Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap

NASA Astrophysics Data System (ADS)

Spiwok, Vojtěch; Králová, Blanka

2011-12-01

Atomic motions in molecules are not linear. This infers that nonlinear dimensionality reduction methods can outperform linear ones in analysis of collective atomic motions. In addition, nonlinear collective motions can be used as potentially efficient guides for biased simulation techniques. Here we present a simulation with a bias potential acting in the directions of collective motions determined by a nonlinear dimensionality reduction method. Ad hoc generated conformations of trans,trans-1,2,4-trifluorocyclooctane were analyzed by Isomap method to map these 72-dimensional coordinates to three dimensions, as described by Brown and co-workers [J. Chem. Phys. 129, 064118 (2008)]. Metadynamics employing the three-dimensional embeddings as collective variables was applied to explore all relevant conformations of the studied system and to calculate its conformational free energy surface. The method sampled all relevant conformations (boat, boat-chair, and crown) and corresponding transition structures inaccessible by an unbiased simulation. This scheme allows to use essentially any parameter of the system as a collective variable in biased simulations. Moreover, the scheme we used for mapping out-of-sample conformations from the 72D to 3D space can be used as a general purpose mapping for dimensionality reduction, beyond the context of molecular modeling.

Methodology issues concerning the accuracy of kinematic data collection and analysis using the ariel performance analysis system

NASA Technical Reports Server (NTRS)

Wilmington, R. P.; Klute, Glenn K. (Editor); Carroll, Amy E. (Editor); Stuart, Mark A. (Editor); Poliner, Jeff (Editor); Rajulu, Sudhakar (Editor); Stanush, Julie (Editor)

1992-01-01

Kinematics, the study of motion exclusive of the influences of mass and force, is one of the primary methods used for the analysis of human biomechanical systems as well as other types of mechanical systems. The Anthropometry and Biomechanics Laboratory (ABL) in the Crew Interface Analysis section of the Man-Systems Division performs both human body kinematics as well as mechanical system kinematics using the Ariel Performance Analysis System (APAS). The APAS supports both analysis of analog signals (e.g. force plate data collection) as well as digitization and analysis of video data. The current evaluations address several methodology issues concerning the accuracy of the kinematic data collection and analysis used in the ABL. This document describes a series of evaluations performed to gain quantitative data pertaining to position and constant angular velocity movements under several operating conditions. Two-dimensional as well as three-dimensional data collection and analyses were completed in a controlled laboratory environment using typical hardware setups. In addition, an evaluation was performed to evaluate the accuracy impact due to a single axis camera offset. Segment length and positional data exhibited errors within 3 percent when using three-dimensional analysis and yielded errors within 8 percent through two-dimensional analysis (Direct Linear Software). Peak angular velocities displayed errors within 6 percent through three-dimensional analyses and exhibited errors of 12 percent when using two-dimensional analysis (Direct Linear Software). The specific results from this series of evaluations and their impacts on the methodology issues of kinematic data collection and analyses are presented in detail. The accuracy levels observed in these evaluations are also presented.

Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

NASA Astrophysics Data System (ADS)

Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

2015-03-01

Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Direct Linear Transformation Method for Three-Dimensional Cinematography

ERIC Educational Resources Information Center

Shapiro, Robert

1978-01-01

The ability of Direct Linear Transformation Method for three-dimensional cinematography to locate points in space was shown to meet the accuracy requirements associated with research on human movement. (JD)

Quantitative analysis of eyes and other optical systems in linear optics.

PubMed

Harris, William F; Evans, Tanya; van Gool, Radboud D

2017-05-01

To show that 14-dimensional spaces of augmented point P and angle Q characteristics, matrices obtained from the ray transference, are suitable for quantitative analysis although only the latter define an inner-product space and only on it can one define distances and angles. The paper examines the nature of the spaces and their relationships to other spaces including symmetric dioptric power space. The paper makes use of linear optics, a three-dimensional generalization of Gaussian optics. Symmetric 2 × 2 dioptric power matrices F define a three-dimensional inner-product space which provides a sound basis for quantitative analysis (calculation of changes, arithmetic means, etc.) of refractive errors and thin systems. For general systems the optical character is defined by the dimensionally-heterogeneous 4 × 4 symplectic matrix S, the transference, or if explicit allowance is made for heterocentricity, the 5 × 5 augmented symplectic matrix T. Ordinary quantitative analysis cannot be performed on them because matrices of neither of these types constitute vector spaces. Suitable transformations have been proposed but because the transforms are dimensionally heterogeneous the spaces are not naturally inner-product spaces. The paper obtains 14-dimensional spaces of augmented point P and angle Q characteristics. The 14-dimensional space defined by the augmented angle characteristics Q is dimensionally homogenous and an inner-product space. A 10-dimensional subspace of the space of augmented point characteristics P is also an inner-product space. The spaces are suitable for quantitative analysis of the optical character of eyes and many other systems. Distances and angles can be defined in the inner-product spaces. The optical systems may have multiple separated astigmatic and decentred refracting elements. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.

An efficient closed-form solution for acoustic emission source location in three-dimensional structures

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

Li, Xibing; Dong, Longjun, E-mail: csudlj@163.com; Australian Centre for Geomechanics, The University of Western Australia, Crawley, 6009

This paper presents an efficient closed-form solution (ECS) for acoustic emission(AE) source location in three-dimensional structures using time difference of arrival (TDOA) measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.

A low-cost and portable realization on fringe projection three-dimensional measurement

NASA Astrophysics Data System (ADS)

Xiao, Suzhi; Tao, Wei; Zhao, Hui

2015-12-01

Fringe projection three-dimensional measurement is widely applied in a wide range of industrial application. The traditional fringe projection system has the disadvantages of high expense, big size, and complicated calibration requirements. In this paper we introduce a low-cost and portable realization on three-dimensional measurement with Pico projector. It has the advantages of low cost, compact physical size, and flexible configuration. For the proposed fringe projection system, there is no restriction to camera and projector's relative alignment on parallelism and perpendicularity for installation. Moreover, plane-based calibration method is adopted in this paper that avoids critical requirements on calibration system such as additional gauge block or precise linear z stage. What is more, error sources existing in the proposed system are introduced in this paper. The experimental results demonstrate the feasibility of the proposed low cost and portable fringe projection system.

A new method to acquire 3-D images of a dental cast

NASA Astrophysics Data System (ADS)

Li, Zhongke; Yi, Yaxing; Zhu, Zhen; Li, Hua; Qin, Yongyuan

2006-01-01

This paper introduced our newly developed method to acquire three-dimensional images of a dental cast. A rotatable table, a laser-knife, a mirror, a CCD camera and a personal computer made up of a three-dimensional data acquiring system. A dental cast is placed on the table; the mirror is installed beside the table; a linear laser is projected to the dental cast; the CCD camera is put up above the dental cast, it can take picture of the dental cast and the shadow in the mirror; while the table rotating, the camera records the shape of the laser streak projected on the dental cast, and transmit the data to the computer. After the table rotated one circuit, the computer processes the data, calculates the three-dimensional coordinates of the dental cast's surface. In data processing procedure, artificial neural networks are enrolled to calibrate the lens distortion, map coordinates form screen coordinate system to world coordinate system. According to the three-dimensional coordinates, the computer reconstructs the stereo image of the dental cast. It is essential for computer-aided diagnosis and treatment planning in orthodontics. In comparison with other systems in service, for example, laser beam three-dimensional scanning system, the characteristic of this three-dimensional data acquiring system: a. celerity, it casts only 1 minute to scan a dental cast; b. compact, the machinery is simple and compact; c. no blind zone, a mirror is introduced ably to reduce blind zone.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

NASA Astrophysics Data System (ADS)

Ouannas, Adel; Grassi, Giuseppe

2016-09-01

A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Hénon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Hénon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).

System and method to create three-dimensional images of non-linear acoustic properties in a region remote from a borehole

DOEpatents

Vu, Cung; Nihei, Kurt T.; Schmitt, Denis P.; Skelt, Christopher; Johnson, Paul A.; Guyer, Robert; TenCate, James A.; Le Bas, Pierre-Yves

2013-01-01

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

NASA Ames potential flow analysis (POTFAN) geometry program (POTGEM), version 1

NASA Technical Reports Server (NTRS)

Medan, R. T.; Bullock, R. B.

1976-01-01

A computer program known as POTGEM is reported which has been developed as an independent segment of a three-dimensional linearized, potential flow analysis system and which is used to generate a panel point description of arbitrary, three-dimensional bodies from convenient engineering descriptions consisting of equations and/or tables. Due to the independent, modular nature of the program, it may be used to generate corner points for other computer programs.

Three-dimensional passive sensing photon counting for object classification

NASA Astrophysics Data System (ADS)

Yeom, Seokwon; Javidi, Bahram; Watson, Edward

2007-04-01

In this keynote address, we address three-dimensional (3D) distortion-tolerant object recognition using photon-counting integral imaging (II). A photon-counting linear discriminant analysis (LDA) is discussed for classification of photon-limited images. We develop a compact distortion-tolerant recognition system based on the multiple-perspective imaging of II. Experimental and simulation results have shown that a low level of photons is sufficient to classify out-of-plane rotated objects.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap.

PubMed

Spiwok, Vojtěch; Králová, Blanka

2011-12-14

Atomic motions in molecules are not linear. This infers that nonlinear dimensionality reduction methods can outperform linear ones in analysis of collective atomic motions. In addition, nonlinear collective motions can be used as potentially efficient guides for biased simulation techniques. Here we present a simulation with a bias potential acting in the directions of collective motions determined by a nonlinear dimensionality reduction method. Ad hoc generated conformations of trans,trans-1,2,4-trifluorocyclooctane were analyzed by Isomap method to map these 72-dimensional coordinates to three dimensions, as described by Brown and co-workers [J. Chem. Phys. 129, 064118 (2008)]. Metadynamics employing the three-dimensional embeddings as collective variables was applied to explore all relevant conformations of the studied system and to calculate its conformational free energy surface. The method sampled all relevant conformations (boat, boat-chair, and crown) and corresponding transition structures inaccessible by an unbiased simulation. This scheme allows to use essentially any parameter of the system as a collective variable in biased simulations. Moreover, the scheme we used for mapping out-of-sample conformations from the 72D to 3D space can be used as a general purpose mapping for dimensionality reduction, beyond the context of molecular modeling. © 2011 American Institute of Physics

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three-dimensional radar imaging techniques and systems for near-field applications

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

Sheen, David M.; Hall, Thomas E.; McMakin, Douglas L.

2016-05-12

The Pacific Northwest National Laboratory has developed three-dimensional holographic (synthetic aperture) radar imaging techniques and systems for a wide variety of near-field applications. These applications include radar cross-section (RCS) imaging, personnel screening, standoff concealed weapon detection, concealed threat detection, through-barrier imaging, ground penetrating radar (GPR), and non-destructive evaluation (NDE). Sequentially-switched linear arrays are used for many of these systems to enable high-speed data acquisition and 3-D imaging. In this paper, the techniques and systems will be described along with imaging results that demonstrate the utility of near-field 3-D radar imaging for these compelling applications.

A new three-dimensional nonscanning laser imaging system based on the illumination pattern of a point-light-source array

NASA Astrophysics Data System (ADS)

Xia, Wenze; Ma, Yayun; Han, Shaokun; Wang, Yulin; Liu, Fei; Zhai, Yu

2018-06-01

One of the most important goals of research on three-dimensional nonscanning laser imaging systems is the improvement of the illumination system. In this paper, a new three-dimensional nonscanning laser imaging system based on the illumination pattern of a point-light-source array is proposed. This array is obtained using a fiber array connected to a laser array with each unit laser having independent control circuits. This system uses a point-to-point imaging process, which is realized using the exact corresponding optical relationship between the point-light-source array and a linear-mode avalanche photodiode array detector. The complete working process of this system is explained in detail, and the mathematical model of this system containing four equations is established. A simulated contrast experiment and two real contrast experiments which use the simplified setup without a laser array are performed. The final results demonstrate that unlike a conventional three-dimensional nonscanning laser imaging system, the proposed system meets all the requirements of an eligible illumination system. Finally, the imaging performance of this system is analyzed under defocusing situations, and analytical results show that the system has good defocusing robustness and can be easily adjusted in real applications.

[Correlation between gaseous exchange rate, body temperature, and mitochondrial protein content in the liver of mice].

PubMed

Muradian, Kh K; Utko, N O; Mozzhukhina, T H; Pishel', I M; Litoshenko, O Ia; Bezrukov, V V; Fraĭfel'd, V E

2002-01-01

Correlative and regressive relations between the gaseous exchange, thermoregulation and mitochondrial protein content were analyzed by two- and three-dimensional statistics in mice. It has been shown that the pair wise linear methods of analysis did not reveal any significant correlation between the parameters under exploration. However, it became evident at three-dimensional and non-linear plotting for which the coefficients of multivariable correlation reached and even exceeded 0.7-0.8. The calculations based on partial differentiation of the multivariable regression equations allow to conclude that at certain values of VO2, VCO2 and body temperature negative relations between the systems of gaseous exchange and thermoregulation become dominating.

Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action.

PubMed

Marvel, Seth A; Mirollo, Renato E; Strogatz, Steven H

2009-12-01

Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems by proving that the governing equations are generated by the action of the Mobius group, a three-parameter subgroup of fractional linear transformations that map the unit disk to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into three-dimensional invariant manifolds (the group orbits). The N-3 constants of motion associated with this foliation are the N-3 functionally independent cross ratios of the oscillator phases. No further reduction is possible, in general; numerical experiments on models of Josephson junction arrays suggest that the invariant manifolds often contain three-dimensional regions of neutrally stable chaos.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Storm Observations of Persistent Three-Dimensional Shoreline Morphology and Bathymetry Along a Geologically Influenced Shoreface Using X-Band Radar (BASIR)

NASA Astrophysics Data System (ADS)

Brodie, K. L.; McNinch, J. E.

2008-12-01

Accurate predictions of shoreline response to storms are contingent upon coastal-morphodynamic models effectively synthesizing the complex evolving relationships between beach topography, sandbar morphology, nearshore bathymetry, underlying geology, and the nearshore wave-field during storm events. Analysis of "pre" and "post" storm data sets have led to a common theory for event response of the nearshore system: pre-storm three-dimensional bar and shoreline configurations shift to two-dimensional, linear forms post- storm. A lack of data during storms has unfortunately left a gap in our knowledge of how the system explicitly changes during the storm event. This work presents daily observations of the beach and nearshore during high-energy storm events over a spatially extensive field site (order of magnitude: 10 km) using Bar and Swash Imaging Radar (BASIR), a mobile x-band radar system. The field site contains a complexity of features including shore-oblique bars and troughs, heterogeneous sediment, and an erosional hotspot. BASIR data provide observations of the evolution of shoreline and bar morphology, as well as nearshore bathymetry, throughout the storm events. Nearshore bathymetry is calculated using a bathymetry inversion from radar- derived wave celerity measurements. Preliminary results show a relatively stable but non-linear shore-parallel bar and a non-linear shoreline with megacusp and embayment features (order of magnitude: 1 km) that are enhanced during the wave events. Both the shoreline and shore-parallel bar undulate at a similar spatial frequency to the nearshore shore- oblique bar-field. Large-scale shore-oblique bars and troughs remain relatively static in position and morphology throughout the storm events. The persistence of a three-dimensional shoreline, shore-parallel bar, and large-scale shore-oblique bars and troughs, contradicts the idea of event-driven shifts to two- dimensional morphology and suggests that beach and nearshore response to storms may be location specific. We hypothesize that the influence of underlying geology, defined by (1) the introduction of heterogeneous sediment and (2) the possible creation of shore-oblique bars and troughs in the nearshore, may be responsible for the persistence of three-dimensional forms and the associated shoreline hotspots during storm events.

Layout optimization using the homogenization method

NASA Technical Reports Server (NTRS)

Suzuki, Katsuyuki; Kikuchi, Noboru

1993-01-01

A generalized layout problem involving sizing, shape, and topology optimization is solved by using the homogenization method for three-dimensional linearly elastic shell structures in order to seek a possibility of establishment of an integrated design system of automotive car bodies, as an extension of the previous work by Bendsoe and Kikuchi. A formulation of a three-dimensional homogenized shell, a solution algorithm, and several examples of computing the optimum layout are presented in this first part of the two articles.

Linear instability in the wake of an elliptic wing

NASA Astrophysics Data System (ADS)

He, Wei; Tendero, Juan Ángel; Paredes, Pedro; Theofilis, Vassilis

2017-12-01

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of Rec=1750 and two angles of attack, {AoA}=0° and 5°. Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.

Three-Dimensional Non-Fermi-Liquid Behavior from One-Dimensional Quantum Critical Local Moments

DOE PAGES

Classen, Laura; Zaliznyak, Igor; Tsvelik, Alexei M.

2018-04-10

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb 2Pt 2Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S = 1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the twomore » interacting subsystems. Lastly, we characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.« less

Three-Dimensional Non-Fermi-Liquid Behavior from One-Dimensional Quantum Critical Local Moments

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

Classen, Laura; Zaliznyak, Igor; Tsvelik, Alexei M.

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb 2Pt 2Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S = 1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the twomore » interacting subsystems. Lastly, we characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.« less

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Three dimensional tracking with misalignment between display and control axes

NASA Technical Reports Server (NTRS)

Ellis, Stephen R.; Tyler, Mitchell; Kim, Won S.; Stark, Lawrence

1992-01-01

Human operators confronted with misaligned display and control frames of reference performed three dimensional, pursuit tracking in virtual environment and virtual space simulations. Analysis of the components of the tracking errors in the perspective displays presenting virtual space showed that components of the error due to visual motor misalignment may be linearly separated from those associated with the mismatch between display and control coordinate systems. Tracking performance improved with several hours practice despite previous reports that such improvement did not take place.

3-d finite element model development for biomechanics: a software demonstration

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

Hollerbach, K.; Hollister, A.M.; Ashby, E.

1997-03-01

Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models,more » using human hand and knee examples, and will demonstrate their software tools.« less

Design of three-dimensional nonimaging concentrators with inhomogeneous media

NASA Astrophysics Data System (ADS)

Minano, J. C.

1986-09-01

A three-dimensional nonimaging concentrator is an optical system that transforms a given four-parametric manifold of rays reaching a surface (entry aperture) into another four-parametric manifold of rays reaching the receiver. A procedure of design of such concentrators is developed. In general, the concentrators use mirrors and inhomogeneous media (i.e., gradient-index media). The concentrator has the maximum concentration allowed by the theorem of conservation of phase-space volume. This is the first known concentrator with such properties. The Welford-Winston edge-ray principle in three-dimensional geometry is proven under several assumptions. The linear compound parabolic concentrator is derived as a particular case of the procedure of design.

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

Three-dimensional head anthropometric analysis

NASA Astrophysics Data System (ADS)

Enciso, Reyes; Shaw, Alex M.; Neumann, Ulrich; Mah, James

2003-05-01

Currently, two-dimensional photographs are most commonly used to facilitate visualization, assessment and treatment of facial abnormalities in craniofacial care but are subject to errors because of perspective, projection, lack metric and 3-dimensional information. One can find in the literature a variety of methods to generate 3-dimensional facial images such as laser scans, stereo-photogrammetry, infrared imaging and even CT however each of these methods contain inherent limitations and as such no systems are in common clinical use. In this paper we will focus on development of indirect 3-dimensional landmark location and measurement of facial soft-tissue with light-based techniques. In this paper we will statistically evaluate and validate a current three-dimensional image-based face modeling technique using a plaster head model. We will also develop computer graphics tools for indirect anthropometric measurements in a three-dimensional head model (or polygonal mesh) including linear distances currently used in anthropometry. The measurements will be tested against a validated 3-dimensional digitizer (MicroScribe 3DX).

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

GPU implementation of the linear scaling three dimensional fragment method for large scale electronic structure calculations

NASA Astrophysics Data System (ADS)

Jia, Weile; Wang, Jue; Chi, Xuebin; Wang, Lin-Wang

2017-02-01

LS3DF, namely linear scaling three-dimensional fragment method, is an efficient linear scaling ab initio total energy electronic structure calculation code based on a divide-and-conquer strategy. In this paper, we present our GPU implementation of the LS3DF code. Our test results show that the GPU code can calculate systems with about ten thousand atoms fully self-consistently in the order of 10 min using thousands of computing nodes. This makes the electronic structure calculations of 10,000-atom nanosystems routine work. This speed is 4.5-6 times faster than the CPU calculations using the same number of nodes on the Titan machine in the Oak Ridge leadership computing facility (OLCF). Such speedup is achieved by (a) carefully re-designing of the computationally heavy kernels; (b) redesign of the communication pattern for heterogeneous supercomputers.

An Energy Model of Place Cell Network in Three Dimensional Space.

PubMed

Wang, Yihong; Xu, Xuying; Wang, Rubin

2018-01-01

Place cells are important elements in the spatial representation system of the brain. A considerable amount of experimental data and classical models are achieved in this area. However, an important question has not been addressed, which is how the three dimensional space is represented by the place cells. This question is preliminarily surveyed by energy coding method in this research. Energy coding method argues that neural information can be expressed by neural energy and it is convenient to model and compute for neural systems due to the global and linearly addable properties of neural energy. Nevertheless, the models of functional neural networks based on energy coding method have not been established. In this work, we construct a place cell network model to represent three dimensional space on an energy level. Then we define the place field and place field center and test the locating performance in three dimensional space. The results imply that the model successfully simulates the basic properties of place cells. The individual place cell obtains unique spatial selectivity. The place fields in three dimensional space vary in size and energy consumption. Furthermore, the locating error is limited to a certain level and the simulated place field agrees to the experimental results. In conclusion, this is an effective model to represent three dimensional space by energy method. The research verifies the energy efficiency principle of the brain during the neural coding for three dimensional spatial information. It is the first step to complete the three dimensional spatial representing system of the brain, and helps us further understand how the energy efficiency principle directs the locating, navigating, and path planning function of the brain.

Using the application visualization system to view HALOE three-dimensional satellite data

NASA Technical Reports Server (NTRS)

Luo, Mingzhao; Schiano, Allen V. R.; Russell, James M., III; Gordley, Larry L.; Stone, Kenneth A.; Cicerone, Ralph J.

1995-01-01

The Application Visualization System (AVS) is used to view a three-dimensional data field containing the volume mixing ratios of a chemical species in the middle atmosphere obtained by the Halogen Occultation Experiment (HALOE) aboard the Upper Atmosphere Research Satellite (UARS). Since launch in September 1991, HALOE has been collecting data on approximately 30 sunrise/sunset events in two narrow latitude bands each day. The vertical volume mixing ratio profiles are retrieved for eight species for each event. The accumulated data for approximately 30 days cover most of the globe (limited by sunlit latitudes), and this monthly data block can be described as the volume mixing ratio of a specific species in the atmosphere as a function of latitude, longitude, and height. The data were remapped using linear interpolation for pressure levels and Gaussian weighted binning from sampling locations to a three-dimensional grid. An AVS network is constructed that allows for viewing the three-dimensional field with rendered slices at constant latitudes, longitudes or pressure levels. Discussions are given on the advantages and some disadvantages learned about from experiences applying AVS to visualize HALOE three dimensional data.

Equivalence between a generalized dendritic network and a set of one-dimensional networks as a ground of linear dynamics.

PubMed

Koda, Shin-ichi

2015-05-28

It has been shown by some existing studies that some linear dynamical systems defined on a dendritic network are equivalent to those defined on a set of one-dimensional networks in special cases and this transformation to the simple picture, which we call linear chain (LC) decomposition, has a significant advantage in understanding properties of dendrimers. In this paper, we expand the class of LC decomposable system with some generalizations. In addition, we propose two general sufficient conditions for LC decomposability with a procedure to systematically realize the LC decomposition. Some examples of LC decomposable linear dynamical systems are also presented with their graphs. The generalization of the LC decomposition is implemented in the following three aspects: (i) the type of linear operators; (ii) the shape of dendritic networks on which linear operators are defined; and (iii) the type of symmetry operations representing the symmetry of the systems. In the generalization (iii), symmetry groups that represent the symmetry of dendritic systems are defined. The LC decomposition is realized by changing the basis of a linear operator defined on a dendritic network into bases of irreducible representations of the symmetry group. The achievement of this paper makes it easier to utilize the LC decomposition in various cases. This may lead to a further understanding of the relation between structure and functions of dendrimers in future studies.

Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Fedorov, A. V.

2017-08-01

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar-turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier-Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton-Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar-turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar-turbulent transition.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

On a model of three-dimensional bursting and its parallel implementation

NASA Astrophysics Data System (ADS)

Tabik, S.; Romero, L. F.; Garzón, E. M.; Ramos, J. I.

2008-04-01

A mathematical model for the simulation of three-dimensional bursting phenomena and its parallel implementation are presented. The model consists of four nonlinearly coupled partial differential equations that include fast and slow variables, and exhibits bursting in the absence of diffusion. The differential equations have been discretized by means of a second-order accurate in both space and time, linearly-implicit finite difference method in equally-spaced grids. The resulting system of linear algebraic equations at each time level has been solved by means of the Preconditioned Conjugate Gradient (PCG) method. Three different parallel implementations of the proposed mathematical model have been developed; two of these implementations, i.e., the MPI and the PETSc codes, are based on a message passing paradigm, while the third one, i.e., the OpenMP code, is based on a shared space address paradigm. These three implementations are evaluated on two current high performance parallel architectures, i.e., a dual-processor cluster and a Shared Distributed Memory (SDM) system. A novel representation of the results that emphasizes the most relevant factors that affect the performance of the paralled implementations, is proposed. The comparative analysis of the computational results shows that the MPI and the OpenMP implementations are about twice more efficient than the PETSc code on the SDM system. It is also shown that, for the conditions reported here, the nonlinear dynamics of the three-dimensional bursting phenomena exhibits three stages characterized by asynchronous, synchronous and then asynchronous oscillations, before a quiescent state is reached. It is also shown that the fast system reaches steady state in much less time than the slow variables.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

Offset-electrode profile acquisition strategy for electrical resistivity tomography

NASA Astrophysics Data System (ADS)

Robbins, Austin R.; Plattner, Alain

2018-04-01

We present an electrode layout strategy that allows electrical resistivity profiles to image the third dimension close to the profile plane. This "offset-electrode profile" approach involves laterally displacing electrodes away from the profile line in an alternating fashion and then inverting the resulting data using three-dimensional electrical resistivity tomography software. In our synthetic and field surveys, the offset-electrode method succeeds in revealing three-dimensional structures in the vicinity of the profile plane, which we could not achieve using three-dimensional inversions of linear profiles. We confirm and explain the limits of linear electrode profiles through a discussion of the three-dimensional sensitivity patterns: For a homogeneous starting model together with a linear electrode layout, all sensitivities remain symmetric with respect to the profile plane through each inversion step. This limitation can be overcome with offset-electrode layouts by breaking the symmetry pattern among the sensitivities. Thanks to freely available powerful three-dimensional resistivity tomography software and cheap modern computing power, the requirement for full three-dimensional calculations does not create a significant burden and renders the offset-electrode approach a cost-effective method. By offsetting the electrodes in an alternating pattern, as opposed to laying the profile out in a U-shape, we minimize shortening the profile length.

Polarization-dependent plasmonic photocurrents in two-dimensional electron systems

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

Popov, V. V., E-mail: popov-slava@yahoo.co.uk; Saratov State University, Saratov 410012; Saratov Scientific Center of the Russian Academy of Sciences, Saratov 410028

2016-06-27

Plasmonic polarization dependent photocurrents in a homogeneous two-dimensional electron system are studied. Those effects are completely different from the photon drag and electronic photogalvanic effects as well as from the plasmonic ratchet effect in a density modulated two-dimensional electron system. Linear and helicity-dependent contributions to the photocurrent are found. The linear contribution can be interpreted as caused by the longitudinal and transverse plasmon drag effect. The helicity-dependent contribution originates from the non-linear electron convection and changes its sign with reversing the plasmonic field helicity. It is shown that the helicity-dependent component of the photocurrent can exceed the linear one bymore » several orders of magnitude in high-mobility two-dimensional electron systems. The results open possibilities for all-electronic detection of the radiation polarization states by exciting the plasmonic photocurrents in two-dimensional electron systems.« less

Effect of Prestresses on the Dispersion of Quasi-Lamb Waves in the System Consisting of an Ideal Liquid Layer and a Compressible Elastic Layer

NASA Astrophysics Data System (ADS)

Bagno, A. M.

2017-03-01

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer interacting with a layer of an ideal compressible fluid is studied. The three-dimensional equations of linearized elasticity and the assumption of finite strains for the elastic layer and the three-dimensional linearized Euler equations for the fluid are used. The dispersion curves for the quasi-Lamb modes are plotted over a wide frequency range. The effect of prestresses and the thickness of the elastic and liquid layers on the frequency spectrum of normal quasi-Lamb waves is analyzed. The localization properties of the lower quasi-Lamb modes in the elastic-fluid waveguides are studied. The numerical results are presented in the form of graphs and analyzed

Microwave imaging by three-dimensional Born linearization of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Caorsi, S.; Gragnani, G. L.; Pastorino, M.

1990-11-01

An approach to microwave imaging is proposed that uses a three-dimensional vectorial form of the Born approximation to linearize the equation of electromagnetic scattering. The inverse scattering problem is numerically solved for three-dimensional geometries by means of the moment method. A pseudoinversion algorithm is adopted to overcome ill conditioning. Results show that the method is well suited for qualitative imaging purposes, while its capability for exactly reconstructing the complex dielectric permittivity is affected by the limitations inherent in the Born approximation and in ill conditioning.

Linear optical response of carbon nanotubes under axial magnetic field

NASA Astrophysics Data System (ADS)

Moradian, Rostam; Chegel, Raad; Behzad, Somayeh

2010-04-01

We considered single walled carbon naotubes (SWCNTs) as real three dimensional (3D) systems in a cylindrical coordinate. The optical matrix elements and linear susceptibility, χ(ω), in the tight binding approximation in terms of one-dimensional wave vector, kz and subband index, l are calculated. In an external axial magnetic field optical frequency dependence of linear susceptibility are investigated. We found that axial magnetic field has two effects on the imaginary part of the linear susceptibility spectrum, in agreement with experimental results. The first effect is broadening and the second, splitting. Also we found that for all metallic zigzag and armchair SWCNTs, the axial magnetic field leads to the creation of a peak with energy less than 1.5 eV, contrary to what is observed in the absence of a magnetic field.

Linear stability theory and three-dimensional boundary layer transition

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Malik, Mujeeb R.

1992-01-01

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

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

NASA Technical Reports Server (NTRS)

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

1997-01-01

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

Fractal Dimensionality of Pore and Grain Volume of a Siliciclastic Marine Sand

NASA Astrophysics Data System (ADS)

Reed, A. H.; Pandey, R. B.; Lavoie, D. L.

Three-dimensional (3D) spatial distributions of pore and grain volumes were determined from high-resolution computer tomography (CT) images of resin-impregnated marine sands. Using a linear gradient extrapolation method, cubic three-dimensional samples were constructed from two-dimensional CT images. Image porosity (0.37) was found to be consistent with the estimate of porosity by water weight loss technique (0.36). Scaling of the pore volume (Vp) with the linear size (L), V~LD provides the fractal dimensionalities of the pore volume (D=2.74+/-0.02) and grain volume (D=2.90+/-0.02) typical for sedimentary materials.

Three-dimensional accuracy of plastic transfer impression copings for three implant systems.

