in three computer codes are outlined. Evaluations of geometric capability and speed are provided for these codes. Although no code development work is included several suggestions for significantly improving complex geometry codes are offered.

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

PubMed Central

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

2011-01-01

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

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.

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.

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.

Morphing the feature-based multi-blocks of normative/healthy vertebral geometries to scoliosis vertebral geometries: development of personalized finite element models.

PubMed

Hadagali, Prasannaah; Peters, James R; Balasubramanian, Sriram

2018-03-01

Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.

A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, A.; Mokhtari, J.; Koochi, A.; Abadyan, M.

2015-06-01

In this paper, the impact of the Casimir attraction on the electromechanical stability of nanowire-fabricated nanotweezers is investigated using a theoretical continuum mechanics model. The Dirichlet mode is considered and an asymptotic solution, based on path integral approach, is applied to consider the effect of vacuum fluctuations in the model. The Euler-Bernoulli beam theory is employed to derive the nonlinear governing equation of the nanotweezers. The governing equations are solved by three different approaches, i.e. the modified variation iteration method, generalized differential quadrature method and using a lumped parameter model. Various perspectives of the problem, including the comparison with the van der Waals force regime, the variation of instability parameters and effects of geometry are addressed in present paper. The proposed approach is beneficial for the precise determination of the electrostatic response of the nanotweezers in the presence of Casimir force.

Geometry and Erdkinder.

ERIC Educational Resources Information Center

McDonald, Nathaniel J.

2001-01-01

Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…

A simple method for in vivo measurement of implant rod three-dimensional geometry during scoliosis surgery.

PubMed

Salmingo, Remel A; Tadano, Shigeru; Fujisaki, Kazuhiro; Abe, Yuichiro; Ito, Manabu

2012-05-01

Scoliosis is defined as a spinal pathology characterized as a three-dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-dimensional geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective geometry has been shown to be successful in the reconstruction of a three-dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-dimensional geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-dimensional geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-dimensional geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-dimensional implant rod geometry in vivo.

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.

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.

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.

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

A Bidirectional Coupling Procedure Applied to Multiscale Respiratory Modeling☆

PubMed Central

Kuprat, A.P.; Kabilan, S.; Carson, J.P.; Corley, R.A.; Einstein, D.R.

2012-01-01

In this study, we present a novel multiscale computational framework for efficiently linking multiple lower-dimensional models describing the distal lung mechanics to imaging-based 3D computational fluid dynamics (CFD) models of the upper pulmonary airways in order to incorporate physiologically appropriate outlet boundary conditions. The framework is an extension of the Modified Newton’s Method with nonlinear Krylov accelerator developed by Carlson and Miller [1, 2, 3]. Our extensions include the retention of subspace information over multiple timesteps, and a special correction at the end of a timestep that allows for corrections to be accepted with verified low residual with as little as a single residual evaluation per timestep on average. In the case of a single residual evaluation per timestep, the method has zero additional computational cost compared to uncoupled or unidirectionally coupled simulations. We expect these enhancements to be generally applicable to other multiscale coupling applications where timestepping occurs. In addition we have developed a “pressure-drop” residual which allows for stable coupling of flows between a 3D incompressible CFD application and another (lower-dimensional) fluid system. We expect this residual to also be useful for coupling non-respiratory incompressible fluid applications, such as multiscale simulations involving blood flow. The lower-dimensional models that are considered in this study are sets of simple ordinary differential equations (ODEs) representing the compliant mechanics of symmetric human pulmonary airway trees. To validate the method, we compare the predictions of hybrid CFD-ODE models against an ODE-only model of pulmonary airflow in an idealized geometry. Subsequently, we couple multiple sets of ODEs describing the distal lung to an imaging-based human lung geometry. Boundary conditions in these models consist of atmospheric pressure at the mouth and intrapleural pressure applied to the multiple sets of ODEs. In both the simplified geometry and in the imaging-based geometry, the performance of the method was comparable to that of monolithic schemes, in most cases requiring only a single CFD evaluation per time step. Thus, this new accelerator allows us to begin combining pulmonary CFD models with lower-dimensional models of pulmonary mechanics with little computational overhead. Moreover, because the CFD and lower-dimensional models are totally separate, this framework affords great flexibility in terms of the type and breadth of the adopted lower-dimensional model, allowing the biomedical researcher to appropriately focus on model design. Research funded by the National Heart and Blood Institute Award 1RO1HL073598. PMID:24347680

A bidirectional coupling procedure applied to multiscale respiratory modeling

NASA Astrophysics Data System (ADS)

Kuprat, A. P.; Kabilan, S.; Carson, J. P.; Corley, R. A.; Einstein, D. R.

2013-07-01

In this study, we present a novel multiscale computational framework for efficiently linking multiple lower-dimensional models describing the distal lung mechanics to imaging-based 3D computational fluid dynamics (CFDs) models of the upper pulmonary airways in order to incorporate physiologically appropriate outlet boundary conditions. The framework is an extension of the modified Newton's method with nonlinear Krylov accelerator developed by Carlson and Miller [1], Miller [2] and Scott and Fenves [3]. Our extensions include the retention of subspace information over multiple timesteps, and a special correction at the end of a timestep that allows for corrections to be accepted with verified low residual with as little as a single residual evaluation per timestep on average. In the case of a single residual evaluation per timestep, the method has zero additional computational cost compared to uncoupled or unidirectionally coupled simulations. We expect these enhancements to be generally applicable to other multiscale coupling applications where timestepping occurs. In addition we have developed a "pressure-drop" residual which allows for stable coupling of flows between a 3D incompressible CFD application and another (lower-dimensional) fluid system. We expect this residual to also be useful for coupling non-respiratory incompressible fluid applications, such as multiscale simulations involving blood flow. The lower-dimensional models that are considered in this study are sets of simple ordinary differential equations (ODEs) representing the compliant mechanics of symmetric human pulmonary airway trees. To validate the method, we compare the predictions of hybrid CFD-ODE models against an ODE-only model of pulmonary airflow in an idealized geometry. Subsequently, we couple multiple sets of ODEs describing the distal lung to an imaging-based human lung geometry. Boundary conditions in these models consist of atmospheric pressure at the mouth and intrapleural pressure applied to the multiple sets of ODEs. In both the simplified geometry and in the imaging-based geometry, the performance of the method was comparable to that of monolithic schemes, in most cases requiring only a single CFD evaluation per time step. Thus, this new accelerator allows us to begin combining pulmonary CFD models with lower-dimensional models of pulmonary mechanics with little computational overhead. Moreover, because the CFD and lower-dimensional models are totally separate, this framework affords great flexibility in terms of the type and breadth of the adopted lower-dimensional model, allowing the biomedical researcher to appropriately focus on model design. Research funded by the National Heart and Blood Institute Award 1RO1HL073598.

Spinorial Geometry and Branes

NASA Astrophysics Data System (ADS)

Sloane, Peter

2007-09-01

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, "The spinorial geometry of supersymmetric backgrounds," Class. Quant. Grav. 22 (2005) 1033 [ arXiv:hep-th/0410155

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.

Effective field renormalization group approach for Ising lattice spin systems

NASA Astrophysics Data System (ADS)

Fittipaldi, Ivon P.

1994-03-01

A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

Effect of nose shape on three-dimensional stagnation region streamlines and heating rates

NASA Technical Reports Server (NTRS)

Hassan, Basil; Dejarnette, Fred R.; Zoby, E. V.

1991-01-01

A new method for calculating the three-dimensional inviscid surface streamlines and streamline metrics using Cartesian coordinates and time as the independent variable of integration has been developed. The technique calculates the streamline from a specified point on the body to a point near the stagnation point by using a prescribed pressure distribution in the Euler equations. The differential equations, which are singular at the stagnation point, are of the two point boundary value problem type. Laminar heating rates are calculated using the axisymmetric analog concept for three-dimensional boundary layers and approximate solutions to the axisymmetric boundary layer equations. Results for elliptic conic forebody geometries show that location of the point of maximum heating depends on the type of conic in the plane of symmetry and the angle of attack, and that this location is in general different from the stagnation point. The new method was found to give smooth predictions of heat transfer in the nose region where previous methods gave oscillatory results.

Bacillus subtilis spreads by surfing on waves of surfactant

PubMed Central

Angelini, Thomas E.; Roper, Marcus; Kolter, Roberto; Weitz, David A.; Brenner, Michael P.

2009-01-01

The bacterium Bacillus subtilis produces the molecule surfactin, which is known to enhance the spreading of multicellular colonies on nutrient substrates by lowering the surface tension of the surrounding fluid, and to aid in the formation of aerial structures. Here we present experiments and a mathematical model that demonstrate how the differential accumulation rates induced by the geometry of the bacterial film give rise to surfactant waves. The spreading flux increases with increasing biofilm viscosity. Community associations are known to protect bacterial populations from environmental challenges such as predation, heat, or chemical stresses, and enable digestion of a broader range of nutritive sources. This study provides evidence of enhanced dispersal through cooperative motility, and points to nonintuitive methods for controlling the spread of biofilms. PMID:19826092

Modeling a Single SEP Event from Multiple Vantage Points Using the iPATH Model

NASA Astrophysics Data System (ADS)

Hu, Junxiang; Li, Gang; Fu, Shuai; Zank, Gary; Ao, Xianzhi

2018-02-01

Using the recently extended 2D improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, we model an example gradual solar energetic particle event as observed at multiple locations. Protons and ions that are energized via the diffusive shock acceleration mechanism are followed at a 2D coronal mass ejection-driven shock where the shock geometry varies across the shock front. The subsequent transport of energetic particles, including cross-field diffusion, is modeled by a Monte Carlo code that is based on a stochastic differential equation method. Time intensity profiles and particle spectra at multiple locations and different radial distances, separated in longitudes, are presented. The results shown here are relevant to the upcoming Parker Solar Probe mission.

Projectile motion without calculus

NASA Astrophysics Data System (ADS)

Rizcallah, Joseph A.

2018-07-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary techniques, which can hardly be assumed of the targeted audience. In the literature, several attempts have been undertaken to avoid calculus altogether and keep the exposition entirely within the realm of algebra and/or geometry. In this paper, we propose yet another non-calculus approach which uses the projectile’s travel times to shed new light on these problems and provide instructors with an alternate method to address them with their students.

Quantum Metric of Classic Physics

NASA Astrophysics Data System (ADS)

Machusky, Eugene

2017-09-01

By methods of differential geometry and number theory the following has been established: All fundamental physical constants are the medians of quasi-harmonic functions of relative space and relative time. Basic quantum units are, in fact, the gradients of normal distribution of standing waves between the points of pulsating spherical spiral, which are determined only by functional bonds of transcendental numbers PI and E. Analytically obtained values of rotational speed, translational velocity, vibrational speed, background temperature and molar mass give the possibility to evaluate all basic quantum units with practically unlimited accuracy. Metric of quantum physics really is two-dimensional image of motion of waves in three-dimensional space. Standard physical model is correct, but SI metric system is insufficiently exact at submillimeter distances.

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.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Spectrally resolved interferometric observations of α Cephei and physical modeling of fast rotating stars

NASA Astrophysics Data System (ADS)

Delaa, O.; Zorec, J.; Domiciano de Souza, A.; Mourard, D.; Perraut, K.; Stee, Ph.; Frémat, Y.; Monnier, J.; Kraus, S.; Che, X.; Bério, Ph.; Bonneau, D.; Clausse, J. M.; Challouf, M.; Ligi, R.; Meilland, A.; Nardetto, N.; Spang, A.; McAlister, H.; ten Brummelaar, T.; Sturmann, J.; Sturmann, L.; Turner, N.; Farrington, C.; Goldfinger, P. J.

2013-07-01

Context. When a given observational quantity depends on several stellar physical parameters, it is generally very difficult to obtain observational constraints for each of them individually. Therefore, we studied under which conditions constraints for some individual parameters can be achieved for fast rotators, knowing that their geometry is modified by the rapid rotation which causes a non-uniform surface brightness distribution. Aims: We aim to study the sensitivity of interferometric observables on the position angle of the rotation axis (PA) of a rapidly rotating star, and whether other physical parameters can influence the determination of PA, and also the influence of the surface differential rotation on the determination of the β exponent in the gravity darkening law that enters the interpretation of interferometric observations, using α Cep as a test star. Methods: We used differential phases obtained from observations carried out in the Hα absorption line of α Cep with the VEGA/CHARA interferometer at high spectral resolution, R = 30 000 to study the kinematics in the atmosphere of the star. Results: We studied the influence of the gravity darkening effect (GDE) on the determination of the PA of the rotation axis of α Cep and determined its value, PA = -157-10°+17°. We conclude that the GDE has a weak influence on the dispersed phases. We showed that the surface differential rotation can have a rather strong influence on the determination of the gravity darkening exponent. A new method of determining the inclination angle of the stellar rotational axis is suggested. We conclude that differential phases obtained with spectro-interferometry carried out on the Hα line can in principle lead to an estimate of the stellar inclination angle i. However, to determine both i and the differential rotation parameter α, lines free from the Stark effect and that have collision-dominated source functions are to be preferred.

Transfer matrix approach to electron transport in monolayer MoS2/MoO x heterostructures

NASA Astrophysics Data System (ADS)

Li, Gen

2018-05-01

Oxygen plasma treatment can introduce oxidation into monolayer MoS2 to transfer MoS2 into MoO x , causing the formation of MoS2/MoO x heterostructures. We find the MoS2/MoO x heterostructures have the similar geometry compared with GaAs/Ga1‑x Al x As semiconductor superlattice. Thus, We employ the established transfer matrix method to analyse the electron transport in the MoS2/MoO x heterostructures with double-well and step-well geometries. We also considere the coupling between transverse and longitudinal kinetic energy because the electron effective mass changes spatially in the MoS2/MoO x heterostructures. We find the resonant peaks show red shift with the increasing of transverse momentum, which is similar to the previous work studying the transverse-momentum-dependent transmission in GaAs/Ga1‑x Al x As double-barrier structure. We find electric field can enhance the magnitude of peaks and intensify the coupling between longitudinal and transverse momentums. Moreover, higher bias is applied to optimize resonant tunnelling condition to show negative differential effect can be observed in the MoS2/MoO x system.

Integrand Reduction Reloaded: Algebraic Geometry and Finite Fields

NASA Astrophysics Data System (ADS)

Sameshima, Ray D.; Ferroglia, Andrea; Ossola, Giovanni

2017-01-01

The evaluation of scattering amplitudes in quantum field theory allows us to compare the phenomenological prediction of particle theory with the measurement at collider experiments. The study of scattering amplitudes, in terms of their symmetries and analytic properties, provides a theoretical framework to develop techniques and efficient algorithms for the evaluation of physical cross sections and differential distributions. Tree-level calculations have been known for a long time. Loop amplitudes, which are needed to reduce the theoretical uncertainty, are more challenging since they involve a large number of Feynman diagrams, expressed as integrals of rational functions. At one-loop, the problem has been solved thanks to the combined effect of integrand reduction, such as the OPP method, and unitarity. However, plenty of work is still needed at higher orders, starting with the two-loop case. Recently, integrand reduction has been revisited using algebraic geometry. In this presentation, we review the salient features of integrand reduction for dimensionally regulated Feynman integrals, and describe an interesting technique for their reduction based on multivariate polynomial division. We also show a novel approach to improve its efficiency by introducing finite fields. Supported in part by the National Science Foundation under Grant PHY-1417354.