PubMed

Teo, Juin Wei; Tan, Keson B; Nicholls, Jack I; Wong, Keng Mun; Uy, Joanne

2014-01-01

The purpose of this study was to compare the three-dimensional accuracy of indirect plastic impression copings and direct implant-level impression copings from three implant systems (Nobel Biocare [NB], Biomet 3i [3i], and Straumann [STR]) at three interimplant buccolingual angulations (0, 8, and 15 degrees). Two-implant master models were used to simulate a three-unit implant fixed partial denture. Test models were made from Impregum impressions using direct implant-level impression copings (DR). Abutments were then connected to the master models for impressions using the plastic impression copings (INDR) at three different angulations for a total of 18 test groups (n = 5 in each group). A coordinate measuring machine was used to measure linear distortions, three-dimensional (3D) distortions, angular distortions, and absolute angular distortions between the master and test models. Three-way analysis of variance showed that the implant system had a significant effect on 3D distortions and absolute angular distortions in the x- and y-axes. Interimplant angulation had a significant effect on 3D distortions and absolute angular distortions in the y-axis. Impression technique had a significant effect on absolute angular distortions in the y-axis. With DR, the NB and 3i systems were not significantly different. With INDR, 3i appeared to have less distortion than the other systems. Interimplant angulations did not significantly affect the accuracy of NBDR, 3iINDR, and STRINDR. The accuracy of INDR and DR was comparable at all interimplant angulations for 3i and STR. For NB, INDR was comparable to DR at 0 and 8 degrees but was less accurate at 15 degrees. Three-dimensional accuracy of implant impressions varied with implant system, interimplant angulation, and impression technique.

Development of a Linearized Unsteady Euler Analysis with Application to Wake/Blade-Row Interactions

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Chuang, H. Andrew

1999-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide a comprehensive and efficient unsteady aerodynamic analysis for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. The mathematical models needed to describe nonlinear and linearized, inviscid, unsteady flows through a blade row operating within a cylindrical annular duct are presented in this report. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to far-field eigen analyses, is also described. The linearized aerodynamic and numerical models have been implemented into the three-dimensional unsteady flow code, LINFLUX. This code is applied herein to predict unsteady subsonic flows driven by wake or vortical excitations. The intent is to validate the LINFLUX analysis via numerical results for simple benchmark unsteady flows and to demonstrate this analysis via application to a realistic wake/blade-row interaction. Detailed numerical results for a three-dimensional version of the 10th Standard Cascade and a fan exit guide vane indicate that LINFLUX is becoming a reliable and useful unsteady aerodynamic prediction capability that can be applied, in the future, to assess the three-dimensional flow physics important to blade-row, aeroacoustic and aeroelastic responses.

Three-dimensional finite element analysis of a newly designed onplant miniplate anchorage system.

PubMed

Liu, Lin; Qu, Yin-Ying; Jiang, Li-Jun; Zhou, Qian; Tang, Tian-Qi

2016-06-01

The purpose of this research was to evaluate the structural stress and deformation of a newly designed onplant miniplate anchorage system compared to a standard anchorage system. A bone block integrated with a novel miniplate and fixation screw system was simulated in a three-dimensional model and subjected to force at different directions. The stress distribution and deformation of the miniplate system and cortical bone were evaluated using the three-dimensional finite element method. The results showed that the stress on the plate system and bone was linearly proportional to the force magnitude and was higher when the force was in a vertical direction (Y-axis). Stress and deformation values of the two screws (screw 1 and 2) were asymmetric when the force was added along Y-axis and was greater in screw 1. The highest deformation value of the screws was 7.5148 μm, much smaller than the limit value. The load was decreased for each single miniscrew, and the ability of the new anchorage system to bear the load was also enhanced to some degree. It was suggested that the newly designed onplant miniplate anchorage system is effective, easily implanted and minimally invasive.

Investigation of the Nicole model

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

Adam, C.; Sanchez-Guillen, J.; Vazquez, R.A.

2006-05-15

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP{sup 1} Lagrangian density to the non-integer power (3/2) - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behavior to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemimore » model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.« less

Optical conductivity of three and two dimensional topological nodal-line semimetals

NASA Astrophysics Data System (ADS)

Barati, Shahin; Abedinpour, Saeed H.

2017-10-01

The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.

Linearized compressible-flow theory for sonic flight speeds

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard; Spreiter, John R

1950-01-01

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)

Decentralization, stabilization, and estimation of large-scale linear systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Vukcevic, M. B.

1976-01-01

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level. A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1996-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic response characteristics of axial-flow turbomachinery blading. The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. In addition, a numerical model for linearized inviscid unsteady flow, which is based upon an existing nonlinear, implicit, wave-split, finite volume analysis, is described. These aerodynamic and numerical models have been implemented into an unsteady flow code, called LINFLUX. A preliminary version of the LINFLUX code is applied herein to selected, benchmark three-dimensional, subsonic, unsteady flows, to illustrate its current capabilities and to uncover existing problems and deficiencies. The numerical results indicate that good progress has been made toward developing a reliable and useful three-dimensional prediction capability. However, some problems, associated with the implementation of an unsteady displacement field and numerical errors near solid boundaries, still exist. Also, accurate far-field conditions must be incorporated into the FINFLUX analysis, so that this analysis can be applied to unsteady flows driven be external aerodynamic excitations.

One dimensional wavefront distortion sensor comprising a lens array system

DOEpatents

Neal, Daniel R.; Michie, Robert B.

1996-01-01

A 1-dimensional sensor for measuring wavefront distortion of a light beam as a function of time and spatial position includes a lens system which incorporates a linear array of lenses, and a detector system which incorporates a linear array of light detectors positioned from the lens system so that light passing through any of the lenses is focused on at least one of the light detectors. The 1-dimensional sensor determines the slope of the wavefront by location of the detectors illuminated by the light. The 1 dimensional sensor has much greater bandwidth that 2 dimensional systems.

One dimensional wavefront distortion sensor comprising a lens array system

DOEpatents

Neal, D.R.; Michie, R.B.

1996-02-20

A 1-dimensional sensor for measuring wavefront distortion of a light beam as a function of time and spatial position includes a lens system which incorporates a linear array of lenses, and a detector system which incorporates a linear array of light detectors positioned from the lens system so that light passing through any of the lenses is focused on at least one of the light detectors. The 1-dimensional sensor determines the slope of the wavefront by location of the detectors illuminated by the light. The 1 dimensional sensor has much greater bandwidth that 2 dimensional systems. 8 figs.

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

NASA Technical Reports Server (NTRS)

Lin, Ray-Sing; Reed, Helen L.

1993-01-01

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Theory of bimolecular reactions in a solution with linear traps: Application to the problem of target search on DNA.

PubMed

Turkin, Alexander; van Oijen, Antoine M; Turkin, Anatoliy A

2015-01-01

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

NASA Technical Reports Server (NTRS)

Tessler, A.; Annett, M. S.; Gendron, G.

2001-01-01

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Compilation of Abstracts of Theses Submitted by Candidates for Degrees: October 1988 to September 1989

DTIC Science & Technology

1989-09-30

to accommodate peripherally non -uniform flow modelling free of experimental uncertainties. It was effects (blockage) in the throughflow code...combines that experimental control functions with a detail in this thesis, and the results of a computer menu-driven, diagnostic subsystem to ensure...equations and design a complete (DSL) for both linear and non -linear models and automatic control system for the three dimensional compared. Cross

NASTRAN computer system level 12.1

NASA Technical Reports Server (NTRS)

Butler, T. G.

1971-01-01

Program uses finite element displacement method for solving linear response of large, three-dimensional structures subject to static, dynamic, thermal, and random loadings. Program adapts to computers of different manufacture, permits up-dating and extention, allows interchange of output and input information between users, and is extensively documented.

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

NASA Astrophysics Data System (ADS)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

Tricuspid Annular Geometry: A Three-Dimensional Transesophageal Echocardiographic Study

PubMed Central

Mahmood, Feroze; Kim, Han; Chaudary, Bilal; Bergman, Remco; Matyal, Robina; Gerstle, Jeniffer; Gorman, Joseph H.; Gorman, Robert C.; Khabbaz, Kamal R.

2013-01-01

Objective To demonstrate the clinical feasibility of accurately measuring tricuspid annular area by 3-dimensional (3D) transesophageal echocardiography (TEE) and to assess the geometric differences based on the presence of tricuspid regurgitation (TR). Also, the shape of the tricuspid annulus was compared with previous descriptions in the literature. Design Prospective. Setting Tertiary care university hospital. Interventions Three-dimensional TEE. Participants Patients undergoing cardiac surgery. Measurements and Main Results Volumetric data sets from 20 patients were acquired by 3D TEE and prospectively analyzed. Comparisons in annular geometry were made between groups based on the presence of TR. The QLab (Philips Medical Systems, Andover, MA) software package was used to calculate tricuspid annular area by both linear elliptical dimensions and planimetry. Further analyses were performed in the 4D Cardio-View (TomTec Corporation GmBH, Munich, Germany) and MATLAB (Natick, MA) software environments to accurately assess annular shape. It was found that patients with greater TR had an eccentrically dilated annulus with a larger annular area. Also, the area as measured by the linear ellipse method was overestimated as compared to the planimetry method. Furthermore, the irregular saddle-shaped geometry of the tricuspid annulus was confirmed through the mathematic model developed by the authors. Conclusions Three-dimensional TEE can be used to measure the tricuspid annular area in a clinically feasible fashion, with an eccentric dilation seen in patients with TR. The tricuspid annulus shape is complex, with annular high and low points, and annular area calculation based on linear measurements significantly overestimates 3D planimetered area. PMID:23725682

Migdal's theorem and electron-phonon vertex corrections in Dirac materials

NASA Astrophysics Data System (ADS)

Roy, Bitan; Sau, Jay D.; Das Sarma, S.

2014-04-01

Migdal's theorem plays a central role in the physics of electron-phonon interactions in metals and semiconductors, and has been extensively studied theoretically for parabolic band electronic systems in three-, two-, and one-dimensional systems over the last fifty years. In the current work, we theoretically study the relevance of Migdal's theorem in graphene and Weyl semimetals which are examples of 2D and 3D Dirac materials, respectively, with linear and chiral band dispersion. Our work also applies to 2D and 3D topological insulator systems. In Fermi liquids, the renormalization of the electron-phonon vertex scales as the ratio of sound (vs) to Fermi (vF) velocity, which is typically a small quantity. In two- and three-dimensional quasirelativistic systems, such as undoped graphene and Weyl semimetals, the one loop electron-phonon vertex renormalization, which also scales as η =vs/vF as η →0, is, however, enhanced by an ultraviolet logarithmic divergent correction, arising from the linear, chiral Dirac band dispersion. Such enhancement of the electron-phonon vertex can be significantly softened due to the logarithmic increment of the Fermi velocity, arising from the long range Coulomb interaction, and therefore, the electron-phonon vertex correction does not have a logarithmic divergence at low energy. Otherwise, the Coulomb interaction does not lead to any additional renormalization of the electron-phonon vertex. Therefore, electron-phonon vertex corrections in two- and three-dimensional Dirac fermionic systems scale as vs/vF0, where vF0 is the bare Fermi velocity, and small when vs≪vF0. These results, although explicitly derived for the intrinsic undoped systems, should hold even when the chemical potential is tuned away from the Dirac points.

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Linear and quadratic static response functions and structure functions in Yukawa liquids.

PubMed

Magyar, Péter; Donkó, Zoltán; Kalman, Gabor J; Golden, Kenneth I

2014-08-01

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Evaluation of a 3D stereophotogrammetric technique to measure the stone casts of patients with unilateral cleft lip and palate.

PubMed

Sforza, Chiarella; De Menezes, Marcio; Bresciani, Elena; Cerón-Zapata, Ana M; López-Palacio, Ana M; Rodriguez-Ardila, Myriam J; Berrio-Gutiérrez, Lina M

2012-07-01

To assess a three-dimensional stereophotogrammetric method for palatal cast digitization of children with unilateral cleft lip and palate. As part of a collaboration between the University of Milan (Italy) and the University CES of Medellin (Colombia), 96 palatal cast models obtained from neonatal patients with unilateral cleft lip and palate were obtained and digitized using a three-dimensional stereophotogrammetric imaging system. Three-dimensional measurements (cleft width, depth, length) were made separately for the longer and shorter cleft segments on the digital dental cast surface between landmarks, previously marked. Seven linear measurements were computed. Systematic and random errors between operators' tracings, and accuracy on geometric objects of known size were calculated. In addition, mean measurements from three-dimensional stereophotographs were compared statistically with those from direct anthropometry. The three-dimensional method presented good accuracy error (<0.9%) on measuring geometric objects. No systematic errors between operators' measurements were found (p > .05). Statistically significant differences (p < 5%) were noted for different methods (caliper versus stereophotogrammetry) for almost all distances analyzed, with mean absolute difference values ranging between 0.22 and 3.41 mm. Therefore, rates for the technical error of measurement and relative error magnitude were scored as moderate for Ag-Am and poor for Ag-Pg and Am-Pm distances. Generally, caliper values were larger than three-dimensional stereophotogrammetric values. Three-dimensional stereophotogrammetric systems have some advantages over direct anthropometry, and therefore the method could be sufficiently precise and accurate on palatal cast digitization with unilateral cleft lip and palate. This would be useful for clinical analyses in maxillofacial, plastic, and aesthetic surgery.

Thermal elastoplastic structural analysis of non-metallic thermal protection systems

NASA Technical Reports Server (NTRS)

Chung, T. J.; Yagawa, G.

1972-01-01

An incremental theory and numerical procedure to analyze a three-dimensional thermoelastoplastic structure subjected to high temperature, surface heat flux, and volume heat supply as well as mechanical loadings are presented. Heat conduction equations and equilibrium equations are derived by assuming a specific form of incremental free energy, entropy, stresses and heat flux together with the first and second laws of thermodynamics, von Mises yield criteria and Prandtl-Reuss flow rule. The finite element discretization using the linear isotropic three-dimensional element for the space domain and a difference operator corresponding to a linear variation of temperature within a small time increment for the time domain lead to systematic solutions of temperature distribution and displacement and stress fields. Various boundary conditions such as insulated surfaces and convection through uninsulated surface can be easily treated. To demonstrate effectiveness of the present formulation a number of example problems are presented.

Weyl solitons in three-dimensional optical lattices

NASA Astrophysics Data System (ADS)

Shang, Ce; Zheng, Yuanlin; Malomed, Boris A.

2018-04-01

Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.

Hamiltonian structure of three-dimensional gravity in Vielbein formalism

NASA Astrophysics Data System (ADS)

Hajihashemi, Mahdi; Shirzad, Ahmad

2018-01-01

Considering Chern-Simons like gravity theories in three dimensions as first order systems, we analyze the Hamiltonian structure of three theories Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity. We show that these systems demonstrate a new feature of the constrained systems in which a new kind of constraints emerge due to factorization of determinant of the matrix of Poisson brackets of constraints. We find the desired number of degrees of freedom as well as the generating functional of local Lorentz transformations and diffeomorphism through canonical structure of the system. We also compare the Hamiltonian structure of linearized version of the considered models with the original ones.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

NASA Astrophysics Data System (ADS)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Wang, Ya-Guang

2008-03-01

Compressible vortex sheets are fundamental waves, along with shocks and rarefaction waves, in entropy solutions to multidimensional hyperbolic systems of conservation laws. Understanding the behavior of compressible vortex sheets is an important step towards our full understanding of fluid motions and the behavior of entropy solutions. For the Euler equations in two-dimensional gas dynamics, the classical linearized stability analysis on compressible vortex sheets predicts stability when the Mach number M > sqrt{2} and instability when M < sqrt{2} ; and Artola and Majda’s analysis reveals that the nonlinear instability may occur if planar vortex sheets are perturbed by highly oscillatory waves even when M > sqrt{2} . For the Euler equations in three dimensions, every compressible vortex sheet is violently unstable and this instability is the analogue of the Kelvin Helmholtz instability for incompressible fluids. The purpose of this paper is to understand whether compressible vortex sheets in three dimensions, which are unstable in the regime of pure gas dynamics, become stable under the magnetic effect in three-dimensional magnetohydrodynamics (MHD). One of the main features is that the stability problem is equivalent to a free-boundary problem whose free boundary is a characteristic surface, which is more delicate than noncharacteristic free-boundary problems. Another feature is that the linearized problem for current-vortex sheets in MHD does not meet the uniform Kreiss Lopatinskii condition. These features cause additional analytical difficulties and especially prevent a direct use of the standard Picard iteration to the nonlinear problem. In this paper, we develop a nonlinear approach to deal with these difficulties in three-dimensional MHD. We first carefully formulate the linearized problem for the current-vortex sheets to show rigorously that the magnetic effect makes the problem weakly stable and establish energy estimates, especially high-order energy estimates, in terms of the nonhomogeneous terms and variable coefficients. Then we exploit these results to develop a suitable iteration scheme of the Nash Moser Hörmander type to deal with the loss of the order of derivative in the nonlinear level and establish its convergence, which leads to the existence and stability of compressible current-vortex sheets, locally in time, in three-dimensional MHD.

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Ermakov's Superintegrable Toy and Nonlocal Symmetries

NASA Astrophysics Data System (ADS)

Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.

2005-11-01

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.

Evaluation of out-of-core computer programs for the solution of symmetric banded linear equations. [simultaneous equations

NASA Technical Reports Server (NTRS)

Dunham, R. S.

1976-01-01

FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.

Novel Three-Dimensional Understanding of Maxillary Cleft Distraction.

PubMed

Vaughan, Stephen Michael; Kau, Chung How; Waite, Peter Daniel

2016-09-01

To set forth a universal standard methodology for quantifying volumetric and linear changes in the craniofacial complex, utilizing three-dimensional data captured from a cleft-lip palate patient who underwent rigid external device (RED) distraction. Cone beam computed tomography images of a 14-year-old patient were captured using a Kodak 9500 (Atlanta, GA) Cone Beam system device and a stereophotogrammetric system (3dMDface(TM) Atlanta, GA). The subject was a nonsyndromic unilateral cleft-lip palate patient who received RED distraction as part of maxillary advancement in conjunction with orthodontic treatment. Preop (T1) and postop (T2) images were superimposed using Invivo 5.2.3 (San Jose, CA) software. Volumetric rendering of the airway, bone, and soft tissues, as well as linear measurements were analyzed. Each measurement was captured 10 times to ensure reliability and reproducibility of methodology. Data from T1 to T2 revealed mean differences as follows: airway total volume +5250 mm, minimum cross-sectional area +67.84 mm; bone +1719 mm, soft tissue +44,432 mm. Mean of linear measurements: Pronasale 1.98 mm, Subnasale 3.35 mm, Labial superius 10.79 mm, Labial inferius 4.13 mm, Right alare 5.71 mm, Right cheilion 7.83 mm, Left alare 4.97 mm, Left cheilion 5.50 mm, Pogonion 3.01 mm, B-point 2.49 mm, U1-U1 9.77 mm, and L1-L1 0.00 mm. P values are <0.001 for each analysis. This paper represents a novel and innovative way to look at prepost RED distractions in a three-dimensional format. A universal standard analysis of the craniofacial complex can be implemented using the techniques and method outlined in this study.

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

NASA Technical Reports Server (NTRS)

Manro, M. E.

1983-01-01

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

Nasolabial Morphology Following Nasoalveolar Molding in Infants With Unilateral Cleft Lip and Palate.

PubMed

Nur Yilmaz, Rahime Burcu; Germeç Çakan, Derya

2018-06-01

The aim of the present study is to evaluate the effects of nasoalveolar molding (NAM) therapy on nasolabial morphology three dimensionally, and compare the nasolabial linear and surface distance measurements in infants with unilateral cleft lip and palate. Facial plaster casts of 42 infants with unilateral cleft lip and palate taken at the onset (pre-NAM) and finishing stage (post-NAM) of NAM were scanned with 3dMDface stereophotogrammetry system (3dMD, Atlanta, GA). Nineteen nasolabial linear and surface distance measurements were performed on three-dimensional images. In addition to standard descriptive statistical calculations (means and SDs), pre- and post-NAM measurements were evaluated by paired t test. All measurements except lip gap, nostril floor width, and nostril diameter increased between pre-NAM and post-NAM. Nostril and lip height increased significantly on the cleft side (P < 0.05). No differences were present between linear and surface distance measurements except for nasal width measurement. Nasal and lip symmetry improved with NAM. The use of surface distance measurements may be advised particularly for continuous and curved anatomic structures in which circumference differences are expected.

Segmented amplifier configurations for laser amplifier

DOEpatents

Hagen, Wilhelm F.

1979-01-01

An amplifier system for high power lasers, the system comprising a compact array of segments which (1) preserves high, large signal gain with improved pumping efficiency and (2) allows the total amplifier length to be shortened by as much as one order of magnitude. The system uses a three dimensional array of segments, with the plane of each segment being oriented at substantially the amplifier medium Brewster angle relative to the incident laser beam and with one or more linear arrays of flashlamps positioned between adjacent rows of amplifier segments, with the plane of the linear array of flashlamps being substantially parallel to the beam propagation direction.

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

A Glimpse in the Third Dimension for Electrical Resistivity Profiles

NASA Astrophysics Data System (ADS)

Robbins, A. R.; Plattner, A.

2017-12-01

We present an electrode layout strategy designed to enhance the popular two-dimensional electrical resistivity profile. Offsetting electrodes from the traditional linear layout and using 3-D inversion software allows for mapping the three-dimensional electrical resistivity close to the profile plane. We established a series of synthetic tests using simulated data generated from chosen resistivity distributions with a three-dimensional target feature. All inversions and simulations were conducted using freely-available ERT software, BERT and E4D. Synthetic results demonstrate the effectiveness of the offset electrode approach, whereas the linear layout failed to resolve the three-dimensional character of our subsurface feature. A field survey using trench backfill as a known resistivity contrast confirmed our synthetic tests. As we show, 3-D inversions of linear layouts for starting models without previously known structure are futile ventures because they generate symmetric resistivity solutions with respect to the profile plane. This is a consequence of the layout's inherent symmetrical sensitivity patterns. An offset electrode layout is not subject to the same limitation, as the collective measurements do not share a common sensitivity symmetry. For practitioners, this approach presents a low-cost improvement of a traditional geophysical method which is simple to use yet may provide critical information about the three dimensional structure of the subsurface close to the profile.

On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

2017-04-01

We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis

NASA Astrophysics Data System (ADS)

Brandão, Rodolfo; Dias, Eduardo O.; Miranda, José A.

2018-03-01

We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.

Continuous Three-Dimensional Control of a Virtual Helicopter Using a Motor Imagery Based Brain-Computer Interface

PubMed Central

Doud, Alexander J.; Lucas, John P.; Pisansky, Marc T.; He, Bin

2011-01-01

Brain-computer interfaces (BCIs) allow a user to interact with a computer system using thought. However, only recently have devices capable of providing sophisticated multi-dimensional control been achieved non-invasively. A major goal for non-invasive BCI systems has been to provide continuous, intuitive, and accurate control, while retaining a high level of user autonomy. By employing electroencephalography (EEG) to record and decode sensorimotor rhythms (SMRs) induced from motor imaginations, a consistent, user-specific control signal may be characterized. Utilizing a novel method of interactive and continuous control, we trained three normal subjects to modulate their SMRs to achieve three-dimensional movement of a virtual helicopter that is fast, accurate, and continuous. In this system, the virtual helicopter's forward-backward translation and elevation controls were actuated through the modulation of sensorimotor rhythms that were converted to forces applied to the virtual helicopter at every simulation time step, and the helicopter's angle of left or right rotation was linearly mapped, with higher resolution, from sensorimotor rhythms associated with other motor imaginations. These different resolutions of control allow for interplay between general intent actuation and fine control as is seen in the gross and fine movements of the arm and hand. Subjects controlled the helicopter with the goal of flying through rings (targets) randomly positioned and oriented in a three-dimensional space. The subjects flew through rings continuously, acquiring as many as 11 consecutive rings within a five-minute period. In total, the study group successfully acquired over 85% of presented targets. These results affirm the effective, three-dimensional control of our motor imagery based BCI system, and suggest its potential applications in biological navigation, neuroprosthetics, and other applications. PMID:22046274

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

NASA Technical Reports Server (NTRS)

Rogers, Michael M.; Moser, Robert D.

1991-01-01

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

A synchrotron radiation microtomography system for the analysis of trabecular bone samples.

PubMed

Salomé, M; Peyrin, F; Cloetens, P; Odet, C; Laval-Jeantet, A M; Baruchel, J; Spanne, P

1999-10-01

X-ray computed microtomography is particularly well suited for studying trabecular bone architecture, which requires three-dimensional (3-D) images with high spatial resolution. For this purpose, we describe a three-dimensional computed microtomography (microCT) system using synchrotron radiation, developed at ESRF. Since synchrotron radiation provides a monochromatic and high photon flux x-ray beam, it allows high resolution and a high signal-to-noise ratio imaging. The principle of the system is based on truly three-dimensional parallel tomographic acquisition. It uses a two-dimensional (2-D) CCD-based detector to record 2-D radiographs of the transmitted beam through the sample under different angles of view. The 3-D tomographic reconstruction, performed by an exact 3-D filtered backprojection algorithm, yields 3-D images with cubic voxels. The spatial resolution of the detector was experimentally measured. For the application to bone investigation, the voxel size was set to 6.65 microm, and the experimental spatial resolution was found to be 11 microm. The reconstructed linear attenuation coefficient was calibrated from hydroxyapatite phantoms. Image processing tools are being developed to extract structural parameters quantifying trabecular bone architecture from the 3-D microCT images. First results on human trabecular bone samples are presented.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Recent Developments In Theory Of Balanced Linear Systems

NASA Technical Reports Server (NTRS)

Gawronski, Wodek

1994-01-01

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

Self-Assembly of Emulsion Droplets into Polymer Chains

NASA Astrophysics Data System (ADS)

Bargteil, Dylan; McMullen, Angus; Brujic, Jasna

We experimentally investigate `beads-on-a-string' models of polymers using the spontaneous assembly of emulsion droplets into linear chains. Droplets functionalized with surface-mobile DNA allow for programmable 'monomers' through which we can influence the three-dimensional structure of the assembled 'polymer'. Such model polymers can be used to study conformational changes of polypeptides and the principles governing protein folding. In our system, we find that droplets bind via complementary DNA strands that are recruited into adhesion patches. Recruitment is driven by the DNA hybridization energy, and is limited by the energy cost of surface deformation and the entropy loss of the mobile linkers, yielding adhesion patches of a characteristic size with a given number of linkers. By tuning the initial surface coverage of linkers, we control valency between the droplets to create linear or branched polymer chains. We additionally control the flexibility of the model polymers by varying the salt concentration and study their dynamics between extended and collapsed states. This system opens the possibility of programming stable three-dimensional structures, such as those found within folded proteins.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

The high performance parallel algorithm for Unified Gas-Kinetic Scheme

NASA Astrophysics Data System (ADS)

Li, Shiyi; Li, Qibing; Fu, Song; Xu, Jinxiu

2016-11-01

A high performance parallel algorithm for UGKS is developed to simulate three-dimensional flows internal and external on arbitrary grid system. The physical domain and velocity domain are divided into different blocks and distributed according to the two-dimensional Cartesian topology with intra-communicators in physical domain for data exchange and other intra-communicators in velocity domain for sum reduction to moment integrals. Numerical results of three-dimensional cavity flow and flow past a sphere agree well with the results from the existing studies and validate the applicability of the algorithm. The scalability of the algorithm is tested both on small (1-16) and large (729-5832) scale processors. The tested speed-up ratio is near linear ashind thus the efficiency is around 1, which reveals the good scalability of the present algorithm.

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Projection of angular momentum via linear algebra

DOE PAGES

Johnson, Calvin W.; O'Mara, Kevin D.

2017-12-01

Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. Here, we show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications tomore » $$^{48}$$Cr and $$^{60}$$Fe in the $pf$ shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.« less

Projection of angular momentum via linear algebra

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

Johnson, Calvin W.; O'Mara, Kevin D.

Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. Here, we show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications tomore » $$^{48}$$Cr and $$^{60}$$Fe in the $pf$ shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.« less

Projection of angular momentum via linear algebra

NASA Astrophysics Data System (ADS)

Johnson, Calvin W.; O'Mara, Kevin D.

2017-12-01

Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. We show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications to 48Cr and 60Fe in the p f shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.

Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths.

PubMed

Ness, H; Stella, L; Lorenz, C D; Kantorovich, L

2017-04-28

We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference ΔT between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (T≳500 K) and temperature differences (ΔT≳500 K), the chains, with N>18 atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (T≲500 K) and temperature differences (ΔT≲400 K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (N≤15). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Characterization of iron ferromagnetism by the local atomic volume: from three-dimensional structures to isolated atoms.

PubMed

Zhang, Lei; Sob, M; Wu, Zhe; Zhang, Ying; Lu, Guang-Hong

2014-02-26

We present a comprehensive study of the relationship between the ferromagnetism and the structural properties of Fe systems from three-dimensional ones to isolated atoms based on the spin-density functional theory. We have found a relation between the magnetic moment and the volume of the Voronoi polyhedron, determining, in most cases, the value of the total magnetic moment as a function of this volume with an average accuracy of ±0.28 μ(B) and of the 3d magnetic moment with an average accuracy of ±0.07 μ(B) when the atomic volume is larger than 22 ų. It is demonstrated that this approach is applicable for many three-dimensional systems, including high-symmetry structures of perfect body-centered cubic (bcc), face-centered cubic (fcc), hexagonal close-packed (hcp), double hexagonal close-packed (dhcp), and simple cubic (sc) crystals, as well as for lower-symmetry ones, for example atoms near a grain boundary (GB) or a surface, around a vacancy or in a linear chain (for low-dimensional cases, we provide a generalized definition of the Voronoi polyhedron). Also, we extend the validity of the Stoner model to low-dimensional structures, such as atomic chains, free-standing monolayers and surfaces, determining the Stoner parameter for these systems. The ratio of the 3d-exchange splitting to the magnetic moment, corresponding to the Stoner parameter, is found to be I(3d) = (0.998 ± 0.006) eV /μ(B) for magnetic moments up to 3.0 μ(B). Further, the 3d exchange splitting changes nearly linearly in the region of higher magnetic moments (3.0-4.0 μ(B)) and the corresponding Stoner exchange parameter equals I(h)(3d) = (0.272 ± 0.006) eV /μ(B). The existence of these two regions reflects the fact that, with increasing Voronoi volume, the 3d bands separate first and, consequently, the 3d magnetic moment increases. When the Voronoi volume is sufficiently large (≥22 ų), the separation of the 3d bands is complete and the magnetic moment reaches a value of 3.0 μ(B). Then, when the volume further increases, the 4s bands start to separate, increasing thus the 4s magnetic moment. Surprisingly, in the region of higher magnetic moments (≥3.0 μ(B)), there is also a linear relationship between the 4s exchange splitting and the total magnetic moment with a slope of I(h)(4s) = (1.053 ± 0.016) eV /μ(B), which is nearly identical to I(3d) for magnetic moments up to 3.0 μB. These linear relations can be considered as an extension of the Stoner model for low-dimensional systems.

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

NASA Technical Reports Server (NTRS)

Strelkov, S. A.; Sushkevich, T. A.

1983-01-01

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Estimating oxygen distribution from vasculature in three-dimensional tumour tissue

PubMed Central

Kannan, Pavitra; Warren, Daniel R.; Markelc, Bostjan; Bates, Russell; Muschel, Ruth; Partridge, Mike

2016-01-01

Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution. PMID:26935806

Estimating oxygen distribution from vasculature in three-dimensional tumour tissue.

PubMed

Grimes, David Robert; Kannan, Pavitra; Warren, Daniel R; Markelc, Bostjan; Bates, Russell; Muschel, Ruth; Partridge, Mike

2016-03-01

Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution. © 2016 The Authors.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Asymmetries and three-dimensional features of vestibular cross-coupled stimuli illuminated through modeling

PubMed Central

Holly, Jan E.; Masood, M. Arjumand; Bhandari, Chiran S.