Study of two-phase flow in helical and spiral coils

NASA Technical Reports Server (NTRS)

Keshock, Edward G.; Yan, AN; Omrani, Adel

1990-01-01

The principal purposes of the present study were to: (1) observe and develop a fundamental understanding of the flow regimes and their transitions occurring in helical and spiral coils; and (2) obtain pressure drop measurements of such flows, and, if possible, develop a method for predicting pressure drop in these flow geometries. Elaborating upon the above, the general intent is to develop criteria (preferably generalized) for establishing the nature of the flow dynamics (e.g. flow patterns) and the magnitude of the pressure drop in such configurations over a range of flow rates and fluid properties. Additionally, the visualization and identification of flow patterns were a fundamental objective of the study. From a practical standpoint, the conditions under which an annular flow pattern exists is of particular practical importance. In the possible practical applications which would implement these geometries, the working fluids are likely to be refrigerant fluids. In the present study the working fluids were an air-water mixture, and refrigerant 113 (R-113). In order to obtain records of flow patterns and their transitions, video photography was employed extensively. Pressure drop measurements were made using pressure differential transducers connected across pressure taps in lines immediately preceding and following the various test sections.

A Comparative Study on the Effectiveness of the Computer Assisted Method and the Interactionist Approach to Teaching Geometry Shapes to Young Children

ERIC Educational Resources Information Center

Zaranis, Nicholas; Synodi, Evanthia

2017-01-01

The purpose of this study is to compare and evaluate the effectiveness of computer assisted teaching of geometry shapes and an interactionist approach to teaching geometry in kindergarten versus other more traditional teaching methods. Our research compares the improvement of the children's geometrical competence using two teaching approaches. The…

Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry

ERIC Educational Resources Information Center

Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo

2014-01-01

The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…

Geometry of Thin Nematic Elastomer Sheets

NASA Astrophysics Data System (ADS)

Aharoni, Hillel; Sharon, Eran; Kupferman, Raz

A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods.

Subsonic panel method for designing wing surfaces from pressure distribution

NASA Technical Reports Server (NTRS)

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

1983-01-01

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

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.

A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

NASA Astrophysics Data System (ADS)

Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John

2016-07-01

In this paper, we present a method for performing uniformly high-order direct numerical simulations of high-speed flows over arbitrary geometries. The method was developed with the goal of simulating and studying the effects of complex isolated roughness elements on the stability of hypersonic boundary layers. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-stencil method. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries and a third-order Runge-Kutta method is used for time advancement. A multi-zone refinement method was also utilized to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme in space and third order in time. Results confirming the method's high order of convergence are shown. Two-dimensional and three-dimensional test cases are presented and show good agreement with previous results. A simulation of Mach 3 flow over the logo of the Ubuntu Linux distribution is shown to demonstrate the method's capabilities for handling complex geometries. Results for Mach 6 wall-bounded flow over a three-dimensional cylindrical roughness element are also presented. The results demonstrate that the method is a promising tool for the study of hypersonic roughness-induced transition.

On the transformations of the dynamical equations

NASA Astrophysics Data System (ADS)

Levi-Civita, T.

2009-08-01

In this issue we bring to the reader’s attention a translation of Levi-Civita’s work “Sulle trasformazioni delle equazioni dinamiche”. This paper, written by Levi-Civita at the onset of his career, is remarkable in many respects. Both the main result and the method developed in the paper brought the author in line with the greatest mathematicians of his day and seriously influenced the further progress of geometry and the theory of integrable systems. Speaking modern language the main result of his paper is the deduction of the general geodesic equivalence equation in invariant form and local classification of geodesically equivalent Riemannian metrics in the case of arbitrary dimension, i.e., metrics having the same geodesics considered as unparameterized curves (this classification problem was formulated by Beltrami in 1865). Levi-Civita’s work produced a great impact on further development of the theory of geodesically equivalent metrics and geodesic mappings, and still remains one of the most important tools in this area of differential geometry. In this paper the author uses a new method based on the concept of Riemannian connection, which later has been also referred to as the Levi-Civita connection. This paper is truly a pioneering work in the sense that the real power of covariant differentiation techniques in solving a concrete and highly nontrivial problem from the theory of dynamical systems was demonstrated. The author skillfully operates and weaves together many of the most advanced (for that times) algebraic, geometric and analytic methods. Moreover, an attentive reader can also notice several forerunning ideas of the method of moving frames, which was developed a few decades later by E. Cartan. We hope that the reader will appreciate the style of exposition as well. This work, focused on the essence of the problem and free of manipulation with abstract mathematical terms, is a good example of a classical text of the late 19th century. Owing to this, the paper is easy to read and understand in spite of some different notation and terminology. The Editorial Board is very grateful to Professor Sergio Benenti for the translation of the original Italian text and valuable comments (see marginal notes at the end of the text, p. 612).

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

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.

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.

Single-cell mechanics--An experimental-computational method for quantifying the membrane-cytoskeleton elasticity of cells.

PubMed

Tartibi, M; Liu, Y X; Liu, G-Y; Komvopoulos, K

2015-11-01

The membrane-cytoskeleton system plays a major role in cell adhesion, growth, migration, and differentiation. F-actin filaments, cross-linkers, binding proteins that bundle F-actin filaments to form the actin cytoskeleton, and integrins that connect the actin cytoskeleton network to the cell plasma membrane and extracellular matrix are major cytoskeleton constituents. Thus, the cell cytoskeleton is a complex composite that can assume different shapes. Atomic force microscopy (AFM)-based techniques have been used to measure cytoskeleton material properties without much attention to cell shape. A recently developed surface chemical patterning method for long-term single-cell culture was used to seed individual cells on circular patterns. A continuum-based cell model, which uses as input the force-displacement response obtained with a modified AFM setup and relates the membrane-cytoskeleton elastic behavior to the cell geometry, while treating all other subcellular components suspended in the cytoplasmic liquid (gel) as an incompressible fluid, is presented and validated by experimental results. The developed analytical-experimental methodology establishes a framework for quantifying the membrane-cytoskeleton elasticity of live cells. This capability may have immense implications in cell biology, particularly in studies seeking to establish correlations between membrane-cytoskeleton elasticity and cell disease, mortality, differentiation, and migration, and provide insight into cell infiltration through nonwoven fibrous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscoelasticity, examine the role of other subcellular components (e.g., nucleus envelope) in cell elasticity, and elucidate the effects of mechanical stimuli on cell differentiation and motility. This is the first study to decouple the membrane-cytoskeleton elasticity from cell stiffness and introduce an effective approach for measuring the elastic modulus. The novelty of this study is the development of new technology for quantifying the elastic stiffness of the membrane-cytoskeleton system of cells. This capability could have immense implications in cell biology, particularly in establishing correlations between various cell diseases, mortality, and differentiation with membrane-cytoskeleton elasticity, examining through-tissue cell migration, and understanding cell infiltration in porous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscous behavior, identify the contribution of other subcellular components (e.g., nucleus envelope) to load sharing, and elucidate mechanotransduction effects due to repetitive compressive loading and unloading on cell differentiation and motility. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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!

Method for Determining Optimum Injector Inlet Geometry

NASA Technical Reports Server (NTRS)

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

2015-01-01

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 method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.

On the inverse problem of blade design for centrifugal pumps and fans

NASA Astrophysics Data System (ADS)

Kruyt, N. P.; Westra, R. W.

2014-06-01

The inverse problem of blade design for centrifugal pumps and fans has been studied. The solution to this problem provides the geometry of rotor blades that realize specified performance characteristics, together with the corresponding flow field. Here a three-dimensional solution method is described in which the so-called meridional geometry is fixed and the distribution of the azimuthal angle at the three-dimensional blade surface is determined for blades of infinitesimal thickness. The developed formulation is based on potential-flow theory. Besides the blade impermeability condition at the pressure and suction side of the blades, an additional boundary condition at the blade surface is required in order to fix the unknown blade geometry. For this purpose the mean-swirl distribution is employed. The iterative numerical method is based on a three-dimensional finite element method approach in which the flow equations are solved on the domain determined by the latest estimate of the blade geometry, with the mean-swirl distribution boundary condition at the blade surface being enforced. The blade impermeability boundary condition is then used to find an improved estimate of the blade geometry. The robustness of the method is increased by specific techniques, such as spanwise-coupled solution of the discretized impermeability condition and the use of under-relaxation in adjusting the estimates of the blade geometry. Various examples are shown that demonstrate the effectiveness and robustness of the method in finding a solution for the blade geometry of different types of centrifugal pumps and fans. The influence of the employed mean-swirl distribution on the performance characteristics is also investigated.

Probing the Inner Core with P'P'

NASA Astrophysics Data System (ADS)

Day, E. A.; Irving, J. C. E.

2015-12-01

Geophysical observations of the inner core today improve our understanding not just of the processes occurring in the core at the present, but also those that have occurred in the past. As the inner core freezes it may record clues as to the state of the Earth at the time of growth, although the texture of the inner core may also be modified through post-solidification mechanisms. The seismic structure of the inner core is not simple; the dominant pattern is one of anisotropic and isotropic differences between the Eastern and Western 'hemispheres' of the inner core. Additionally, there is evidence for an innermost inner core, layering of the uppermost inner core, and possibly super-rotation of the inner core relative to the mantle. Most body wave studies of inner core structure use PKP-PKIKP differential travel times to constrain velocity variations within the inner core. However, body wave studies are inherently limited by the geometry of fixed sources and stations, and thus there are some areas of the inner core that are relatively under-sampled, even in today's data-rich world. Here, we examine the differential travel times of the different branches of P'P' (PKIKPPKIKP and PKPPKP), comparing the arrival time of inner core sensitive branch, P'P'df, with the arrival times of branches that only reach the outer core. By using P'P' we are able to exploit alternative ray geometries and sample different regions of the inner core to those areas accessible to studies which utilize PKIKP. We use both linear and non-linear stacking methods to make observations of small amplitude P'P' phases. These measurements match the broad scale hemispherical pattern of anisotropy in the inner core.

Efficient road geometry identification from digital vector data

NASA Astrophysics Data System (ADS)

Andrášik, Richard; Bíl, Michal

2016-07-01

A new method for the automatic identification of road geometry from digital vector data is presented. The method is capable of efficiently identifying circular curves with their radii and tangents (straight sections). The average error of identification ranged from 0.01 to 1.30 % for precisely drawn data and 4.81 % in the case of actual road data with noise in the location of vertices. The results demonstrate that the proposed method is faster and more precise than commonly used techniques. This approach can be used by road administrators to complete their databases with information concerning the geometry of roads. It can also be utilized by transport engineers or traffic safety analysts to investigate the possible dependence of traffic accidents on road geometries. The method presented is applicable as well to railroads and rivers or other line features.

An Ejector Air Intake Design Method for a Novel Rocket-Based Combined-Cycle Rocket Nozzle

NASA Astrophysics Data System (ADS)

Waung, Timothy S.

Rocket-based combined-cycle (RBCC) vehicles have the potential to reduce launch costs through the use of several different air breathing engine cycles, which reduce fuel consumption. The rocket-ejector cycle, in which air is entrained into an ejector section by the rocket exhaust, is used at flight speeds below Mach 2. This thesis develops a design method for an air intake geometry around a novel RBCC rocket nozzle design for the rocket-ejector engine cycle. This design method consists of a geometry creation step in which a three-dimensional intake geometry is generated, and a simple flow analysis step which predicts the air intake mass flow rate. The air intake geometry is created using the rocket nozzle geometry and eight primary input parameters. The input parameters are selected to give the user significant control over the air intake shape. The flow analysis step uses an inviscid panel method and an integral boundary layer method to estimate the air mass flow rate through the intake geometry. Intake mass flow rate is used as a performance metric since it directly affects the amount of thrust a rocket-ejector can produce. The design method results for the air intake operating at several different points along the subsonic portion of the Ariane 4 flight profile are found to under predict mass flow rate by up to 8.6% when compared to three-dimensional computational fluid dynamics simulations for the same air intake.

Vehicle response-based track geometry assessment using multi-body simulation

NASA Astrophysics Data System (ADS)

Kraft, Sönke; Causse, Julien; Coudert, Frédéric

2018-02-01

The assessment of the geometry of railway tracks is an indispensable requirement for safe rail traffic. Defects which represent a risk for the safety of the train have to be identified and the necessary measures taken. According to current standards, amplitude thresholds are applied to the track geometry parameters measured by recording cars. This geometry-based assessment has proved its value but suffers from the low correlation between the geometry parameters and the vehicle reactions. Experience shows that some defects leading to critical vehicle reactions are underestimated by this approach. The use of vehicle responses in the track geometry assessment process allows identifying critical defects and improving the maintenance operations. This work presents a vehicle response-based assessment method using multi-body simulation. The choice of the relevant operation conditions and the estimation of the simulation uncertainty are outlined. The defects are identified from exceedances of track geometry and vehicle response parameters. They are then classified using clustering methods and the correlation with vehicle response is analysed. The use of vehicle responses allows the detection of critical defects which are not identified from geometry parameters.

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.

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.

Propellant-Flow-Actuated Rocket Engine Igniter

NASA Technical Reports Server (NTRS)

Wollen, Mark

2013-01-01

A rocket engine igniter has been created that uses a pneumatically driven hammer that, by specialized geometry, is induced into an oscillatory state that can be used to either repeatedly impact a piezoelectric crystal with sufficient force to generate a spark capable of initiating combustion, or can be used with any other system capable of generating a spark from direct oscillatory motion. This innovation uses the energy of flowing gaseous propellant, which by means of pressure differentials and kinetic motion, causes a hammer object to oscillate. The concept works by mass flows being induced through orifices on both sides of a cylindrical tube with one or more vent paths. As the mass flow enters the chamber, the pressure differential is caused because the hammer object is supplied with flow on one side and the other side is opened with access to the vent path. The object then crosses the vent opening and begins to slow because the pressure differential across the ball reverses due to the geometry in the tube. Eventually, the object stops because of the increasing pressure differential on the object until all of the kinetic energy has been transferred to the gas via compression. This is the point where the object reverses direction because of the pressure differential. This behavior excites a piezoelectric crystal via direct impact from the hammer object. The hammer strikes a piezoelectric crystal, then reverses direction, and the resultant high voltage created from the crystal is transferred via an electrode to a spark gap in the ignition zone, thereby providing a spark to ignite the engine. Magnets, or other retention methods, might be employed to favorably position the hammer object prior to start, but are not necessary to maintain the oscillatory behavior. Various manifestations of the igniter have been developed and tested to improve device efficiency, and some improved designs are capable of operation at gas flow rates of a fraction of a gram per second (0.001 lb/s) and pressure drops on the order of 30 to 50 kilopascal (a few psi). An analytical model has been created and tested in conjunction with a precisely calibrated reference model. The analytical model accurately captures the overall behavior of this innovation. The model is a simple "volume-orifice" concept, with each chamber considered a single temperature and pressure "node" connected to adjacent nodes, or to vent paths through flow control orifices. Mass and energy balances are applied to each node, with gas flow predicted using simple compressible flow equations.