2017-01-01

Head movements during sustained rotation can cause angular cross-coupling which leads to tumbling illusions. Even though angular vectors predict equal magnitude illusions for head movements in opposite directions, the magnitudes of the illusions are often surprisingly asymmetric, such as during leftward versus rightward yaw while horizontal in a centrifuge. This paper presents a comprehensive investigation of the angular-linear stimulus combinations from eight different published papers in which asymmetries were found. Interactions between all angular and linear vectors, including gravity, are taken into account to model the three-dimensional consequences of the stimuli. Three main results followed. First, for every pair of head yaw movements, an asymmetry was found in the stimulus itself when considered in a fully three-dimensional manner, and the direction of the asymmetry matched the subjectively reported magnitude asymmetry. Second, for pitch and roll head movements for which motion sickness was measured, the stimulus was found symmetric in every case except one, and motion sickness generally aligned with other factors such as the existence of a head rest. Third, three-dimensional modeling predicted subjective inconsistency in the direction of perceived rotation when linear and angular components were oppositely-directed, and predicted surplus illusory rotation in the direction of head movement. PMID:27814310

Application of Least-Squares Adjustment Technique to Geometric Camera Calibration and Photogrammetric Flow Visualization

NASA Technical Reports Server (NTRS)

Chen, Fang-Jenq

1997-01-01

Flow visualization produces data in the form of two-dimensional images. If the optical components of a camera system are perfect, the transformation equations between the two-dimensional image and the three-dimensional object space are linear and easy to solve. However, real camera lenses introduce nonlinear distortions that affect the accuracy of transformation unless proper corrections are applied. An iterative least-squares adjustment algorithm is developed to solve the nonlinear transformation equations incorporated with distortion corrections. Experimental applications demonstrate that a relative precision on the order of 40,000 is achievable without tedious laboratory calibrations of the camera.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Specific heat of (C 6H 11NH 3) CuCl 3 (CHAC), a system of ferromagnetic chains

NASA Astrophysics Data System (ADS)

Schouten, J. C.; van der Geest, G. J.; de Jonge, W. J. M.; Kopinga, K.

1980-08-01

The heat capacity of (C 6H 11NH 3) CuCl 3 (CHAC) has been measured for 0.45 < T < 60 K. Three-dimensional ordering is observed at T = 2.214 K. The data in the paramagnetic region can be described by a ferromagnetic S = {1}/{2} Heisenberg linear chain model system with J/ k = +45 ± 5K.

Beam tracking phase tomography with laboratory sources

NASA Astrophysics Data System (ADS)

Vittoria, F. A.; Endrizzi, M.; Kallon, G. K. N.; Hagen, C. K.; Diemoz, P. C.; Zamir, A.; Olivo, A.

2018-04-01

An X-ray phase-contrast laboratory system is presented, based on the beam-tracking method. Beam-tracking relies on creating micro-beamlets of radiation by placing a structured mask before the sample, and analysing them by using a detector with sufficient resolution. The system is used in tomographic configuration to measure the three dimensional distribution of the linear attenuation coefficient, difference from unity of the real part of the refractive index, and of the local scattering power of specimens. The complementarity of the three signals is investigated, together with their potential use for material discrimination.

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew-Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.

Reduced-Order Models Based on POD-Tpwl for Compositional Subsurface Flow Simulation

NASA Astrophysics Data System (ADS)

Durlofsky, L. J.; He, J.; Jin, L. Z.

2014-12-01

A reduced-order modeling procedure applicable for compositional subsurface flow simulation will be described and applied. The technique combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide highly efficient surrogate models. The method is based on a molar formulation (which uses pressure and overall component mole fractions as the primary variables) and is applicable for two-phase, multicomponent systems. The POD-TPWL procedure expresses new solutions in terms of linearizations around solution states generated and saved during previously simulated 'training' runs. High-dimensional states are projected into a low-dimensional subspace using POD. Thus, at each time step, only a low-dimensional linear system needs to be solved. Results will be presented for heterogeneous three-dimensional simulation models involving CO2 injection. Both enhanced oil recovery and carbon storage applications (with horizontal CO2 injectors) will be considered. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations will be demonstrated for 'test' runs in which the well controls differ from those used for training. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to about 3-4 full-order runs. Runtime speedups using POD-TPWL are, however, very significant - typically O(100-1000). The use of POD-TPWL for well control optimization will also be illustrated. For this application, some amount of retraining during the course of the optimization is required, which leads to smaller, but still significant, speedup factors.

Cross Flow Effects on Glaze Ice Roughness Formation

NASA Technical Reports Server (NTRS)

Tsao, Jen-Ching

2004-01-01

The present study examines the impact of large-scale cross flow on the creation of ice roughness elements on the leading edge of a swept wing under glaze icing conditions. A three-dimensional triple-deck structure is developed to describe the local interaction of a 3 D air boundary layer with ice sheets and liquid films. A linear stability analysis is presented here. It is found that, as the sweep angle increases, the local icing instabilities enhance and the most linearly unstable modes are strictly three dimensional.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Exploring the CAESAR database using dimensionality reduction techniques

NASA Astrophysics Data System (ADS)

Mendoza-Schrock, Olga; Raymer, Michael L.

2012-06-01

The Civilian American and European Surface Anthropometry Resource (CAESAR) database containing over 40 anthropometric measurements on over 4000 humans has been extensively explored for pattern recognition and classification purposes using the raw, original data [1-4]. However, some of the anthropometric variables would be impossible to collect in an uncontrolled environment. Here, we explore the use of dimensionality reduction methods in concert with a variety of classification algorithms for gender classification using only those variables that are readily observable in an uncontrolled environment. Several dimensionality reduction techniques are employed to learn the underlining structure of the data. These techniques include linear projections such as the classical Principal Components Analysis (PCA) and non-linear (manifold learning) techniques, such as Diffusion Maps and the Isomap technique. This paper briefly describes all three techniques, and compares three different classifiers, Naïve Bayes, Adaboost, and Support Vector Machines (SVM), for gender classification in conjunction with each of these three dimensionality reduction approaches.

A computational study for investigating acoustic streaming and tissue heating during high intensity focused ultrasound through blood vessel with an obstacle

NASA Astrophysics Data System (ADS)

Parvin, Salma; Sultana, Aysha

2017-06-01

The influence of High Intensity Focused Ultrasound (HIFU) on the obstacle through blood vessel is studied numerically. A three-dimensional acoustics-thermal-fluid coupling model is employed to compute the temperature field around the obstacle through blood vessel. The model construction is based on the linear Westervelt and conjugate heat transfer equations for the obstacle through blood vessel. The system of equations is solved using Finite Element Method (FEM). We found from this three-dimensional numerical study that the rate of heat transfer is increasing from the obstacle and both the convective cooling and acoustic streaming can considerably change the temperature field.

Validation of in vitro assays in three-dimensional human dermal constructs.

PubMed

Idrees, Ayesha; Chiono, Valeria; Ciardelli, Gianluca; Shah, Siegfried; Viebahn, Richard; Zhang, Xiang; Salber, Jochen

2018-05-01

Three-dimensional cell culture systems are urgently needed for cytocompatibility testing of biomaterials. This work aimed at the development of three-dimensional in vitro dermal skin models and their optimization for cytocompatibility evaluation. Initially "murine in vitro dermal construct" based on L929 cells was generated, leading to the development of "human in vitro dermal construct" consisting of normal human dermal fibroblasts in rat tail tendon collagen type I. To assess the viability of the cells, different assays CellTiter-Blue ® , RealTime-Glo ™ MT, and CellTiter-Glo ® (Promega) were evaluated to optimize the best-suited assay to the respective cell type and three-dimensional system. Z-stack imaging (Live/Dead and Phalloidin/DAPI-Promokine) was performed to visualize normal human dermal fibroblasts inside matrix revealing filopodia-like morphology and a uniform distribution of normal human dermal fibroblasts in matrix. CellTiter-Glo was found to be the optimal cell viability assay among those analyzed. CellTiter-Blue reagent affected the cell morphology of normal human dermal fibroblasts (unlike L929), suggesting an interference with cell biological activity, resulting in less reliable viability data. On the other hand, RealTime-Glo provided a linear signal only with a very low cell density, which made this assay unsuitable for this system. CellTiter-Glo adapted to three-dimensional dermal construct by optimizing the "shaking time" to enhance the reagent penetration and maximum adenosine triphosphate release, indicating 2.4 times higher viability value by shaking for 60 min than for 5 min. In addition, viability results showed that cells were viable inside the matrix. This model would be further advanced with more layers of skin to make a full thickness model.

The three-dimensional evolution of a plane mixing layer. Part 2: Pairing and transition to turbulence

NASA Technical Reports Server (NTRS)

Moser, Robert D.; Rogers, Michael M.

1992-01-01

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings was simulated numerically. Initial conditions for all simulations consisted of a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found both to inhibit the growth of infinitesimal three-dimensional disturbances and to trigger the transition to turbulence in highly three dimensional flows. The mechanisms responsible for the growth of three-dimensionality as well as the initial phases of the transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of span wise vorticity, which undergo a secondary roll up. Transition also produces an increase in the degree of scalar mixing, in agreement with experimental observations of mixing transition. Simulations were also conducted to investigate changes in span wise length scale that may occur in response to the change in stream wise length scale during a pairing. The linear mechanism for this process was found to be very slow, requiring roughly three pairings to complete a doubling of the span wise scale. Stronger three-dimensionality can produce more rapid scale changes but is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one span wise scale to a similar array at a larger span wise scale.

System and method to estimate compressional to shear velocity (VP/VS) ratio in a region remote from a borehole

DOEpatents

Vu, Cung; Nihei, Kurt T; Schmitt, Denis P; Skelt, Christopher; Johnson, Paul A; Guyer, Robert; TenCate, James A; Le Bas, Pierre-Yves

2012-10-16

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

Real-time spectro-ellipsometric approach to distinguish between two-dimensional Ge layer growth and Ge dot formation on SiO2 substrates

NASA Astrophysics Data System (ADS)

Akazawa, Housei

2018-04-01

Morphological evolution of Ge layers on SiO2 substrates grown by photo-excited chemical vapor deposition from GeH4 was monitored in real time by recording (Ψ, Δ) angles of spectroscopic ellipsometry and ex-situ analyzed by atomic force microscopy (AFM). Distinct Ψ-Δ trajectory shapes were demonstrated to discriminate the two-dimensional (2D) and three-dimensional (3D) growth modes. While the trajectory of 2D growth is characterized by a one-turn spiral, that of 3D growth consisted of three sections corresponding to initial wetting of the SiO2 surface, creation of nucleation centers, and dot growth. The critical point where the system turns into 2D or 3D growth can be in situ identified in terms of the directions of the Ψ-Δ trajectories. AFM images revealed characteristic changes in the microstructure, including self-assembling dots and dots merging with one another. While the root-mean-square surface roughness increased linearly against film thickness, the maximum peak-to-valley height deviated once from linear dependence and later returned back to it, which reflected coarsening of dots and embedding of valleys between dots.

Optimum Particle Size for Gold-Catalyzed CO Oxidation

PubMed Central

2018-01-01

The structure sensitivity of gold-catalyzed CO oxidation is presented by analyzing in detail the dependence of CO oxidation rate on particle size. Clusters with less than 14 gold atoms adopt a planar structure, whereas larger ones adopt a three-dimensional structure. The CO and O2 adsorption properties depend strongly on particle structure and size. All of the reaction barriers relevant to CO oxidation display linear scaling relationships with CO and O2 binding strengths as main reactivity descriptors. Planar and three-dimensional gold clusters exhibit different linear scaling relationship due to different surface topologies and different coordination numbers of the surface atoms. On the basis of these linear scaling relationships, first-principles microkinetics simulations were conducted to determine CO oxidation rates and possible rate-determining step of Au particles. Planar Au9 and three-dimensional Au79 clusters present the highest CO oxidation rates for planar and three-dimensional clusters, respectively. The planar Au9 cluster is much more active than the optimum Au79 cluster. A common feature of optimum CO oxidation performance is the intermediate binding strengths of CO and O2, resulting in intermediate coverages of CO, O2, and O. Both these optimum particles present lower performance than maximum Sabatier performance, indicating that there is sufficient room for improvement of gold catalysts for CO oxidation. PMID:29707098

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Force system generated by elastic archwires with vertical V bends: a three-dimensional analysis.

PubMed

Upadhyay, Madhur; Shah, Raja; Peterson, Donald; Asaki, Takafumi; Yadav, Sumit; Agarwal, Sachin

2017-04-01

Our previous understanding of V-bend mechanics is primarily from two-dimensional (2D) analysis of archwire bracket interactions in the second order. These analyses do not take into consideration the three-dimensional (3D) nature of orthodontic appliances involving the third order. To quantify the force system generated in a 3D two bracket set up involving the molar and incisors with vertical V-bends. Maxillary molar and incisor brackets were arranged in a dental arch form and attached to load cells capable of measuring forces and moments in all three planes (x, y, and z) of space. Symmetrical V-bends (right and left sides) were placed at 11 different locations along rectangular beta-titanium archwires of various sizes at an angle of 150degrees. Each wire was evaluated for the 11 bend positions. Specifically, the vertical forces (Fz) and anterio-posterior moments (Mx) were analysed. Descriptive statistics were used to interpret the results. With increasing archwire size, Fz and Mx increased at the two brackets (P < 0.05). The vertical forces were linear and symmetric in nature, increasing in magnitude as the bends moved closer to either bracket. The Mx curves were asymmetric and non-linear displaying higher magnitudes for molar bracket. As the bends were moved closer to either bracket a distinct flattening of the incisor Mx curve was noted, implying no change in its magnitude. This article provides critical information on V-bend mechanics involving second order and third order archwire-bracket interactions. A model for determining this force system is described that might allow for easier translation to actual clinical practice. © The Author 2016. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: journals.permissions@oup.com

Dynamic System Coupler Program (DYSCO 4.1). Volume 1. Theoretical Manual

DTIC Science & Technology

1989-01-01

present analysis is as follows: 1. Triplet X, Y, Z represents an inertia frame, R. The R system coordinates are the rotor shaft axes when there is...small perturbation analysis . 2.5 3-D MODAL STRUCTURE - CFM3 A three-dimensional structure is represented as a linear combination of orth­ ogonal modes...Include rotor blade damage modeling, Elgen analysis development, general time history solution development, frequency domain solution development

Three-dimensional repositioning accuracy of semiadjustable articulator cast mounting systems.

PubMed

Tan, Ming Yi; Ung, Justina Youlin; Low, Ada Hui Yin; Tan, En En; Tan, Keson Beng Choon

2014-10-01

In spite of its importance in prosthesis precision and quality, the 3-dimensional repositioning accuracy of cast mounting systems has not been reported in detail. The purpose of this study was to quantify the 3-dimensional repositioning accuracy of 6 selected cast mounting systems. Five magnetic mounting systems were compared with a conventional screw-on system. Six systems on 3 semiadjustable articulators were evaluated: Denar Mark II with conventional screw-on mounting plates (DENSCR) and magnetic mounting system with converter plates (DENCON); Denar Mark 330 with in-built magnetic mounting system (DENMAG) and disposable mounting plates; and Artex CP with blue (ARTBLU), white (ARTWHI), and black (ARTBLA) magnetic mounting plates. Test casts with 3 high-precision ceramic ball bearings at the mandibular central incisor (Point I) and the right and left second molar (Point R; Point L) positions were mounted on 5 mounting plates (n=5) for all 6 systems. Each cast was repositioned 10 times by 4 operators in random order. Nine linear (Ix, Iy, Iz; Rx, Ry, Rz; Lx, Ly, Lz) and 3 angular (anteroposterior, mediolateral, twisting) displacements were measured with a coordinate measuring machine. The mean standard deviations of the linear and angular displacements defined repositioning accuracy. Anteroposterior linear repositioning accuracy ranged from 23.8 ±3.7 μm (DENCON) to 4.9 ±3.2 μm (DENSCR). Mediolateral linear repositioning accuracy ranged from 46.0 ±8.0 μm (DENCON) to 3.7 ±1.5 μm (ARTBLU), and vertical linear repositioning accuracy ranged from 7.2 ±9.6 μm (DENMAG) to 1.5 ±0.9 μm (ARTBLU). Anteroposterior angular repositioning accuracy ranged from 0.0084 ±0.0080 degrees (DENCON) to 0.0020 ±0.0006 degrees (ARTBLU), and mediolateral angular repositioning accuracy ranged from 0.0120 ±0.0111 degrees (ARTWHI) to 0.0027 ±0.0008 degrees (ARTBLU). Twisting angular repositioning accuracy ranged from 0.0419 ±0.0176 degrees (DENCON) to 0.0042 ±0.0038 degrees (ARTBLA). One-way ANOVA found significant differences (P<.05) among all systems for Iy, Ry, Lx, Ly, and twisting. Generally, vertical linear displacements were less likely to reach the threshold of clinical detectability compared with anteroposterior or mediolateral linear displacements. The overall repositioning accuracy of DENSCR was comparable with 4 magnetic mounting systems (DENMAG, ARTBLU, ARTWHI, ARTBLA). DENCON exhibited the worst repositioning accuracy for Iy, Ry, Lx, Ly, and twisting. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems

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

Ng, C.; Bhattacharjee, A.; Skiff, F.

2006-05-15

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show thatmore » the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered as true eigenmodes (which they are not in the collisionless theory). For BGK modes, our interest is motivated by recent discoveries of electrostatic solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is quite mature, there appear to be no exact three-dimensional solutions in the literature (except for the limiting case when the magnetic field is sufficiently strong so that one can apply the guiding-center approximation). We show, in fact, that two- and three-dimensional solutions that depend only on energy do not exist. However, if solutions depend on both energy and angular momentum, we can construct exact three-dimensional solutions for the unmagnetized case, and two-dimensional solutions for the case with a finite magnetic field. The latter are shown to be exact, fully electromagnetic solutions of the steady-state Vlasov-Poisson-Ampere system.« less

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Linear solver performance in elastoplastic problem solution on GPU cluster

NASA Astrophysics Data System (ADS)

Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.

2017-12-01

Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

Visual analysis of mass cytometry data by hierarchical stochastic neighbour embedding reveals rare cell types.

PubMed

van Unen, Vincent; Höllt, Thomas; Pezzotti, Nicola; Li, Na; Reinders, Marcel J T; Eisemann, Elmar; Koning, Frits; Vilanova, Anna; Lelieveldt, Boudewijn P F

2017-11-23

Mass cytometry allows high-resolution dissection of the cellular composition of the immune system. However, the high-dimensionality, large size, and non-linear structure of the data poses considerable challenges for the data analysis. In particular, dimensionality reduction-based techniques like t-SNE offer single-cell resolution but are limited in the number of cells that can be analyzed. Here we introduce Hierarchical Stochastic Neighbor Embedding (HSNE) for the analysis of mass cytometry data sets. HSNE constructs a hierarchy of non-linear similarities that can be interactively explored with a stepwise increase in detail up to the single-cell level. We apply HSNE to a study on gastrointestinal disorders and three other available mass cytometry data sets. We find that HSNE efficiently replicates previous observations and identifies rare cell populations that were previously missed due to downsampling. Thus, HSNE removes the scalability limit of conventional t-SNE analysis, a feature that makes it highly suitable for the analysis of massive high-dimensional data sets.

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Bond, J. Richard; Mersini-Houghton, Laura, E-mail: j.braden@ucl.ac.uk, E-mail: bond@cita.utoronto.ca, E-mail: mersini@physics.unc.edu

2015-08-01

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Department of Physics, University of Toronto,60 St. George Street, Toronto, ON, M5S 3H8; Department of Physics and Astronomy, University College London,Gower Street, London, WC1E 6BT

2015-08-26

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory A.

2017-01-01

In this paper we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three-band model, while leaving the flat band dispersionless. We find a small gap is also opened at the quadratic band touching point by two-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this three-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

Effects of biomotor structures on performance of competitive gymnastics elements in elementary school female sixth-graders.

PubMed

Delas, Suncica; Babin, Josip; Katić, Ratko

2007-12-01

In order to identify biomotor systems that determine performance of competitive gymnastics elements in elementary school female sixth-graders, factor structures of morphological characteristics and basic motor abilities were determined first, followed by relations of the morphological-motor system factors obtained with a set of criterion variables evaluating specific motor skills in competitive gymnastics in 126 female children aged 12 years +/- 3 months. Factor analysis of 17 morphological measures yielded three morphological factors: factor of mesoendomorphy and/or adipose body voluminosity; factor of longitudinal body dimensionality; and factor of transverse arm dimensionality. Factor analysis of 16 motor variables produced four motor factors: general motoricity factor (motor system); general speed factor; factor of explosive strength of throwing type (arm explosiveness); and factor of arm and leg flexibility. Three significant canonical correlations, i.e. linear combinations, explained the association between the set of seven latent variables of the morphological and basic motor system, and five variables evaluating the knowledge in competitive gymnastics. The first canonical linear combination was based on a favorable and predominant impact of the general motor factor (a system integrating whole body coordination, leg explosiveness, relative arm strength, arm movement frequency and body flexibility) on performance of gymnastics elements, cartwheel, handstand and backward pullover mount in particular, and to a lesser extent front scale and double leg pirouette for 180 degrees. The relation of the second pair of canonical factors additionally explained the role of transverse dimensionality of arm skeleton, arm flexibility and explosiveness in performing cartwheel and squat vault, whereas the relation of the third pair of canonical factors explained the unfavorable impact of adipose voluminosity on the performance of squat vault and backward pullover mount.

Three-dimensional modeling of flexible pavements : research implementation plan.

DOT National Transportation Integrated Search

2006-02-14

Many of the asphalt pavement analysis programs are based on linear elastic models. A linear viscoelastic models : would be superior to linear elastic models for analyzing the response of asphalt concrete pavements to loads. There : is a need to devel...

Application of Linear Discriminant Analysis in Dimensionality Reduction for Hand Motion Classification

NASA Astrophysics Data System (ADS)

Phinyomark, A.; Hu, H.; Phukpattaranont, P.; Limsakul, C.

2012-01-01

The classification of upper-limb movements based on surface electromyography (EMG) signals is an important issue in the control of assistive devices and rehabilitation systems. Increasing the number of EMG channels and features in order to increase the number of control commands can yield a high dimensional feature vector. To cope with the accuracy and computation problems associated with high dimensionality, it is commonplace to apply a processing step that transforms the data to a space of significantly lower dimensions with only a limited loss of useful information. Linear discriminant analysis (LDA) has been successfully applied as an EMG feature projection method. Recently, a number of extended LDA-based algorithms have been proposed, which are more competitive in terms of both classification accuracy and computational costs/times with classical LDA. This paper presents the findings of a comparative study of classical LDA and five extended LDA methods. From a quantitative comparison based on seven multi-feature sets, three extended LDA-based algorithms, consisting of uncorrelated LDA, orthogonal LDA and orthogonal fuzzy neighborhood discriminant analysis, produce better class separability when compared with a baseline system (without feature projection), principle component analysis (PCA), and classical LDA. Based on a 7-dimension time domain and time-scale feature vectors, these methods achieved respectively 95.2% and 93.2% classification accuracy by using a linear discriminant classifier.

Supercomputer algorithms for efficient linear octree encoding of three-dimensional brain images.

PubMed

Berger, S B; Reis, D J

1995-02-01

We designed and implemented algorithms for three-dimensional (3-D) reconstruction of brain images from serial sections using two important supercomputer architectures, vector and parallel. These architectures were represented by the Cray YMP and Connection Machine CM-2, respectively. The programs operated on linear octree representations of the brain data sets, and achieved 500-800 times acceleration when compared with a conventional laboratory workstation. As the need for higher resolution data sets increases, supercomputer algorithms may offer a means of performing 3-D reconstruction well above current experimental limits.

Matter-wave solitons supported by quadrupole-quadrupole interactions and anisotropic discrete lattices

NASA Astrophysics Data System (ADS)

Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin

2018-04-01

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Enhanced Spectral Anisotropies Near the Proton-Cyclotron Scale: Possible Two-Component Structure in Hall-FLR MHD Turbulence Simulations

NASA Technical Reports Server (NTRS)

Ghosh, Sanjoy; Goldstein, Melvyn L.

2011-01-01

Recent analysis of the magnetic correlation function of solar wind fluctuations at 1 AU suggests the existence of two-component structure near the proton-cyclotron scale. Here we use two-and-one-half dimensional and three-dimensional compressible MHD models to look for two-component structure adjacent the proton-cyclotron scale. Our MHD system incorporates both Hall and Finite Larmor Radius (FLR) terms. We find that strong spectral anisotropies appear adjacent the proton-cyclotron scales depending on selections of initial condition and plasma beta. These anisotropies are enhancements on top of related anisotropies that appear in standard MHD turbulence in the presence of a mean magnetic field and are suggestive of one turbulence component along the inertial scales and another component adjacent the dissipative scales. We compute the relative strengths of linear and nonlinear accelerations on the velocity and magnetic fields to gauge the relative influence of terms that drive the system with wave-like (linear) versus turbulent (nonlinear) dynamics.

Three-dimensional finite amplitude electroconvection in dielectric liquids

NASA Astrophysics Data System (ADS)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Unsteady transonic flows - Introduction, current trends, applications

NASA Technical Reports Server (NTRS)

Yates, E. C., Jr.

1985-01-01

The computational treatment of unsteady transonic flows is discussed, reviewing the historical development and current techniques. The fundamental physical principles are outlined; the governing equations are introduced; three-dimensional linearized and two-dimensional linear-perturbation theories in frequency domain are described in detail; and consideration is given to frequency-domain FEMs and time-domain finite-difference and integral-equation methods. Extensive graphs and diagrams are included.

The linear sizes tolerances and fits system modernization

NASA Astrophysics Data System (ADS)

Glukhov, V. I.; Grinevich, V. A.; Shalay, V. V.

2018-04-01

The study is carried out on the urgent topic for technical products quality providing in the tolerancing process of the component parts. The aim of the paper is to develop alternatives for improving the system linear sizes tolerances and dimensional fits in the international standard ISO 286-1. The tasks of the work are, firstly, to classify as linear sizes the elements additionally linear coordinating sizes that determine the detail elements location and, secondly, to justify the basic deviation of the tolerance interval for the element's linear size. The geometrical modeling method of real details elements, the analytical and experimental methods are used in the research. It is shown that the linear coordinates are the dimensional basis of the elements linear sizes. To standardize the accuracy of linear coordinating sizes in all accuracy classes, it is sufficient to select in the standardized tolerance system only one tolerance interval with symmetrical deviations: Js for internal dimensional elements (holes) and js for external elements (shafts). The main deviation of this coordinating tolerance is the average zero deviation, which coincides with the nominal value of the coordinating size. Other intervals of the tolerance system are remained for normalizing the accuracy of the elements linear sizes with a fundamental change in the basic deviation of all tolerance intervals is the maximum deviation corresponding to the limit of the element material: EI is the lower tolerance for the of the internal elements (holes) sizes and es is the upper tolerance deviation for the outer elements (shafts) sizes. It is the sizes of the material maximum that are involved in the of the dimensional elements mating of the shafts and holes and determine the fits type.

Pairing phase diagram of three holes in the generalized Hubbard model

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

Navarro, O.; Espinosa, J.E.

Investigations of high-{Tc} superconductors suggest that the electronic correlation may play a significant role in the formation of pairs. Although the main interest is on the physic of two-dimensional highly correlated electron systems, the one-dimensional models related to high temperature superconductivity are very popular due to the conjecture that properties of the 1D and 2D variants of certain models have common aspects. Within the models for correlated electron systems, that attempt to capture the essential physics of high-temperature superconductors and parent compounds, the Hubbard model is one of the simplest. Here, the pairing problem of a three electrons system hasmore » been studied by using a real-space method and the generalized Hubbard Hamiltonian. This method includes the correlated hopping interactions as an extension of the previously proposed mapping method, and is based on mapping the correlated many body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem was solved in a non-perturbative way. In a linear chain, the authors analyzed the pairing phase diagram of three correlated holes for different values of the Hamiltonian parameters. For some value of the hopping parameters they obtain an analytical solution for all kind of interactions.« less

A plasma source driven predator-prey like mechanism as a potential cause of spiraling intermittencies in linear plasma devices

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

Reiser, D.; Ohno, N.; Tanaka, H.

2014-03-15

Three-dimensional global drift fluid simulations are carried out to analyze coherent plasma structures appearing in the NAGDIS-II linear device (nagoya divertor plasma Simulator-II). The numerical simulations reproduce several features of the intermittent spiraling structures observed, for instance, statistical properties, rotation frequency, and the frequency of plasma expulsion. The detailed inspection of the three-dimensional plasma dynamics allows to identify the key mechanism behind the formation of these intermittent events. The resistive coupling between electron pressure and parallel electric field in the plasma source region gives rise to a quasilinear predator-prey like dynamics where the axisymmetric mode represents the prey and themore » spiraling structure with low azimuthal mode number represents the predator. This interpretation is confirmed by a reduced one-dimensional quasilinear model derived on the basis of the findings in the full three-dimensional simulations. The dominant dynamics reveals certain similarities to the classical Lotka-Volterra cycle.« less

True orbit simulation of piecewise linear and linear fractional maps of arbitrary dimension using algebraic numbers

NASA Astrophysics Data System (ADS)

Saito, Asaki; Yasutomi, Shin-ichi; Tamura, Jun-ichi; Ito, Shunji

2015-06-01

We introduce a true orbit generation method enabling exact simulations of dynamical systems defined by arbitrary-dimensional piecewise linear fractional maps, including piecewise linear maps, with rational coefficients. This method can generate sufficiently long true orbits which reproduce typical behaviors (inherent behaviors) of these systems, by properly selecting algebraic numbers in accordance with the dimension of the target system, and involving only integer arithmetic. By applying our method to three dynamical systems—that is, the baker's transformation, the map associated with a modified Jacobi-Perron algorithm, and an open flow system—we demonstrate that it can reproduce their typical behaviors that have been very difficult to reproduce with conventional simulation methods. In particular, for the first two maps, we show that we can generate true orbits displaying the same statistical properties as typical orbits, by estimating the marginal densities of their invariant measures. For the open flow system, we show that an obtained true orbit correctly converges to the stable period-1 orbit, which is inherently possessed by the system.

A moist Boussinesq shallow water equations set for testing atmospheric models

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

Zerroukat, M., E-mail: mohamed.zerroukat@metoffice.gov.uk; Allen, T.

The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allowmore » the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics–physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. - Highlights: • Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations. • The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations. • This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy. • Like full models, temperature and moistures are advected as tracers that interact through a simplified yet realistic phase-change model. • This model is a unique tool to test numerical methods for atmospheric models, and physics–dynamics coupling, in a very realistic and simple way.« less

The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Evans, K. S.

1974-01-01

The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria.

Static stability of a three-dimensional space truss. M.S. Thesis - Case Western Reserve Univ., 1994

NASA Technical Reports Server (NTRS)

Shaker, John F.

1995-01-01

In order to deploy large flexible space structures it is necessary to develop support systems that are strong and lightweight. The most recent example of this aerospace design need is vividly evident in the space station solar array assembly. In order to accommodate both weight limitations and strength performance criteria, ABLE Engineering has developed the Folding Articulating Square Truss (FASTMast) support structure. The FASTMast is a space truss/mechanism hybrid that can provide system support while adhering to stringent packaging demands. However, due to its slender nature and anticipated loading, stability characterization is a critical part of the design process. Furthermore, the dire consequences surely to result from a catastrophic instability quickly provide the motivation for careful examination of this problem. The fundamental components of the space station solar array system are the (1) solar array blanket system, (2) FASTMast support structure, and (3) mast canister assembly. The FASTMast once fully deployed from the canister will provide support to the solar array blankets. A unique feature of this structure is that the system responds linearly within a certain range of operating loads and nonlinearly when that range is exceeded. The source of nonlinear behavior in this case is due to a changing stiffness state resulting from an inability of diagonal members to resist applied loads. The principal objective of this study was to establish the failure modes involving instability of the FASTMast structure. Also of great interest during this effort was to establish a reliable analytical approach capable of effectively predicting critical values at which the mast becomes unstable. Due to the dual nature of structural response inherent to this problem, both linear and nonlinear analyses are required to characterize the mast in terms of stability. The approach employed herein is one that can be considered systematic in nature. The analysis begins with one and two-dimensional failure models of the system and its important components. From knowledge gained through preliminary analyses a foundation is developed for three-dimensional analyses of the FASTMast structure. The three-dimensional finite element (FE) analysis presented here involves a FASTMast system one-tenth the size of the actual flight unit. Although this study does not yield failure analysis results that apply directly to the flight article, it does establish a method by which the full-scale mast can be evaluated.

Static stability of a three-dimensional space truss

NASA Astrophysics Data System (ADS)

Shaker, John F.