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…

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)

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

NASA Astrophysics Data System (ADS)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first meeting with the name `Symmetries and Integrability of Discrete Equations (SIDE)' was held in Estérel, Québec, Canada. This was organized by D Levi, P Winternitz and L Vinet. After the success of the first meeting the scientific community decided to hold bi-annual SIDE meetings. They were held in 1996 at the University of Kent (UK), 1998 in Sabaudia (Italy), 2000 at the University of Tokyo (Japan), 2002 in Giens (France), 2004 in Helsinki (Finland) and in 2006 at the University of Melbourne (Australia). In 2008 the SIDE 8 meeting was again organized near Montreal, in Ste-Adèle, Québec, Canada. The SIDE 8 International Advisory Committee (also the SIDE steering committee) consisted of Frank Nijhoff, Alexander Bobenko, Basil Grammaticos, Jarmo Hietarinta, Nalini Joshi, Decio Levi, Vassilis Papageorgiou, Junkichi Satsuma, Yuri Suris, Claude Vialet and Pavel Winternitz. The local organizing committee consisted of Pavel Winternitz, John Harnad, Véronique Hussin, Decio Levi, Peter Olver and Luc Vinet. Financial support came from the Centre de Recherches Mathématiques in Montreal and the National Science Foundation (through the University of Minnesota). Proceedings of the first three SIDE meetings were published in the LMS Lecture Note series. Since 2000 the emphasis has been on publishing selected refereed articles in response to a general call for papers issued after the conference. This allows for a wider author base, since the call for papers is not restricted to conference participants. The SIDE topics thus are represented in special issues of Journal of Physics A: Mathematical and General 34 (48) and Journal of Physics A: Mathematical and Theoretical, 40 (42) (SIDE 4 and SIDE 7, respectively), Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2) (SIDE 5 and SIDE 6 respectively). The SIDE 8 meeting was organized around several topics and the contributions to this special issue reflect the diversity presented during the meeting. The papers presented at the SIDE 8 meeting were organized into the following special sessions: geometry of discrete and continuous Painlevé equations; continuous symmetries of discrete equations—theory and computational applications; algebraic aspects of discrete equations; singularity confinement, algebraic entropy and Nevanlinna theory; discrete differential geometry; discrete integrable systems and isomonodromy transformations; special functions as solutions of difference and q-difference equations. This special issue of the journal is organized along similar lines. The first three articles are topical review articles appearing in alphabetical order (by first author). The article by Doliwa and Nieszporski describes the Darboux transformations in a discrete setting, namely for the discrete second order linear problem. The article by Grammaticos, Halburd, Ramani and Viallet concentrates on the integrability of the discrete systems, in particular they describe integrability tests for difference equations such as singularity confinement, algebraic entropy (growth and complexity), and analytic and arithmetic approaches. The topical review by Konopelchenko explores the relationship between the discrete integrable systems and deformations of associative algebras. All other articles are presented in alphabetical order (by first author). The contributions were solicited from all participants as well as from the general scientific community. The contributions published in this special issue can be loosely grouped into several overlapping topics, namely: •Geometry of discrete and continuous Painlevé equations (articles by Spicer and Nijhoff and by Lobb and Nijhoff). •Continuous symmetries of discrete equations—theory and applications (articles by Dorodnitsyn and Kozlov; Levi, Petrera and Scimiterna; Scimiterna; Ste-Marie and Tremblay; Levi and Yamilov; Rebelo and Winternitz). •Yang--Baxter maps (article by Xenitidis and Papageorgiou). •Algebraic aspects of discrete equations (articles by Doliwa and Nieszporski; Konopelchenko; Tsarev and Wolf). •Singularity confinement, algebraic entropy and Nevanlinna theory (articles by Grammaticos, Halburd, Ramani and Viallet; Grammaticos, Ramani and Tamizhmani). •Discrete integrable systems and isomonodromy transformations (article by Dzhamay). •Special functions as solutions of difference and q-difference equations (articles by Atakishiyeva, Atakishiyev and Koornwinder; Bertola, Gekhtman and Szmigielski; Vinet and Zhedanov). •Other topics (articles by Atkinson; Grünbaum Nagai, Kametaka and Watanabe; Nagiyev, Guliyeva and Jafarov; Sahadevan and Uma Maheswari; Svinin; Tian and Hu; Yao, Liu and Zeng). This issue is the result of the collaboration of many individuals. We would like to thank the authors who contributed and everyone else involved in the preparation of this special issue.

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.

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.

Unfitted Two-Phase Flow Simulations in Pore-Geometries with Accurate

NASA Astrophysics Data System (ADS)

Heimann, Felix; Engwer, Christian; Ippisch, Olaf; Bastian, Peter

2013-04-01

The development of better macro scale models for multi-phase flow in porous media is still impeded by the lack of suitable methods for the simulation of such flow regimes on the pore scale. The highly complicated geometry of natural porous media imposes requirements with regard to stability and computational efficiency which current numerical methods fail to meet. Therefore, current simulation environments are still unable to provide a thorough understanding of porous media in multi-phase regimes and still fail to reproduce well known effects like hysteresis or the more peculiar dynamics of the capillary fringe with satisfying accuracy. Although flow simulations in pore geometries were initially the domain of Lattice-Boltzmann and other particle methods, the development of Galerkin methods for such applications is important as they complement the range of feasible flow and parameter regimes. In the recent past, it has been shown that unfitted Galerkin methods can be applied efficiently to topologically demanding geometries. However, in the context of two-phase flows, the interface of the two immiscible fluids effectively separates the domain in two sub-domains. The exact representation of such setups with multiple independent and time depending geometries exceeds the functionality of common unfitted methods. We present a new approach to pore scale simulations with an unfitted discontinuous Galerkin (UDG) method. Utilizing a recursive sub-triangulation algorithm, we extent the UDG method to setups with multiple independent geometries. This approach allows an accurate representation of the moving contact line and the interface conditions, i.e. the pressure jump across the interface. Example simulations in two and three dimensions illustrate and verify the stability and accuracy of this approach.

Optimizing the Entrainment Geometry of a Dry Powder Inhaler: Methodology and Preliminary Results.

PubMed

Kopsch, Thomas; Murnane, Darragh; Symons, Digby

2016-11-01

For passive dry powder inhalers (DPIs) entrainment and emission of the aerosolized drug dose depends strongly on device geometry and the patient's inhalation manoeuvre. We propose a computational method for optimizing the entrainment part of a DPI. The approach assumes that the pulmonary delivery location of aerosol can be determined by the timing of dose emission into the tidal airstream. An optimization algorithm was used to iteratively perform computational fluid dynamic (CFD) simulations of the drug emission of a DPI. The algorithm seeks to improve performance by changing the device geometry. Objectives were to achieve drug emission that was: A) independent of inhalation manoeuvre; B) similar to a target profile. The simulations used complete inhalation flow-rate profiles generated dependent on the device resistance. The CFD solver was OpenFOAM with drug/air flow simulated by the Eulerian-Eulerian method. To demonstrate the method, a 2D geometry was optimized for inhalation independence (comparing two breath profiles) and an early-bolus delivery. Entrainment was both shear-driven and gas-assisted. Optimization for a delay in the bolus delivery was not possible with the chosen geometry. Computational optimization of a DPI geometry for most similar drug delivery has been accomplished for an example entrainment geometry.

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.

Teaching Geometry: An Experiential and Artistic Approach.

ERIC Educational Resources Information Center

Ogletree, Earl J.

The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

NASA Astrophysics Data System (ADS)

Liu, X.; Banerjee, J. R.

2017-03-01

A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

Classical versus Computer Algebra Methods in Elementary Geometry

ERIC Educational Resources Information Center

Pech, Pavel

2005-01-01

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

Aspects géométriques et intégrables des modèles de matrices aléatoires

NASA Astrophysics Data System (ADS)

Marchal, Olivier

2010-12-01

This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to "quantum algebraic geometry" and to the generalization of symplectic invariants to "quantum curves". Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold.

WE-EF-207-09: Single-Scan Dual-Energy CT Using Primary Modulation

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

Petrongolo, M; Zhu, L

Purpose: Compared with conventional CT, dual energy CT (DECT) provides better material differentiation but requires projection data with two different effective x-ray spectra. Current DECT scanners use either a two-scan setting or costly imaging components, which are not feasible or available on open-gantry cone-beam CT systems. We propose a hardware-based method which utilizes primary modulation to enable single-scan DECT on a conventional CT scanner. The CT imaging geometry of primary modulation is identical to that used in our previous method for scatter removal, making it possible for future combination with effective scatter correction on the same CT scanner. Methods: Wemore » insert an attenuation sheet with a spatially-varying pattern - primary modulator-between the x-ray source and the imaged object. During the CT scan, the modulator selectively hardens the x-ray beam at specific detector locations. Thus, the proposed method simultaneously acquires high and low energy data. High and low energy CT images are then reconstructed from projections with missing data via an iterative CT reconstruction algorithm with gradient weighting. Proof-of-concept studies are performed using a copper modulator on a cone-beam CT system. Results: Our preliminary results on the Catphan(c) 600 phantom indicate that the proposed method for single-scan DECT is able to successfully generate high-quality high and low energy CT images and distinguish different materials through basis material decomposition. By applying correction algorithms and using all of the acquired projection data, we can reconstruct a single CT image of comparable image quality to conventional CT images, i.e., without primary modulation. Conclusion: This work shows great promise in using a primary modulator to perform high-quality single-scan DECT imaging. Future studies will test method performance on anthropomorphic phantoms and perform quantitative analyses on image qualities and DECT decomposition accuracy. We will use simulations to optimize the modulator material and geometry parameters.« less

Three methods to retrieve slant total electron content measurements from ground-based GPS receivers and performance assessment

NASA Astrophysics Data System (ADS)

Zhang, Baocheng

2016-07-01

The high sampling rate along with the global coverage of ground-based receivers makes Global Positioning System (GPS) data particularly ideal for sensing the Earth's ionosphere. Retrieval of slant total electron content measurements (TECMs) constitutes a key first step toward extracting various ionospheric parameters from GPS data. Within the ionospheric community, the interpretation of TECM is widely recognized as the slant total electron content along the satellite receiver line of sight, biased by satellite and receiver differential code biases (DCBs). The Carrier-to-Code Leveling (CCL) has long been used as a geometry-free method for retrieving TECM, mainly because of its simplicity and effectiveness. In fact, however, the CCL has proven inaccurate as it may give rise to TECM very susceptible to so-called leveling errors. With the goal of attaining more accurate TECM retrieval, we report in this contribution two other methods than the CCL, namely, the Precise Point Positioning (PPP) and the Array-aided PPP (A-PPP). The PPP further exploits the International GPS Service (IGS) orbit and clock products and turns out to be a geometry-based method. The A-PPP is designed to retrieve TECM from an array of colocated receivers, taking advantage of the broadcast orbit and clock products. Moreover, A-PPP also takes into account the fact that the ionospheric effects measured from one satellite to all colocated receivers ought to be the same, thus leading to the estimability of interreceiver DCB. We perform a comparative study of the formal precision and the empirical accuracy of the TECM that are retrieved, respectively, by three methods from the same set of GPS data. Results of such a study can be used to assess the actual performance of the three methods. In addition, we check the temporal stability in A-PPP-derived interreceiver DCB estimates over time periods ranging from 1 to 3 days.

Lower extremity EMG-driven modeling of walking with automated adjustment of musculoskeletal geometry

PubMed Central

Meyer, Andrew J.; Patten, Carolynn

2017-01-01

Neuromusculoskeletal disorders affecting walking ability are often difficult to manage, in part due to limited understanding of how a patient’s lower extremity muscle excitations contribute to the patient’s lower extremity joint moments. To assist in the study of these disorders, researchers have developed electromyography (EMG) driven neuromusculoskeletal models utilizing scaled generic musculoskeletal geometry. While these models can predict individual muscle contributions to lower extremity joint moments during walking, the accuracy of the predictions can be hindered by errors in the scaled geometry. This study presents a novel EMG-driven modeling method that automatically adjusts surrogate representations of the patient’s musculoskeletal geometry to improve prediction of lower extremity joint moments during walking. In addition to commonly adjusted neuromusculoskeletal model parameters, the proposed method adjusts model parameters defining muscle-tendon lengths, velocities, and moment arms. We evaluated our EMG-driven modeling method using data collected from a high-functioning hemiparetic subject walking on an instrumented treadmill at speeds ranging from 0.4 to 0.8 m/s. EMG-driven model parameter values were calibrated to match inverse dynamic moments for five degrees of freedom in each leg while keeping musculoskeletal geometry close to that of an initial scaled musculoskeletal model. We found that our EMG-driven modeling method incorporating automated adjustment of musculoskeletal geometry predicted net joint moments during walking more accurately than did the same method without geometric adjustments. Geometric adjustments improved moment prediction errors by 25% on average and up to 52%, with the largest improvements occurring at the hip. Predicted adjustments to musculoskeletal geometry were comparable to errors reported in the literature between scaled generic geometric models and measurements made from imaging data. Our results demonstrate that with appropriate experimental data, joint moment predictions for walking generated by an EMG-driven model can be improved significantly when automated adjustment of musculoskeletal geometry is included in the model calibration process. PMID:28700708

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

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 quantum Hall states: Gravitational anomaly and transport coefficients

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

Can, Tankut, E-mail: tcan@scgp.stonybrook.edu; Laskin, Michael; Wiegmann, Paul B.

2015-11-15

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iteratingmore » a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.« less

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.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Quantitative three-dimensional photoacoustic tomography of the finger joints: an in vivo study

NASA Astrophysics Data System (ADS)

Sun, Yao; Sobel, Eric; Jiang, Huabei

2009-11-01

We present for the first time in vivo full three-dimensional (3-D) photoacoustic tomography (PAT) of the distal interphalangeal joint in a human subject. Both absorbed energy density and absorption coefficient images of the joint are quantitatively obtained using our finite-element-based photoacoustic image reconstruction algorithm coupled with the photon diffusion equation. The results show that major anatomical features in the joint along with the side arteries can be imaged with a 1-MHz transducer in a spherical scanning geometry. In addition, the cartilages associated with the joint can be quantitatively differentiated from the phalanx. This in vivo study suggests that the 3-D PAT method described has the potential to be used for early diagnosis of joint diseases such as osteoarthritis and rheumatoid arthritis.