1995-05-01

In order to deploy large flexible space structures it is necessary to develop support systems that are strong and lightweight. The most recent example of this aerospace design need is vividly evident in the space station solar array assembly. In order to accommodate both weight limitations and strength performance criteria, ABLE Engineering has developed the Folding Articulating Square Truss (FASTMast) support structure. The FASTMast is a space truss/mechanism hybrid that can provide system support while adhering to stringent packaging demands. However, due to its slender nature and anticipated loading, stability characterization is a critical part of the design process. Furthermore, the dire consequences surely to result from a catastrophic instability quickly provide the motivation for careful examination of this problem. The fundamental components of the space station solar array system are the (1) solar array blanket system, (2) FASTMast support structure, and (3) mast canister assembly. The FASTMast once fully deployed from the canister will provide support to the solar array blankets. A unique feature of this structure is that the system responds linearly within a certain range of operating loads and nonlinearly when that range is exceeded. The source of nonlinear behavior in this case is due to a changing stiffness state resulting from an inability of diagonal members to resist applied loads. The principal objective of this study was to establish the failure modes involving instability of the FASTMast structure. Also of great interest during this effort was to establish a reliable analytical approach capable of effectively predicting critical values at which the mast becomes unstable. Due to the dual nature of structural response inherent to this problem, both linear and nonlinear analyses are required to characterize the mast in terms of stability. The approach employed herein is one that can be considered systematic in nature. The analysis begins with one and two-dimensional failure models of the system and its important components. From knowledge gained through preliminary analyses a foundation is developed for three-dimensional analyses of the FASTMast structure. The three-dimensional finite element (FE) analysis presented here involves a FASTMast system one-tenth the size of the actual flight unit. Although this study does not yield failure analysis results that apply directly to the flight article, it does establish a method by which the full-scale mast can be evaluated.

Development and verification of global/local analysis techniques for laminated composites

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.

1991-01-01

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.

Determinism in synthesized chaotic waveforms.

PubMed

Corron, Ned J; Blakely, Jonathan N; Hayes, Scott T; Pethel, Shawn D

2008-03-01

The output of a linear filter driven by a randomly polarized square wave, when viewed backward in time, is shown to exhibit determinism at all times when embedded in a three-dimensional state space. Combined with previous results establishing exponential divergence equivalent to a positive Lyapunov exponent, this result rigorously shows that such reverse-time synthesized waveforms appear equally to have been produced by a deterministic chaotic system.

[Development of a system for ultrasonic three-dimensional reconstruction of fetus].

PubMed

Baba, K

1989-04-01

We have developed a system for ultrasonic three-dimensional (3-D) fetus reconstruction using computers. Either a real-time linear array probe or a convex array probe of an ultrasonic scanner was mounted on a position sensor arm of a manual compound scanner in order to detect the position of the probe. A microcomputer was used to convert the position information to what could be recorded on a video tape as an image. This image was superimposed on the ultrasonic tomographic image simultaneously with a superimposer and recorded on a video tape. Fetuses in utero were scanned in seven cases. More than forty ultrasonic section image on the video tape were fed into a minicomputer. The shape of the fetus was displayed three-dimensionally by means of computer graphics. The computer-generated display produced a 3-D image of the fetus and showed the usefulness and accuracy of this system. Since it took only a few seconds for data collection by ultrasonic inspection, fetal movement did not adversely affect the results. Data input took about ten minutes for 40 slices, and 3-D reconstruction and display took about two minutes. The system made it possible to observe and record the 3-D image of the fetus in utero non-invasively and therefore is expected to make it much easier to obtain a 3-D picture of the fetus in utero.

Defects in regular nanosystems and interference spectra at reemission of electromagnetic field attosecond pulses

NASA Astrophysics Data System (ADS)

Matveev, V. I.; Makarov, D. N.

2017-01-01

The effect of defects in nanostructured targets on interference spectra at the reemission of attosecond electromagnetic pulses has been considered. General expressions have been obtained for calculations of spectral distributions for one-, two-, and three-dimensional multiatomic nanosystems consisting of identical complex atoms with defects such as bends, vacancies, and breaks. Changes in interference spectra by a linear chain with several removed atoms (chain with breaks) and by a linear chain with a bend have been calculated as examples allowing a simple analytical representation. Generalization to two- and three-dimensional nanosystems has been developed.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

A three dimensional Dirichlet-to-Neumann map for surface waves over topography

NASA Astrophysics Data System (ADS)

Nachbin, Andre; Andrade, David

2016-11-01

We consider three dimensional surface water waves in the potential theory regime. The bottom topography can have a quite general profile. In the case of linear waves the Dirichlet-to-Neumann operator is formulated in a matrix decomposition form. Computational simulations illustrate the performance of the method. Two dimensional periodic bottom variations are considered in both the Bragg resonance regime as well as the rapidly varying (homogenized) regime. In the three-dimensional case we use the Luneburg lens-shaped submerged mound, which promotes the focusing of the underlying rays. FAPERJ Cientistas do Nosso Estado Grant 102917/2011 and ANP/PRH-32.

Three-dimensional disc-satellite interaction: torques, migration, and observational signatures

NASA Astrophysics Data System (ADS)

Arzamasskiy, Lev; Zhu, Zhaohuan; Stone, James M.

2018-04-01

The interaction of a satellite with a gaseous disc results in the excitation of spiral density waves, which remove angular momentum from the orbit. In addition, if the orbit is not coplanar with the disc, three-dimensional effects will excite bending and eccentricity waves. We perform three-dimensional hydrodynamic simulations to study nonlinear disc-satellite interaction in inviscid protoplanetary discs for a variety of orbital inclinations from 0° to 180°. It is well known that three-dimensional effects are important even for zero inclination. In this work, we (1) show that for planets with small inclinations (as in the Solar system), effects such as the total torque and migration rate strongly depend on the inclination and are significantly different (about 2.5 times smaller) from the two-dimensional case, (2) give formulae for the migration rate, inclination damping, and precession rate of planets with different inclination angles in disc with different scale heights, and (3) present the observational signatures of a planet on an inclined orbit with respect to the protoplanetary disc. For misaligned planets, we find good agreement with linear theory in the limit of small inclinations, and with dynamical friction estimates for intermediate inclinations. We find that in the latter case, the dynamical friction force is not parallel to the relative planetary velocity. Overall, the derived formulae will be important for studying exoplanets with obliquity.

A panning DLT procedure for three-dimensional videography.

PubMed

Yu, B; Koh, T J; Hay, J G

1993-06-01

The direct linear transformation (DLT) method [Abdel-Aziz and Karara, APS Symposium on Photogrammetry. American Society of Photogrammetry, Falls Church, VA (1971)] is widely used in biomechanics to obtain three-dimensional space coordinates from film and video records. This method has some major shortcomings when used to analyze events which take place over large areas. To overcome these shortcomings, a three-dimensional data collection method based on the DLT method, and making use of panning cameras, was developed. Several small single control volumes were combined to construct a large total control volume. For each single control volume, a regression equation (calibration equation) is developed to express each of the 11 DLT parameters as a function of camera orientation, so that the DLT parameters can then be estimated from arbitrary camera orientations. Once the DLT parameters are known for at least two cameras, and the associated two-dimensional film or video coordinates of the event are obtained, the desired three-dimensional space coordinates can be computed. In a laboratory test, five single control volumes (in a total control volume of 24.40 x 2.44 x 2.44 m3) were used to test the effect of the position of the single control volume on the accuracy of the computed three dimensional space coordinates. Linear and quadratic calibration equations were used to test the effect of the order of the equation on the accuracy of the computed three dimensional space coordinates. For four of the five single control volumes tested, the mean resultant errors associated with the use of the linear calibration equation were significantly larger than those associated with the use of the quadratic calibration equation. The position of the single control volume had no significant effect on the mean resultant errors in computed three dimensional coordinates when the quadratic calibration equation was used. Under the same data collection conditions, the mean resultant errors in the computed three dimensional coordinates associated with the panning and stationary DLT methods were 17 and 22 mm, respectively. The major advantages of the panning DLT method lie in the large image sizes obtained and in the ease with which the data can be collected. The method also has potential for use in a wide variety of contexts. The major shortcoming of the method is the large amount of digitizing necessary to calibrate the total control volume. Adaptations of the method to reduce the amount of digitizing required are being explored.

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Kaul, Upender K.

2005-01-01

A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Phase-locked scroll waves defy turbulence induced by negative filament tension.

PubMed

Li, Teng-Chao; Gao, Xiang; Zheng, Fei-Fei; Cai, Mei-Chun; Li, Bing-Wei; Zhang, Hong; Dierckx, Hans

2016-01-01

Scroll waves in a three-dimensional media may develop into turbulence due to negative tension of the filament. Such negative tension-induced instability of scroll waves has been observed in the Belousov-Zhabotinsky reaction systems. Here we propose a method to restabilize scroll wave turbulence caused by negative tension in three-dimensional chemical excitable media using a circularly polarized (rotating) external field. The stabilization mechanism is analyzed in terms of phase-locking caused by the external field, which makes the effective filament tension positive. The phase-locked scroll waves that have positive tension and higher frequency defy the turbulence and finally restore order. A linear theory for the change of filament tension caused by a generic rotating external field is presented and its predictions closely agree with numerical simulations.

UWB Tracking System Design with TDOA Algorithm

NASA Technical Reports Server (NTRS)

Ni, Jianjun; Arndt, Dickey; Ngo, Phong; Phan, Chau; Gross, Julia; Dusl, John; Schwing, Alan

2006-01-01

This presentation discusses an ultra-wideband (UWB) tracking system design effort using a tracking algorithm TDOA (Time Difference of Arrival). UWB technology is exploited to implement the tracking system due to its properties, such as high data rate, fine time resolution, and low power spectral density. A system design using commercially available UWB products is proposed. A two-stage weighted least square method is chosen to solve the TDOA non-linear equations. Matlab simulations in both two-dimensional space and three-dimensional space show that the tracking algorithm can achieve fine tracking resolution with low noise TDOA data. The error analysis reveals various ways to improve the tracking resolution. Lab experiments demonstrate the UWBTDOA tracking capability with fine resolution. This research effort is motivated by a prototype development project Mini-AERCam (Autonomous Extra-vehicular Robotic Camera), a free-flying video camera system under development at NASA Johnson Space Center for aid in surveillance around the International Space Station (ISS).

Effects of Laboratory Disinfecting Agents on Dimensional Stability of Three Commercially Available Heat-Cured Denture Acrylic Resins in India: An In-Vitro Study

PubMed Central

Jujare, Ravikanth Haridas; Varghese, Rana Kalappattil; Singh, Vishwa Deepak; Gaurav, Amit

2016-01-01

Introduction Dental professionals are exposed to a wide variety of microorganisms which calls for use of effective infection control procedures in the dental office and laboratories that can prevent cross-contamination that could extend to dentists, dental office staff, dental technicians as well as patients. This concern has led to a renewed interest in denture sterilization and disinfection. Heat polymerized dentures exhibit dimensional change during disinfection procedure. Aim The purpose of this study was to determine the influence of different types of widely used laboratory disinfecting agents on the dimensional stability of heat-cured denture acrylic resins and to compare the dimensional stability of three commercially available heat-cured denture acrylic resins in India. Materials and Methods Twelve specimens of uniform dimension each of three different brands namely Stellon, Trevalon and Acralyn-H were prepared using circular metal disc. Chemical disinfectants namely 2% alkaline glutaraldehyde, 1% povidone-iodine, 0.5% sodium hypochlorite and water as control group were used. Diameter of each specimen was measured before immersion and after immersion with time interval of 1 hour and 12 hours. The data was evaluated statistically using one way analysis of variance. Results All the specimens in three disinfectants and in water exhibited very small amount of linear expansion. Among three disinfectants, specimens in 2% alkaline glutaraldehyde exhibited least(0.005mm) and water showed highest (0.009mm) amount of dimensional change. Among resins, Trevalon showed least (0.067mm) and Acralyn-H exhibited highest (0.110mm) amount of dimensional change. Conclusion Although, all the specimens of three different brands of heat-cured denture acrylic resins exhibited increase in linear dimensional change in all the disinfectants and water, they were found to be statistically insignificant. PMID:27134996

[Preliminary construction of three-dimensional visual educational system for clinical dentistry based on world wide web webpage].

PubMed

Hu, Jian; Xu, Xiang-yang; Song, En-min; Tan, Hong-bao; Wang, Yi-ning

2009-09-01

To establish a new visual educational system of virtual reality for clinical dentistry based on world wide web (WWW) webpage in order to provide more three-dimensional multimedia resources to dental students and an online three-dimensional consulting system for patients. Based on computer graphics and three-dimensional webpage technologies, the software of 3Dsmax and Webmax were adopted in the system development. In the Windows environment, the architecture of whole system was established step by step, including three-dimensional model construction, three-dimensional scene setup, transplanting three-dimensional scene into webpage, reediting the virtual scene, realization of interactions within the webpage, initial test, and necessary adjustment. Five cases of three-dimensional interactive webpage for clinical dentistry were completed. The three-dimensional interactive webpage could be accessible through web browser on personal computer, and users could interact with the webpage through rotating, panning and zooming the virtual scene. It is technically feasible to implement the visual educational system of virtual reality for clinical dentistry based on WWW webpage. Information related to clinical dentistry can be transmitted properly, visually and interactively through three-dimensional webpage.

Score-level fusion of two-dimensional and three-dimensional palmprint for personal recognition systems

NASA Astrophysics Data System (ADS)

Chaa, Mourad; Boukezzoula, Naceur-Eddine; Attia, Abdelouahab

2017-01-01

Two types of scores extracted from two-dimensional (2-D) and three-dimensional (3-D) palmprint for personal recognition systems are merged, introducing a local image descriptor for 2-D palmprint-based recognition systems, named bank of binarized statistical image features (B-BSIF). The main idea of B-BSIF is that the extracted histograms from the binarized statistical image features (BSIF) code images (the results of applying the different BSIF descriptor size with the length 12) are concatenated into one to produce a large feature vector. 3-D palmprint contains the depth information of the palm surface. The self-quotient image (SQI) algorithm is applied for reconstructing illumination-invariant 3-D palmprint images. To extract discriminative Gabor features from SQI images, Gabor wavelets are defined and used. Indeed, the dimensionality reduction methods have shown their ability in biometrics systems. Given this, a principal component analysis (PCA)+linear discriminant analysis (LDA) technique is employed. For the matching process, the cosine Mahalanobis distance is applied. Extensive experiments were conducted on a 2-D and 3-D palmprint database with 10,400 range images from 260 individuals. Then, a comparison was made between the proposed algorithm and other existing methods in the literature. Results clearly show that the proposed framework provides a higher correct recognition rate. Furthermore, the best results were obtained by merging the score of B-BSIF descriptor with the score of the SQI+Gabor wavelets+PCA+LDA method, yielding an equal error rate of 0.00% and a recognition rate of rank-1=100.00%.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

NASA Astrophysics Data System (ADS)

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

PubMed

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Statistics of the stochastically forced Lorenz attractor by the Fokker-Planck equation and cumulant expansions.

PubMed

Allawala, Altan; Marston, J B

2016-11-01

We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: a self-adjoint construction of the linear operator and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants. A comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation. Theoretical and computational aspects of the Fokker-Planck and cumulant expansion methods are discussed.

Reconstruction of three-dimensional ultrasound images based on cyclic Savitzky-Golay filters

NASA Astrophysics Data System (ADS)

Toonkum, Pollakrit; Suwanwela, Nijasri C.; Chinrungrueng, Chedsada

2011-01-01

We present a new algorithm for reconstructing a three-dimensional (3-D) ultrasound image from a series of two-dimensional B-scan ultrasound slices acquired in the mechanical linear scanning framework. Unlike most existing 3-D ultrasound reconstruction algorithms, which have been developed and evaluated in the freehand scanning framework, the new algorithm has been designed to capitalize the regularity pattern of the mechanical linear scanning, where all the B-scan slices are precisely parallel and evenly spaced. The new reconstruction algorithm, referred to as the cyclic Savitzky-Golay (CSG) reconstruction filter, is an improvement on the original Savitzky-Golay filter in two respects: First, it is extended to accept a 3-D array of data as the filter input instead of a one-dimensional data sequence. Second, it incorporates the cyclic indicator function in its least-squares objective function so that the CSG algorithm can simultaneously perform both smoothing and interpolating tasks. The performance of the CSG reconstruction filter compared to that of most existing reconstruction algorithms in generating a 3-D synthetic test image and a clinical 3-D carotid artery bifurcation in the mechanical linear scanning framework are also reported.

A multilayered sharp interface model of coupled freshwater and saltwater flow in coastal systems: Model development and application

USGS Publications Warehouse

Essaid, Hedeff I.

1990-01-01

A quasi three-dimensional, finite difference model, that simulates freshwater and saltwater flow separated by a sharp interface, has been developed to study layered coastal aquifer systems. The model allows for regional simulation of coastal groundwater conditions, including the effects of saltwater dynamics on the freshwater system. Vertically integrated freshwater and saltwater flow equations incorporating the interface boundary condition are solved within each aquifer. Leakage through confining layers is calculated by Darcy's law, accounting for density differences across the layer. The locations of the interface tip and toe, within grid blocks, are tracked by linearly extrapolating the position of the interface. The model has been verified using available analytical solutions and experimental results. Application of the model to the Soquel-Aptos basin, Santa Cruz County, California, illustrates the use of the quasi three-dimensional, sharp interface approach for the examination of freshwater-saltwater dynamics in regional systems. Simulation suggests that the interface, today, is still responding to long-term Pleistocene sea level fluctuations and has not achieved equilibrium with present day sea level conditions.

A parallel reaction-transport model applied to cement hydration and microstructure development

NASA Astrophysics Data System (ADS)

Bullard, Jeffrey W.; Enjolras, Edith; George, William L.; Satterfield, Steven G.; Terrill, Judith E.

2010-03-01

A recently described stochastic reaction-transport model on three-dimensional lattices is parallelized and is used to simulate the time-dependent structural and chemical evolution in multicomponent reactive systems. The model, called HydratiCA, uses probabilistic rules to simulate the kinetics of diffusion, homogeneous reactions and heterogeneous phenomena such as solid nucleation, growth and dissolution in complex three-dimensional systems. The algorithms require information only from each lattice site and its immediate neighbors, and this localization enables the parallelized model to exhibit near-linear scaling up to several hundred processors. Although applicable to a wide range of material systems, including sedimentary rock beds, reacting colloids and biochemical systems, validation is performed here on two minerals that are commonly found in Portland cement paste, calcium hydroxide and ettringite, by comparing their simulated dissolution or precipitation rates far from equilibrium to standard rate equations, and also by comparing simulated equilibrium states to thermodynamic calculations, as a function of temperature and pH. Finally, we demonstrate how HydratiCA can be used to investigate microstructure characteristics, such as spatial correlations between different condensed phases, in more complex microstructures.

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

NASA Technical Reports Server (NTRS)

Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

1995-01-01

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

The Stability Region for Feedback Control of the Wake Behind Twin Oscillating Cylinders

NASA Astrophysics Data System (ADS)

Borggaard, Jeff; Gugercin, Serkan; Zietsman, Lizette

2016-11-01

Linear feedback control has the ability to stabilize vortex shedding behind twin cylinders where cylinder rotation is the actuation mechanism. Complete elimination of the wake is only possible for certain Reynolds numbers and cylinder spacing. This is related to the presence of asymmetric unstable modes in the linearized system. We investigate this region of parameter space using a number of closed-loop simulations that bound this region. We then consider the practical issue of designing feedback controls based on limited state measurements by building a nonlinear compensator using linear robust control theory with and incorporating the nonlinear terms in the compensator (e.g., using the extended Kalman filter). Interpolatory model reduction methods are applied to the large discretized, linearized Navier-Stokes system and used for computing the control laws and compensators. Preliminary closed-loop simulations of a three-dimensional version of this problem will also be presented. Supported in part by the National Science Foundation.

Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.

PubMed

Mustafa, M; Mushtaq, A; Hayat, T; Alsaedi, A

2016-01-01

Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4-water ferrofluid is larger in comparison to the pure fluid even at low particle concentration.

Symmetry-Breaking Phase Transition without a Peierls Instability in Conducting Monoatomic Chains

NASA Astrophysics Data System (ADS)

Blumenstein, C.; Schäfer, J.; Morresi, M.; Mietke, S.; Matzdorf, R.; Claessen, R.

2011-10-01

The one-dimensional (1D) model system Au/Ge(001), consisting of linear chains of single atoms on a surface, is scrutinized for lattice instabilities predicted in the Peierls paradigm. By scanning tunneling microscopy and electron diffraction we reveal a second-order phase transition at 585 K. It leads to charge ordering with transversal and vertical displacements and complex interchain correlations. However, the structural phase transition is not accompanied by the electronic signatures of a charge density wave, thus precluding a Peierls instability as origin. Instead, this symmetry-breaking transition exhibits three-dimensional critical behavior. This reflects a dichotomy between the decoupled 1D electron system and the structural elements that interact via the substrate. Such substrate-mediated coupling between the wires thus appears to have been underestimated also in related chain systems.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Local reduction of certain wave operators to one-dimensional form

NASA Technical Reports Server (NTRS)

Roe, Philip

1994-01-01

It is noted that certain common linear wave operators have the property that linear variation of the initial data gives rise to one-dimensional evolution in a plane defined by time and some direction in space. The analysis is given For operators arising in acoustics, electromagnetics, elastodynamics, and an abstract system.

Design and Fabrication of a Miniaturized GMI Magnetic Sensor Based on Amorphous Wire by MEMS Technology

PubMed Central

Chen, Jiawen; Li, Jianhua; Li, Yiyuan; Chen, Yulong

2018-01-01

A miniaturized Co-based amorphous wire GMI (Giant magneto-impedance) magnetic sensor was designed and fabricated in this paper. The Co-based amorphous wire was used as the sense element due to its high sensitivity to the magnetic field. A three-dimensional micro coil surrounding the Co-based amorphous wire was fabricated by MEMS (Micro-Electro-Mechanical System) technology, which was used to extract the electrical signal. The three-dimensional micro pick-up coil was designed and simulated with HFSS (High Frequency Structure Simulator) software to determine the key parameters. Surface micro machining MEMS (Micro-Electro-Mechanical System) technology was employed to fabricate the three-dimensional coil. The size of the developed amorphous wire magnetic sensor is 5.6 × 1.5 × 1.1 mm3. Helmholtz coil was used to characterize the performance of the device. The test results of the sensor sample show that the voltage change is 130 mV/Oe and the linearity error is 4.83% in the range of 0~45,000 nT. The results indicate that the developed miniaturized magnetic sensor has high sensitivity. By testing the electrical resistance of the samples, the results also showed high uniformity of each device. PMID:29494477

Thermal convection in three-dimensional fractured porous media

NASA Astrophysics Data System (ADS)

Mezon, C.; Mourzenko, V. V.; Thovert, J.-F.; Antoine, R.; Fontaine, F.; Finizola, A.; Adler, P. M.

2018-01-01

Thermal convection is numerically computed in three-dimensional (3D) fluid saturated isotropically fractured porous media. Fractures are randomly inserted as two-dimensional (2D) convex polygons. Flow is governed by Darcy's 2D and 3D laws in the fractures and in the porous medium, respectively; exchanges take place between these two structures. Results for unfractured porous media are in agreement with known theoretical predictions. The influence of parameters such as the fracture aperture (or fracture transmissivity) and the fracture density on the heat released by the whole system is studied for Rayleigh numbers up to 150 in cubic boxes with closed-top conditions. Then, fractured media are compared to homogeneous porous media with the same macroscopic properties. Three major results could be derived from this study. The behavior of the system, in terms of heat release, is determined as a function of fracture density and fracture transmissivity. First, the increase in the output flux with fracture density is linear over the range of fracture density tested. Second, the increase in output flux as a function of fracture transmissivity shows the importance of percolation. Third, results show that the effective approach is not always valid, and that the mismatch between the full calculations and the effective medium approach depends on the fracture density in a crucial way.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Large Scale Laser Two-Photon Polymerization Structuring for Fabrication of Artificial Polymeric Scaffolds for Regenerative Medicine

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

Malinauskas, M.; Purlys, V.; Zukauskas, A.

2010-11-10

We present a femtosecond Laser Two-Photon Polymerization (LTPP) system of large scale three-dimensional structuring for applications in tissue engineering. The direct laser writing system enables fabrication of artificial polymeric scaffolds over a large area (up to cm in lateral size) with sub-micrometer resolution which could find practical applications in biomedicine and surgery. Yb:KGW femtosecond laser oscillator (Pharos, Light Conversion. Co. Ltd.) is used as an irradiation source (75 fs, 515 nm (frequency doubled), 80 MHz). The sample is mounted on wide range linear motor driven stages having 10 nm sample positioning resolution (XY--ALS130-100, Z--ALS130-50, Aerotech, Inc.). These stages guarantee anmore » overall travelling range of 100 mm into X and Y directions and 50 mm in Z direction and support the linear scanning speed up to 300 mm/s. By moving the sample three-dimensionally the position of laser focus in the photopolymer is changed and one is able to write complex 3D (three-dimensional) structures. An illumination system and CMOS camera enables online process monitoring. Control of all equipment is automated via custom made computer software ''3D-Poli'' specially designed for LTPP applications. Structures can be imported from computer aided design STereoLihography (stl) files or programmed directly. It can be used for rapid LTPP structuring in various photopolymers (SZ2080, AKRE19, PEG-DA-258) which are known to be suitable for bio-applications. Microstructured scaffolds can be produced on different substrates like glass, plastic and metal. In this paper, we present microfabricated polymeric scaffolds over a large area and growing of adult rabbit myogenic stem cells on them. Obtained results show the polymeric scaffolds to be applicable for cell growth practice. It exhibit potential to use it for artificial pericardium in the experimental model in the future.« less

Large Scale Laser Two-Photon Polymerization Structuring for Fabrication of Artificial Polymeric Scaffolds for Regenerative Medicine

NASA Astrophysics Data System (ADS)

Malinauskas, M.; Purlys, V.; Žukauskas, A.; Rutkauskas, M.; Danilevičius, P.; Paipulas, D.; Bičkauskaitė, G.; Bukelskis, L.; Baltriukienė, D.; Širmenis, R.; Gaidukevičiutė, A.; Bukelskienė, V.; Gadonas, R.; Sirvydis, V.; Piskarskas, A.

2010-11-01

We present a femtosecond Laser Two-Photon Polymerization (LTPP) system of large scale three-dimensional structuring for applications in tissue engineering. The direct laser writing system enables fabrication of artificial polymeric scaffolds over a large area (up to cm in lateral size) with sub-micrometer resolution which could find practical applications in biomedicine and surgery. Yb:KGW femtosecond laser oscillator (Pharos, Light Conversion. Co. Ltd.) is used as an irradiation source (75 fs, 515 nm (frequency doubled), 80 MHz). The sample is mounted on wide range linear motor driven stages having 10 nm sample positioning resolution (XY—ALS130-100, Z—ALS130-50, Aerotech, Inc.). These stages guarantee an overall travelling range of 100 mm into X and Y directions and 50 mm in Z direction and support the linear scanning speed up to 300 mm/s. By moving the sample three-dimensionally the position of laser focus in the photopolymer is changed and one is able to write complex 3D (three-dimensional) structures. An illumination system and CMOS camera enables online process monitoring. Control of all equipment is automated via custom made computer software "3D-Poli" specially designed for LTPP applications. Structures can be imported from computer aided design STereoLihography (stl) files or programmed directly. It can be used for rapid LTPP structuring in various photopolymers (SZ2080, AKRE19, PEG-DA-258) which are known to be suitable for bio-applications. Microstructured scaffolds can be produced on different substrates like glass, plastic and metal. In this paper, we present microfabricated polymeric scaffolds over a large area and growing of adult rabbit myogenic stem cells on them. Obtained results show the polymeric scaffolds to be applicable for cell growth practice. It exhibit potential to use it for artificial pericardium in the experimental model in the future.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

DOE PAGES

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

2015-01-01

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

Teaching veterinary obstetrics using three-dimensional animation technology.

PubMed

Scherzer, Jakob; Buchanan, M Flint; Moore, James N; White, Susan L

2010-01-01

In this three-year study, test scores for students taught veterinary obstetrics in a classroom setting with either traditional media (photographs, text, and two-dimensional graphical presentations) were compared with those for students taught by incorporating three-dimensional (3D) media (linear animations and interactive QuickTime Virtual Reality models) into the classroom lectures. Incorporation of the 3D animations and interactive models significantly increased students' scores on essay questions designed to assess their comprehension of the subject matter. This approach to education may help to better prepare students for dealing with obstetrical cases during their final clinical year and after graduation.

The three-dimensional compressible flow in a radial inflow turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Tabakoff, W.; Malak, M.

1984-01-01

This work presents the results of an analytical study and an experimental investigation of the three-dimensional flow in a turbine scroll. The finite element method is used in the iterative numerical solution of the locally linearized governing equations for the three-dimensional velocity potential field. The results of the numerical computations are compared with the experimental measurements in the scroll cross sections, which were obtained using laser Doppler velocimetry and hot wire techniques. The results of the computations show a variation in the flow conditions around the rotor periphery which was found to depend on the scroll geometry.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

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

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

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.

Multiple-channel ultra-violet absorbance detector for two-dimensional chromatographic separations.

PubMed

Lynch, Kyle B; Yang, Yu; Ren, Jiangtao; Liu, Shaorong

2018-05-01

In recent years, much research has gone into developing online comprehensive two-dimensional liquid chromatographic systems allowing for high peak capacities in comparable separation times to that of one-dimensional liquid chromatographic systems. However, the speed requirements in the second dimension (2nd-D) still remain one challenge for complex biological samples due to the current configuration of two column/two detector systems. Utilization of multiple 2nd-D columns can mitigate this challenge. To adapt this approach, we need a multiple channel detector. Here we develop a versatile multichannel ultraviolet (UV) light absorbance detector that is capable of simultaneously monitoring separations in 12 columns. The detector consists of a deuterium lighthouse, a flow cell assembly (a 13-channel flow cell fitted with a 13-photodiode-detection system), and a data acquisition and monitoring terminal. Through the use of a custom high optical quality furcated fiber to improve light transmission, precise machining of a flow cell to reduce background stray light through precision alignment, and sensitive electronic circuitry to reduce electronic noise through an active low pass filter, the background noise level is measured in the tens of µAU. We obtain a linear dynamic range of close to three orders of magnitude. Compared to a commercialized multichannel UV light absorbance detector like the Waters 2488 UV/Vis, our device provides an increase in channel detection while residing within the same noise region and linear range. Copyright © 2018 Elsevier B.V. All rights reserved.

Quantum error-correcting code for ternary logic

NASA Astrophysics Data System (ADS)

Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; Sur-Kolay, Susmita

2018-05-01

Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 ×2 ) -dimensional and (3 ×3 ) -dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 ×2 ) -dimensional as well as (3 ×3 ) -dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.

Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

NASA Astrophysics Data System (ADS)

Han, B.; Li, Y.

2016-12-01

We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera

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

Zhu Feipeng; Shi Hongjian; Bai Pengxiang

In fringe projection, the CCD camera and the projector are often placed at equal height. In this paper, we will study the calibration of an unequal arrangement of the CCD camera and the projector. The principle of fringe projection with two-dimensional digital image correlation to acquire the profile of object surface is described in detail. By formula derivation and experiment, the linear relationship between the out-of-plane calibration coefficient and the y coordinate is clearly found. To acquire the three-dimensional (3D) information of an object correctly, this paper presents an effective calibration method with linear least-squares fitting, which is very simplemore » in principle and calibration. Experiments are implemented to validate the availability and reliability of the calibration method.« less

High-Dimensional Quantum Information Processing with Linear Optics

NASA Astrophysics Data System (ADS)

Fitzpatrick, Casey A.

Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for carrying out quantum walks on arbitrary graph structures, a powerful tool for any quantum computer. It is shown that the novel architecture provides new, efficient capabilities for the optical quantum simulation of Hamiltonians and topologically protected states. Further, these simulations use exponentially fewer resources than feedforward techniques, scale linearly to higher-dimensional systems, and use only linear optics, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

Streamline-curvature effect in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Reed, Helen L.; Lin, Ray-Sing; Petraglia, Media M.

1992-01-01

The effect of including wall and streamline curvature terms in swept-wing boundary-layer stability calculations is studied. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in this formulation and approximated by their local finite-difference values. Convex-wall curvature has a stabilizing effect, while streamline curvature is destabilizing if the curvature exceeds a critical value.

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

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

1996-01-01

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Three dimensional, non-linear, finite element analysis of compactable soil interaction with a hyperelastic wheel

NASA Astrophysics Data System (ADS)

Chiroux, Robert Charles

The objective of this research was to produce a three dimensional, non-linear, dynamic simulation of the interaction between a hyperelastic wheel rolling over compactable soil. The finite element models developed to produce the simulation utilized the ABAQUS/Explicit computer code. Within the simulation two separate bodies were modeled, the hyperelastic wheel and a compactable soil-bed. Interaction between the bodies was achieved by allowing them to come in contact but not to penetrate the contact surface. The simulation included dynamic loading of a hyperelastic, rubber tire in contact with compactable soil with an applied constant angular velocity or torque, including a tow load, applied to the wheel hub. The constraints on the wheel model produced a straight and curved path. In addition the simulation included a shear limit between the tire and soil allowing for the introduction of slip. Soil properties were simulated using the Drucker-Prager, Cap Plasticity model available within the ABAQUS/Explicit program. Numerical results obtained from the three dimensional model were compared with related experimental data and showed good correlation for similar conditions. Numerical and experimental data compared well for both stress and wheel rut formation depth under a weight of 5.8 kN and a constant angular velocity applied to the wheel hub. The simulation results provided a demonstration of the benefit of three-dimensional simulation in comparison to previous two-dimensional, plane strain simulations.

Reversible gelling culture media for in-vitro cell culture in three-dimensional matrices

DOEpatents

An, Yuehuei H.; Mironov, Vladimir A.; Gutowska, Anna

2000-01-01

A gelling cell culture medium useful for forming a three dimensional matrix for cell culture in vitro is prepared by copolymerizing an acrylamide derivative with a hydrophilic comonomer to form a reversible (preferably thermally reversible) gelling linear random copolymer in the form of a plurality of linear chains having a plurality of molecular weights greater than or equal to a minimum gelling molecular weight cutoff, mixing the copolymer with an aqueous solvent to form a reversible gelling solution and adding a cell culture medium to the gelling solution to form the gelling cell culture medium. Cells such as chondrocytes or hepatocytes are added to the culture medium to form a seeded culture medium, and temperature of the medium is raised to gel the seeded culture medium and form a three dimensional matrix containing the cells. After propagating the cells in the matrix, the cells may be recovered by lowering the temperature to dissolve the matrix and centrifuging.

On-line analysis of algae in water by discrete three-dimensional fluorescence spectroscopy.

PubMed

Zhao, Nanjing; Zhang, Xiaoling; Yin, Gaofang; Yang, Ruifang; Hu, Li; Chen, Shuang; Liu, Jianguo; Liu, Wenqing

2018-03-19

In view of the problem of the on-line measurement of algae classification, a method of algae classification and concentration determination based on the discrete three-dimensional fluorescence spectra was studied in this work. The discrete three-dimensional fluorescence spectra of twelve common species of algae belonging to five categories were analyzed, the discrete three-dimensional standard spectra of five categories were built, and the recognition, classification and concentration prediction of algae categories were realized by the discrete three-dimensional fluorescence spectra coupled with non-negative weighted least squares linear regression analysis. The results show that similarities between discrete three-dimensional standard spectra of different categories were reduced and the accuracies of recognition, classification and concentration prediction of the algae categories were significantly improved. By comparing with that of the chlorophyll a fluorescence excitation spectra method, the recognition accuracy rate in pure samples by discrete three-dimensional fluorescence spectra is improved 1.38%, and the recovery rate and classification accuracy in pure diatom samples 34.1% and 46.8%, respectively; the recognition accuracy rate of mixed samples by discrete-three dimensional fluorescence spectra is enhanced by 26.1%, the recovery rate of mixed samples with Chlorophyta 37.8%, and the classification accuracy of mixed samples with diatoms 54.6%.

Handy elementary algebraic properties of the geometry of entanglement

NASA Astrophysics Data System (ADS)

Blair, Howard A.; Alsing, Paul M.

2013-05-01

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

Low-Dimensional Model of a Cylinder Wake

NASA Astrophysics Data System (ADS)

Luchtenburg, Mark; Cohen, Kelly; Siegel, Stefan; McLaughlin, Tom

2003-11-01

In a two-dimensional cylinder wake, self-excited oscillations in the form of periodic shedding of vortices are observed above a critical Reynolds number of about 47. These flow-induced non-linear oscillations lead to some undesirable effects associated with unsteady pressures such as fluid-structure interactions. An effective way of suppressing the self-excited flow oscillations is by the incorporation of closed-loop flow control. In this effort, a low dimensional, proper orthogonal decomposition (POD) model is based on data obtained from direct numerical simulations of the Navier Stokes equations for the two dimensional circular cylinder wake at a Reynolds number of 100. Three different conditions are examined, namely, the unforced wake experiencing steady-state vortex shedding, the transient behavior of the unforced wake at the startup of the simulation, and transient response to open-loop harmonic forcing by translation. We discuss POD mode selection and the number of modes that need to be included in the low-dimensional model. It is found that the transient dynamics need to be represented by a coupled system that includes an aperiodic mean-flow mode, an aperiodic shift mode and the periodic von Karman modes. Finally, a least squares mapping method is introduced to develop the non-linear state equations. The predictive capability of the state equations demonstrates the ability of the above approach to model the transient dynamics of the wake.

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

The dynamics and control of large flexible space structures - 13

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Li, Feiyue; Xu, Jianke

1990-01-01

The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.

Three dimensional steady subsonic Euler flows in bounded nozzles

NASA Astrophysics Data System (ADS)

Chen, Chao; Xie, Chunjing

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization.

PubMed

Yang, C; Jiang, W; Chen, D-H; Adiga, U; Ng, E G; Chiu, W

2009-03-01

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Self-diffusion in a stochastically heated two-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2016-09-01

Diffusion in a two-dimensional dusty plasma liquid (i.e., a Yukawa liquid) is studied experimentally. The dusty plasma liquid is heated stochastically by a surrounding three-dimensional toroidal dusty plasma gas which acts as a thermal reservoir. The measured dust velocity distribution functions are isotropic Maxwellians, giving a well-defined kinetic temperature. The mean-square displacement for dust particles is found to increase linearly with time, indicating normal diffusion. The measured diffusion coefficients increase approximately linearly with temperature. The effective collision rate is dominated by collective dust-dust interactions rather than neutral gas drag, and is comparable to the dusty-plasma frequency.

Three-dimensional to two-dimensional transition in mode-I fracture microbranching in a perturbed hexagonal close-packed lattice

NASA Astrophysics Data System (ADS)

Heizler, Shay I.; Kessler, David A.

2017-06-01

Mode-I fracture exhibits microbranching in the high velocity regime where the simple straight crack is unstable. For velocities below the instability, classic modeling using linear elasticity is valid. However, showing the existence of the instability and calculating the dynamics postinstability within the linear elastic framework is difficult and controversial. The experimental results give several indications that the microbranching phenomenon is basically a three-dimensional (3D) phenomenon. Nevertheless, the theoretical effort has been focused mostly on two-dimensional (2D) modeling. In this paper we study the microbranching instability using three-dimensional atomistic simulations, exploring the difference between the 2D and the 3D models. We find that the basic 3D fracture pattern shares similar behavior with the 2D case. Nevertheless, we exhibit a clear 3D-2D transition as the crack velocity increases, whereas as long as the microbranches are sufficiently small, the behavior is pure 3D behavior, whereas at large driving, as the size of the microbranches increases, more 2D-like behavior is exhibited. In addition, in 3D simulations, the quantitative features of the microbranches, separating the regimes of steady-state cracks (mirror) and postinstability (mist-hackle) are reproduced clearly, consistent with the experimental findings.

Magnetotransport in two dimensional electron systems under microwave excitation and in highly oriented pyrolytic graphite

NASA Astrophysics Data System (ADS)

Ramanayaka, Aruna N.

This thesis consists of two parts. The first part considers the effect of microwave radiation on magnetotransport in high quality GaAs/AlGaAs heterostructure two dimensional electron systems. The effect of microwave (MW) radiation on electron temperature was studied by investigating the amplitude of the Shubnikov de Haas (SdH) oscillations in a regime where the cyclotron frequency o c and the MW angular frequency o satisfy 2o ≤ o c ≤ 3.5o. The results indicate negligible electron heating under modest MW photoexcitation, in agreement with theoretical predictions. Next, the effect of the polarization direction of the linearly polarized MWs on the MW induced magnetoresistance oscillation amplitude was investigated. The results demonstrate the first indications of polarization dependence of MW induced magnetoresistance oscillations. In the second part, experiments on the magnetotransport of three dimensional highly oriented pyrolytic graphite (HOPG) reveal a non-zero Berry phase for HOPG. Furthermore, a novel phase relation between oscillatory magneto- and Hall- resistances was discovered from the studies of the HOPG specimen. INDEX WORDS: Two dimensional electron systems, Magnetoresistance, Microwave induced magnetoresistance oscillations, Graphite, Quantum Hall effect, Hall effect, Resistivity rule, Shubnikov de Haas effect, Shubnikov de Haas oscillation.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Implementation of webcam-based hyperspectral imaging system

NASA Astrophysics Data System (ADS)

Balooch, Ali; Nazeri, Majid; Abbasi, Hamed

2018-02-01

In the present work, a hyperspectral imaging system (imaging spectrometer) using a commercial webcam has been designed and developed. This system was able to capture two-dimensional spectra (in emission, transmission and reflection modes) directly from the scene in the desired wavelengths. Imaging of the object is done directly by linear sweep (pushbroom method). To do so, the spectrometer is equipped with a suitable collecting lens and a linear travel stage. A 1920 x 1080 pixel CMOS webcam was used as a detector. The spectrometer has been calibrated by the reference spectral lines of standard lamps. The spectral resolution of this system was about 2nm and its spatial resolution was about 1 mm for a 10 cm long object. The hardware solution is based on data acquisition working on the USB platform and controlled by a LabVIEW program. In this system, the initial output was a three-dimensional matrix in which two dimensions of the matrix were related to the spatial information of the object and the third dimension was the spectrum of any point of the object. Finally, the images in different wavelengths were created by reforming the data of the matrix. The free spectral range (FSR) of the system was 400 to 1100 nm. The system was successfully tested for some applications, such as plasma diagnosis as well as applications in food and agriculture sciences.

Linear and nonlinear interpretation of the direct strike lightning response of the NASA F106B thunderstorm research aircraft

NASA Technical Reports Server (NTRS)

Rudolph, T. H.; Perala, R. A.

1983-01-01

The objective of the work reported here is to develop a methodology by which electromagnetic measurements of inflight lightning strike data can be understood and extended to other aircraft. A linear and time invariant approach based on a combination of Fourier transform and three dimensional finite difference techniques is demonstrated. This approach can obtain the lightning channel current in the absence of the aircraft for given channel characteristic impedance and resistive loading. The model is applied to several measurements from the NASA F106B lightning research program. A non-linear three dimensional finite difference code has also been developed to study the response of the F106B to a lightning leader attachment. This model includes three species air chemistry and fluid continuity equations and can incorporate an experimentally based streamer formulation. Calculated responses are presented for various attachment locations and leader parameters. The results are compared qualitatively with measured inflight data.

Three-dimensional thermocapillary flow regimes with evaporation

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2017-10-01

A three-dimensional problem of evaporative convection in a system of the immiscible media with a common thermocapillary interface is studied. New exact solution, which is a generalization of the Ostroumov - Birikh solution of the Navier - Stokes equations in the Oberbeck - Boussinesq approximation, is presented in order to describe the joint flows of the liquid and gas - vapor mixture in an infinite channel with a rectangular cross-section. The motion occurs in the bulk force field under action of a constant longitudinal temperature gradient. The velocity components depend only on the transverse coordinates. The functions of pressure, temperature and concentration of vapor in the gas are characterized by the linear dependence on the longitudinal coordinate. In the framework of the problem statement, which takes into account diffusive mass flux through the interface and zero vapor flux at the upper boundary of the channel, the influence of the gravity and intensity of the thermal action on flow structure is studied. The original three-dimensional problem is reduced to a chain of two-dimensional problems which are solved numerically with help of modification of the method of alternating directions. Arising flows can be characterized as a translational-rotational motion, under that the symmetrical double, quadruple or sextuple vortex structures are formed. Quantity, shape and structure of the vortexes also depend on properties of the working media.

Application of Linear and Non-Linear Harmonic Methods for Unsteady Transonic Flow

NASA Astrophysics Data System (ADS)

Gundevia, Rayomand

This thesis explores linear and non-linear computational methods for solving unsteady flow. The eventual goal is to apply these methods to two-dimensional and three-dimensional flutter predictions. In this study the quasi-one-dimensional nozzle is used as a framework for understanding these methods and their limitations. Subsonic and transonic cases are explored as the back-pressure is forced to oscillate with known amplitude and frequency. A steady harmonic approach is used to solve this unsteady problem for which perturbations are said to be small in comparison to the mean flow. The use of a linearized Euler equations (LEE) scheme is good at capturing the flow characteristics but is limited by accuracy to relatively small amplitude perturbations. The introduction of time-averaged second-order terms in the Non-Linear Harmonic (NLH) method means that a better approximation of the mean-valued solution, upon which the linearization is based, can be made. The nonlinear time-accurate Euler solutions are used for comparison and to establish the regimes of unsteadiness for which these schemes fails. The usefulness of the LEE and NLH methods lie in the gains in computational efficiency over the full equations.

Self-force on a point charge and linear source in the space of a screw dislocation

NASA Astrophysics Data System (ADS)

Azevedo, Sérgio; Moraes, Fernando

2000-03-01

Using a description of defect in solids in terms of three-dimensional gravity, we determine the eletrostatic self-force acting on a point teste charge and a linear source in the presence of a screw dislocation.

Computation of the three-dimensional medial surface dynamics of the vocal folds.

PubMed

Döllinger, Michael; Berry, David A

2006-01-01

To increase our understanding of pathological and healthy voice production, quantitative measurement of the medial surface dynamics of the vocal folds is significant, albeit rarely performed because of the inaccessibility of the vocal folds. Using an excised hemilarynx methodology, a new calibration technique, herein referred to as the linear approximate (LA) method, was introduced to compute the three-dimensional coordinates of fleshpoints along the entire medial surface of the vocal fold. The results were compared with results from the direct linear transform. An associated error estimation was presented, demonstrating the improved accuracy of the new method. A test on real data was reported including computation of quantitative measurements of vocal fold dynamics.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Morphometry of the ear in Down's syndrome subjects. A three-dimensional computerized assessment.

PubMed

Sforza, C; Dellavia, C; Tartaglia, G M; Ferrario, V F

2005-07-01

The three-dimensional coordinates of 13 soft-tissue landmarks on the ears were obtained by a computerized digitizer in 28 subjects with Down's syndrome aged 12-45 years, and in 449 sex, age and ethnic group matched controls. From the landmarks, left and right linear distances (ear width and length), ratios (ear width-to-ear length), areas (ear area), angles (angle of the auricle versus the facial midplane) and the three-dimensional symmetry index were calculated. For both males and females, all linear dimensions and areas were significantly (Analysis of Variance, P < 0.001) larger in the reference subjects than in the subjects with Down's syndrome. All values significantly increased as a function of age (P < 0.05); the increment was larger in the reference subjects than in the subjects with Down's syndrome. On both sides of the face, the subjects with Down's syndrome had larger ear width-to-ear length ratios, and larger angles of the auricle versus the facial midplane than the reference subjects. The three-dimensional symmetry index was significantly larger in the reference subjects and in the older persons. In conclusion, ear dimensions, position and shape significantly differed in subjects with Down's syndrome when compared to sex, age and ethnic group matched controls. Some of the differences were sex and age related.

Hyoid Bone Development: An Assessment Of Optimal CT Scanner Parameters and Three-Dimensional Volume Rendering Techniques.

PubMed

Cotter, Meghan M; Whyms, Brian J; Kelly, Michael P; Doherty, Benjamin M; Gentry, Lindell R; Bersu, Edward T; Vorperian, Houri K

2015-08-01

The hyoid bone anchors and supports the vocal tract. Its complex shape is best studied in three dimensions, but it is difficult to capture on computed tomography (CT) images and three-dimensional volume renderings. The goal of this study was to determine the optimal CT scanning and rendering parameters to accurately measure the growth and developmental anatomy of the hyoid and to determine whether it is feasible and necessary to use these parameters in the measurement of hyoids from in vivo CT scans. Direct linear and volumetric measurements of skeletonized hyoid bone specimens were compared with corresponding CT images to determine the most accurate scanning parameters and three-dimensional rendering techniques. A pilot study was undertaken using in vivo scans from a retrospective CT database to determine feasibility of quantifying hyoid growth. Scanning parameters and rendering technique affected accuracy of measurements. Most linear CT measurements were within 10% of direct measurements; however, volume was overestimated when CT scans were acquired with a slice thickness greater than 1.25 mm. Slice-by-slice thresholding of hyoid images decreased volume overestimation. The pilot study revealed that the linear measurements tested correlate with age. A fine-tuned rendering approach applied to small slice thickness CT scans produces the most accurate measurements of hyoid bones. However, linear measurements can be accurately assessed from in vivo CT scans at a larger slice thickness. Such findings imply that investigation into the growth and development of the hyoid bone, and the vocal tract as a whole, can now be performed using these techniques. © 2015 Wiley Periodicals, Inc.

Two-component dark-bright solitons in three-dimensional atomic Bose-Einstein condensates.

PubMed

Wang, Wenlong; Kevrekidis, P G

2017-03-01

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.

Modeling and Analysis of Large Amplitude Flight Maneuvers

NASA Technical Reports Server (NTRS)

Anderson, Mark R.

2004-01-01

Analytical methods for stability analysis of large amplitude aircraft motion have been slow to develop because many nonlinear system stability assessment methods are restricted to a state-space dimension of less than three. The proffered approach is to create regional cell-to-cell maps for strategically located two-dimensional subspaces within the higher-dimensional model statespace. These regional solutions capture nonlinear behavior better than linearized point solutions. They also avoid the computational difficulties that emerge when attempting to create a cell map for the entire state-space. Example stability results are presented for a general aviation aircraft and a micro-aerial vehicle configuration. The analytical results are consistent with characteristics that were discovered during previous flight-testing.

Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

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

Yan, R.; Aluie, H.; Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14627

The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume.

Linear stability of three-dimensional boundary layers - Effects of curvature and non-parallelism

NASA Technical Reports Server (NTRS)

Malik, M. R.; Balakumar, P.

1993-01-01

In this paper we study the effect of in-plane (wavefront) curvature on the stability of three-dimensional boundary layers. It is found that this effect is stabilizing or destabilizing depending upon the sign of the crossflow velocity profile. We also investigate the effects of surface curvature and nonparallelism on crossflow instability. Computations performed for an infinite-swept cylinder show that while convex curvature stabilizes the three-dimensional boundary layer, nonparallelism is, in general, destabilizing and the net effect of the two depends upon meanflow and disturbance parameters. It is also found that concave surface curvature further destabilizes the crossflow instability.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System

NASA Astrophysics Data System (ADS)

Li, Chun-Lai; Li, Wen; Zhang, Jing; Xie, Yuan-Xi; Zhao, Yi-Bo

2016-09-01

A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincaré map, power spectrum, Kaplan-Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. Supported by Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ4036, University Natural Science Foundation of Jiangsu Province under Grant No. 14KJB120007 and the National Natural Science Foundation of China under Grant Nos. 11504176 and 11602084

Gamma/x-ray linear pushbroom stereo for 3D cargo inspection

NASA Astrophysics Data System (ADS)

Zhu, Zhigang; Hu, Yu-Chi

2006-05-01

For evaluating the contents of trucks, containers, cargo, and passenger vehicles by a non-intrusive gamma-ray or X-ray imaging system to determine the possible presence of contraband, three-dimensional (3D) measurements could provide more information than 2D measurements. In this paper, a linear pushbroom scanning model is built for such a commonly used gamma-ray or x-ray cargo inspection system. Accurate 3D measurements of the objects inside a cargo can be obtained by using two such scanning systems with different scanning angles to construct a pushbroom stereo system. A simple but robust calibration method is proposed to find the important parameters of the linear pushbroom sensors. Then, a fast and automated stereo matching algorithm based on free-form deformable registration is developed to obtain 3D measurements of the objects under inspection. A user interface is designed for 3D visualization of the objects in interests. Experimental results of sensor calibration, stereo matching, 3D measurements and visualization of a 3D cargo container and the objects inside, are presented.

Three Dimensional Integration and On-Wafer Packaging for Heterogeneous Wafer-Scale Circuit Architectures

DTIC Science & Technology

2006-11-01

Chip Level CMOS Chip High resistivity Si Metal Interconnect 25μm 24GHz fully integrated receiver CMOS transimpedance Amplifier (13GHz BW, 52dBΩ...power of a high-resistivity SiGe power amplifier chip with the wide operating frequency range and compactness of a CMOS mixed signal chip operating...With good RF channel selectivity, system specifications such as the linearity of the low noise amplifier (LNA), the phase noise of the voltage

Prediction of high-dimensional states subject to respiratory motion: a manifold learning approach

NASA Astrophysics Data System (ADS)

Liu, Wenyang; Sawant, Amit; Ruan, Dan

2016-07-01

The development of high-dimensional imaging systems in image-guided radiotherapy provides important pathways to the ultimate goal of real-time full volumetric motion monitoring. Effective motion management during radiation treatment usually requires prediction to account for system latency and extra signal/image processing time. It is challenging to predict high-dimensional respiratory motion due to the complexity of the motion pattern combined with the curse of dimensionality. Linear dimension reduction methods such as PCA have been used to construct a linear subspace from the high-dimensional data, followed by efficient predictions on the lower-dimensional subspace. In this study, we extend such rationale to a more general manifold and propose a framework for high-dimensional motion prediction with manifold learning, which allows one to learn more descriptive features compared to linear methods with comparable dimensions. Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where accurate and efficient prediction can be performed. A fixed-point iterative pre-image estimation method is used to recover the predicted value in the original state space. We evaluated and compared the proposed method with a PCA-based approach on level-set surfaces reconstructed from point clouds captured by a 3D photogrammetry system. The prediction accuracy was evaluated in terms of root-mean-squared-error. Our proposed method achieved consistent higher prediction accuracy (sub-millimeter) for both 200 ms and 600 ms lookahead lengths compared to the PCA-based approach, and the performance gain was statistically significant.

Application of Hyperspectral Techniques to Monitoring and Management of Invasive Plant Species Infestation

DTIC Science & Technology

2008-01-01

the sensor is a data cloud in multi- dimensional space with each band generating an axis of dimension. When the data cloud is viewed in two or three...endmember of interest is not a true endmember in the data space . A ) B) Figure 8: Linear mixture models. A ) two- dimensional ...multi- dimensional space . A classifier is a computer algorithm that takes

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

NASA Astrophysics Data System (ADS)

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Noack, Bernd R.

2017-04-01

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

NASA Astrophysics Data System (ADS)

Benhaiem, David; Joyce, Michael; Sicard, François

2013-03-01

One-dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three-dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three-dimensional Einstein-de Sitter (EdS) model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two-point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalization of the so-called stable clustering hypothesis in three dimensions; and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the `stable clustering' region from the `universal' region is very well approximated by a `critical' value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of `universality' of non-linear clustering in this context.

Maintenance of headland-associated linear sandbanks: modelling the secondary flows and sediment transport

NASA Astrophysics Data System (ADS)

Berthot, Alexis; Pattiaratchi, Charitha

2005-12-01

Linear sandbanks are located globally in areas where there are strong currents and an abundance of sand. In the recent years, these sandbanks have become of strategic interest as a potential source of marine aggregates (sand and gravel) and mineral deposits. They form the seaward boundary of the nearshore zone and therefore are important for the stability of the coastal system. They also commonly reach the sea surface and thus pose a threat to navigation. Headland-associated linear sandbanks are a specific type of sandbanks which are located in the lee of coastal topographic features such as headlands and islands. Interaction between tidal currents and topographic features generate complex three-dimensional circulation patterns that significantly influence the distribution of sediments in the vicinity of the feature. Field and numerical model investigations of the three-dimensional flow structure have been undertaken on the Levillain Shoal, a headland-associated linear sandbank present in the lee of Cape Levillain (Shark Bay, Western Australia). The field data indicated the presence of secondary flows near the tip of the cape and around the bank which were re-produced in the numerical simulations. Numerical results have shown that residual eddies are not representative of the sediment transport and that secondary currents enhance the convergence of sediment towards the sandbank. Maintenance processes have been investigated. Sediment transport paths near the cape and the bank indicate that the sandbank is part of a sand circulation cell where the sand is circulating around the bank with exchanges between the sandbank and the headland.

Vertical Distribution of Radiation Stress for Non-linear Shoaling Waves

NASA Astrophysics Data System (ADS)

Webb, B. M.; Slinn, D. N.

2004-12-01

The flux of momentum directed shoreward by an incident wave field, commonly referred to as the radiation stress, plays a significant role in nearshore circulation and, therefore, has a profound impact on the transport of pollutants, biota, and sediment in nearshore systems. Having received much attention since the seminal work of Longuet-Higgins and Stewart in the early 1960's, use of the radiation stress concept continues to be refined and evidence of its utility is widespread in literature pertaining to coastal and ocean science. A number of investigations, both numerical and analytical in nature, have used the concept of the radiation stress to derive appropriate forcing mechanisms that initiate cross-shore and longshore circulation, but typically in a depth-averaged sense due to a lack of information concerning the vertical distribution of the wave stresses. While depth-averaged nearshore circulation models are still widely used today, advancements in technology have permitted the adaptation of three-dimensional (3D) modeling techniques to study flow properties of complex nearshore circulation systems. It has been shown that the resulting circulation in these 3D models is very sensitive to the vertical distribution of the nearshore forcing, which have often been implemented as either depth-uniform or depth-linear distributions. Recently, analytical expressions describing the vertical structure of radiation stress components have appeared in the literature (see Mellor, 2003; Xia et al., 2004) but do not fully describe the magnitude and structure in the region bound by the trough and crest of non-linear, propagating waves. Utilizing a three-dimensional, non-linear, numerical model that resolves the time-dependent free surface, we present mean flow properties resulting from a simulation of Visser's (1984, 1991) laboratory experiment on uniform longshore currents. More specifically, we provide information regarding the vertical distribution of radiation stress components (Sxx and Sxy) resulting from obliquely incident, non-linear shoaling waves. Vertical profiles of the radiation stress components predicted by the numerical model are compared with published analytical solutions, expressions given by linear theory, and observations from an investigation employing second-order cnoidal wave theory.

Three-dimensional imaging and remote sensing imaging; Proceedings of the Meeting, Los Angeles, CA, Jan. 14, 15, 1988

NASA Astrophysics Data System (ADS)

Robbins, Woodrow E.

1988-01-01

The present conference discusses topics in novel technologies and techniques of three-dimensional imaging, human factors-related issues in three-dimensional display system design, three-dimensional imaging applications, and image processing for remote sensing. Attention is given to a 19-inch parallactiscope, a chromostereoscopic CRT-based display, the 'SpaceGraph' true three-dimensional peripheral, advantages of three-dimensional displays, holographic stereograms generated with a liquid crystal spatial light modulator, algorithms and display techniques for four-dimensional Cartesian graphics, an image processing system for automatic retina diagnosis, the automatic frequency control of a pulsed CO2 laser, and a three-dimensional display of magnetic resonance imaging of the spine.

Exact solutions of a hierarchy of mixing speeds models

NASA Astrophysics Data System (ADS)

Cornille, H.; Platkowski, T.

1992-07-01

This paper presents several new aspects of discrete kinetic theory (DKT). First a hierarchy of d-dimensional (d=1,2,3) models is proposed with (2d+3) velocities and three moduli speeds: 0, 2, and a third one that can be arbitrary. It is assumed that the particles at rest have an internal energy which, for microscopic collisions, supplies for the loss of the kinetic energy. In a more general way than usual, collisions are allowed that mix particles with different speeds. Second, for the (1+1)-dimensional restriction of the systems of PDE for these models which have two independent quadratic collision terms we construct different exact solutions. The usual types of exact solutions are studied: periodic solutions and shock wave solutions obtained from the standard linearization of the scalar Riccati equations called Riccatian shock waves. Then other types of solutions of the coupled Riccati equations are found called non-Riccatian shock waves and they are compared with the previous ones. The main new result is that, between the upstream and downstream states, these new solutions are not necessarily monotonous. Further, for the shock problem, a two-dimensional dynamical system of ODE is solved numerically with limit values corresponding to the upstream and downstream states. As a by-product of this study two new linearizations for the Riccati coupled equations with two functions are proposed.

Three-dimensional representations of photo-induced electron transfer rates in pyrene-(CH2)n-N,N'-dimethylaniline systems obtained by three electron transfer theories.

PubMed

Rujkorakarn, Rong; Tanaka, Fumio

2009-01-01

The observed rates of photo-induced electron transfer (ET) from N,N'-dimethylaniline (DMA) to the excited pyrene (Py) in confined systems of pyrene-(CH(2))(n)-N,N'- dimethylaniline (PnD: n=1-3) were studied by molecular dynamic simulation (MD) and three kinds of electron transfer theories. ET parameters contained in Marcus theory (M theory), Bixon and Jortner theory (BJ theory) and Kakitani and Mataga theory (KM theory) were determined so as to fit the calculated fluorescence intensities with those obtained by the observed ET rates, according to a non-linear least squares method. Three-dimensional profiles of logarithm of calculated ET rates depending on two of three ET parameters, R, epsilon(0) and -DeltaG degrees were systematically examined with best-fit ET parameters of P1D. Bell shape dependencies of ET rate were predicted on R and on epsilon(0), and on -DeltaG degrees as well, by M theory and KM theory. The profiles of logarithm of ET rate calculated by BJ theory exhibited oscillatory dependencies not only on -DeltaG degrees , but also on R and on epsilon(0). Relationship between ET state and charge transfer complex was discussed with BJ theory.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

Study of three-dimensional effects on vortex breakdown

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1988-01-01

The incompressible axisymmetric steady Navier-Stokes equations in primitive variables are used to simulate vortex breakdown. The equations, discretized using a second-order, central-difference scheme, are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers, based on vortex-core radius, as high as 1500. An attempt to study the stability of the axisymmetric solutions against three-dimensional perturbations is discussed.

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations

NASA Astrophysics Data System (ADS)

Huck, Thierry; Vallis, Geoffrey K.

2001-08-01

What can we learn from performing a linear stability analysis of the large-scale ocean circulation? Can we predict from the basic state the occurrence of interdecadal oscillations, such as might be found in a forward integration of the full equations of motion? If so, do the structure and period of the linearly unstable modes resemble those found in a forward integration? We pursue here a preliminary study of these questions for a case in idealized geometry, in which the full nonlinear behavior can also be explored through forward integrations. Specifically, we perform a three-dimensional linear stability analysis of the thermally-driven circulation of the planetary geostrophic equations. We examine the resulting eigenvalues and eigenfunctions, comparing them with the structure of the interdecadal oscillations found in the fully nonlinear model in various parameter regimes. We obtain a steady state by running the time-dependent, nonlinear model to equilibrium using restoring boundary conditions on surface temperature. If the surface heat fluxes are then diagnosed, and these values applied as constant flux boundary conditions, the nonlinear model switches into a state of perpetual, finite amplitude, interdecadal oscillations. We construct a linearized version of the model by empirically evaluating the tangent linear matrix at the steady state, under both restoring and constant-flux boundary conditions. An eigen-analysis shows there are no unstable eigenmodes of the linearized model with restoring conditions. In contrast, under constant flux conditions, we find a single unstable eigenmode that shows a striking resemblance to the fully-developed oscillations in terms of three-dimensional structure, period and growth rate. The mode may be damped through either surface restoring boundary conditions or sufficiently large horizontal tracer diffusion. The success of this simple numerical method in idealized geometry suggests applications in the study of the stability of the ocean circulation in more realistic configurations, and the possibility of predicting potential oceanic modes, even weakly damped, that might be excited by stochastic atmospheric forcing or mesoscale ocean eddies.

Evaluation of the 3dMDface system as a tool for soft tissue analysis.