The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers' Transformational Geometry Success

ERIC Educational Resources Information Center

Yilmaz, Gül Kaleli

2015-01-01

This study aims to investigate the effects of using Dynamic Geometry Software (DGS) Cabri II Plus and physical manipulatives on the transformational geometry achievement of candidate teachers. In this study, the semi-experimental method was used, consisting of two experimental and one control groups. The samples of this study were 117 students. A…

Using 3D Computer Graphics Multimedia to Motivate Preservice Teachers' Learning of Geometry and Pedagogy

ERIC Educational Resources Information Center

Goodson-Espy, Tracy; Lynch-Davis, Kathleen; Schram, Pamela; Quickenton, Art

2010-01-01

This paper describes the genesis and purpose of our geometry methods course, focusing on a geometry-teaching technology we created using NVIDIA[R] Chameleon demonstration. This article presents examples from a sequence of lessons centered about a 3D computer graphics demonstration of the chameleon and its geometry. In addition, we present data…

BOOK REVIEW: Partial Differential Equations in General Relativity

NASA Astrophysics Data System (ADS)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed proofs of the main results in a self-contained book of reasonable length. Instead, the author concentrates on providing key definitions together with their motivations and explaining the main results, tools and difficulties for each topic. There is a section at the end of each chapter which points the reader to appropriate literature for further details. In this way, Rendall manages to describe the central issues concerning many subjects. Each of the twelve chapters (except for one on functional analysis) contains an important application to general relativity. For example, the chapter on ODEs discusses Bianchi spacetimes and the Einstein constraint equations are discussed in the chapter on elliptic equations. In the chapter on hyperbolic equations, the Einstein dust system is considered in the context of Leray hyperbolicity and Gowdy spacetimes are analysed in the section on Fuchsian methods. The book concludes with four chapters purely on applications to general relativity, namely The Cauchy problem for the Einstein equations, Global results, The Einstein-Vlasov system and The Einstein-scalar field systems. On reading this book, someone with a basic understanding of relativity could rapidly develop a picture, painted in broad brush strokes, of the main problems and tools in the area. It would be particularly useful for someone, such as a graduate student, just entering the field, or for someone who wants a general idea of the main issues. For those who want to go further, a lot more reading will be necessary but the author has sign-posted appropriate entry points to the literature throughout the book. Ultimately, this is a very technical subject and this book can only provide an overview. I believe that Alan Rendall's book is a valuable contribution to the field of mathematical relativity.

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.

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

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.

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.

Optimization of magnet end-winding geometry

NASA Astrophysics Data System (ADS)

Reusch, Michael F.; Weissenburger, Donald W.; Nearing, James C.

1994-03-01

A simple, almost entirely analytic, method for the optimization of stress-reduced magnet-end winding paths for ribbon-like superconducting cable is presented. This technique is based on characterization of these paths as developable surfaces, i.e., surfaces whose intrinsic geometry is flat. The method is applicable to winding mandrels of arbitrary geometry. Computational searches for optimal winding paths are easily implemented via the technique. Its application to the end configuration of cylindrical Superconducting Super Collider (SSC)-type magnets is discussed. The method may be useful for other engineering problems involving the placement of thin sheets of material.

Geometry control of long-span continuous girder concrete bridge during construction through finite element model updating

NASA Astrophysics Data System (ADS)

Wu, Jie; Yan, Quan-sheng; Li, Jian; Hu, Min-yi

2016-04-01

In bridge construction, geometry control is critical to ensure that the final constructed bridge has the consistent shape as design. A common method is by predicting the deflections of the bridge during each construction phase through the associated finite element models. Therefore, the cambers of the bridge during different construction phases can be determined beforehand. These finite element models are mostly based on the design drawings and nominal material properties. However, the accuracy of these bridge models can be large due to significant uncertainties of the actual properties of the materials used in construction. Therefore, the predicted cambers may not be accurate to ensure agreement of bridge geometry with design, especially for long-span bridges. In this paper, an improved geometry control method is described, which incorporates finite element (FE) model updating during the construction process based on measured bridge deflections. A method based on the Kriging model and Latin hypercube sampling is proposed to perform the FE model updating due to its simplicity and efficiency. The proposed method has been applied to a long-span continuous girder concrete bridge during its construction. Results show that the method is effective in reducing construction error and ensuring the accuracy of the geometry of the final constructed bridge.

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.

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.

Realistic sampling of amino acid geometries for a multipolar polarizable force field

PubMed Central

Hughes, Timothy J.; Cardamone, Salvatore

2015-01-01

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. PMID:26235784

Synergism of the method of characteristics and CAD technology for neutron transport calculation

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

Chen, Z.; Wang, D.; He, T.

2013-07-01

The method of characteristics (MOC) is a very popular methodology in neutron transport calculation and numerical simulation in recent decades for its unique advantages. One of the key problems determining whether the MOC can be applied in complicated and highly heterogeneous geometry is how to combine an effective geometry processing method with MOC. Most of the existing MOC codes describe the geometry by lines and arcs with extensive input data, such as circles, ellipses, regular polygons and combination of them. Thus they have difficulty in geometry modeling, background meshing and ray tracing for complicated geometry domains. In this study, amore » new idea making use of a CAD solid modeler MCAM which is a CAD/Image-based Automatic Modeling Program for Neutronics and Radiation Transport developed by FDS Team in China was introduced for geometry modeling and ray tracing of particle transport to remove these geometrical limitations mentioned above. The diamond-difference scheme was applied to MOC to reduce the spatial discretization error of the flat flux approximation in theory. Based on MCAM and MOC, a new MOC code was developed and integrated into SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical testing results demonstrated the feasibility and effectiveness of the new idea for geometry treatment in SuperMC. (authors)« less

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.

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

Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology

PubMed Central

Ukwatta, Eranga; Arevalo, Hermenegild; Rajchl, Martin; White, James; Pashakhanloo, Farhad; Prakosa, Adityo; Herzka, Daniel A.; McVeigh, Elliot; Lardo, Albert C.; Trayanova, Natalia A.; Vadakkumpadan, Fijoy

2015-01-01

Purpose: Accurate three-dimensional (3D) reconstruction of myocardial infarct geometry is crucial to patient-specific modeling of the heart aimed at providing therapeutic guidance in ischemic cardiomyopathy. However, myocardial infarct imaging is clinically performed using two-dimensional (2D) late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) techniques, and a method to build accurate 3D infarct reconstructions from the 2D LGE-CMR images has been lacking. The purpose of this study was to address this need. Methods: The authors developed a novel methodology to reconstruct 3D infarct geometry from segmented low-resolution (Lo-res) clinical LGE-CMR images. Their methodology employed the so-called logarithm of odds (LogOdds) function to implicitly represent the shape of the infarct in segmented image slices as LogOdds maps. These 2D maps were then interpolated into a 3D image, and the result transformed via the inverse of LogOdds to a binary image representing the 3D infarct geometry. To assess the efficacy of this method, the authors utilized 39 high-resolution (Hi-res) LGE-CMR images, including 36 in vivo acquisitions of human subjects with prior myocardial infarction and 3 ex vivo scans of canine hearts following coronary ligation to induce infarction. The infarct was manually segmented by trained experts in each slice of the Hi-res images, and the segmented data were downsampled to typical clinical resolution. The proposed method was then used to reconstruct 3D infarct geometry from the downsampled images, and the resulting reconstructions were compared with the manually segmented data. The method was extensively evaluated using metrics based on geometry as well as results of electrophysiological simulations of cardiac sinus rhythm and ventricular tachycardia in individual hearts. Several alternative reconstruction techniques were also implemented and compared with the proposed method. Results: The accuracy of the LogOdds method in reconstructing 3D infarct geometry, as measured by the Dice similarity coefficient, was 82.10% ± 6.58%, a significantly higher value than those of the alternative reconstruction methods. Among outcomes of electrophysiological simulations with infarct reconstructions generated by various methods, the simulation results corresponding to the LogOdds method showed the smallest deviation from those corresponding to the manual reconstructions, as measured by metrics based on both activation maps and pseudo-ECGs. Conclusions: The authors have developed a novel method for reconstructing 3D infarct geometry from segmented slices of Lo-res clinical 2D LGE-CMR images. This method outperformed alternative approaches in reproducing expert manual 3D reconstructions and in electrophysiological simulations. PMID:26233186

Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology

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

Ukwatta, Eranga, E-mail: eukwatt1@jhu.edu; Arevalo, Hermenegild; Pashakhanloo, Farhad

Purpose: Accurate three-dimensional (3D) reconstruction of myocardial infarct geometry is crucial to patient-specific modeling of the heart aimed at providing therapeutic guidance in ischemic cardiomyopathy. However, myocardial infarct imaging is clinically performed using two-dimensional (2D) late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) techniques, and a method to build accurate 3D infarct reconstructions from the 2D LGE-CMR images has been lacking. The purpose of this study was to address this need. Methods: The authors developed a novel methodology to reconstruct 3D infarct geometry from segmented low-resolution (Lo-res) clinical LGE-CMR images. Their methodology employed the so-called logarithm of odds (LogOdds) function to implicitlymore » represent the shape of the infarct in segmented image slices as LogOdds maps. These 2D maps were then interpolated into a 3D image, and the result transformed via the inverse of LogOdds to a binary image representing the 3D infarct geometry. To assess the efficacy of this method, the authors utilized 39 high-resolution (Hi-res) LGE-CMR images, including 36 in vivo acquisitions of human subjects with prior myocardial infarction and 3 ex vivo scans of canine hearts following coronary ligation to induce infarction. The infarct was manually segmented by trained experts in each slice of the Hi-res images, and the segmented data were downsampled to typical clinical resolution. The proposed method was then used to reconstruct 3D infarct geometry from the downsampled images, and the resulting reconstructions were compared with the manually segmented data. The method was extensively evaluated using metrics based on geometry as well as results of electrophysiological simulations of cardiac sinus rhythm and ventricular tachycardia in individual hearts. Several alternative reconstruction techniques were also implemented and compared with the proposed method. Results: The accuracy of the LogOdds method in reconstructing 3D infarct geometry, as measured by the Dice similarity coefficient, was 82.10% ± 6.58%, a significantly higher value than those of the alternative reconstruction methods. Among outcomes of electrophysiological simulations with infarct reconstructions generated by various methods, the simulation results corresponding to the LogOdds method showed the smallest deviation from those corresponding to the manual reconstructions, as measured by metrics based on both activation maps and pseudo-ECGs. Conclusions: The authors have developed a novel method for reconstructing 3D infarct geometry from segmented slices of Lo-res clinical 2D LGE-CMR images. This method outperformed alternative approaches in reproducing expert manual 3D reconstructions and in electrophysiological simulations.« 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.

Investigation of converging and collimated beam instrument geometry on specular gloss measurements

NASA Astrophysics Data System (ADS)

Zwinkels, Joanne C.; Côté, Éric; Morgan, John

2018-02-01

Specular gloss is an important appearance property of a wide variety of manufactured goods. Depending upon the application, e.g. paints, paper, ceramics, etc. different instrument designs and measurement geometries are specified in standard test methods. For a given specular angle, these instrument designs can be broadly classified as converging beam (TAPPI method) and collimated beam (DIN method). In recent comparisons of specular gloss measurements using different glossmeters, very large standard deviations have been reported, well exceeding the manufacturers claims. In this paper, we investigate the effect of instrument beam geometry on gloss measurements. These results indicate that this difference in beam geometry can give the magnitude of gloss differences reported in these comparisons and highlights the importance of educating the user community of best measurement practices and obtaining appropriate traceability for their glossmeters.

Computational Cardiac Anatomy Using MRI

PubMed Central

Beg, Mirza Faisal; Helm, Patrick A.; McVeigh, Elliot; Miller, Michael I.; Winslow, Raimond L.

2005-01-01

Ventricular geometry and fiber orientation may undergo global or local remodeling in cardiac disease. However, there are as yet no mathematical and computational methods for quantifying variation of geometry and fiber orientation or the nature of their remodeling in disease. Toward this goal, a landmark and image intensity-based large deformation diffeomorphic metric mapping (LDDMM) method to transform heart geometry into common coordinates for quantification of shape and form was developed. Two automated landmark placement methods for modeling tissue deformations expected in different cardiac pathologies are presented. The transformations, computed using the combined use of landmarks and image intensities, yields high-registration accuracy of heart anatomies even in the presence of significant variation of cardiac shape and form. Once heart anatomies have been registered, properties of tissue geometry and cardiac fiber orientation in corresponding regions of different hearts may be quantified. PMID:15508155

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

ESTIMATING STREAMFLOW AND ASSOCIATED HYDRAULIC GEOMETRY, THE MID-ATLANTIC REGION, USA

EPA Science Inventory

Methods to estimate streamflow and channel hydraulic geometry were developed for ungaged streams in the Mid-Atlantic Region. Observed mean annual streamflow and associated hydraulic geometry data from 75 gaging stations located in the Appalachian Plateau, the Ridge and Valley, an...

Euclid and Descartes: A Partnership.

ERIC Educational Resources Information Center

Wasdovich, Dorothy Hoy

1991-01-01

Presented is a method of reorganizing a high school geometry course to integrate coordinate geometry together with Euclidean geometry at an earlier stage in the course, thus enabling students to prove subsequent theorems from either perspective. Several examples contrasting different proofs from both perspectives are provided. (MDH)

Gary O's Fence Question.

ERIC Educational Resources Information Center

Daniels, David S.

1993-01-01

Discusses the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

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.

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.

The prediction of the noise of supersonic propellers in time domain - New theoretical results

NASA Technical Reports Server (NTRS)

Farassat, F.

1983-01-01

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Multimodal biometric method that combines veins, prints, and shape of a finger

NASA Astrophysics Data System (ADS)

Kang, Byung Jun; Park, Kang Ryoung; Yoo, Jang-Hee; Kim, Jeong Nyeo

2011-01-01

Multimodal biometrics provides high recognition accuracy and population coverage by using various biometric features. A single finger contains finger veins, fingerprints, and finger geometry features; by using multimodal biometrics, information on these multiple features can be simultaneously obtained in a short time and their fusion can outperform the use of a single feature. This paper proposes a new finger recognition method based on the score-level fusion of finger veins, fingerprints, and finger geometry features. This research is novel in the following four ways. First, the performances of the finger-vein and fingerprint recognition are improved by using a method based on a local derivative pattern. Second, the accuracy of the finger geometry recognition is greatly increased by combining a Fourier descriptor with principal component analysis. Third, a fuzzy score normalization method is introduced; its performance is better than the conventional Z-score normalization method. Fourth, finger-vein, fingerprint, and finger geometry recognitions are combined by using three support vector machines and a weighted SUM rule. Experimental results showed that the equal error rate of the proposed method was 0.254%, which was lower than those of the other methods.

Impact of Acoustic Radiation Force Excitation Geometry on Shear Wave Dispersion and Attenuation Estimates.