PubMed

Hong, C; Choi, K; Kachroo, Y; Kwon, T; Nguyen, A; McComb, R; Moon, W

2017-06-01

To evaluate the accuracy of three-dimensional stereophotogrammetry by comparing values obtained from direct anthropometry and the 3dMDface system. To achieve a more comprehensive evaluation of the reliability of 3dMD, both linear and surface measurements were examined. UCLA Section of Orthodontics. Mannequin head as model for anthropometric measurements. Image acquisition and analysis were carried out on a mannequin head using 16 anthropometric landmarks and 21 measured parameters for linear and surface distances. 3D images using 3dMDface system were made at 0, 1 and 24 hours; 1, 2, 3 and 4 weeks. Error magnitude statistics used include mean absolute difference, standard deviation of error, relative error magnitude and root mean square error. Intra-observer agreement for all measurements was attained. Overall mean errors were lower than 1.00 mm for both linear and surface parameter measurements, except in 5 of the 21 measurements. The three longest parameter distances showed increased variation compared to shorter distances. No systematic errors were observed for all performed paired t tests (P<.05). Agreement values between two observers ranged from 0.91 to 0.99. Measurements on a mannequin confirmed the accuracy of all landmarks and parameters analysed in this study using the 3dMDface system. Results indicated that 3dMDface system is an accurate tool for linear and surface measurements, with potentially broad-reaching applications in orthodontics, surgical treatment planning and treatment evaluation. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

New infinite-dimensional hidden symmetries for heterotic string theory

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

Gao Yajun

The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected.

Singularities of interference of three waves with different polarization states.

PubMed

Kurzynowski, Piotr; Woźniak, Władysław A; Zdunek, Marzena; Borwińska, Monika

2012-11-19

We presented the interference setup which can produce interesting two-dimensional patterns in polarization state of the resulting light wave emerging from the setup. The main element of our setup is the Wollaston prism which gives two plane, linearly polarized waves (eigenwaves of both Wollaston's wedges) with linearly changed phase difference between them (along the x-axis). The third wave coming from the second arm of proposed polarization interferometer is linearly or circularly polarized with linearly changed phase difference along the y-axis. The interference of three plane waves with different polarization states (LLL - linear-linear-linear or LLC - linear-linear-circular) and variable change difference produce two-dimensional light polarization and phase distributions with some characteristic points and lines which can be claimed to constitute singularities of different types. The aim of this article is to find all kind of these phase and polarization singularities as well as their classification. We postulated in our theoretical simulations and verified in our experiments different kinds of polarization singularities, depending on which polarization parameter was considered (the azimuth and ellipticity angles or the diagonal and phase angles). We also observed the phase singularities as well as the isolated zero intensity points which resulted from the polarization singularities when the proper analyzer was used at the end of the setup. The classification of all these singularities as well as their relationships were analyzed and described.

Simulating Fatigue Crack Growth in Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Spievak, Lisa E.; Wawrzynek, Paul A.; Ingraffea, Anthony R.

2000-01-01

The majority of helicopter transmission systems utilize spiral bevel gears to convert the horizontal power from the engine into vertical power for the rotor. Due to the cyclical loading on a gear's tooth, fatigue crack propagation can occur. In rotorcraft applications, a crack's trajectory determines whether the gear failure will be benign or catastrophic for the aircraft. As a result, the capability to predict crack growth in gears is significant. A spiral bevel gear's complex shape requires a three dimensional model of the geometry and cracks. The boundary element method in conjunction with linear elastic fracture mechanics theories is used to predict arbitrarily shaped three dimensional fatigue crack trajectories in a spiral bevel pinion under moving load conditions. The predictions are validated by comparison to experimental results. The sensitivity of the predictions to variations in loading conditions and crack growth rate model parameters is explored. Critical areas that must be understood in greater detail prior to predicting more accurate crack trajectories and crack growth rates in three dimensions are identified.

Anchorage in Orthodontics: Three-dimensional Scanner Input.

PubMed

Nabbout, Fidele; Baron, Pascal

2018-01-01

The aim of this article is to re-evaluate anchorage coefficient values in orthodontics and their influence in the treatment decision through the usage of three-dimensional (3D) scanner. A sample of 80 patients was analyzed with the 3D scanner using the C2000 and Cepha 3DT softwares (CIRAD Montpellier, France). Tooth anatomy parameters (linear measurements, root, and crown volumes) were then calculated to determine new anchorage coefficients based on root volume. Data were collected and statistically evaluated with the StatView software (version 5.0). The anchorage coefficient values found in this study are compared to those established in previous studies. These new values affect and modify our approach in orthodontic treatment from the standpoint of anchorage. The use of new anchorage coefficient values has significant clinical implications in conventional and in microimplants-assisted orthodontic mechanics through the selection and delivery of the optimal force system (magnitude and moment) for an adequate biological response.

Three-Dimensional Genome Organization and Function in Drosophila

PubMed Central

Schwartz, Yuri B.; Cavalli, Giacomo

2017-01-01

Understanding how the metazoan genome is used during development and cell differentiation is one of the major challenges in the postgenomic era. Early studies in Drosophila suggested that three-dimensional (3D) chromosome organization plays important regulatory roles in this process and recent technological advances started to reveal connections at the molecular level. Here we will consider general features of the architectural organization of the Drosophila genome, providing historical perspective and insights from recent work. We will compare the linear and spatial segmentation of the fly genome and focus on the two key regulators of genome architecture: insulator components and Polycomb group proteins. With its unique set of genetic tools and a compact, well annotated genome, Drosophila is poised to remain a model system of choice for rapid progress in understanding principles of genome organization and to serve as a proving ground for development of 3D genome-engineering techniques. PMID:28049701

Fiber pushout test: A three-dimensional finite element computational simulation

NASA Technical Reports Server (NTRS)

Mital, Subodh K.; Chamis, Christos C.

1990-01-01

A fiber pushthrough process was computationally simulated using three-dimensional finite element method. The interface material is replaced by an anisotropic material with greatly reduced shear modulus in order to simulate the fiber pushthrough process using a linear analysis. Such a procedure is easily implemented and is computationally very effective. It can be used to predict fiber pushthrough load for a composite system at any temperature. The average interface shear strength obtained from pushthrough load can easily be separated into its two components: one that comes from frictional stresses and the other that comes from chemical adhesion between fiber and the matrix and mechanical interlocking that develops due to shrinkage of the composite because of phase change during the processing. Step-by-step procedures are described to perform the computational simulation, to establish bounds on interfacial bond strength and to interpret interfacial bond quality.

Extending generalized Kubelka-Munk to three-dimensional radiative transfer.

PubMed

Sandoval, Christopher; Kim, Arnold D

2015-08-10

The generalized Kubelka-Munk (gKM) approximation is a linear transformation of the double spherical harmonics of order one (DP₁) approximation of the radiative transfer equation. Here, we extend the gKM approximation to study problems in three-dimensional radiative transfer. In particular, we derive the gKM approximation for the problem of collimated beam propagation and scattering in a plane-parallel slab composed of a uniform absorbing and scattering medium. The result is an 8×8 system of partial differential equations that is much easier to solve than the radiative transfer equation. We compare the solutions of the gKM approximation with Monte Carlo simulations of the radiative transfer equation to identify the range of validity for this approximation. We find that the gKM approximation is accurate for isotropic scattering media that are sufficiently thick and much less accurate for anisotropic, forward-peaked scattering media.

The terminal area simulation system. Volume 1: Theoretical formulation

NASA Technical Reports Server (NTRS)

Proctor, F. H.

1987-01-01

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Essential uncontrollability of discrete linear, time-invariant, dynamical systems

NASA Technical Reports Server (NTRS)

Cliff, E. M.

1975-01-01

The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

NASA Technical Reports Server (NTRS)

Robertson, D. K.

1985-01-01

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

Flyby Error Analysis Based on Contour Plots for the Cassini Tour

NASA Technical Reports Server (NTRS)

Stumpf, P. W.; Gist, E. M.; Goodson, T. D.; Hahn, Y.; Wagner, S. V.; Williams, P. N.

2008-01-01

The maneuver cancellation analysis consists of cost contour plots employed by the Cassini maneuver team. The plots are two-dimensional linear representations of a larger six-dimensional solution to a multi-maneuver, multi-encounter mission at Saturn. By using contours plotted with the dot product of vectors B and R and the dot product of vectors B and T components, it is possible to view the effects delta V on for various encounter positions in the B-plane. The plot is used in operations to help determine if the Approach Maneuver (ensuing encounter minus three days) and/or the Cleanup Maneuver (ensuing encounter plus three days) can be cancelled and also is a linear check of an integrated solution.

Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

NASA Technical Reports Server (NTRS)

Weinberg, B. C.; Mcdonald, H.

1980-01-01

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils.

The Goertler vortex instability mechanism in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.

1984-01-01

The two dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

NASA Astrophysics Data System (ADS)

Zhu, Lianhua; Yang, Xiaofan; Guo, Zhaoli

2017-12-01

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios.

Reflections on the nature of non-linear responses of the climate to forcing

NASA Astrophysics Data System (ADS)

Ditlevsen, Peter

2017-04-01

On centennial to multi-millennial time scales the paleoclimatic record shows that climate responds in a very non-linear way to the external forcing. Perhaps most puzzling is the change in glacial period duration at the Middle Pleistocene Transition. From a dynamical systems perspective, this could be a change in frequency locking between the orbital forcing and the climatic response or it could be a non-linear resonance phenomenon. In both cases the climate system shows a non-trivial oscillatory behaviour. From the records it seems that this behaviour can be described by an effective dynamics on a low-dimensional slow manifold. These different possible dynamical behaviours will be discussed. References: Arianna Marchionne, Peter Ditlevsen, and Sebastian Wieczorek, "Three types of nonlinear resonances", arXiv:1605.00858 Peter Ashwin and Peter Ditlevsen, "The middle Pleistocene transition as a generic bifurcation on a slow manifold", Climate Dynamics, 45, 2683, 2015. Peter D. Ditlevsen, "The bifurcation structure and noise assisted transitions in the Pleistocene glacial cycles", Paleoceanography, 24, PA3204, 2009

Transition records of stationary Markov chains.

PubMed

Naudts, Jan; Van der Straeten, Erik

2006-10-01

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

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

Yan, R.; Betti, R.; Sanz, J.

The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. As a result, the vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume.

Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space.

PubMed

Dubček, Tena; Kennedy, Colin J; Lu, Ling; Ketterle, Wolfgang; Soljačić, Marin; Buljan, Hrvoje

2015-06-05

We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases.

A web service system supporting three-dimensional post-processing of medical images based on WADO protocol.

PubMed

He, Longjun; Xu, Lang; Ming, Xing; Liu, Qian

2015-02-01

Three-dimensional post-processing operations on the volume data generated by a series of CT or MR images had important significance on image reading and diagnosis. As a part of the DIOCM standard, WADO service defined how to access DICOM objects on the Web, but it didn't involve three-dimensional post-processing operations on the series images. This paper analyzed the technical features of three-dimensional post-processing operations on the volume data, and then designed and implemented a web service system for three-dimensional post-processing operations of medical images based on the WADO protocol. In order to improve the scalability of the proposed system, the business tasks and calculation operations were separated into two modules. As results, it was proved that the proposed system could support three-dimensional post-processing service of medical images for multiple clients at the same moment, which met the demand of accessing three-dimensional post-processing operations on the volume data on the web.

Magnetic resonance imaging findings are useful for evaluating the three-dimensional development and follow-up of linear lupus erythematosus profundus.

PubMed

Ogawa, M; Muro, Y; Sugiura, K; Sakakibara, A; Akiyama, M

2015-10-01

Lupus erythematosus profundus (LEP), which is a variant of chronic cutaneous lupus erythematosus (CLE), is seen in approximately 2∼3% of CLE patients, and only 10% to 20% of LEP patients present with systemic LE (SLE). LEP shows subcutaneous nodules with or without discoid LE (DLE). Linear LEP, a very rare variant of LEP, was first reported in 1991 in Japanese and in 1998 in English. Since LEP sometimes leaves skin depressions or scars as a result of atrophy of adipose tissue, early and adequate treatments are necessary. Here, we introduce an LEP case in which magnetic resonance imaging (MRI) was quite effective in evaluating a lesion that had been considered to be linear DLE. © The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

A higher order panel method for linearized supersonic flow

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Epton, M. A.; Johnson, F. T.; Magnus, A. E.; Rubbert, P. E.

1979-01-01

The basic integral equations of linearized supersonic theory for an advanced supersonic panel method are derived. Methods using only linear varying source strength over each panel or only quadratic doublet strength over each panel gave good agreement with analytic solutions over cones and zero thickness cambered wings. For three dimensional bodies and wings of general shape, combined source and doublet panels with interior boundary conditions to eliminate the internal perturbations lead to a stable method providing good agreement experiment. A panel system with all edges contiguous resulted from dividing the basic four point non-planar panel into eight triangular subpanels, and the doublet strength was made continuous at all edges by a quadratic distribution over each subpanel. Superinclined panels were developed and tested on s simple nacelle and on an airplane model having engine inlets, with excellent results.

Automatic Reconstruction of Spacecraft 3D Shape from Imagery

NASA Astrophysics Data System (ADS)

Poelman, C.; Radtke, R.; Voorhees, H.

We describe a system that computes the three-dimensional (3D) shape of a spacecraft from a sequence of uncalibrated, two-dimensional images. While the mathematics of multi-view geometry is well understood, building a system that accurately recovers 3D shape from real imagery remains an art. A novel aspect of our approach is the combination of algorithms from computer vision, photogrammetry, and computer graphics. We demonstrate our system by computing spacecraft models from imagery taken by the Air Force Research Laboratory's XSS-10 satellite and DARPA's Orbital Express satellite. Using feature tie points (each identified in two or more images), we compute the relative motion of each frame and the 3D location of each feature using iterative linear factorization followed by non-linear bundle adjustment. The "point cloud" that results from this traditional shape-from-motion approach is typically too sparse to generate a detailed 3D model. Therefore, we use the computed motion solution as input to a volumetric silhouette-carving algorithm, which constructs a solid 3D model based on viewpoint consistency with the image frames. The resulting voxel model is then converted to a facet-based surface representation and is texture-mapped, yielding realistic images from arbitrary viewpoints. We also illustrate other applications of the algorithm, including 3D mensuration and stereoscopic 3D movie generation.

Improvement in airborne position measurements based on an ultrasonic linear-period-modulated wave by 1-bit signal processing

NASA Astrophysics Data System (ADS)

Thong-un, Natee; Hirata, Shinnosuke; Kurosawa, Minoru K.

2015-07-01

In this paper, we describe an expansion of the airborne ultrasonic systems for object localization in the three-dimensional spaces of navigation. A system, which revises the microphone arrangement and algorithm, can expand the object-position measurement from +90° in a previous method up to +180° for both the elevation and azimuth angles. The proposed system consists of a sound source and four acoustical receivers. Moreover, the system is designed to utilize low-cost devices, and low-cost computation relying on 1-bit signal processing is used to support the real-time application on a field-programmable gate array (FPGA). An object location is identified using spherical coordinates. A spherical object, which has a curved surface, is considered a target for this system. The transmit pulse to the target is a linear-period-modulated ultrasonic wave with a chirp rate of 50-20 kHz. Statistical evaluation of this work is the experimental investigation under repeatability.

Investigation on dynamical interaction between a heavy vehicle and road pavement

NASA Astrophysics Data System (ADS)

Yang, Shaopu; Li, Shaohua; Lu, Yongjie

2010-08-01

This paper presents a model for three-dimensional, heavy vehicle-pavement-foundation coupled system, which is modelled as a seven-DOF vehicle moving along a simply supported double-layer rectangular thin plate on a linear viscoelastic foundation. The vertical tyre force is described by a single point-contact model, while the pavement-foundation is modelled as a double-layer plate on a linear viscoelastic foundation. Using the Galerkin method and quick direct integral method, the dynamical behaviour of the vehicle-pavement-foundation coupled system is investigated numerically and compared with that of traditional vehicle system and pavement system. The effects of coupling action on vehicle body vertical acceleration, suspension deformations, tyre forces and pavement displacements are also obtained. The investigation shows that the coupling action could not be neglected even on a smooth road surface, such as highway. Thus, it is necessary to investigate the dynamics of vehicle and pavement simultaneously based on the vehicle-pavement-foundation coupled system.

Use of 3-dimensional surface acquisition to study facial morphology in 5 populations.

PubMed

Kau, Chung How; Richmond, Stephen; Zhurov, Alexei; Ovsenik, Maja; Tawfik, Wael; Borbely, Peter; English, Jeryl D

2010-04-01

The aim of this study was to assess the use of 3-dimensional facial averages for determining morphologic differences from various population groups. We recruited 473 subjects from 5 populations. Three-dimensional images of the subjects were obtained in a reproducible and controlled environment with a commercially available stereo-photogrammetric camera capture system. Minolta VI-900 (Konica Minolta, Tokyo, Japan) and 3dMDface (3dMD LLC, Atlanta, Ga) systems were used. Each image was obtained as a facial mesh and orientated along a triangulated axis. All faces were overlaid, one on top of the other, and a complex mathematical algorithm was performed until average composite faces of 1 man and 1 woman were achieved for each subgroup. These average facial composites were superimposed based on a previously validated superimposition method, and the facial differences were quantified. Distinct facial differences were observed among the groups. The linear differences between surface shells ranged from 0.37 to 1.00 mm for the male groups. The linear differences ranged from 0.28 and 0.87 mm for the women. The color histograms showed that the similarities in facial shells between the subgroups by sex ranged from 26.70% to 70.39% for men and 36.09% to 79.83% for women. The average linear distance from the signed color histograms for the male subgroups ranged from -6.30 to 4.44 mm. The female subgroups ranged from -6.32 to 4.25 mm. Average faces can be efficiently and effectively created from a sample of 3-dimensional faces. Average faces can be used to compare differences in facial morphologies for various populations and sexes. Facial morphologic differences were greatest when totally different ethnic variations were compared. Facial morphologic similarities were present in comparable groups, but there were large variations in concentrated areas of the face. Copyright 2010 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.

Systems Biology Approaches for Understanding Genome Architecture.

PubMed

Sewitz, Sven; Lipkow, Karen

2016-01-01

The linear and three-dimensional arrangement and composition of chromatin in eukaryotic genomes underlies the mechanisms directing gene regulation. Understanding this organization requires the integration of many data types and experimental results. Here we describe the approach of integrating genome-wide protein-DNA binding data to determine chromatin states. To investigate spatial aspects of genome organization, we present a detailed description of how to run stochastic simulations of protein movements within a simulated nucleus in 3D. This systems level approach enables the development of novel questions aimed at understanding the basic mechanisms that regulate genome dynamics.

Infiltrating a thin or single-layer opal with an atomic vapour: Sub-Doppler signals and crystal optics

NASA Astrophysics Data System (ADS)

Moufarej, Elias; Maurin, Isabelle; Zabkov, Ilya; Laliotis, Athanasios; Ballin, Philippe; Klimov, Vasily; Bloch, Daniel

2014-10-01

Artificial thin glass opals can be infiltrated with a resonant alkali-metal vapour, providing novel types of hybrid systems. The reflection at the interface between the substrate and the opal yields a resonant signal, which exhibits sub-Doppler structures in linear spectroscopy for a range of oblique incidences. This result is suspected to originate in an effect of the three-dimensional confinement of the vapour in the opal interstices. It is here extended to a situation where the opal is limited to a few- or even a single-layer opal film, which is a kind of bidimensional grating. We have developed a flexible one-dimensional layered optical model, well suited for a Langmuir-Blodgett opal. Once extended to the case of a resonant infiltration, the model reproduces quick variations of the lineshape with incidence angle or polarization. Alternately, for an opal limited to a single layer of identical spheres, a three-dimensional numerical calculation was developed. It predicts crystalline anisotropy, which is demonstrated through diffraction on an empty opal made of a single layer of polystyrene spheres.

Aerodynamic preliminary analysis system. Part 1: Theory. [linearized potential theory

NASA Technical Reports Server (NTRS)

Bonner, E.; Clever, W.; Dunn, K.

1978-01-01

A comprehensive aerodynamic analysis program based on linearized potential theory is described. The solution treats thickness and attitude problems at subsonic and supersonic speeds. Three dimensional configurations with or without jet flaps having multiple non-planar surfaces of arbitrary planform and open or closed slender bodies of non-circular contour may be analyzed. Longitudinal and lateral-directional static and rotary derivative solutions may be generated. The analysis was implemented on a time sharing system in conjunction with an input tablet digitizer and an interactive graphics input/output display and editing terminal to maximize its responsiveness to the preliminary analysis problem. Nominal case computation time of 45 CPU seconds on the CDC 175 for a 200 panel simulation indicates the program provides an efficient analysis for systematically performing various aerodynamic configuration tradeoff and evaluation studies.

Multiphysics Modeling of an Annular Linear Induction Pump With Applications to Space Nuclear Power Systems

NASA Technical Reports Server (NTRS)

Kilbane, J.; Polzin, K. A.

2014-01-01

An annular linear induction pump (ALIP) that could be used for circulating liquid-metal coolant in a fission surface power reactor system is modeled in the present work using the computational COMSOL Multiphysics package. The pump is modeled using a two-dimensional, axisymmetric geometry and solved under conditions similar to those used during experimental pump testing. Real, nonlinear, temperature-dependent material properties can be incorporated into the model for both the electrically-conducting working fluid in the pump (NaK-78) and structural components of the pump. The intricate three-phase coil configuration of the pump is implemented in the model to produce an axially-traveling magnetic wave that is qualitatively similar to the measured magnetic wave. The model qualitatively captures the expected feature of a peak in efficiency as a function of flow rate.

Versatile low-Reynolds-number swimmer with three-dimensional maneuverability.

PubMed

Jalali, Mir Abbas; Alam, Mohammad-Reza; Mousavi, SeyyedHossein

2014-11-01

We design and simulate the motion of a swimmer, the Quadroar, with three-dimensional translation and reorientation capabilities in low-Reynolds-number conditions. The Quadroar is composed of an I-shaped frame whose body link is a simple linear actuator and four disks that can rotate about the axes of flange links. The time symmetry is broken by a combination of disk rotations and the one-dimensional expansion or contraction of the body link. The Quadroar propels on forward and transverse straight lines and performs full three-dimensional reorientation maneuvers, which enable it to swim along arbitrary trajectories. We find continuous operation modes that propel the swimmer on planar and three-dimensional periodic and quasiperiodic orbits. Precessing quasiperiodic orbits consist of slow lingering phases with cardioid or multiloop turns followed by directional propulsive phases. Quasiperiodic orbits allow the swimmer to access large parts of its neighboring space without using complex control strategies. We also discuss the feasibility of fabricating a nanoscale Quadroar by photoactive molecular rotors.

Thermal Non-Equilibrium Flows in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Zeng, Yanni

2016-01-01

We study the equations describing the motion of a thermal non-equilibrium gas in three space dimensions. It is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that the Shizuta-Kawashima criterion is violated. This implies that a perturbation of a constant equilibrium state consists of two parts: one decays in time while the other stays. In fact, the entropy wave grows weakly along the particle path as the process is irreversible. We study thermal properties related to the well-posedness of the nonlinear system. We also obtain a detailed pointwise estimate on the Green's function for the Cauchy problem when the system is linearized around an equilibrium constant state. The Green's function provides a complete picture of the wave pattern, with an exact and explicit leading term. Comparing with existing results for one dimensional flows, our results reveal a new feature of three dimensional flows: not only does the entropy wave not decay, but the velocity also contains a non-decaying part, strongly coupled with its decaying one. The new feature is supported by the second order approximation via the Chapman-Enskog expansions, which are the Navier-Stokes equations with vanished shear viscosity and heat conductivity.

Electromagnetic density of modes for a finite-size three-dimensional structure.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Centini, Marco; Scalora, Michael; Bloemer, Mark J

2004-05-01

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

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

Yu, W.; Jiang, Y.; Yang, J.

A three-dimensional (3D) Dirac semimetal (DS) is an analogue of graphene, but with linear energy dispersion in all (three) momentum directions. 3D DSs have been a fertile playground in discovering novel quantum particles, for example Weyl fermions, in solid state systems. Many 3D DSs were theoretically predicted and experimentally confirmed. Here, we report here the results in exfoliated ZrTe 5 thin flakes from the studies of aberration-corrected scanning transmission electron microscopy and low temperature magneto-transport measurements. We observed several unique results. First, a π Berry phase was obtained from the Landau fan diagram of the Shubnikov-de Haas oscillations in themore » longitudinal conductivity σ xx. Second, the longitudinal resistivity ρ xx shows a linear magnetic field dependence in the quantum limit regime. Most surprisingly, quantum oscillations were also observed at fractional Landau level indices N = 5/3 and 7/5, demonstrating strong electron-electron interaction effects in ZrTe 5.« less

Analysis on the multi-dimensional spectrum of the thrust force for the linear motor feed drive system in machine tools

NASA Astrophysics Data System (ADS)

Yang, Xiaojun; Lu, Dun; Ma, Chengfang; Zhang, Jun; Zhao, Wanhua

2017-01-01

The motor thrust force has lots of harmonic components due to the nonlinearity of drive circuit and motor itself in the linear motor feed drive system. What is more, in the motion process, these thrust force harmonics may vary with the position, velocity, acceleration and load, which affects the displacement fluctuation of the feed drive system. Therefore, in this paper, on the basis of the thrust force spectrum obtained by the Maxwell equation and the electromagnetic energy method, the multi-dimensional variation of each thrust harmonic is analyzed under different motion parameters. Then the model of the servo system is established oriented to the dynamic precision. The influence of the variation of the thrust force spectrum on the displacement fluctuation is discussed. At last the experiments are carried out to verify the theoretical analysis above. It can be found that the thrust harmonics show multi-dimensional spectrum characteristics under different motion parameters and loads, which should be considered to choose the motion parameters and optimize the servo control parameters in the high-speed and high-precision machine tools equipped with the linear motor feed drive system.

On the dimensionally correct kinetic theory of turbulence for parallel propagation

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

Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Ziebell, L. F., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Yoon, P. H., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br

2015-03-15

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectivelymore » emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.« less

Finite-difference interblock transmissivity for unconfined aquifers and for aquifers having smoothly varying transmissivity

USGS Publications Warehouse

Goode, D.J.; Appel, C.A.

1992-01-01

More accurate alternatives to the widely used harmonic mean interblock transmissivity are proposed for block-centered finite-difference models of ground-water flow in unconfined aquifers and in aquifers having smoothly varying transmissivity. The harmonic mean is the exact interblock transmissivity for steady-state one-dimensional flow with no recharge if the transmissivity is assumed to be spatially uniform over each finite-difference block, changing abruptly at the block interface. However, the harmonic mean may be inferior to other means if transmissivity varies in a continuous or smooth manner between nodes. Alternative interblock transmissivity functions are analytically derived for the case of steady-state one-dimensional flow with no recharge. The second author has previously derived the exact interblock transmissivity, the logarithmic mean, for one-dimensional flow when transmissivity is a linear function of distance in the direction of flow. We show that the logarithmic mean transmissivity is also exact for uniform flow parallel to the direction of changing transmissivity in a two- or three-dimensional model, regardless of grid orientation relative to the flow vector. For the case of horizontal flow in a homogeneous unconfined or water-table aquifer with a horizontal bottom and with areally distributed recharge, the exact interblock transmissivity is the unweighted arithmetic mean of transmissivity at the nodes. This mean also exhibits no grid-orientation effect for unidirectional flow in a two-dimensional model. For horizontal flow in an unconfined aquifer with no recharge where hydraulic conductivity is a linear function of distance in the direction of flow the exact interblock transmissivity is the product of the arithmetic mean saturated thickness and the logarithmic mean hydraulic conductivity. For several hypothetical two- and three-dimensional cases with smoothly varying transmissivity or hydraulic conductivity, the harmonic mean is shown to yield the least accurate solution to the flow equation of the alternatives considered. Application of the alternative interblock transmissivities to a regional aquifer system model indicates that the changes in computed heads and fluxes are typically small, relative to model calibration error. For this example, the use of alternative interblock transmissivities resulted in an increase in computational effort of less than 3 percent. Numerical algorithms to compute alternative interblock transmissivity functions in a modular three-dimensional flow model are presented and documented.

Three-Dimensional Magnetic Analysis Technique Developed for Evaluating Stirling Convertor Linear Alternators

NASA Technical Reports Server (NTRS)

Geng, Steven M.

2003-01-01

The Department of Energy, the Stirling Technology Company (STC), and the NASA Glenn Research Center are developing Stirling convertors for Stirling radioisotope generators to provide electrical power for future NASA deep space missions. STC is developing the 55-We technology demonstration convertor (TDC) under contract to the Department of Energy. The Department of Energy recently named Lockheed Martin as the system integration contractor for the Stirling radioisotope generator development project. Lockheed Martin will develop the Stirling radioisotope generator engineering unit and has contract options to develop the qualification unit and the first flight unit. Glenn s role includes an in-house project to provide convertor, component, and materials testing and evaluation in support of the overall power system development. As a part of this work, Glenn has established an in-house Stirling research laboratory for testing, analyzing, and evaluating Stirling machines. STC has built four 55-We convertors for NASA, and these are being tested at Glenn. A cross-sectional view of the 55-We TDC is shown in the figure. Of critical importance to the successful development of the Stirling convertor for space power applications is the development of a lightweight and highly efficient linear alternator. In support, Glenn has been developing finite element analysis and finite element method tools for performing various linear alternator thermal and electromagnetic analyses and evaluating design configurations. A three-dimensional magnetostatic finite element model of STC's 55-We TDC linear alternator was developed to evaluate the demagnetization fields affecting the alternator magnets. Since the actual linear alternator hardware is symmetric to the quarter section about the axis of motion, only a quarter section of the alternator was modeled. The components modeled included the mover laminations, the neodymium-iron-boron magnets, the stator laminations, and the copper coils. The three-dimensional magnetostatic model was then coupled with a circuit simulator model of the alternator load and convertor controller. The coupled model was then used to generate alternator terminal voltage and current predictions. The predicted voltage and current waveforms agreed well with the experimental data, which tended to validate the accuracy of the coupled model. The model was then used to generate predictions of the demagnetization fields acting on the alternator magnets for the alternator under load. The preliminary model predictions indicate that the highest potential for demagnetization is along the inside surface of the uncovered magnets. The demagnetization field for the uncovered magnets when the mover is positioned at the end of a stroke is higher than it is when the mover is at the position of maximum induced voltage or maximum alternator current. Assuming normal load conditions, the model predicted that the onset of demagnetization is most likely to occur for magnet temperatures above 101 C.

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5

PubMed Central

Chen, Zhi-Guo; Chen, R. Y.; Zhong, R. D.; Schneeloch, John; Zhang, C.; Huang, Y.; Qu, Fanming; Yu, Rui; Gu, G. D.; Wang, N. L.

2017-01-01

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe5, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [∼33,000 cm2/(V ⋅ s)] multilayer ZrTe5 flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ∼10 meV and a B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Our results not only provide spectroscopic evidence for the TI state in ZrTe5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials. PMID:28096330

Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe 5

DOE PAGES

Chen, Zhi -Guo; Chen, R. Y.; Zhong, R. D.; ...

2017-01-17

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe 5, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [~33,000 cm 2/(V • s)] multilayer ZrTe 5 flakemore » at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ~10 meV and a √B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Finally, our results not only provide spectroscopic evidence for the TI state in ZrTe 5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials.« less

Stress Induced in Periodontal Ligament under Orthodontic Loading (Part II): A Comparison of Linear Versus Non-Linear Fem Study.

PubMed

Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B

2015-09-01

Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. This shows that the force level required for non-linear analysis is lesser than that of linear analysis.

[Clinical effect of three dimensional human body scanning system BurnCalc in the evaluation of burn wound area].

PubMed

Lu, J; Wang, L; Zhang, Y C; Tang, H T; Xia, Z F

2017-10-20

Objective: To validate the clinical effect of three dimensional human body scanning system BurnCalc developed by our research team in the evaluation of burn wound area. Methods: A total of 48 burn patients treated in the outpatient department of our unit from January to June 2015, conforming to the study criteria, were enrolled in. For the first 12 patients, one wound on the limbs or torso was selected from each patient. The stability of the system was tested by 3 attending physicians using three dimensional human body scanning system BurnCalc to measure the area of wounds individually. For the following 36 patients, one wound was selected from each patient, including 12 wounds on limbs, front torso, and side torso, respectively. The area of wounds was measured by the same attending physician using transparency tracing method, National Institutes of Health (NIH) Image J method, and three dimensional human body scanning system BurnCalc, respectively. The time for getting information of 36 wounds by three methods was recorded by stopwatch. The stability among the testers was evaluated by the intra-class correlation coefficient (ICC). Data were processed with randomized blocks analysis of variance and Bonferroni test. Results: (1) Wound area of patients measured by three physicians using three dimensional human body scanning system BurnCalc was (122±95), (121±95), and (123±96) cm(2,) respectively, and there was no statistically significant difference among them ( F =1.55, P >0.05). The ICC among 3 physicians was 0.999. (2) The wound area of limbs of patients measured by transparency tracing method, NIH Image J method, and three dimensional human body scanning system BurnCalc was (84±50), (76±46), and (84±49) cm(2,) respectively. There was no statistically significant difference in the wound area of limbs of patients measured by transparency tracing method and three dimensional human body scanning system BurnCalc ( P >0.05). The wound area of limbs of patients measured by NIH Image J method was smaller than that measured by transparency tracing method and three dimensional human body scanning system BurnCalc (with P values below 0.05). There was no statistically significant difference in the wound area of front torso of patients measured by transparency tracing method, NIH Image J method, and three dimensional human body scanning system BurnCalc ( F =0.33, P >0.05). The wound area of side torso of patients measured by transparency tracing method, NIH Image J method, and three dimensional human body scanning system BurnCalc was (169±88), (150±80), and (169±86) cm(2,) respectively. There was no statistically significant difference in the wound area of side torso of patients measured by transparency tracing method and three dimensional human body scanning system BurnCalc ( P >0.05). The wound area of side torso of patients measured by NIH Image J method was smaller than that measured by transparency tracing method and three dimensional human body scanning system BurnCalc (with P values below 0.05). (3) The time for getting information of wounds of patients by transparency tracing method, NIH Image J method, and three dimensional human body scanning system BurnCalc was (77±14), (10±3), and (9±3) s, respectively. The time for getting information of wounds of patients by transparency tracing method was longer than that by NIH Image J method and three dimensional human body scanning system BurnCalc (with P values below 0.05). The time for getting information of wounds of patients by three dimensional human body scanning system BurnCalc was close to that by NIH Image J method ( P >0.05). Conclusions: The three dimensional human body scanning system BurnCalc is stable and can accurately evaluate the wound area on limbs and torso of burn patients.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

The Linear Parameters and the Decoupling Matrix for Linearly Coupled Motion in 6 Dimensional Phase Space

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

Parzen, George

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4- dimensional phase space, wheremore » R has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix. This set of equations also allows the linear parameters, the β i,α i, i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters,β i,α i, i = 1, 3, and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters α i and β i, i = 1, 3, and the elements of the decoupling matrix R. The procedure presented here for studying coupled motion in 6-dimensional phase space can also be applied to coupled motion in 4-dimensional phase space, where it may be a useful alternative procedure to the procedure presented by Edwards and Teng. In particular, it gives a simpler programing procedure for computing the beta functions and the emittances for coupled motion in 4-dimensional phase space.« less

The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space. Informal report

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

Parzen, G.

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 {times} 6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6 {times} 6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4-dimensional phase space, where Rmore » has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix. This set of equations also allows the linear parameters, {beta}{sub i}, {alpha}{sub i} = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters, the {beta}{sub i}, {alpha}{sub i} i = 1, 3, and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters {alpha}{sub i} and {beta}{sub i}, i = 1, 3, and the elements of the decoupling matrix R. The procedure presented here for studying coupled motion in 6-dimensional phase space can also be applied to coupled motion in 4-dimensional phase space, where it may be a useful alternative procedure to the procedure presented by Edwards and Teng. In particular, it gives a simpler programming procedure for computing the beta functions and the emittances for coupled motion in 4-dimensional phase space.« less

General methods for determining the linear stability of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.

1988-01-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

General methods for determining the linear stability of coronal magnetic fields

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

Craig, I.J.D.; Sneyd, A.D.; McClymont, A.N.

1988-12-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak. 19 references.

A new global approach to obtain three-dimensional displacement maps by integrating GPS and DInSAR data

NASA Astrophysics Data System (ADS)

Guglielmino, F.; Nunnari, G.; Puglisi, G.; Spata, A.

2009-04-01

We propose a new technique, based on the elastic theory, to efficiently produce an estimate of three-dimensional surface displacement maps by integrating sparse Global Position System (GPS) measurements of deformations and Differential Interferometric Synthetic Aperture Radar (DInSAR) maps of movements of the Earth's surface. The previous methodologies known in literature, for combining data from GPS and DInSAR surveys, require two steps: the first, in which sparse GPS measurements are interpolated in order to fill in GPS displacements at the DInSAR grid, and the second, to estimate the three-dimensional surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach is that both these steps are unified. We propose a linear matrix equation which accounts for both GPS and DInSAR data whose solution provide simultaneously the strain tensor, the displacement field and the rigid body rotation tensor throughout the entire investigated area. The mentioned linear matrix equation is solved by using the Weighted Least Square (WLS) thus assuring both numerical robustness and high computation efficiency. The proposed methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mt. Etna. The goodness of the results has been evaluated by using standard errors. These tests also allow optimising the choice of specific parameters of this algorithm. This "open" structure of the method will allow in the near future to take account of other available data sets, such as additional interferograms, or other geodetic data (e.g. levelling, tilt, etc.), in order to achieve even higher accuracy.

Three-dimensional analysis for liquid hydrogen in a cryogenic storage tank with heat pipe pump system

NASA Astrophysics Data System (ADS)

Ho, Son H.; Rahman, Muhammad M.

2008-01-01

This paper presents a study on fluid flow and heat transfer of liquid hydrogen in a zero boil-off cryogenic storage tank in a microgravity environment. The storage tank is equipped with an active cooling system consisting of a heat pipe and a pump-nozzle unit. The pump collects cryogen at its inlet and discharges it through its nozzle onto the evaporator section of the heat pipe in order to prevent the cryogen from boiling off due to the heat leaking through the tank wall from the surroundings. A three-dimensional (3-D) finite element model is employed in a set of numerical simulations to solve for velocity and temperature fields of liquid hydrogen in steady state. Complex structures of 3-D velocity and temperature distributions determined from the model are presented. Simulations with an axisymmetric model were also performed for comparison. Parametric study results from both models predict that as the speed of the cryogenic fluid discharged from the nozzle increases, the mean or bulk cryogenic fluid speed increases linearly and the maximum temperature within the cryogenic fluid decreases.

Three-dimensional analysis of magnetometer array data

NASA Technical Reports Server (NTRS)

Richmond, A. D.; Baumjohann, W.

1984-01-01

A technique is developed for mapping magnetic variation fields in three dimensions using data from an array of magnetometers, based on the theory of optimal linear estimation. The technique is applied to data from the Scandinavian Magnetometer Array. Estimates of the spatial power spectra for the internal and external magnetic variations are derived, which in turn provide estimates of the spatial autocorrelation functions of the three magnetic variation components. Statistical errors involved in mapping the external and internal fields are quantified and displayed over the mapping region. Examples of field mapping and of separation into external and internal components are presented. A comparison between the three-dimensional field separation and a two-dimensional separation from a single chain of stations shows that significant differences can arise in the inferred internal component.

Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

Three-dimensional spatiotemporal focusing of holographic patterns

PubMed Central

Hernandez, Oscar; Papagiakoumou, Eirini; Tanese, Dimitrii; Fidelin, Kevin; Wyart, Claire; Emiliani, Valentina

2016-01-01

Two-photon excitation with temporally focused pulses can be combined with phase-modulation approaches, such as computer-generated holography and generalized phase contrast, to efficiently distribute light into two-dimensional, axially confined, user-defined shapes. Adding lens-phase modulations to 2D-phase holograms enables remote axial pattern displacement as well as simultaneous pattern generation in multiple distinct planes. However, the axial confinement linearly degrades with lateral shape area in previous reports where axially shifted holographic shapes were not temporally focused. Here we report an optical system using two spatial light modulators to independently control transverse- and axial-target light distribution. This approach enables simultaneous axial translation of single or multiple spatiotemporally focused patterns across the sample volume while achieving the axial confinement of temporal focusing. We use the system's capability to photoconvert tens of Kaede-expressing neurons with single-cell resolution in live zebrafish larvae. PMID:27306044

Three-dimensional image acquisition and reconstruction system on a mobile device based on computer-generated integral imaging.

PubMed

Erdenebat, Munkh-Uchral; Kim, Byeong-Jun; Piao, Yan-Ling; Park, Seo-Yeon; Kwon, Ki-Chul; Piao, Mei-Lan; Yoo, Kwan-Hee; Kim, Nam

2017-10-01

A mobile three-dimensional image acquisition and reconstruction system using a computer-generated integral imaging technique is proposed. A depth camera connected to the mobile device acquires the color and depth data of a real object simultaneously, and an elemental image array is generated based on the original three-dimensional information for the object, with lens array specifications input into the mobile device. The three-dimensional visualization of the real object is reconstructed on the mobile display through optical or digital reconstruction methods. The proposed system is implemented successfully and the experimental results certify that the system is an effective and interesting method of displaying real three-dimensional content on a mobile device.

A new two-dimensional theory for vibrations of piezoelectric crystal plates with electroded faces

NASA Astrophysics Data System (ADS)

Lee, P. C. Y.; Yu, J. D.; Lin, W. S.

1998-02-01

A system of two-dimensional (2-D) governing equations for piezoelectric plates with general crystal symmetry and with electroded faces is deduced from the three-dimensional (3-D) equations of linear piezoelectricity by expansion in series of trigonometric functions of thickness coordinate. The essential difference of the present derivation from the earlier studies by trigonometrical series expansion is that the antisymmetric in-plane displacements induced by gradients of the bending deflection (the zero-order component of transverse displacement) are expressed by the linear functions of the thickness coordinate, and the rest of displacements are expanded in cosine series of the thickness coordinate. For the electric potential, a sine-series expansion is used for it is well suited for satisfying the electrical conditions at the faces covered with conductive electrodes. A system of approximate first-order equations is extracted from the infinite system of 2-D equations. Dispersion curves for thickness shear, flexure, and face-shear modes varying along x1 and those for thickness twist and face shear varying along x3 for AT-cut quartz plates are calculated from the present 2-D equations as well as from the 3-D equations, and comparison shows that the agreement is very close without introducing any corrections. Predicted frequency spectra by the present equations are shown to agree closely with the experimental data by Koga and Fukuyo [J. Inst. Elec. Comm. Engrs. of Japan 36, 59 (1953)] and those by Nakazawa, Horiuchi, and Ito [Proceedings of 1990 IEEE Ultrasonics Symposium (IEEE, New York, 1990)].

Image Processing Research

DTIC Science & Technology

1975-09-30

systems a linear model results in an object f being mappad into an image _ by a point spread function matrix H. Thus with noise j +Hf +n (1) The simplest... linear models for imaging systems are given by space invariant point spread functions (SIPSF) in which case H is block circulant. If the linear model is...Ij,...,k-IM1 is a set of two dimensional indices each distinct and prior to k. Modeling Procedare: To derive the linear predictor (block LP of figure

Ultrahigh resolution optical coherence tomography for quantitative topographic mapping of retinal and intraretinal architectural morphology

NASA Astrophysics Data System (ADS)

Ko, Tony H.; Hartl, Ingmar; Drexler, Wolfgang; Ghanta, Ravi K.; Fujimoto, James G.

2002-06-01

Quantitative, three-dimensional mapping of retinal architectural morphology was achieved using an ultrahigh resolution ophthalmic OCT system. This OCT system utilizes a broad bandwidth titanium-sapphire laser light source generating bandwidths of up to 300 nm near 800 nm center wavelength. The system enables real-time cross-sectional imaging of the retina with ~3 micrometers axial resolution. The macula and the papillomacular axis of a normal human subject were systematically mapped using a series of linear scans. Edge detection and segmentation algorithms were developed to quantify retinal and intraretinal thicknesses. Topographic mapping of the total retinal thickness and the total ganglion cell/inner plexiform layer thickness was achieved around the macula. A topographic mapping quantifying the progressive thickening of the nerve fiber layer (NFL) nasally approaching the optic disk was also demonstrated. The ability to create three-dimensional topographic mapping of retinal architectural morphology at ~3 micrometers axial resolution will be relevant for the diagnosis of many retinal diseases. The topographic quantification of these structures can serve as a powerful tool for developing algorithms and clinical scanning protocols for the screening and staging of ophthalmic diseases such as glaucoma.

Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

NASA Astrophysics Data System (ADS)

Zhu, Yan-Qing; Zhang, Dan-Wei; Yan, Hui; Xing, Ding-Yu; Zhu, Shi-Liang

2017-09-01

The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct two- and three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named as Maxwell fermions. We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions, Maxwell points may have nontrivial monopole charges of ±2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

Geometric mean for subspace selection.

PubMed

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2009-02-01

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

Three dimensional reliability analyses of currently used methods for assessment of sagittal jaw discrepancy

PubMed Central

Almaqrami, Bushra-Sufyan; Alhammadi, Maged-Sultan

2018-01-01

Background The objective of this study was to analyse three dimensionally the reliability and correlation of angular and linear measurements in assessment of anteroposterior skeletal discrepancy. Material and Methods In this retrospective cross sectional study, a sample of 213 subjects were three-dimensionally analysed from cone-beam computed tomography scans. The sample was divided according to three dimensional measurement of anteroposterior relation (ANB angle) into three groups (skeletal Class I, Class II and Class III). The anterior-posterior cephalometric indicators were measured on volumetric images using Anatomage software (InVivo5.2). These measurements included three angular and seven linear measurements. Cross tabulations were performed to correlate the ANB angle with each method. Intra-class Correlation Coefficient (ICC) test was applied for the difference between the two reliability measurements. P value of < 0.05 was considered significant. Results There was a statistically significant (P<0.05) agreement between all methods used with variability in assessment of different anteroposterior relations. The highest correlation was between ANB and DSOJ (0.913), strong correlation with AB/FH, AB/SN/, MM bisector, AB/PP, Wits appraisal (0.896, 0.890, 0.878, 0.867,and 0.858, respectively), moderate with AD/SN and Beta angle (0.787 and 0.760), and weak correlation with corrected ANB angle (0.550). Conclusions Conjunctive usage of ANB angle with DSOJ, AB/FH, AB/SN/, MM bisector, AB/PP and Wits appraisal in 3D cephalometric analysis provide a more reliable and valid indicator of the skeletal anteroposterior relationship. Clinical relevance: Most of orthodontic literature depends on single method (ANB) with its drawbacks in assessment of skeletal discrepancy which is a cardinal factors for proper treatment planning, this study assessed three dimensionally the degree of correlation between all available methods to make clinical judgement more accurate based on more than one method of assessment. Key words:Anteroposterior relationships, ANB angle, Three-dimension, CBCT. PMID:29750096

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

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

Crenshaw, Michael E., E-mail: michael.e.crenshaw4.civ@mail.mil

2014-04-15

In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derivemore » electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.« less

Non-linear 3D evaluation of different oral implant-abutment connections.

PubMed

Streckbein, P; Streckbein, R G; Wilbrand, J F; Malik, C Y; Schaaf, H; Howaldt, H P; Flach, M

2012-12-01

Micro-gaps and osseous overload in the implant-abutment connection are the most common causes of peri-implant bone resorption and implant failure. These undesirable events can be visualized on standardized three-dimensional finite element models and by radiographic methods. The present study investigated the influence of 7 available implant systems (Ankylos, Astra, Bego, Brånemark, Camlog, Straumann, and Xive) with different implant-abutment connections on bone overload and the appearance of micro-gaps in vitro. The individual geometries of the implants were transferred to three-dimensional finite element models. In a non-linear analysis considering the pre-loading of the occlusion screw, friction between the implant and abutment, the influence of the cone angle on bone strain, and the appearance of micro-gaps were determined. Increased bone strains were correlated with small (< 15°) cone angles. Conical implant-abutment connections efficiently avoided micro-gaps but had a negative effect on peri-implant bone strain. Bone strain was reduced in implants with greater wall thickness (Ankylos) or a smaller cone angle (Bego). The results of our in silico study provide a solid basis for the reduction of peri-implant bone strain and micro-gaps in the implant-abutment connection to improve long-term stability.

Effect of Surface Waviness on Transition in Three-Dimensional Boundary-Layer Flow

NASA Technical Reports Server (NTRS)

Masad, Jamal A.

1996-01-01

The effect of a surface wave on transition in three-dimensional boundary-layer flow over an infinite swept wing was studied. The mean flow computed using interacting boundary-layer theory, and transition was predicted using linear stability theory coupled with the empirical eN method. It was found that decreasing the wave height, sweep angle, or freestream unit Reynolds number, and increasing the freestream Mach number or suction level all stabilized the flow and moved transition onset to downstream locations.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1980-01-01

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.

Three-dimensional Navier-Stokes analysis of turbine passage heat transfer

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Arnone, Andrea

1991-01-01

The three-dimensional Reynolds-averaged Navier-Stokes equations are numerically solved to obtain the pressure distribution and heat transfer rates on the endwalls and the blades of two linear turbine cascades. The TRAF3D code which has recently been developed in a joint project between researchers from the University of Florence and NASA Lewis Research Center is used. The effect of turbulence is taken into account by using the eddy viscosity hypothesis and the two-layer mixing length model of Baldwin and Lomax. Predictions of surface heat transfer are made for Langston's cascade and compared with the data obtained for that cascade by Graziani. The comparison was found to be favorable. The code is also applied to a linear transonic rotor cascade to predict the pressure distributions and heat transfer rates.

Linear and Nonlinear Analysis of Magnetic Bearing Bandwidth Due to Eddy Current Limitations

NASA Technical Reports Server (NTRS)

Kenny, Andrew; Palazzolo, Alan

2000-01-01

Finite element analysis was used to study the bandwidth of alloy hyperco50a and silicon iron laminated rotors and stators in magnetic bearings. A three dimensional model was made of a heteropolar bearing in which all the flux circulated in the plane of the rotor and stator laminate. A three dimensional model of a plate similar to the region of a pole near the gap was also studied with a very fine mesh. Nonlinear time transient solutions for the net flux carried by the plate were compared to steady state time harmonic solutions. Both linear and quasi-nonlinear steady state time harmonic solutions were calculated and compared. The finite element solutions for power loss and flux bandwidth were compared to those determined from classical analytical solutions to Maxwell's equations.

Simple Procedure to Compute the Inductance of a Toroidal Ferrite Core from the Linear to the Saturation Regions

PubMed Central

Salas, Rosa Ana; Pleite, Jorge

2013-01-01

We propose a specific procedure to compute the inductance of a toroidal ferrite core as a function of the excitation current. The study includes the linear, intermediate and saturation regions. The procedure combines the use of Finite Element Analysis in 2D and experimental measurements. Through the two dimensional (2D) procedure we are able to achieve convergence, a reduction of computational cost and equivalent results to those computed by three dimensional (3D) simulations. The validation is carried out by comparing 2D, 3D and experimental results. PMID:28809283

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Three-Dimensional Transgenic Cell Models to Quantify Space Genotoxic Effects

NASA Technical Reports Server (NTRS)

Gonda, S.; Wu, H.; Pingerelli, P.; Glickman, B.

2000-01-01

In this paper we describe a three-dimensional, multicellular tissue-equivalent model, produced in NASA-designed, rotating wall bioreactors using mammalian cells engineered for genomic containment of mUltiple copies of defined target genes for genotoxic assessment. The Rat 2(lambda) fibroblasts (Stratagene, Inc.) were genetically engineered to contain high-density target genes for mutagenesis. Stable three-dimensional, multicellular spheroids were formed when human mammary epithelial cells and Rat 2(lambda) fibroblasts were cocultured on Cytodex 3 Beads in a rotating wall bioreactor. The utility of this spheroidal model for genotoxic assessment was indicated by a linear dose response curve and by results of gene sequence analysis of mutant clones from 400micron diameter spheroids following low-dose, high-energy, neon radiation exposure

From N=4 Galilean superparticle to three-dimensional non-relativistic N=4 superfields

NASA Astrophysics Data System (ADS)

Fedoruk, Sergey; Ivanov, Evgeny; Lukierski, Jerzy

2018-05-01

We consider the general N=4 , d = 3 Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization techniques, we introduce a class of actions for N=4 three-dimensional non-relativistic superparticle, such that they are linear in the central charge Maurer-Cartan one-forms. As a prerequisite to the quantization, we analyze the phase space constraints structure of our model for various choices of the central charges. The first class constraints generate gauge transformations, involving fermionic κ-gauge transformations. The quantization of the model gives rise to the collection of free N=4 , d = 3 Galilean superfields, which can be further employed, e.g., for description of three-dimensional non-relativistic N=4 supersymmetric theories.

A numerical study of transition control by periodic suction-blowing

NASA Technical Reports Server (NTRS)

Biringen, Sedat

1987-01-01

The applicability of active control of transition by periodic suction-blowing is investigated via direct numerical simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that, for relatively small three dimensional amplitudes, a two dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the flow dynamics during transition.

On the strain energy of laminated composite plates

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Multidimensionally encoded magnetic resonance imaging.

PubMed

Lin, Fa-Hsuan

2013-07-01

Magnetic resonance imaging (MRI) typically achieves spatial encoding by measuring the projection of a q-dimensional object over q-dimensional spatial bases created by linear spatial encoding magnetic fields (SEMs). Recently, imaging strategies using nonlinear SEMs have demonstrated potential advantages for reconstructing images with higher spatiotemporal resolution and reducing peripheral nerve stimulation. In practice, nonlinear SEMs and linear SEMs can be used jointly to further improve the image reconstruction performance. Here, we propose the multidimensionally encoded (MDE) MRI to map a q-dimensional object onto a p-dimensional encoding space where p > q. MDE MRI is a theoretical framework linking imaging strategies using linear and nonlinear SEMs. Using a system of eight surface SEM coils with an eight-channel radiofrequency coil array, we demonstrate the five-dimensional MDE MRI for a two-dimensional object as a further generalization of PatLoc imaging and O-space imaging. We also present a method of optimizing spatial bases in MDE MRI. Results show that MDE MRI with a higher dimensional encoding space can reconstruct images more efficiently and with a smaller reconstruction error when the k-space sampling distribution and the number of samples are controlled. Copyright © 2012 Wiley Periodicals, Inc.

Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors

NASA Astrophysics Data System (ADS)

Wei, Zhouchao; Rajagopal, Karthikeyan; Zhang, Wei; Kingni, Sifeu Takougang; Akgül, Akif

2018-04-01

Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke-Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications.

MUSTA fluxes for systems of conservation laws

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2006-08-01

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporate GFORCE in the framework of the MUSTA approach [E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003], resulting in a version that we call GMUSTA. For non-linear systems this gives results that are comparable to those of the Godunov method in conjunction with the exact Riemann solver or complete approximate Riemann solvers, noting however that in our approach, the solution of the Riemann problem in the conventional sense is avoided. Both the GFORCE and GMUSTA fluxes are extended to multi-dimensional non-linear systems in a straightforward unsplit manner, resulting in linearly stable schemes that have the same stability regions as the straightforward multi-dimensional extension of Godunov's method. The methods are applicable to general meshes. The schemes of this paper share with the family of centred methods the common properties of being simple and applicable to a large class of hyperbolic systems, but the schemes of this paper are distinctly more accurate. Finally, we proceed to the practical implementation of our numerical fluxes in the framework of high-order finite volume WENO methods for multi-dimensional non-linear hyperbolic systems. Numerical results are presented for the Euler equations and for the equations of magnetohydrodynamics.

Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials

NASA Astrophysics Data System (ADS)

Choi, Jin-Ho; Cui, Ping; Lan, Haiping; Zhang, Zhenyu

2015-08-01

The exciton is one of the most crucial physical entities in the performance of optoelectronic and photonic devices, and widely varying exciton binding energies have been reported in different classes of materials. Using first-principles calculations within the G W -Bethe-Salpeter equation approach, here we investigate the excitonic properties of two recently discovered layered materials: phosphorene and graphene fluoride. We first confirm large exciton binding energies of, respectively, 0.85 and 2.03 eV in these systems. Next, by comparing these systems with several other representative two-dimensional materials, we discover a striking linear relationship between the exciton binding energy and the band gap and interpret the existence of the linear scaling law within a simple hydrogenic picture. The broad applicability of this novel scaling law is further demonstrated by using strained graphene fluoride. These findings are expected to stimulate related studies in higher and lower dimensions, potentially resulting in a deeper understanding of excitonic effects in materials of all dimensionalities.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

An automatic robotic system for three-dimensional tooth crown preparation using a picosecond laser.

PubMed

Wang, Lei; Wang, Dangxiao; Zhang, Yuru; Ma, Lei; Sun, Yuchun; Lv, Peijun

2014-09-01

Laser techniques have been introduced into dentistry to overcome the drawbacks of traditional treatment methods. The existing methods in dental clinical operations for tooth crown preparation have several drawbacks which affect the long-term success of the dental treatment. To develop an improved robotic system to manipulate the laser beam to achieve safe and accurate three-dimensional (3D) tooth ablation, and thus to realize automatic tooth crown preparation in clinical operations. We present an automatic laser ablation system for tooth crown preparation in dental restorative operations. The system, combining robotics and laser technology, is developed to control the laser focus in three-dimensional motion aiming for high speed and accuracy crown preparation. The system consists of an end-effector, a real-time monitor and a tooth fixture. A layer-by-layer ablation method is developed to control the laser focus during the crown preparation. Experiments are carried out with picosecond laser on wax resin and teeth. The accuracy of the system is satisfying, achieving the average linear errors of 0.06 mm for wax resin and 0.05 mm for dentin. The angle errors are 4.33° for wax resin and 0.5° for dentin. The depth errors for wax resin and dentin are both within 0.1 mm. The ablation time is 1.5 hours for wax resin and 3.5 hours for dentin. The ablation experimental results show that the movement range and the resolution of the robotic system can meet the requirements of typical dental operations for tooth crown preparation. Also, the errors of tooth shape and preparation angle are able to satisfy the requirements of clinical crown preparation. Although the experimental results illustrate the potential of using picosecond lasers for 3D tooth crown preparation, many research issues still need to be studied before the system can be applied to clinical operations. © 2014 Wiley Periodicals, Inc.

Trajectory tracking in quadrotor platform by using PD controller and LQR control approach

NASA Astrophysics Data System (ADS)

Islam, Maidul; Okasha, Mohamed; Idres, Moumen Mohammad

2017-11-01

The purpose of the paper is to discuss a comparative evaluation of performance of two different controllers i.e. Proportional-Derivative Controller (PD) and Linear Quadratic Regulation (LQR) in Quadrotor dynamic system that is under-actuated with high nonlinearity. As only four states can be controlled at the same time in the Quadrotor, the trajectories are designed on the basis of the four states whereas three dimensional position and rotation along an axis, known as yaw movement are considered. In this work, both the PD controller and LQR control approach are used for Quadrotor nonlinear model to track the trajectories. LQR control approach for nonlinear model is designed on the basis of a linear model of the Quadrotor because the performance of linear model and nonlinear model around certain nominal point is almost similar. Simulink and MATLAB software is used to design the controllers and to evaluate the performance of both the controllers.

That Deceptive Line: Plato, Linear Perspective, Visual Perception, and Tragedy

ERIC Educational Resources Information Center

Killian, Jeremy

2012-01-01

In "The Renaissance Rediscovery of Linear Perspective," one of Samuel Edgerton's claims is that Filippo Brunelleschi and his contemporaries did not develop a three-dimensional style of representing the world in painting as much as they reappropriated a way to depict the natural world in painting that most mirrored the human perception of it.…

SU-E-T-279: Realization of Three-Dimensional Conformal Dose Planning in Prostate Brachytherapy

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

Li, Z; Jiang, S; Yang, Z

2014-06-01

Purpose: Successful clinical treatment in prostate brachytherapy is largely dependent on the effectiveness of pre-surgery dose planning. Conventional dose planning method could hardly arrive at a satisfy result. In this abstract, a three-dimensional conformal localized dose planning method is put forward to ensure the accuracy and effectiveness of pre-implantation dose planning. Methods: Using Monte Carlo method, the pre-calculated 3-D dose map for single source is obtained. As for multiple seeds dose distribution, the maps are combined linearly to acquire the 3-D distribution. The 3-D dose distribution is exhibited in the form of isodose surface together with reconstructed 3-D organs groupmore » real-timely. Then it is possible to observe the dose exposure to target volume and normal tissues intuitively, thus achieving maximum dose irradiation to treatment target and minimum healthy tissues damage. In addition, the exfoliation display of different isodose surfaces can be realized applying multi-values contour extraction algorithm based on voxels. The needles could be displayed in the system by tracking the position of the implanted seeds in real time to conduct block research in optimizing insertion trajectory. Results: This study extends dose planning from two-dimensional to three-dimensional, realizing the three-dimensional conformal irradiation, which could eliminate the limitations of 2-D images and two-dimensional dose planning. A software platform is developed using VC++ and Visualization Toolkit (VTK) to perform dose planning. The 3-D model reconstruction time is within three seconds (on a Intel Core i5 PC). Block research could be conducted to avoid inaccurate insertion into sensitive organs or internal obstructions. Experiments on eight prostate cancer cases prove that this study could make the dose planning results more reasonable. Conclusion: The three-dimensional conformal dose planning method could improve the rationality of dose planning by safely reducing the large target margin and avoiding dose dead zones for prostate cancer treatment. 1) National Natural Science Foundation of People's Republic of China (No. 51175373); 2) New Century Educational Talents Plan of Chinese Education Ministry (NCET-10-0625); 3) Scientific and Technological Major Project, Tianjin (No. 12ZCDZSY10600)« less

A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure

NASA Astrophysics Data System (ADS)

Albertazzi, A.; Viotti, M. R.; Veiga, C. L. N.; Fantin, A. V.

2016-08-01

Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Dimensions and geometry of the temporomandibular joint and masseter muscles.

PubMed

Zurowski, R; Gosek, M; Aleksandrowicz, R

1976-01-01

The bio-engineering team presents its suggestion of a method for the measurement of the temporomandibular joint and masseter muscles in order to determine the parameters necessary for exact sciences and indispensable for unified and objective cognitive studies. Ten formalin-fixed human cadavers served for the studies. The preparations were prepared by the modified method of anatomical procedure. Linear and angular measurements of temporomandibular joint and masseter muscles were carried out with the use of the three-dimensional Cartesian system of OXYZ coordinates in relation to frontal, sagittal and horizontal planes. The physiological cross-sections of the masseter, temporal, lateral and medial pterygoid muscles were also determined. The collected data make it possible to develop a mathematical three-dimensioned model of the osseo-articulo-muscular system of the mastication organ.

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The equations of momentum annd continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in Earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The equations of momentum and continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

3D DNS and LES of Breaking Inertia-Gravity Waves

NASA Astrophysics Data System (ADS)

Remmler, S.; Fruman, M. D.; Hickel, S.; Achatz, U.