PubMed

Lipman, Samantha L; Rouze, Ned C; Palmeri, Mark L; Nightingale, Kathryn R

2018-04-01

Shear wave elasticity imaging (SWEI) characterizes the mechanical properties of human tissues to differentiate healthy from diseased tissue. Commercial scanners tend to reconstruct shear wave speeds for a region of interest using time-of-flight methods reporting a single shear wave speed (or elastic modulus) to the end user under the assumptions that tissue is elastic and shear wave speeds are not dependent on the frequency content of the shear waves. Human tissues, however, are known to be viscoelastic, resulting in dispersion and attenuation. Shear wave spectroscopy and spectral methods have been previously reported in the literature to quantify shear wave dispersion and attenuation, commonly making an assumption that the acoustic radiation force excitation acts as a cylindrical source with a known geometric shear wave amplitude decay. This work quantifies the bias in shear dispersion and attenuation estimates associated with making this cylindrical wave assumption when applied to shear wave sources with finite depth extents, as commonly occurs with realistic focal geometries, in elastic and viscoelastic media. Bias is quantified using analytically derived shear wave data and shear wave data generated using finite-element method models. Shear wave dispersion and attenuation bias (up to 15% for dispersion and 41% for attenuation) is greater for more tightly focused acoustic radiation force sources with smaller depths of field relative to their lateral extent (height-to-width ratios <16). Dispersion and attenuation errors associated with assuming a cylindrical geometric shear wave decay in SWEI can be appreciable and should be considered when analyzing the viscoelastic properties of tissues with acoustic radiation force source distributions with limited depths of field. Copyright © 2018 World Federation for Ultrasound in Medicine and Biology. Published by Elsevier Inc. All rights reserved.

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Nitsche Extended Finite Element Methods for Earthquake Simulation

NASA Astrophysics Data System (ADS)

Coon, Ethan T.

Modeling earthquakes and geologically short-time-scale events on fault networks is a difficult problem with important implications for human safety and design. These problems demonstrate a. rich physical behavior, in which distributed loading localizes both spatially and temporally into earthquakes on fault systems. This localization is governed by two aspects: friction and fault geometry. Computationally, these problems provide a stern challenge for modelers --- static and dynamic equations must be solved on domains with discontinuities on complex fault systems, and frictional boundary conditions must be applied on these discontinuities. The most difficult aspect of modeling physics on complicated domains is the mesh. Most numerical methods involve meshing the geometry; nodes are placed on the discontinuities, and edges are chosen to coincide with faults. The resulting mesh is highly unstructured, making the derivation of finite difference discretizations difficult. Therefore, most models use the finite element method. Standard finite element methods place requirements on the mesh for the sake of stability, accuracy, and efficiency. The formation of a mesh which both conforms to fault geometry and satisfies these requirements is an open problem, especially for three dimensional, physically realistic fault. geometries. In addition, if the fault system evolves over the course of a dynamic simulation (i.e. in the case of growing cracks or breaking new faults), the geometry must he re-meshed at each time step. This can be expensive computationally. The fault-conforming approach is undesirable when complicated meshes are required, and impossible to implement when the geometry is evolving. Therefore, meshless and hybrid finite element methods that handle discontinuities without placing them on element boundaries are a desirable and natural way to discretize these problems. Several such methods are being actively developed for use in engineering mechanics involving crack propagation and material failure. While some theory and application of these methods exist, implementations for the simulation of networks of many cracks have not yet been considered. For my thesis, I implement and extend one such method, the eXtended Finite Element Method (XFEM), for use in static and dynamic models of fault networks. Once this machinery is developed, it is applied to open questions regarding the behavior of networks of faults, including questions of distributed deformation in fault systems and ensembles of magnitude, location, and frequency in repeat ruptures. The theory of XFEM is augmented to allow for solution of problems with alternating regimes of static solves for elastic stress conditions and short, dynamic earthquakes on networks of faults. This is accomplished using Nitsche's approach for implementing boundary conditions. Finally, an optimization problem is developed to determine tractions along the fault, enabling the calculation of frictional constraints and the rupture front. This method is verified via a series of static, quasistatic, and dynamic problems. Armed with this technique, we look at several problems regarding geometry within the earthquake cycle in which geometry is crucial. We first look at quasistatic simulations on a community fault model of Southern California, and model slip distribution across that system. We find the distribution of deformation across faults compares reasonably well with slip rates across the region, as constrained by geologic data. We find geometry can provide constraints for friction, and consider the minimization of shear strain across the zone as a function of friction and plate loading direction, and infer bounds on fault strength in the region. Then we consider the repeated rupture problem, modeling the full earthquake cycle over the course of many events on several fault geometries. In this work, we look at distributions of events, studying the effect of geometry on statistical metrics of event ensembles. Finally, this thesis is a proof of concept for the XFEM on earthquake cycle models on fault systems. We identify strengths and weaknesses of the method, and identify places for future improvement. We discuss the feasibility of the method's use in three dimensions, and find the method to be a strong candidate for future crustal deformation simulations.

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.

Attenuation correction factors for cylindrical, disc and box geometry

NASA Astrophysics Data System (ADS)

Agarwal, Chhavi; Poi, Sanhita; Mhatre, Amol; Goswami, A.; Gathibandhe, M.

2009-08-01

In the present study, attenuation correction factors have been experimentally determined for samples having cylindrical, disc and box geometry and compared with the attenuation correction factors calculated by Hybrid Monte Carlo (HMC) method [ C. Agarwal, S. Poi, A. Goswami, M. Gathibandhe, R.A. Agrawal, Nucl. Instr. and. Meth. A 597 (2008) 198] and with the near-field and far-field formulations available in literature. It has been observed that the near-field formulae, although said to be applicable at close sample-detector geometry, does not work at very close sample-detector configuration. The advantage of the HMC method is that it is found to be valid for all sample-detector geometries.

Estimation and Mapping of Coastal Mangrove Biomass Using Both Passive and Active Remote Sensing Method

NASA Astrophysics Data System (ADS)

Yiqiong, L.; Lu, W.; Zhou, J.; Gan, W.; Cui, X.; Lin, G., Sr.

2015-12-01

Mangrove forests play an important role in global carbon cycle, but carbon stocks in different mangrove forests are not easily measured at large scale. In this research, both active and passive remote sensing methods were used to estimate the aboveground biomass of dominant mangrove communities in Zhanjiang National Mangrove Nature Reserve in Guangdong, China. We set up a decision tree including spectral, texture, position and geometry indexes to achieve mangrove inter-species classification among 5 main species named Aegiceras corniculatum, Aricennia marina, Bruguiera gymnorrhiza, Kandelia candel, Sonneratia apetala by using 5.8m multispectral ZY-3 images. In addition, Lidar data were collected and used to obtain the canopy height of different mangrove species. Then, regression equations between the field measured aboveground biomass and the canopy height deduced from Lidar data were established for these mangrove species. By combining these results, we were able to establish a relatively accurate method for differentiating mangrove species and mapping their aboveground biomass distribution at the estuary scale, which could be applied to mangrove forests in other regions.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

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

Le Hardy, D.; Favennec, Y., E-mail: yann.favennec@univ-nantes.fr; Rousseau, B.

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken intomore » account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.« less

Wind-driven currents in a shallow lake or sea

NASA Technical Reports Server (NTRS)

Goldstein, M. E.; Gedney, R. T.

1971-01-01

For shallow lakes and seas such as the great lakes (especially Lake Erie) where the depth is not much greater than the Ekman depth, the usual Ekman dynamics cannot be used to predict the wind driven currents. The necessary extension to include shallow bodies of water, given by Welander, leads to a partial differential equation for the surface displacement which in turn determines all other flow quantities. A technique for obtaining exact analytical solutions to Welander's equation for bodies of water with large class of bottom topographies which may or may not contain islands is given. It involves applying conformal mapping methods to an extension of Welander's equation into the complex plane. When the wind stress is constant (which is the usual assumption for lakes) the method leads to general solutions which hold for bodies of water of arbitrary shape (the shape appears in the solutions through a set of constants which are the coefficients in the Laurent expansion of a mapping of the particular lake geometry). The method is applied to an elliptically shaped lake and a circular lake containing an eccentrically located circular island.

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.

A discrete geometric approach for simulating the dynamics of thin viscous threads

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

Audoly, B., E-mail: audoly@lmm.jussieu.fr; Clauvelin, N.; Brun, P.-T.

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistencymore » of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.« less

A Robust Symmetry-Based Approach to Exploit Terra-SAR-X Dual-Pol Data for Targets at Sea Observation

NASA Astrophysics Data System (ADS)

Velotto, D.; Nunziata, F.; Migliaccio, M.; Lehner, S.

2013-08-01

In this study a simple physical property, known as reflection symmetry, is exploited to differentiate the objects in marine scenes, i.e. sea surface and metallic targets. First the reflection property is verified and demonstrated against actual SAR images, by measuring the magnitude of the correlation between cross- polarized channels (i.e. HH/HV or VH/VV). Then, a sensitivity study is performed to show the potential of the proposed method in observing man-made metallic target at sea. The robustness of the proposed technique is demonstrated using coherent dual-polarimetric X- band SAR data acquired by the satellite TerraSAR-X in both cross-polarization combinations, with different incidence angle and weather conditions. Co-located ground truth information provided by Automatic Identification System (AIS) reports and harbor charts are used to locate ships, navigation aids and buoys. The proposed method outperforms standard single polarization SAR targets at sea observation independently of the radar geometry and oceanic phenomena.

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.

Characterization of the geometry and topology of DNA pictured as a discrete collection of atoms

PubMed Central

Olson, Wilma K.

2014-01-01

The structural and physical properties of DNA are closely related to its geometry and topology. The classical mathematical treatment of DNA geometry and topology in terms of ideal smooth space curves was not designed to characterize the spatial arrangements of atoms found in high-resolution and simulated double-helical structures. We present here new and rigorous numerical methods for the rapid and accurate assessment of the geometry and topology of double-helical DNA structures in terms of the constituent atoms. These methods are well designed for large DNA datasets obtained in detailed numerical simulations or determined experimentally at high-resolution. We illustrate the usefulness of our methodology by applying it to the analysis of three canonical double-helical DNA chains, a 65-bp minicircle obtained in recent molecular dynamics simulations, and a crystallographic array of protein-bound DNA duplexes. Although we focus on fully base-paired DNA structures, our methods can be extended to treat the geometry and topology of melted DNA structures as well as to characterize the folding of arbitrary molecules such as RNA and cyclic peptides. PMID:24791158

Shielded resistive electromagnets of arbitrary surface geometry using the boundary element method and a minimum energy constraint.

PubMed

Harris, Chad T; Haw, Dustin W; Handler, William B; Chronik, Blaine A

2013-09-01

Eddy currents are generated in MR by the use of rapidly switched electromagnets, resulting in time varying and spatially varying magnetic fields that must be either minimized or corrected. This problem is further complicated when non-cylindrical insert magnets are used for specialized applications. Interruption of the coupling between an insert coil and the MR system is typically accomplished using active magnetic shielding. A new method of actively shielding insert gradient and shim coils of any surface geometry by use of the boundary element method for coil design with a minimum energy constraint is presented. This method was applied to shield x- and z-gradient coils for two separate cases: a traditional cylindrical primary gradient with cylindrical shield and, to demonstrate its versatility in surface geometry, the same cylindrical primary gradients with a rectangular box-shaped shield. For the cylindrical case this method produced shields that agreed with analytic solutions. For the second case, the rectangular box-shaped shields demonstrated very good shielding characteristics despite having a different geometry than the primary coils. Copyright © 2013 Elsevier Inc. All rights reserved.

A Novel Multi-Camera Calibration Method based on Flat Refractive Geometry

NASA Astrophysics Data System (ADS)

Huang, S.; Feng, M. C.; Zheng, T. X.; Li, F.; Wang, J. Q.; Xiao, L. F.

2018-03-01

Multi-camera calibration plays an important role in many field. In the paper, we present a novel multi-camera calibration method based on flat refractive geometry. All cameras can acquire calibration images of transparent glass calibration board (TGCB) at the same time. The application of TGCB leads to refractive phenomenon which can generate calibration error. The theory of flat refractive geometry is employed to eliminate the error. The new method can solve the refractive phenomenon of TGCB. Moreover, the bundle adjustment method is used to minimize the reprojection error and obtain optimized calibration results. Finally, the four-cameras calibration results of real data show that the mean value and standard deviation of the reprojection error of our method are 4.3411e-05 and 0.4553 pixel, respectively. The experimental results show that the proposed method is accurate and reliable.

Effective Fragment Potential Method for H-Bonding: How To Obtain Parameters for Nonrigid Fragments.

PubMed

Dubinets, Nikita; Slipchenko, Lyudmila V

2017-07-20

Accuracy of the effective fragment potential (EFP) method was explored for describing intermolecular interaction energies in three dimers with strong H-bonded interactions, formic acid, formamide, and formamidine dimers, which are a part of HBC6 database of noncovalent interactions. Monomer geometries in these dimers change significantly as a function of intermonomer separation. Several EFP schemes were considered, in which fragment parameters were prepared for a fragment in its gas-phase geometry or recomputed for each unique fragment geometry. Additionally, a scheme in which gas-phase fragment parameters are shifted according to relaxed fragment geometries is introduced and tested. EFP data are compared against the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) method in a complete basis set (CBS) and the symmetry adapted perturbation theory (SAPT). All considered EFP schemes provide a good agreement with CCSD(T)/CBS for binding energies at equilibrium separations, with discrepancies not exceeding 2 kcal/mol. However, only the schemes that utilize relaxed fragment geometries remain qualitatively correct at shorter than equilibrium intermolecular distances. The EFP scheme with shifted parameters behaves quantitatively similar to the scheme in which parameters are recomputed for each monomer geometry and thus is recommended as a computationally efficient approach for large-scale EFP simulations of flexible systems.

Hydraulic tomography of discrete networks of conduits and fractures in a karstic aquifer by using a deterministic inversion algorithm

NASA Astrophysics Data System (ADS)

Fischer, P.; Jardani, A.; Lecoq, N.

2018-02-01

In this paper, we present a novel inverse modeling method called Discrete Network Deterministic Inversion (DNDI) for mapping the geometry and property of the discrete network of conduits and fractures in the karstified aquifers. The DNDI algorithm is based on a coupled discrete-continuum concept to simulate numerically water flows in a model and a deterministic optimization algorithm to invert a set of observed piezometric data recorded during multiple pumping tests. In this method, the model is partioned in subspaces piloted by a set of parameters (matrix transmissivity, and geometry and equivalent transmissivity of the conduits) that are considered as unknown. In this way, the deterministic optimization process can iteratively correct the geometry of the network and the values of the properties, until it converges to a global network geometry in a solution model able to reproduce the set of data. An uncertainty analysis of this result can be performed from the maps of posterior uncertainties on the network geometry or on the property values. This method has been successfully tested for three different theoretical and simplified study cases with hydraulic responses data generated from hypothetical karstic models with an increasing complexity of the network geometry, and of the matrix heterogeneity.

Numerical algebraic geometry: a new perspective on gauge and string theories

NASA Astrophysics Data System (ADS)

Mehta, Dhagash; He, Yang-Hui; Hauensteine, Jonathan D.

2012-07-01

There is a rich interplay between algebraic geometry and string and gauge theories which has been recently aided immensely by advances in computational algebra. However, symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these shortcomings. The so-called `embarrassing parallelizability' allows us to solve many problems and extract physical information which elude symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.

Measurement of in vitro and in vivo stent geometry and deformation by means of 3D imaging and stereo-photogrammetry.

PubMed

Zwierzak, Iwona; Cosentino, Daria; Narracott, Andrew J; Bonhoeffer, Philipp; Diaz, Vanessa; Fenner, John W; Schievano, Silvia

2014-12-01

To quantify variability of in vitro and in vivo measurement of 3D device geometry using 3D and biplanar imaging. Comparison of stent reconstruction is reported for in vitro coronary stent deployment (using micro-CT and optical stereo-photogrammetry) and in vivo pulmonary valve stent deformation (using 4DCT and biplanar fluoroscopy). Coronary stent strut length and inter-strut angle were compared in the fully deployed configuration. Local (inter-strut angle) and global (dog-boning ratio) measures of stent deformation were reported during stent deployment. Pulmonary valve stent geometry was assessed throughout the cardiac cycle by reconstruction of stent geometry and measurement of stent diameter. Good agreement was obtained between methods for assessment of coronary stent geometry with maximum disagreement of +/- 0.03 mm (length) and +/- 3 degrees (angle). The stent underwent large, non-uniform, local deformations during balloon inflation, which did not always correlate with changes in stent diameter. Three-dimensional reconstruction of the pulmonary valve stent was feasible for all frames of the fluoroscopy and for 4DCT images, with good correlation between the diameters calculated from the two methods. The largest compression of the stent during the cardiac cycle was 6.98% measured from fluoroscopy and 7.92% from 4DCT, both in the most distal ring. Quantitative assessment of stent geometry reconstructed from biplanar imaging methods in vitro and in vivo has shown good agreement with geometry reconstructed from 3D techniques. As a result of their short image acquisition time, biplanar methods may have significant advantages in the measurement of dynamic 3D stent deformation.

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)

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…

Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies of C20-C86fullerene isomers

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

Zheng, Guishan; Irle, Stephan; Morokuma, Keiji

2005-07-20

The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. The performance of both non-iterative (NCC) and self-consistent charge (SCC) versions of the density functional tight binding (DFTB) method, as well as AM1 and PM3 methods, has been compared with the B3LYP method, a hybrid density functional theory (DFT) method, for equilibrium geometries and relative energies of various isomers of C20–C86 fullerenes. Both NCC- and SCCDFTB methods compare very favorablymore » with B3LYP both in geometries and isomer relative energies, while AM1 and PM3 do noticeably worse.« less

Efficiently computing exact geodesic loops within finite steps.

PubMed

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

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.

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.

Study of skin model and geometry effects on thermal performance of thermal protective fabrics

NASA Astrophysics Data System (ADS)

Zhu, Fanglong; Ma, Suqin; Zhang, Weiyuan

2008-05-01

Thermal protective clothing has steadily improved over the years as new materials and improved designs have reached the market. A significant method that has brought these improvements to the fire service is the NFPA 1971 standard on structural fire fighters’ protective clothing. However, this testing often neglects the effects of cylindrical geometry on heat transmission in flame resistant fabrics. This paper deals with methods to develop cylindrical geometry testing apparatus incorporating novel skin bioheat transfer model to test flame resistant fabrics used in firefighting. Results show that fabrics which shrink during the test can have reduced thermal protective performance compared with the qualities measured with a planar geometry tester. Results of temperature differences between skin simulant sensors of planar and cylindrical tester are also compared. This test method provides a new technique to accurately and precisely characterize the thermal performance of thermal protective fabrics.

Hand biometric recognition based on fused hand geometry and vascular patterns.

PubMed

Park, GiTae; Kim, Soowon

2013-02-28

A hand biometric authentication method based on measurements of the user's hand geometry and vascular pattern is proposed. To acquire the hand geometry, the thickness of the side view of the hand, the K-curvature with a hand-shaped chain code, the lengths and angles of the finger valleys, and the lengths and profiles of the fingers were used, and for the vascular pattern, the direction-based vascular-pattern extraction method was used, and thus, a new multimodal biometric approach is proposed. The proposed multimodal biometric system uses only one image to extract the feature points. This system can be configured for low-cost devices. Our multimodal biometric-approach hand-geometry (the side view of the hand and the back of hand) and vascular-pattern recognition method performs at the score level. The results of our study showed that the equal error rate of the proposed system was 0.06%.

Hand Biometric Recognition Based on Fused Hand Geometry and Vascular Patterns

PubMed Central

Park, GiTae; Kim, Soowon

2013-01-01

A hand biometric authentication method based on measurements of the user's hand geometry and vascular pattern is proposed. To acquire the hand geometry, the thickness of the side view of the hand, the K-curvature with a hand-shaped chain code, the lengths and angles of the finger valleys, and the lengths and profiles of the fingers were used, and for the vascular pattern, the direction-based vascular-pattern extraction method was used, and thus, a new multimodal biometric approach is proposed. The proposed multimodal biometric system uses only one image to extract the feature points. This system can be configured for low-cost devices. Our multimodal biometric-approach hand-geometry (the side view of the hand and the back of hand) and vascular-pattern recognition method performs at the score level. The results of our study showed that the equal error rate of the proposed system was 0.06%. PMID:23449119

Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Motta, Mario; Zhang, Shiwei

2018-05-01

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.

Extending rule-based methods to model molecular geometry and 3D model resolution.

PubMed

Hoard, Brittany; Jacobson, Bruna; Manavi, Kasra; Tapia, Lydia

2016-08-01

Computational modeling is an important tool for the study of complex biochemical processes associated with cell signaling networks. However, it is challenging to simulate processes that involve hundreds of large molecules due to the high computational cost of such simulations. Rule-based modeling is a method that can be used to simulate these processes with reasonably low computational cost, but traditional rule-based modeling approaches do not include details of molecular geometry. The incorporation of geometry into biochemical models can more accurately capture details of these processes, and may lead to insights into how geometry affects the products that form. Furthermore, geometric rule-based modeling can be used to complement other computational methods that explicitly represent molecular geometry in order to quantify binding site accessibility and steric effects. We propose a novel implementation of rule-based modeling that encodes details of molecular geometry into the rules and binding rates. We demonstrate how rules are constructed according to the molecular curvature. We then perform a study of antigen-antibody aggregation using our proposed method. We simulate the binding of antibody complexes to binding regions of the shrimp allergen Pen a 1 using a previously developed 3D rigid-body Monte Carlo simulation, and we analyze the aggregate sizes. Then, using our novel approach, we optimize a rule-based model according to the geometry of the Pen a 1 molecule and the data from the Monte Carlo simulation. We use the distances between the binding regions of Pen a 1 to optimize the rules and binding rates. We perform this procedure for multiple conformations of Pen a 1 and analyze the impact of conformation and resolution on the optimal rule-based model. We find that the optimized rule-based models provide information about the average steric hindrance between binding regions and the probability that antibodies will bind to these regions. These optimized models quantify the variation in aggregate size that results from differences in molecular geometry and from model resolution.

Online shaft encoder geometry compensation for arbitrary shaft speed profiles using Bayesian regression

NASA Astrophysics Data System (ADS)

Diamond, D. H.; Heyns, P. S.; Oberholster, A. J.

2016-12-01

The measurement of instantaneous angular speed is being increasingly investigated for its use in a wide range of condition monitoring and prognostic applications. Central to many measurement techniques are incremental shaft encoders recording the arrival times of shaft angular increments. The conventional approach to processing these signals assumes that the angular increments are equidistant. This assumption is generally incorrect when working with toothed wheels and especially zebra tape encoders and has been shown to introduce errors in the estimated shaft speed. There are some proposed methods in the literature that aim to compensate for this geometric irregularity. Some of the methods require the shaft speed to be perfectly constant for calibration, something rarely achieved in practice. Other methods assume the shaft speed to be nearly constant with minor deviations. Therefore existing methods cannot calibrate the entire shaft encoder geometry for arbitrary shaft speeds. The present article presents a method to calculate the shaft encoder geometry for arbitrary shaft speed profiles. The method uses Bayesian linear regression to calculate the encoder increment distances. The method is derived and then tested against simulated and laboratory experiments. The results indicate that the proposed method is capable of accurately determining the shaft encoder geometry for any shaft speed profile.

Geometry of Conservation Laws for a Class of Parabolic Partial Differential Equations

NASA Astrophysics Data System (ADS)

Clelland, Jeanne Nielsen

1996-08-01

I consider the problem of computing the space of conservation laws for a second-order, parabolic partial differential equation for one function of three independent variables. The PDE is formulated as an exterior differential system {cal I} on a 12 -manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of {cal I} modulo the so -called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of equivalence to study the structure of the space of conservation laws. My main result is:. Theorem. Any conservation law for a second-order, parabolic PDE for one function of three independent variables can be represented by a closed 3-form in the differential ideal {cal I} on the original 12-manifold M. I show that if a nontrivial conservation law exists, then {cal I} has a deprolongation to an equivalent system {cal J} on a 7-manifold N, and any conservation law for {cal I} can be expressed as a closed 3-form on N which lies in {cal J}. Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic) equation of the formA(u _{xx}u_{yy}-u_sp {xy}{2}) + B_1u_{xx }+2B_2u_{xy} +B_3u_ {yy}+C=0crwhere A, B_{i}, C are functions of x, y, t, u, u_{x}, u _{y}, u_{t}. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using Cartan's method of equivalence. I show that the non-linearizable equation u_{t} = {1over2}e ^{-u}(u_{xx}+u_ {yy})has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a linear equation, i.e., is linearizable.

Multilevel geometry optimization

NASA Astrophysics Data System (ADS)

Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

2000-02-01

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

Method of grid generation

DOEpatents

Barnette, Daniel W.

2002-01-01

The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.

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.

Virtual reality based adaptive dose assessment method for arbitrary geometries in nuclear facility decommissioning.

PubMed

Liu, Yong-Kuo; Chao, Nan; Xia, Hong; Peng, Min-Jun; Ayodeji, Abiodun

2018-05-17

This paper presents an improved and efficient virtual reality-based adaptive dose assessment method (VRBAM) applicable to the cutting and dismantling tasks in nuclear facility decommissioning. The method combines the modeling strength of virtual reality with the flexibility of adaptive technology. The initial geometry is designed with the three-dimensional computer-aided design tools, and a hybrid model composed of cuboids and a point-cloud is generated automatically according to the virtual model of the object. In order to improve the efficiency of dose calculation while retaining accuracy, the hybrid model is converted to a weighted point-cloud model, and the point kernels are generated by adaptively simplifying the weighted point-cloud model according to the detector position, an approach that is suitable for arbitrary geometries. The dose rates are calculated with the Point-Kernel method. To account for radiation scattering effects, buildup factors are calculated with the Geometric-Progression formula in the fitting function. The geometric modeling capability of VRBAM was verified by simulating basic geometries, which included a convex surface, a concave surface, a flat surface and their combination. The simulation results show that the VRBAM is more flexible and superior to other approaches in modeling complex geometries. In this paper, the computation time and dose rate results obtained from the proposed method were also compared with those obtained using the MCNP code and an earlier virtual reality-based method (VRBM) developed by the same authors. © 2018 IOP Publishing Ltd.

Electronic excitations in long polyenes revisited

NASA Astrophysics Data System (ADS)

Schmidt, Maximilian; Tavan, Paul

2012-03-01

We apply the valence shell model OM2 [W. Weber and W. Thiel, Theor. Chem. Acc. 103, 495, (2000), 10.1007/s002149900083] combined with multireference configuration interaction (MRCI) to compute the vertical excitation energies and transition dipole moments of the low-energy singlet excitations in the polyenes with 4 ⩽ N ⩽ 22π-electrons. We find that the OM2/MRCI descriptions closely resemble those of Pariser-Parr-Pople (PPP) π-electron models [P. Tavan and K. Schulten, Phys. Rev. B 36, 4337, (1987)], if equivalent MRCI procedures and regularly alternating model geometries are used. OM2/MRCI optimized geometries are shown to entail improved descriptions particularly for smaller polyenes (N ⩽ 12), for which sizeable deviations from the regular model geometries are found. With configuration interaction active spaces covering also the σ- in addition to the π-electrons, OM2/MRCI excitation energies turn out to become smaller by at most 0.35 eV for the ionic and 0.15 eV for the covalent excitations. The particle-hole (ph) symmetry, which in Pariser-Parr-Pople models arises from the zero-differential overlap approximation, is demonstrated to be only weakly broken in OM2 such that the oscillator strengths of the covalent 1B_u^- states, which artificially vanish in ph-symmetric models, are predicted to be very small. According to OM2/MRCI and experimental data the 1B_u^- state is the third excited singlet state for N < 12 and becomes the second for N ⩾ 14. By comparisons with results of other theoretical approaches and experimental evidence we argue that deficiencies of the particular MRCI method employed by us, which show up in a poor size consistency of the covalent excitations for N > 12, are caused by its restriction to at most doubly excited references.

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.

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.

Algorithm for lens calculations in the geometrized Maxwell theory

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A physical zero-knowledge object-comparison system for nuclear warhead verification

PubMed Central

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander; d'Errico, Francesco

2016-01-01

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications. PMID:27649477

A physical zero-knowledge object-comparison system for nuclear warhead verification.

PubMed

Philippe, Sébastien; Goldston, Robert J; Glaser, Alexander; d'Errico, Francesco

2016-09-20

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.

A physical zero-knowledge object-comparison system for nuclear warhead verification

NASA Astrophysics Data System (ADS)

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander; D'Errico, Francesco

2016-09-01

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information. More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.

A physical zero-knowledge object-comparison system for nuclear warhead verification

DOE PAGES

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander; ...

2016-09-20

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information.more » More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.« less

A physical zero-knowledge object-comparison system for nuclear warhead verification

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

Philippe, Sébastien; Goldston, Robert J.; Glaser, Alexander

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other sensitive physical data has attracted attention, especially in the field of nuclear arms control. Here we demonstrate a non-electronic fast neutron differential radiography technique using superheated emulsion detectors that can confirm that two objects are identical without revealing their geometry or composition. Such a technique could form the basis of a verification system that could confirm the authenticity of nuclear weapons without sharing any secret design information.more » More broadly, by demonstrating a physical zero-knowledge proof that can compare physical properties of objects, this experiment opens the door to developing other such secure proof-systems for other applications.« less

An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations

NASA Technical Reports Server (NTRS)

Yun, Xiaoping; Kumar, Vijay R.

1991-01-01

An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.

Simplified calculation of solar flux distribution on the side wall of cylindrical cavity solar receivers

NASA Technical Reports Server (NTRS)

Bhandari, P.; Wu, Y. C.; Roschke, E. J.

1989-01-01

A simple solar flux calculation algorithm for a cylindrical cavity type solar receiver has been developed and implemented on an IBM PC-AT. Using cone optics, the contour error method is utilized to handle the slope error of a paraboloidal concentrator. The flux distribution on the side wall is calculated by integration of the energy incident from cones emanating from all the differential elements on the concentrator. The calculations are done for any set of dimensions and properties of the receiver and the concentrator, and account for any spillover on the aperture plate. The results of this algorithm compared excellently with those predicted by more complicated programs. Because of the utilization of axial symmetry and overall simplification, it is extremely fast. It can be esily extended to other axisymmetric receiver geometries.

New graph polynomials in parametric QED Feynman integrals

NASA Astrophysics Data System (ADS)

Golz, Marcel

2017-10-01

In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by the fact that their parametric integrand is much larger and more involved. It is, moreover, only implicitly given as the result of certain differential operators applied to the scalar integrand exp(-ΦΓ /ΨΓ) , where ΨΓ and ΦΓ are the Kirchhoff and Symanzik polynomials of the Feynman graph Γ. In the case of quantum electrodynamics we find that the full parametric integrand inherits a rich combinatorial structure from ΨΓ and ΦΓ. In the end, it can be expressed explicitly as a sum over products of new types of graph polynomials which have a combinatoric interpretation via simple cycle subgraphs of Γ.

A comparative study on different methods of automatic mesh generation of human femurs.

PubMed

Viceconti, M; Bellingeri, L; Cristofolini, L; Toni, A

1998-01-01

The aim of this study was to evaluate comparatively five methods for automating mesh generation (AMG) when used to mesh a human femur. The five AMG methods considered were: mapped mesh, which provides hexahedral elements through a direct mapping of the element onto the geometry; tetra mesh, which generates tetrahedral elements from a solid model of the object geometry; voxel mesh which builds cubic 8-node elements directly from CT images; and hexa mesh that automatically generated hexahedral elements from a surface definition of the femur geometry. The various methods were tested against two reference models: a simplified geometric model and a proximal femur model. The first model was useful to assess the inherent accuracy of the meshes created by the AMG methods, since an analytical solution was available for the elastic problem of the simplified geometric model. The femur model was used to test the AMG methods in a more realistic condition. The femoral geometry was derived from a reference model (the "standardized femur") and the finite element analyses predictions were compared to experimental measurements. All methods were evaluated in terms of human and computer effort needed to carry out the complete analysis, and in terms of accuracy. The comparison demonstrated that each tested method deserves attention and may be the best for specific situations. The mapped AMG method requires a significant human effort but is very accurate and it allows a tight control of the mesh structure. The tetra AMG method requires a solid model of the object to be analysed but is widely available and accurate. The hexa AMG method requires a significant computer effort but can also be used on polygonal models and is very accurate. The voxel AMG method requires a huge number of elements to reach an accuracy comparable to that of the other methods, but it does not require any pre-processing of the CT dataset to extract the geometry and in some cases may be the only viable solution.

Image-based 3D reconstruction and virtual environmental walk-through

NASA Astrophysics Data System (ADS)

Sun, Jifeng; Fang, Lixiong; Luo, Ying

2001-09-01

We present a 3D reconstruction method, which combines geometry-based modeling, image-based modeling and rendering techniques. The first component is an interactive geometry modeling method which recovery of the basic geometry of the photographed scene. The second component is model-based stereo algorithm. We discus the image processing problems and algorithms of walking through in virtual space, then designs and implement a high performance multi-thread wandering algorithm. The applications range from architectural planning and archaeological reconstruction to virtual environments and cinematic special effects.

Quantum mechanics of conformally and minimally coupled Friedmann-Robertson-Walker cosmology

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

1992-10-01

The expansion method by a time-dependent basis of the eigenfunctions for the space-coordinate-dependent sub-Hamiltonian is one of the most natural frameworks for quantum systems, relativistic as well as nonrelativistic. The complete set of wave functions is found in the product integral formulation, whose constants of integration are fixed by Cauchy initial data. The wave functions for the Friedmann-Robertson-Walker (FRW) cosmology conformally and minimally coupled to a scalar field with a power-law potential or a polynomial potential are expanded in terms of the eigenfunctions of the scalar field sub-Hamiltonian part. The resultant gravitational field part which is an ``intrinsic'' timelike variable-dependent matrix-valued differential equation is solved again in the product integral formulation. There are classically allowed regions for the ``intrinsic'' timelike variable depending on the scalar field quantum numbers and these regions increase accordingly as the quantum numbers increase. For a fixed large three-geometry the wave functions corresponding to the low excited (small quantum number) states of the scalar field are exponentially damped or diverging and the wave functions corresponding to the high excited (large quantum number) states are still oscillatory but become eventually exponential as the three-geometry becomes larger. Furthermore, a proposal is advanced that the wave functions exponentially damped for a large three-geometry may be interpreted as ``tunneling out'' wave functions into, and the wave functions exponentially diverging as ``tunneling in'' from, different universes with the same or different topologies, the former being interpreted as the recently proposed Hawking-Page wormhole wave functions. It is observed that there are complex as well as Euclidean actions depending on the quantum numbers of the scalar field part outside the classically allowed region both of the gravitational and scalar fields, suggesting the usefulness of complex geometry and complex trajectories. From the most general wave functions for the FRW cosmology conformally coupled to scalar field, the boundary conditions for the wormhole wave functions are modified so that the modulus of wave functions, instead of the wave functions themselves, should be exponentially damped for a large three-geometry and be regular up to some negative power of the three-geometry as the three-geometry collapses. The wave functions for the FRW cosmology minimally coupled to an inhomogeneous scalar field are similarly found in the product integral formulation. The role of a large number of the inhomogeneous modes of the scalar field is not only to increase the classically allowed regions for the gravitational part but also to provide a mechanism of the decoherence of quantum interferences between the different sizes of the universe.

GENIE(++): A Multi-Block Structured Grid System

NASA Technical Reports Server (NTRS)

Williams, Tonya; Nadenthiran, Naren; Thornburg, Hugh; Soni, Bharat K.

1996-01-01

The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.

A method for validation of finite element forming simulation on basis of a pointwise comparison of distance and curvature

NASA Astrophysics Data System (ADS)

Dörr, Dominik; Joppich, Tobias; Schirmaier, Fabian; Mosthaf, Tobias; Kärger, Luise; Henning, Frank

2016-10-01

Thermoforming of continuously fiber reinforced thermoplastics (CFRTP) is ideally suited to thin walled and complex shaped products. By means of forming simulation, an initial validation of the producibility of a specific geometry, an optimization of the forming process and the prediction of fiber-reorientation due to forming is possible. Nevertheless, applied methods need to be validated. Therefor a method is presented, which enables the calculation of error measures for the mismatch between simulation results and experimental tests, based on measurements with a conventional coordinate measuring device. As a quantitative measure, describing the curvature is provided, the presented method is also suitable for numerical or experimental sensitivity studies on wrinkling behavior. The applied methods for forming simulation, implemented in Abaqus explicit, are presented and applied to a generic geometry. The same geometry is tested experimentally and simulation and test results are compared by the proposed validation method.

Combination of microscopic model and VoF-multiphase approach for numerical simulation of nodular cast iron solidification

NASA Astrophysics Data System (ADS)

Subasic, E.; Huang, C.; Jakumeit, J.; Hediger, F.

2015-06-01

The ongoing increase in the size and capacity of state-of-the-art wind power plants is highlighting the need to reduce the weight of critical components, such as hubs, main shaft bearing housings, gear box housings and support bases. These components are manufactured as nodular iron castings (spheroid graphite iron, or SGI). A weight reduction of up to 20% is achievable by optimizing the geometry to minimize volume, thus enabling significant downsizing of wind power plants. One method for enhancing quality control in the production of thick-walled SGI castings, and thus reducing tolerances and, consequently, enabling castings of smaller volume is via a casting simulation of mould filling and solidification based on a combination of microscopic model and VoF-multiphase approach. Coupled fluid flow with heat transport and phase transformation kinetics during solidification is described by partial differential equations and solved using the finite volume method. The flow of multiple phases is described using a volume of fluid approach. Mass conservation equations are solved separately for both liquid and solid phases. At the micro-level, the diffusion-controlled growth model for grey iron eutectic grains by Wetterfall et al. is combined with a growth model for white iron eutectic grains. The micro-solidification model is coupled with macro-transport equations via source terms in the energy and continuity equations. As a first step the methodology was applied to a simple geometry to investigate the impact of mould-filling on the grey-to-white transition prediction in nodular cast iron.

Three dimensional electrochemical simulation of solid oxide fuel cell cathode based on microstructure reconstructed by marching cubes method

NASA Astrophysics Data System (ADS)

He, An; Gong, Jiaming; Shikazono, Naoki

2018-05-01

In the present study, a model is introduced to correlate the electrochemical performance of solid oxide fuel cell (SOFC) with the 3D microstructure reconstructed by focused ion beam scanning electron microscopy (FIB-SEM) in which the solid surface is modeled by the marching cubes (MC) method. Lattice Boltzmann method (LBM) is used to solve the governing equations. In order to maintain the geometries reconstructed by the MC method, local effective diffusivities and conductivities computed based on the MC geometries are applied in each grid, and partial bounce-back scheme is applied according to the boundary predicted by the MC method. From the tortuosity factor and overpotential calculation results, it is concluded that the MC geometry drastically improves the computational accuracy by giving more precise topology information.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

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.

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.

Methods for Computationally Efficient Structured CFD Simulations of Complex Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Herrick, Gregory P.; Chen, Jen-Ping

2012-01-01

This research presents more efficient computational methods by which to perform multi-block structured Computational Fluid Dynamics (CFD) simulations of turbomachinery, thus facilitating higher-fidelity solutions of complicated geometries and their associated flows. This computational framework offers flexibility in allocating resources to balance process count and wall-clock computation time, while facilitating research interests of simulating axial compressor stall inception with more complete gridding of the flow passages and rotor tip clearance regions than is typically practiced with structured codes. The paradigm presented herein facilitates CFD simulation of previously impractical geometries and flows. These methods are validated and demonstrate improved computational efficiency when applied to complicated geometries and flows.

A survey of the broadband shock associated noise prediction methods

NASA Technical Reports Server (NTRS)

Kim, Chan M.; Krejsa, Eugene A.; Khavaran, Abbas

1992-01-01

Several different prediction methods to estimate the broadband shock associated noise of a supersonic jet are introduced and compared with experimental data at various test conditions. The nozzle geometries considered for comparison include a convergent and a convergent-divergent nozzle, both axisymmetric. Capabilities and limitations of prediction methods in incorporating the two nozzle geometries, flight effect, and temperature effect are discussed. Predicted noise field shows the best agreement for a convergent nozzle geometry under static conditions. Predicted results for nozzles in flight show larger discrepancies from data and more dependable flight data are required for further comparison. Qualitative effects of jet temperature, as observed in experiment, are reproduced in predicted results.

Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem

DOE PAGES

Stefanescu, Razvan; Schmidt, Kathleen; Hite, Jason; ...

2016-12-12

In this paper, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particlemore » swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Finally, marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms.« less

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.

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.

On the Methods of Determining the Radio Emission Geometry in Pulsar Magnetospheres

NASA Technical Reports Server (NTRS)

Dyks, J.; Rudak, B.; Harding, Alice K.

2004-01-01

We present a modification of the relativistic phase shift method of determining the radio emission geometry from pulsar magnetospheres proposed by Gangadhara & Gupta (2001). Our modification provides a method of determining radio emission altitudes which does not depend on the viewing geometry and does not require polarization measurements. We suggest application of the method to the outer edges of averaged radio pulse profiles to identify magnetic field lines associated with'the edges of the pulse and, thereby, to test the geometric method based on the measurement of the pulse width at the lowest intensity level. We show that another relativistic method proposed by Blaskiewicz et al. (1991) provides upper limits for emission altitudes associated with the outer edges of pulse profiles. A comparison of these limits with the altitudes determined with the geometric method may be used to probe the importance of rotational distortions of magnetic field and refraction effects in the pulsar magnetosphere. We provide a comprehensive discussion of the assumptions used in the relativistic methods.

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…

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.

GEOMETRY-INDEPENDENT DETERMINATION OF RADIAL DENSITY DISTRIBUTIONS IN MOLECULAR CLOUD CORES AND OTHER ASTRONOMICAL OBJECTS

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

Krčo, Marko; Goldsmith, Paul F., E-mail: marko@astro.cornell.edu

2016-05-01

We present a geometry-independent method for determining the shapes of radial volume density profiles of astronomical objects whose geometries are unknown, based on a single column density map. Such profiles are often critical to understand the physics and chemistry of molecular cloud cores, in which star formation takes place. The method presented here does not assume any geometry for the object being studied, thus removing a significant source of bias. Instead, it exploits contour self-similarity in column density maps, which appears to be common in data for astronomical objects. Our method may be applied to many types of astronomical objectsmore » and observable quantities so long as they satisfy a limited set of conditions, which we describe in detail. We derive the method analytically, test it numerically, and illustrate its utility using 2MASS-derived dust extinction in molecular cloud cores. While not having made an extensive comparison of different density profiles, we find that the overall radial density distribution within molecular cloud cores is adequately described by an attenuated power law.« less

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.

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\

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.

A method for performance comparison of polycentric knees and its application to the design of a knee for developing countries.

PubMed

Anand, T S; Sujatha, S

2017-08-01

Polycentric knees for transfemoral prostheses have a variety of geometries, but a survey of literature shows that there are few ways of comparing their performance. Our objective was to present a method for performance comparison of polycentric knee geometries and design a new geometry. In this work, we define parameters to compare various commercially available prosthetic knees in terms of their stability, toe clearance, maximum flexion, and so on and optimize the parameters to obtain a new knee design. We use the defined parameters and optimization to design a new knee geometry that provides the greater stability and toe clearance necessary to navigate uneven terrain which is typically encountered in developing countries. Several commercial knees were compared based on the defined parameters to determine their suitability for uneven terrain. A new knee was designed based on optimization of these parameters. Preliminary user testing indicates that the new knee is very stable and easy to use. The methodology can be used for better knee selection and design of more customized knee geometries. Clinical relevance The method provides a tool to aid in the selection and design of polycentric knees for transfemoral prostheses.

A dose assessment method for arbitrary geometries with virtual reality in the nuclear facilities decommissioning

NASA Astrophysics Data System (ADS)

Chao, Nan; Liu, Yong-kuo; Xia, Hong; Ayodeji, Abiodun; Bai, Lu

2018-03-01

During the decommissioning of nuclear facilities, a large number of cutting and demolition activities are performed, which results in a frequent change in the structure and produce many irregular objects. In order to assess dose rates during the cutting and demolition process, a flexible dose assessment method for arbitrary geometries and radiation sources was proposed based on virtual reality technology and Point-Kernel method. The initial geometry is designed with the three-dimensional computer-aided design tools. An approximate model is built automatically in the process of geometric modeling via three procedures namely: space division, rough modeling of the body and fine modeling of the surface, all in combination with collision detection of virtual reality technology. Then point kernels are generated by sampling within the approximate model, and when the material and radiometric attributes are inputted, dose rates can be calculated with the Point-Kernel method. To account for radiation scattering effects, buildup factors are calculated with the Geometric-Progression formula in the fitting function. The effectiveness and accuracy of the proposed method was verified by means of simulations using different geometries and the dose rate results were compared with that derived from CIDEC code, MCNP code and experimental measurements.

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

NASA Technical Reports Server (NTRS)

Moitra, Anutosh

1989-01-01

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

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.

Automatic construction of subject-specific human airway geometry including trifurcations based on a CT-segmented airway skeleton and surface

PubMed Central

Miyawaki, Shinjiro; Tawhai, Merryn H.; Hoffman, Eric A.; Wenzel, Sally E.; Lin, Ching-Long

2016-01-01

We propose a method to construct three-dimensional airway geometric models based on airway skeletons, or centerlines (CLs). Given a CT-segmented airway skeleton and surface, the proposed CL-based method automatically constructs subject-specific models that contain anatomical information regarding branches, include bifurcations and trifurcations, and extend from the trachea to terminal bronchioles. The resulting model can be anatomically realistic with the assistance of an image-based surface; alternatively a model with an idealized skeleton and/or branch diameters is also possible. This method systematically identifies and classifies trifurcations to successfully construct the models, which also provides the number and type of trifurcations for the analysis of the airways from an anatomical point of view. We applied this method to 16 normal and 16 severe asthmatic subjects using their computed tomography images. The average distance between the surface of the model and the image-based surface was 11% of the average voxel size of the image. The four most frequent locations of trifurcations were the left upper division bronchus, left lower lobar bronchus, right upper lobar bronchus, and right intermediate bronchus. The proposed method automatically constructed accurate subject-specific three-dimensional airway geometric models that contain anatomical information regarding branches using airway skeleton, diameters, and image-based surface geometry. The proposed method can construct (i) geometry automatically for population-based studies, (ii) trifurcations to retain the original airway topology, (iii) geometry that can be used for automatic generation of computational fluid dynamics meshes, and (iv) geometry based only on a skeleton and diameters for idealized branches. PMID:27704229

CAD-based Automatic Modeling Method for Geant4 geometry model Through MCAM

NASA Astrophysics Data System (ADS)

Wang, Dong; Nie, Fanzhi; Wang, Guozhong; Long, Pengcheng; LV, Zhongliang; LV, Zhongliang

2014-06-01

Geant4 is a widely used Monte Carlo transport simulation package. Before calculating using Geant4, the calculation model need be established which could be described by using Geometry Description Markup Language (GDML) or C++ language. However, it is time-consuming and error-prone to manually describe the models by GDML. Automatic modeling methods have been developed recently, but there are some problem existed in most of present modeling programs, specially some of them were not accurate or adapted to specifically CAD format. To convert the GDML format models to CAD format accurately, a Geant4 Computer Aided Design (CAD) based modeling method was developed for automatically converting complex CAD geometry model into GDML geometry model. The essence of this method was dealing with CAD model represented with boundary representation (B-REP) and GDML model represented with constructive solid geometry (CSG). At first, CAD model was decomposed to several simple solids which had only one close shell. And then the simple solid was decomposed to convex shell set. Then corresponding GDML convex basic solids were generated by the boundary surfaces getting from the topological characteristic of a convex shell. After the generation of these solids, GDML model was accomplished with series boolean operations. This method was adopted in CAD/Image-based Automatic Modeling Program for Neutronics & Radiation Transport (MCAM), and tested with several models including the examples in Geant4 install package. The results showed that this method could convert standard CAD model accurately, and can be used for Geant4 automatic modeling.

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

Systems and Methods for Designing and Fabricating Contact-Free Support Structures for Overhang Geometries of Parts in Powder-Bed Metal Additive Manufacturing

NASA Technical Reports Server (NTRS)

Cooper, Kenneth (Inventor); Chou, Yuag-Shan (Inventor)

2017-01-01

Systems and methods are provided for designing and fabricating contact-free support structures for overhang geometries of parts fabricated using electron beam additive manufacturing. One or more layers of un-melted metallic powder are disposed in an elongate gap between an upper horizontal surface of the support structure and a lower surface of the overhang geometry. The powder conducts heat from the overhang geometry to the support structure. The support structure acts as a heat sink to enhance heat transfer and reduce the temperature and severe thermal gradients due to poor thermal conductivity of metallic powders underneath the overhang. Because the support structure is not connected to the part, the support structure can be removed freely without any post-processing step.

Integrated Fluorescence

NASA Technical Reports Server (NTRS)

Tuma, Margaret (Inventor); Gruhlke, Russell W. (Inventor)

1998-01-01

A detection method is integrated with a filtering method and an enhancement method to create a fluorescence sensor that can be miniaturized. The fluorescence sensor comprises a thin film geometry including a waveguide layer, a metal film layer and sensor layer. The thin film geometry of the fluorescence sensor allows the detection of fluorescent radiation over a narrow wavelength interval. This enables wavelength discrimination and eliminates the detection of unwanted light from unknown or spurious sources.

Analysis and design of planar and non-planar wings for induced drag minimization

NASA Technical Reports Server (NTRS)

Mortara, K.; Straussfogel, Dennis M.; Maughmer, Mark D.

1991-01-01

The goal of the work was to develop and validate computational tools to be used for the design of planar and non-planar wing geometries for minimum induced drag. Because of the iterative nature of the design problem, it is important that, in addition to being sufficiently accurate for the problem at hand, they are reasonably fast and computationally efficient. Toward this end, a method of predicting induced drag in the presence of a non-rigid wake is coupled with a panel method. The induced drag prediction technique is based on the Kutta-Joukowski law applied at the trailing edge. Until recently, the use of this method has not been fully explored and pressure integration and Trefftz-plane calculations favored. As is shown in this report, however, the Kutta-Joukowski method is able to give better results for a given amount of effort than the more common techniques, particularly when relaxed wakes and non-planar wing geometries are considered. Using these tools, a workable design method is in place which takes into account relaxed wakes and non-planar wing geometries. It is recommended that this method be used to design a wind-tunnel experiment to verify the predicted aerodynamic benefits of non-planar wing geometries.

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.

Geometry definition and grid generation for a complete fighter aircraft

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1986-01-01

Recent advances in computing power and numerical solution procedures have enabled computational fluid dynamicists to attempt increasingly difficult problems. In particular, efforts are focusing on computations of complex three-dimensional flow fields about realistic aerodynamic bodies. To perform such computations, a very accurate and detailed description of the surface geometry must be provided, and a three-dimensional grid must be generated in the space around the body. The geometry must be supplied in a format compatible with the grid generation requirements, and must be verified to be free of inconsistencies. This paper presents a procedure for performing the geometry definition of a fighter aircraft that makes use of a commercial computer-aided design/computer-aided manufacturing system. Furthermore, visual representations of the geometry are generated using a computer graphics system for verification of the body definition. Finally, the three-dimensional grids for fighter-like aircraft are generated by means of an efficient new parabolic grid generation method. This method exhibits good control of grid quality.

Performance characterization of complex fuel port geometries for hybrid rocket fuel grains

NASA Astrophysics Data System (ADS)

Bath, Andrew

This research investigated the 3D printing and burning of fuel grains with complex geometry and the development of software capable of modeling and predicting the regression of a cross-section of these complex fuel grains. The software developed did predict the geometry to a fair degree of accuracy, especially when enhanced corner rounding was turned on. The model does have some drawbacks, notably being relatively slow, and does not perfectly predict the regression. If corner rounding is turned off, however, the model does become much faster; although less accurate, this method does still predict a relatively accurate resulting burn geometry, and is fast enough to be used for performance-tuning or genetic algorithms. In addition to the modeling method, preliminary investigations into the burning behavior of fuel grains with a helical flow path were performed. The helix fuel grains have a regression rate of nearly 3 times that of any other fuel grain geometry, primarily due to the enhancement of the friction coefficient between the flow and flow path.

Geometry definition and grid generation for a complete fighter aircraft

NASA Technical Reports Server (NTRS)

Edwards, Thomas A.

1986-01-01

Recent advances in computing power and numerical solution procedures have enabled computational fluid dynamicists to attempt increasingly difficult problems. In particular, efforts are focusing on computations of complex three-dimensional flow fields about realistic aerodynamic bodies. To perform such computations, a very accurate and detailed description of the surface geometry must be provided, and a three-dimensional grid must be generated in the space around the body. The geometry must be supplied in a format compatible with the grid generation requirements, and must be verified to be free of inconsistencies. A procedure for performing the geometry definition of a fighter aircraft that makes use of a commercial computer-aided design/computer-aided manufacturing system is presented. Furthermore, visual representations of the geometry are generated using a computer graphics system for verification of the body definition. Finally, the three-dimensional grids for fighter-like aircraft are generated by means of an efficient new parabolic grid generation method. This method exhibits good control of grid quality.

Discovering Structural Regularity in 3D Geometry

PubMed Central

Pauly, Mark; Mitra, Niloy J.; Wallner, Johannes; Pottmann, Helmut; Guibas, Leonidas J.

2010-01-01

We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or mesh-based models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis. PMID:21170292

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

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

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.

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.

An ODE-Based Wall Model for Turbulent Flow Simulations

NASA Technical Reports Server (NTRS)

Berger, Marsha J.; Aftosmis, Michael J.

2017-01-01

Fully automated meshing for Reynolds-Averaged Navier-Stokes Simulations, Mesh generation for complex geometry continues to be the biggest bottleneck in the RANS simulation process; Fully automated Cartesian methods routinely used for inviscid simulations about arbitrarily complex geometry; These methods lack of an obvious & robust way to achieve near wall anisotropy; Goal: Extend these methods for RANS simulation without sacrificing automation, at an affordable cost; Note: Nothing here is limited to Cartesian methods, and much becomes simpler in a body-fitted setting.

A Methodology for the Derivation of Unloaded Abdominal Aortic Aneurysm Geometry With Experimental Validation

PubMed Central

Chandra, Santanu; Gnanaruban, Vimalatharmaiyah; Riveros, Fabian; Rodriguez, Jose F.; Finol, Ender A.

2016-01-01

In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140 mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 μm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5–8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment. PMID:27538124

Background-independent condensed matter models for quantum gravity

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Markopoulou, Fotini

2011-09-01

A number of recent proposals on a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such approach. At the conceptual level, there is a clash between the 'timelessness' of general relativity and emergence. Secondly, the lack of a fundamental spacetime renders difficult the straightforward application of well-known methods of statistical physics to the problem. We recently initiated a study of such problems using spin systems based on the evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. In this paper, we review two such models. The first model is a model of emergent (flat) space and matter, and we show how to use methods from quantum information theory to derive features such as the speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This model has primitive notions of gravitational attraction that we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.

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.

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.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code

NASA Astrophysics Data System (ADS)

Chacon, Luis

2006-10-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation. PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 (2^nd order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas, has been developed for resistive MHD, and is currently being extended to Hall MHD. In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries. L. Chac'on, Comput. Phys. Comm., 163 (3), 143-171 (2004) L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002); J. Comput. Phys., 188 (2), 573-592 (2003) L. Chac'on, 32nd EPS Conf. Plasma Physics, Tarragona, Spain, 2005 L. Chac'on et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006

Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfaces

PubMed Central

Wang, Chenglong; Xu, Fei; Hsu, Ming-Chen; Krishnamurthy, Adarsh

2017-01-01

Computational fluid dynamics (CFD) simulations of flow over complex objects have been performed traditionally using fluid-domain meshes that conform to the shape of the object. However, creating shape conforming meshes for complicated geometries like automobiles require extensive geometry preprocessing. This process is usually tedious and requires modifying the geometry, including specialized operations such as defeaturing and filling of small gaps. Hsu et al. (2016) developed a novel immersogeometric fluid-flow method that does not require the generation of a boundary-fitted mesh for the fluid domain. However, their method used the NURBS parameterization of the surfaces for generating the surface quadrature points to enforce the boundary conditions, which required the B-rep model to be converted completely to NURBS before analysis can be performed. This conversion usually leads to poorly parameterized NURBS surfaces and can lead to poorly trimmed or missing surface features. In addition, converting simple geometries such as cylinders to NURBS imposes a performance penalty since these geometries have to be dealt with as rational splines. As a result, the geometry has to be inspected again after conversion to ensure analysis compatibility and can increase the computational cost. In this work, we have extended the immersogeometric method to generate surface quadrature points directly using analytic surfaces. We have developed quadrature rules for all four kinds of analytic surfaces: planes, cones, spheres, and toroids. We have also developed methods for performing adaptive quadrature on trimmed analytic surfaces. Since analytic surfaces have frequently been used for constructing solid models, this method is also faster to generate quadrature points on real-world geometries than using only NURBS surfaces. To assess the accuracy of the proposed method, we perform simulations of a benchmark problem of flow over a torpedo shape made of analytic surfaces and compare those to immersogeometric simulations of the same model with NURBS surfaces. We also compare the results of our immersogeometric method with those obtained using boundary-fitted CFD of a tessellated torpedo shape, and quantities of interest such as drag coefficient are in good agreement. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of a truck that has a large percentage of analytic surfaces. Using analytic surfaces over NURBS avoids unnecessary surface type conversion and significantly reduces model-preprocessing time, while providing the same accuracy for the aerodynamic quantities of interest. PMID:29051678

Bootstrapping on Undirected Binary Networks Via Statistical Mechanics

NASA Astrophysics Data System (ADS)

Fushing, Hsieh; Chen, Chen; Liu, Shan-Yu; Koehl, Patrice

2014-09-01

We propose a new method inspired from statistical mechanics for extracting geometric information from undirected binary networks and generating random networks that conform to this geometry. In this method an undirected binary network is perceived as a thermodynamic system with a collection of permuted adjacency matrices as its states. The task of extracting information from the network is then reformulated as a discrete combinatorial optimization problem of searching for its ground state. To solve this problem, we apply multiple ensembles of temperature regulated Markov chains to establish an ultrametric geometry on the network. This geometry is equipped with a tree hierarchy that captures the multiscale community structure of the network. We translate this geometry into a Parisi adjacency matrix, which has a relative low energy level and is in the vicinity of the ground state. The Parisi adjacency matrix is then further optimized by making block permutations subject to the ultrametric geometry. The optimal matrix corresponds to the macrostate of the original network. An ensemble of random networks is then generated such that each of these networks conforms to this macrostate; the corresponding algorithm also provides an estimate of the size of this ensemble. By repeating this procedure at different scales of the ultrametric geometry of the network, it is possible to compute its evolution entropy, i.e. to estimate the evolution of its complexity as we move from a coarse to a fine description of its geometric structure. We demonstrate the performance of this method on simulated as well as real data networks.

A dissipative particle dynamics method for arbitrarily complex geometries

NASA Astrophysics Data System (ADS)

Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em

2018-02-01

Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor-corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid-solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier-Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry - the "Brown Pacman" microfluidic device - to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles, which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration. In addition to stationary arbitrary-shape objects, the new method is particularly useful for problems involving moving and deformable boundaries, because it only uses local information of neighboring particles and satisfies the desired boundary conditions on-the-fly.

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.

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

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

2013-05-01

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