2012-04-01

As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and correspondingly large horizontal wavelength to be strongly influenced by the Coriolis force. Inertia-gravity waves are very active in the middle atmosphere and their breaking is potentially an important influence on the circulation in this region. The parametrization of this process requires a good theoretical understanding, which we want to enhance with the present study. Primary linear instabilities of an inertia-gravity wave and "2.5-dimensional" nonlinear simulations (where the spatial dependence is two dimensional but the velocity and vorticity fields are three-dimensional) with the wave perturbed by its leading primary instabilities by Achatz [1] have shown that the breaking differs significantly from that of high-frequency gravity waves due to the strongly sheared component of velocity perpendicular to the plane of wave-propagation. Fruman & Achatz [2] investigated the three-dimensionalization of the breaking by computing the secondary linear instabilities of the same waves using singular vector analysis. These secondary instabilities are variations perpendicular to the direction of the primary perturbation and the wave itself, and their wavelengths are an order of magnitude shorter than both. In continuation of this work, we carried out fully three-dimensional nonlinear simulations of inertia-gravity waves perturbed by their leading primary and secondary instabilities. The direct numerical simulation (DNS) was made tractable by restricting the domain size to the dominant scales selected by the linear analyses. The study includes both convectively stable and unstable waves. To the best of our knowledge, this is the first fully three-dimensional nonlinear direct numerical simulation of inertia-gravity waves at realistic Reynolds numbers with complete resolution of the smallest turbulence scales. Previous simulations either were restricted to high frequency gravity waves (e. g. Fritts et al. [3]), or the ratio N/f was artificially reduced (e. g. Lelong & Dunkerton [4]). The present simulations give us insight into the three-dimensional breaking process as well as the emerging turbulence. We assess the possibility of reducing the computational costs of three-dimensional simulations by using an implicit turbulence subgrid-scale parametrization based on the Adaptive Local Deconvolution Method (ALDM) for stratified turbulence [5]. In addition, we have performed ensembles of nonlinear 2.5-dimensional DNS, like those in Achatz [1] but with a small amount of noise superposed to the initial state, and compared the results with coarse-resolution simulations using either ALDM as well as with standard LES schemes. We found that the results of the models with parametrized turbulence, which are orders of magnitude more computationally economical than the DNS, compare favorably with the DNS in terms of the decay of the wave amplitude with time (the quantity most important for application to gravity-wave drag parametrization) suggesting that they may be trusted in future simulations of gravity wave breaking.

Three dimensional dynamics of a flexible Motorised Momentum Exchange Tether

NASA Astrophysics Data System (ADS)

Ismail, N. A.; Cartmell, M. P.

2016-03-01

This paper presents a new flexural model for the three dimensional dynamics of the Motorised Momentum Exchange Tether (MMET) concept. This study has uncovered the relationships between planar and nonplanar motions, and the effect of the coupling between these two parameters on pragmatic circular and elliptical orbits. The tether sub-spans are modelled as stiffened strings governed by partial differential equations of motion, with specific boundary conditions. The tether sub-spans are flexible and elastic, thereby allowing three dimensional displacements. The boundary conditions lead to a specific frequency equation and the eigenvalues from this provide the natural frequencies of the orbiting flexible motorised tether when static, accelerating in monotonic spin, and at terminal angular velocity. A rotation transformation matrix has been utilised to get the position vectors of the system's components in an assumed inertial frame. Spatio-temporal coordinates are transformed to modal coordinates before applying Lagrange's equations, and pre-selected linear modes are included to generate the equations of motion. The equations of motion contain inertial nonlinearities which are essentially of cubic order, and these show the potential for intricate intermodal coupling effects. A simulation of planar and non-planar motions has been undertaken and the differences in the modal responses, for both motions, and between the rigid body and flexible models are highlighted and discussed.

2D and 3D Traveling Salesman Problem

ERIC Educational Resources Information Center

Haxhimusa, Yll; Carpenter, Edward; Catrambone, Joseph; Foldes, David; Stefanov, Emil; Arns, Laura; Pizlo, Zygmunt

2011-01-01

When a two-dimensional (2D) traveling salesman problem (TSP) is presented on a computer screen, human subjects can produce near-optimal tours in linear time. In this study we tested human performance on a real and virtual floor, as well as in a three-dimensional (3D) virtual space. Human performance on the real floor is as good as that on a…

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R.

1985-01-01

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Lift and drag in three-dimensional steady viscous and compressible flow

NASA Astrophysics Data System (ADS)

Liu, L. Q.; Wu, J. Z.; Su, W. D.; Kang, L. L.

2017-11-01

In a recent paper, Liu, Zhu, and Wu ["Lift and drag in two-dimensional steady viscous and compressible flow," J. Fluid Mech. 784, 304-341 (2015)] present a force theory for a body in a two-dimensional, viscous, compressible, and steady flow. In this companion paper, we do the same for three-dimensional flows. Using the fundamental solution of the linearized Navier-Stokes equations, we improve the force formula for incompressible flows originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, which is further proved to be universally true from subsonic to supersonic flows. We call this result the unified force theorem, which states that the forces are always determined by the vector circulation Γϕ of longitudinal velocity and the scalar inflow Qψ of transverse velocity. Since this theorem is not directly observable either experimentally or computationally, a testable version is also derived, which, however, holds only in the linear far field. We name this version the testable unified force formula. After that, a general principle to increase the lift-drag ratio is proposed.

Effect of chordwise forces and deformations and deformations due to steady lift on wing flutter

NASA Technical Reports Server (NTRS)

Boyd, W. N.

1977-01-01

This investigation explores the effects of chordwise forces and deformations and steady-state deformation due to lift on the static and dynamic aeroelastic stability of a uniform cantilever wing. Results of this analysis are believed to have practical applications for high-performance sailplanes and certain RPV's. The airfoil cross section is assumed to be symmetric and camber bending is neglected. Motions in vertical bending, fore-and-aft bending, and torsion are considered. A differential equation model is developed, which included the nonlinear elastic bending-torsion coupling that accompanies even moderate deflections. A linearized expansion in small time-dependent deflections is made about a steady flight condition. The stability determinant of the linearized system then contains coefficients that depend on steady displacements. Loads derived from two-dimensional incompressible aerodynamic theory are used to obtain the majority of the results, but cases using three-dimensional subsonic compressible theory are also studied. The stability analysis is carried out in terms of the dynamically uncoupled natural modes of vibration of the uniform cantilever.

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Three-dimensional polarization states of monochromatic light fields.

PubMed

Azzam, R M A

2011-11-01

The 3×1 generalized Jones vectors (GJVs) [E(x) E(y) E(z)](t) (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3×3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E(s)=T E(i), is briefly introduced. In such a matrix transformation, E(i) and E(s) are the 3×1 GJVs of the incident and scattered waves and T is the 3×3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.

Correlated observations of three triggered lightning flashes

NASA Technical Reports Server (NTRS)

Idone, V. P.; Orville, R. E.; Hubert, P.; Barret, L.; Eybert-Berard, A.

1984-01-01

Three triggered lightning flashes, initiated during the Thunderstorm Research International Program (1981) at Langmuir Laboratory, New Mexico, are examined on the basis of three-dimensional return stroke propagation speeds and peak currents. Nonlinear relationships result between return stroke propagation speed and stroke peak current for 56 strokes, and between return stroke propagation speed and dart leader propagation speed for 32 strokes. Calculated linear correlation coefficients include dart leader propagation speed and ensuing return stroke peak current (32 strokes; r = 0.84); and stroke peak current and interstroke interval (69 strokes; r = 0.57). Earlier natural lightning data do not concur with the weak positive correlation between dart leader propagation speed and interstroke interval. Therefore, application of triggered lightning results to natural lightning phenomena must be made with certain caveats. Mean values are included for the three-dimensional return stroke propagation speed and for the three-dimensional dart leader propagation speed.

A variable-order laminated plate theory based on the variational-asymptotical method

NASA Technical Reports Server (NTRS)

Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.

1993-01-01

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Atmospheric refraction errors in laser ranging systems

NASA Technical Reports Server (NTRS)

Gardner, C. S.; Rowlett, J. R.

1976-01-01

The effects of horizontal refractivity gradients on the accuracy of laser ranging systems were investigated by ray tracing through three dimensional refractivity profiles. The profiles were generated by performing a multiple regression on measurements from seven or eight radiosondes, using a refractivity model which provided for both linear and quadratic variations in the horizontal direction. The range correction due to horizontal gradients was found to be an approximately sinusoidal function of azimuth having a minimum near 0 deg azimuth and a maximum near 180 deg azimuth. The peak to peak variation was approximately 5 centimeters at 10 deg elevation and decreased to less than 1 millimeter at 80 deg elevation.

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

NASA Astrophysics Data System (ADS)

Huyakorn, P. S.; Panday, S.; Wu, Y. S.

1994-06-01

A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.

Tooth-size discrepancy: A comparison between manual and digital methods

PubMed Central

Correia, Gabriele Dória Cabral; Habib, Fernando Antonio Lima; Vogel, Carlos Jorge

2014-01-01

Introduction Technological advances in Dentistry have emerged primarily in the area of diagnostic tools. One example is the 3D scanner, which can transform plaster models into three-dimensional digital models. Objective This study aimed to assess the reliability of tooth size-arch length discrepancy analysis measurements performed on three-dimensional digital models, and compare these measurements with those obtained from plaster models. Material and Methods To this end, plaster models of lower dental arches and their corresponding three-dimensional digital models acquired with a 3Shape R700T scanner were used. All of them had lower permanent dentition. Four different tooth size-arch length discrepancy calculations were performed on each model, two of which by manual methods using calipers and brass wire, and two by digital methods using linear measurements and parabolas. Results Data were statistically assessed using Friedman test and no statistically significant differences were found between the two methods (P > 0.05), except for values found by the linear digital method which revealed a slight, non-significant statistical difference. Conclusions Based on the results, it is reasonable to assert that any of these resources used by orthodontists to clinically assess tooth size-arch length discrepancy can be considered reliable. PMID:25279529

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

Linear decentralized systems with special structure. [for twin lift helicopters

NASA Technical Reports Server (NTRS)

Martin, C. F.

1982-01-01

Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.

Role of upper-level wind shear on the structure and maintenance of derecho-producing convective systems

NASA Astrophysics Data System (ADS)

Coniglio, Michael Charles

Common large-scale environments associated with the development of derecho-producing convective systems from a large number of events are identified using statistical clustering of the 500-mb geopotential heights as guidance. The majority of the events (72%) fall into three main patterns that include a well-defined upstream trough (40%), a ridge (20%), and a zonal, low-amplitude flow (12%), which is defined as an additional warm-season pattern that is not identified in past studies of derecho environments. Through an analysis of proximity soundings, discrepancies are found in both low-level and deep-tropospheric shear parameters between observations and the shear profiles considered favorable for strong, long-lived convective systems in idealized simulations. To explore the role of upper-level shear in derecho environments, a set of two-dimensional simulations of density currents within a dry, neutrally stable environment are used to examine the ability of a cold pool to lift environmental air within a vertically sheared flow. The results confirm that the addition of upper-level shear to a wind profile with weak to moderate low-level shear increases the vertical displacement of low-level parcels despite a decrease in the vertical velocity along the cold pool interface, as suggested by previous studies. Parcels that are elevated above the surface (1-2 km) overturn and are responsible for the deep lifting in the deep-shear environments. This deep overturning caused by the upper-level shear helps to maintain the tilt of the convective systems in more complex two-dimensional and three dimensional simulations. The overturning also is shown to greatly increase the size of the convective systems in the three-dimensional simulations by facilitating the initiation and maintenance of convective cells along the cold pool. When combined with estimates of the cold pool motion and the storm-relative hodograph, these results may best be used for the prediction of the demise of strong, linear mesoscale convective systems (MCSs) and may provide a conceptual model for the persistence of strong MCSs above a surface nocturnal inversion in situations that are not forced by a low-level jet.

A three dimensional finite element formulation for thermoviscoelastic orthotropic media

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

Zocher, M.A.

1997-12-31

A numerical algorithm for the efficient solution of the uncoupled quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation is briefly outlined.

The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps

NASA Astrophysics Data System (ADS)

Simpson, D. J. W.

2018-05-01

In two-parameter bifurcation diagrams of piecewise-linear continuous maps on , mode-locking regions typically have points of zero width known as shrinking points. Near any shrinking point, but outside the associated mode-locking region, a significant proportion of parameter space can be usefully partitioned into a two-dimensional array of annular sectors. The purpose of this paper is to show that in these sectors the dynamics is well-approximated by a three-parameter family of skew sawtooth circle maps, where the relationship between the skew sawtooth maps and the N-dimensional map is fixed within each sector. The skew sawtooth maps are continuous, degree-one, and piecewise-linear, with two different slopes. They approximate the stable dynamics of the N-dimensional map with an error that goes to zero with the distance from the shrinking point. The results explain the complicated radial pattern of periodic, quasi-periodic, and chaotic dynamics that occurs near shrinking points.

APPLE - An aeroelastic analysis system for turbomachines and propfans

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, Milind A.; Srivastava, R.; Mehmed, Oral

1992-01-01

This paper reviews aeroelastic analysis methods for propulsion elements (advanced propellers, compressors and turbines) being developed and used at NASA Lewis Research Center. These aeroelastic models include both structural and aerodynamic components. The structural models include the typical section model, the beam model with and without disk flexibility, and the finite element blade model with plate bending elements. The aerodynamic models are based on the solution of equations ranging from the two-dimensional linear potential equation for a cascade to the three-dimensional Euler equations for multi-blade configurations. Typical results are presented for each aeroelastic model. Suggestions for further research are indicated. All the available aeroelastic models and analysis methods are being incorporated into a unified computer program named APPLE (Aeroelasticity Program for Propulsion at LEwis).

Dynamic aeroelastic stability of vertical-axis wind turbines under constant wind velocity

NASA Astrophysics Data System (ADS)

Nitzsche, Fred

1994-05-01

The flutter problem associated with the blades of a class of vertical-axis wind turbines called Darrieus is studied in detail. The spinning blade is supposed to be initially curved in a particular shape characterized by a state of pure tension at the blade cross section. From this equilibrium position a three-dimensional linear perturbation pattern is superimposed to determine the dynamic aeroelastic stability of the blade in the presence of free wind speed by means of the Floquet-Lyapunov theory for periodic systems.

Environmental pollution as engine of industrialization

NASA Astrophysics Data System (ADS)

Antoci, Angelo; Galeotti, Marcello; Sordi, Serena

2018-05-01

This paper analyzes the dynamics of a small open economy with two sectors (a farming sector and an industrial one), heterogeneous agents (workers and entrepreneurs) and free inter-sectoral labor mobility. Labor productivity in the first sector is negatively affected by environmental pollution generated by both sectors, whereas in the second sector it is positively affected by physical capital accumulated by entrepreneurs. Through a global analysis of the non-linear three-dimensional dynamic system of the model we derive conditions under which industrialization generates a decline in workers' revenues in both sectors.

An optimal analysis for Darcy-Forchheimer 3D flow of Carreau nanofluid with convectively heated surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2018-06-01

Darcy-Forchheimer three dimensional flow of Carreau nanoliquid induced by a linearly stretchable surface with convective boundary condition has been analyzed. Buongiorno model has been employed to elaborate thermophoresis and Brownian diffusion effects. Zero nanoparticles mass flux and convective surface conditions are implemented at the boundary. The governing problems are nonlinear. Optimal homotopic procedure has been used to tackle the governing mathematical system. Graphical results clearly depict the outcome of temperature and concentration fields. Surface drag coefficients and local Nusselt number are also plotted and discussed.

Chosen interval methods for solving linear interval systems with special type of matrix

NASA Astrophysics Data System (ADS)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

Research on three-dimensional real scene technology of Sichuan-Tibet highway

NASA Astrophysics Data System (ADS)

Yin, Peng; Bo, Xianglei; Liu, Fen

2018-04-01

This paper studies the three-dimensional real scene technology in the application of highway simulation, and a system to realize three-dimensional real scene of Sichuan-Tibet highway is presented. This system can improve the defect of the traditional Sichuan-Tibet highway geographic information system from performance and feeling. The Tibet forces can use this system to improve motor adaptive training effect and command decision-making ability.

Three-dimensional shape measurement system applied to superficial inspection of non-metallic pipes for the hydrocarbons transport

NASA Astrophysics Data System (ADS)

Arciniegas, Javier R.; González, Andrés. L.; Quintero, L. A.; Contreras, Carlos R.; Meneses, Jaime E.

2014-05-01

Three-dimensional shape measurement is a subject that consistently produces high scientific interest and provides information for medical, industrial and investigative applications, among others. In this paper, it is proposed to implement a three-dimensional (3D) reconstruction system for applications in superficial inspection of non-metallic pipes for the hydrocarbons transport. The system is formed by a CCD camera, a video-projector and a laptop and it is based on fringe projection technique. System functionality is evidenced by evaluating the quality of three-dimensional reconstructions obtained, which allow observing the failures and defects on the study object surface.

A new method for assessing relative dynamic motion of vertebral bodies during cyclic loading in vitro.

PubMed

Dean, J C; Wilcox, C H; Daniels, A U; Goodwin, R R; Van Wagoner, E; Dunn, H K

1991-01-01

A new experimental technique for measuring generalized three-dimensional motion of vertebral bodies during cyclic loading in vitro is presented. The system consists of an orthogonal array of three lasers mounted rigidly to one vertebra, and a set of three mutually orthogonal charge-coupled devices mounted rigidly to an adjacent vertebra. Each laser strikes a corresponding charge-coupled device screen. The mathematical model of the system is reduced to a linear set of equations with consequent matrix algebra allowing fast real-time data reduction during cyclic movements of the spine. The range and accuracy of the system is well suited for studying thoracolumbar motion segments. Distinct advantages of the system include miniaturization of the components, the elimination of the need for mechanical linkages between the bodies, and a high degree of accuracy which is not dependent on viewing volume as found in photogrammetric systems. More generally, the spectrum of potential applications of systems of this type to the real-time measurement of the relative motion of two bodies is extremely broad.

Design of four-beam IH-RFQ linear accelerator

NASA Astrophysics Data System (ADS)

Ikeda, Shota; Murata, Aki; Hayashizaki, Noriyosu

2017-09-01

The multi-beam acceleration method is an acceleration technique for low-energy high-intensity heavy ion beams, which involves accelerating multiple beams to decrease space charge effects, and then integrating these beams by a beam funneling system. At the Tokyo Institute of Technology a two beam IH-RFQ linear accelerator was developed using a two beam laser ion source with direct plasma injection scheme. This system accelerated a carbon ion beam with a current of 108 mA (54 mA/channel × 2) from 5 up to 60 keV/u. In order to demonstrate that a four-beam IH-RFQ linear accelerator is suitable for high-intensity heavy ion beam acceleration, we have been developing a four-beam prototype. A four-beam IH-RFQ linear accelerator consists of sixteen RFQ electrodes (4 × 4 set) with stem electrodes installed alternately on the upper and lower ridge electrodes. As a part of this development, we have designed a four-beam IH-RFQ linear accelerator using three dimensional electromagnetic simulation software and beam tracking simulation software. From these simulation results, we have designed the stem electrodes, the center plate and the side shells by evaluating the RF properties such as the resonance frequency, the power loss and the electric strength distribution between the RFQ electrodes.

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

REPORT ON AN ORBITAL MAPPING SYSTEM.

USGS Publications Warehouse

Colvocoresses, Alden P.; ,

1984-01-01

During June 1984, the International Society for Photogrammetry and Remote Sensing accepted a committee report that defines an Orbital Mapping System (OMS) to follow Landsat and other Earth-sensing systems. The OMS involves the same orbital parameters of Landsats 1, 2, and 3, three wave bands (two in the visible and one in the near infrared) and continuous stereoscopic capability. The sensors involve solid-state linear arrays and data acquisition (including stereo) designed for one-dimensional data processing. It has a resolution capability of 10-m pixels and is capable of producing 1:50,000-scale image maps with 20-m contours. In addition to mapping, the system is designed to monitor the works of man as well as nature and in a cost-effective manner.

Tracking performance under time sharing conditions with a digit processing task: A feedback control theory analysis. [attention sharing effect on operator performance

NASA Technical Reports Server (NTRS)

Gopher, D.; Wickens, C. D.

1975-01-01

A one dimensional compensatory tracking task and a digit processing reaction time task were combined in a three phase experiment designed to investigate tracking performance in time sharing. Adaptive techniques, elaborate feedback devices, and on line standardization procedures were used to adjust task difficulty to the ability of each individual subject and manipulate time sharing demands. Feedback control analysis techniques were employed in the description of tracking performance. The experimental results show that when the dynamics of a system are constrained, in such a manner that man machine system stability is no longer a major concern of the operator, he tends to adopt a first order control describing function, even with tracking systems of higher order. Attention diversion to a concurrent task leads to an increase in remnant level, or nonlinear power. This decrease in linearity is reflected both in the output magnitude spectra of the subjects, and in the linear fit of the amplitude ratio functions.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

A fast method to compute Three-Dimensional Infrared Radiative Transfer in non scattering medium

NASA Astrophysics Data System (ADS)

Makke, Laurent; Musson-Genon, Luc; Carissimo, Bertrand

2014-05-01

The Atmospheric Radiation field has seen the development of more accurate and faster methods to take into account absoprtion in participating media. Radiative fog appears with clear sky condition due to a significant cooling during the night, so scattering is left out. Fog formation modelling requires accurate enough method to compute cooling rates. Thanks to High Performance Computing, multi-spectral approach of Radiative Transfer Equation resolution is most often used. Nevertheless, the coupling of three-dimensionnal radiative transfer with fluid dynamics is very detrimental to the computational cost. To reduce the time spent in radiation calculations, the following method uses analytical absorption functions fitted by Sasamori (1968) on Yamamoto's charts (Yamamoto,1956) to compute a local linear absorption coefficient. By averaging radiative properties, this method eliminates the spectral integration. For an isothermal atmosphere, analytical calculations lead to an explicit formula between emissivities functions and linear absorption coefficient. In the case of cooling to space approximation, this analytical expression gives very accurate results compared to correlated k-distribution. For non homogeneous paths, we propose a two steps algorithm. One-dimensional radiative quantities and linear absorption coefficient are computed by a two-flux method. Then, three-dimensional RTE under the grey medium assumption is solved with the DOM. Comparisons with measurements of radiative quantities during ParisFOG field (2006) shows the cability of this method to handle strong vertical variations of pressure/temperature and gases concentrations.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

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

NASA Astrophysics Data System (ADS)

Newman, James Charles, III

1997-10-01

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

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory; The CenterComplex Quantum Systems Team

In this work we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flat-band dispersionless. We find a small gap is also opened at the quadratic band touching point by 2-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems. We gratefully acknowledge funding from ARO Grant W911NF-14-1-0579 and NSF DMR-1507621.

Parity-Time Symmetric Nonlocal Metasurfaces: All-Angle Negative Refraction and Volumetric Imaging

NASA Astrophysics Data System (ADS)

Monticone, Francesco; Valagiannopoulos, Constantinos A.; Alù, Andrea

2016-10-01

Lens design for focusing and imaging has been optimized through centuries of developments; however, conventional lenses, even in their most ideal realizations, still suffer from fundamental limitations, such as limits in resolution and the presence of optical aberrations, which are inherent to the laws of refraction. In addition, volume-to-volume imaging of three-dimensional regions of space is not possible with systems based on conventional refractive optics, which are inherently limited to plane-to-plane imaging. Although some of these limitations have been at least theoretically relaxed with the advent of metamaterials, several challenges still stand in the way of ideal imaging of three-dimensional regions of space. Here, we show that the concept of parity-time symmetry, combined with tailored nonlocal responses, enables overcoming some of these challenges, and we propose the design of a loss-immune, linear, transversely invariant, planarized metamaterial lens, with reduced aberrations and the potential to realize volume-to-volume imaging.

Anchorage in Orthodontics: Three-dimensional Scanner Input

PubMed Central

Nabbout, Fidele; Baron, Pascal

2018-01-01

Aims and Objectives: The aim of this article is to re-evaluate anchorage coefficient values in orthodontics and their influence in the treatment decision through the usage of three-dimensional (3D) scanner. Materials and Methods: A sample of 80 patients was analyzed with the 3D scanner using the C2000 and Cepha 3DT softwares (CIRAD Montpellier, France). Tooth anatomy parameters (linear measurements, root, and crown volumes) were then calculated to determine new anchorage coefficients based on root volume. Data were collected and statistically evaluated with the StatView software (version 5.0). Results: The anchorage coefficient values found in this study are compared to those established in previous studies. These new values affect and modify our approach in orthodontic treatment from the standpoint of anchorage. Conclusion: The use of new anchorage coefficient values has significant clinical implications in conventional and in microimplants-assisted orthodontic mechanics through the selection and delivery of the optimal force system (magnitude and moment) for an adequate biological response. PMID:29629323

Heat transport in an anharmonic crystal

NASA Astrophysics Data System (ADS)

Acharya, Shiladitya; Mukherjee, Krishnendu

2018-04-01

We study transport of heat in an ordered, anharmonic crystal in the form of slab geometry in three dimensions. Apart from attaching baths of Langevin type to two extreme surfaces, we also attach baths of same type to the intermediate surfaces of the slab. Since the crystal is uninsulated, it exchanges energy with the intermediate heat baths. We find that both Fourier’s law of heat conduction and the Newton’s law of cooling hold to leading order in anharmonic coupling. The leading behavior of the temperature profile is exponentially falling from high to low temperature surface of the slab. As the anharmonicity increases, profiles fall more below the harmonic one in the log plot. In the thermodynamic limit thermal conductivity remains independent of the environment temperature and its leading order anharmonic contribution is linearly proportional to the temperature change between the two extreme surfaces of the slab. A fast crossover from one-dimensional (1D) to three-dimensional (3D) behavior of the thermal conductivity is observed in the system.

Efficient propagation-inside-layer expansion algorithm for solving the scattering from three-dimensional nested homogeneous dielectric bodies with arbitrary shape.

PubMed

Bellez, Sami; Bourlier, Christophe; Kubické, Gildas

2015-03-01

This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.

Angular velocity discrimination

NASA Technical Reports Server (NTRS)

Kaiser, Mary K.

1990-01-01

Three experiments designed to investigate the ability of naive observers to discriminate rotational velocities of two simultaneously viewed objects are described. Rotations are constrained to occur about the x and y axes, resulting in linear two-dimensional image trajectories. The results indicate that observers can discriminate angular velocities with a competence near that for linear velocities. However, perceived angular rate is influenced by structural aspects of the stimuli.

Simulation Methods for Poisson Processes in Nonstationary Systems.

DTIC Science & Technology

1978-08-01

for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the...and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

NASA Technical Reports Server (NTRS)

Ford, G. E.

1986-01-01

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Multivariable control of a rolling spider drone

NASA Astrophysics Data System (ADS)

Lyu, Haifeng

The research and application of Unmanned Aerial Vehicles (UAVs) has been a hot topic recently. A UAV is dened as an aircraft which is designed not to carry a human pilot or operated with remote electronic input by the flight controller. In this thesis, the design of a control system for a quadcopter named Rolling Spider Drone is conducted. The thesis work presents the design of two kinds of controllers that can control the Drone to keep it balanced and track different kinds of input trajectories. The nonlinear mathematical model for the Drone is derived by the Newton-Euler method. The rotational subsystem and translational system are derived to describe the attitude and position motion of Drone. Techniques from linear control theory are employed to linearize the highly coupled and nonlinear quadcopter plant around equilibrium points and apply the linear feedback controller to stabilize the system. The controller is a digital tracking system that deploys LQR for system stability design. Fixed gain and adaptive gain scheduled controllers are developed and compared with different LQR weights. Step references and reference trajectories involving signicant variation for the yaw angle in the xy-plane and three-dimensional spaces are tracked in the simulation. The physical implementation and an output feedback controller are considered for future work.

Reconstruction 3-dimensional image from 2-dimensional image of status optical coherence tomography (OCT) for analysis of changes in retinal thickness

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

Arinilhaq,; Widita, Rena

2014-09-30

Optical Coherence Tomography is often used in medical image acquisition to diagnose that change due easy to use and low price. Unfortunately, this type of examination produces a two-dimensional retinal image of the point of acquisition. Therefore, this study developed a method that combines and reconstruct 2-dimensional retinal images into three-dimensional images to display volumetric macular accurately. The system is built with three main stages: data acquisition, data extraction and 3-dimensional reconstruction. At data acquisition step, Optical Coherence Tomography produced six *.jpg images of each patient were further extracted with MATLAB 2010a software into six one-dimensional arrays. The six arraysmore » are combined into a 3-dimensional matrix using a kriging interpolation method with SURFER9 resulting 3-dimensional graphics of macula. Finally, system provides three-dimensional color graphs based on the data distribution normal macula. The reconstruction system which has been designed produces three-dimensional images with size of 481 × 481 × h (retinal thickness) pixels.« less

Three species one-dimensional kinetic model for weakly ionized plasmas

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

Gonzalez, J., E-mail: jorge.gonzalez@upm.es; Donoso, J. M.; Tierno, S. P.

2016-06-15

A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting setmore » of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.« less

Self-consistent field theory of tethered polymers: one dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions.

PubMed

Suo, Tongchuan; Whitmore, Mark D

2014-11-28

We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a "mushroom" regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ(1/3) scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ(1/3). In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ(1/3). We also compare the results for two different solvents with each other, and with earlier Θ solvent results.

Hyperbolic Positioning with Antenna Arrays and Multi-Channel Pseudolite for Indoor Localization

PubMed Central

Fujii, Kenjirou; Sakamoto, Yoshihiro; Wang, Wei; Arie, Hiroaki; Schmitz, Alexander; Sugano, Shigeki

2015-01-01

A hyperbolic positioning method with antenna arrays consisting of proximately-located antennas and a multi-channel pseudolite is proposed in order to overcome the problems of indoor positioning with conventional pseudolites (ground-based GPS transmitters). A two-dimensional positioning experiment using actual devices is conducted. The experimental result shows that the positioning accuracy varies centimeter- to meter-level according to the geometric relation between the pseudolite antennas and the receiver. It also shows that the bias error of the carrier-phase difference observables is more serious than their random error. Based on the size of the bias error of carrier-phase difference that is inverse-calculated from the experimental result, three-dimensional positioning performance is evaluated by computer simulation. In addition, in the three-dimensional positioning scenario, an initial value convergence analysis of the non-linear least squares is conducted. Its result shows that initial values that can converge to a right position exist at least under the proposed antenna setup. The simulated values and evaluation methods introduced in this work can be applied to various antenna setups; therefore, by using them, positioning performance can be predicted in advance of installing an actual system. PMID:26437405

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Predicted Realization of Cubic Dirac Fermion in Quasi-One-Dimensional Transition-Metal Monochalcogenides

NASA Astrophysics Data System (ADS)

Liu, Qihang; Zunger, Alex

2017-04-01

We show that the previously predicted "cubic Dirac fermion," composed of six conventional Weyl fermions including three with left-handed and three with right-handed chirality, is realized in a specific, stable solid state system that has been made years ago, but was not appreciated as a "cubically dispersed Dirac semimetal" (CDSM). We identify the crystal symmetry constraints and find the space group P 63/m as one of the two that can support a CDSM, of which the characteristic band crossing has linear dispersion along the principle axis but cubic dispersion in the plane perpendicular to it. We then conduct a material search using density functional theory, identifying a group of quasi-one-dimensional molybdenum monochalcogenide compounds AI(MoXVI)3 (AI=Na , K, Rb, In, Tl; XVI=S , Se, Te) as ideal CDSM candidates. Studying the stability of the A (MoX) 3 family reveals a few candidates such as Rb (MoTe) 3 and Tl (MoTe) 3 that are predicted to be resilient to Peierls distortion, thus retaining the metallic character. Furthermore, the combination of one dimensionality and metallic nature in this family provides a platform for unusual optical signature—polarization-dependent metallic vs insulating response.

Quantum states and optical responses of low-dimensional electron hole systems

NASA Astrophysics Data System (ADS)

Ogawa, Tetsuo

2004-09-01

Quantum states and their optical responses of low-dimensional electron-hole systems in photoexcited semiconductors and/or metals are reviewed from a theoretical viewpoint, stressing the electron-hole Coulomb interaction, the excitonic effects, the Fermi-surface effects and the dimensionality. Recent progress of theoretical studies is stressed and important problems to be solved are introduced. We cover not only single-exciton problems but also few-exciton and many-exciton problems, including electron-hole plasma situations. Dimensionality of the Wannier exciton is clarified in terms of its linear and nonlinear responses. We also discuss a biexciton system, exciton bosonization technique, high-density degenerate electron-hole systems, gas-liquid phase separation in an excited state and the Fermi-edge singularity due to a Mahan exciton in a low-dimensional metal.

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Highly cytocompatible and flexible three-dimensional graphene/polydimethylsiloxane composite for culture and electrochemical detection of L929 fibroblast cells.

PubMed

Waiwijit, Uraiwan; Maturos, Thitima; Pakapongpan, Saithip; Phokharatkul, Ditsayut; Wisitsoraat, Anurat; Tuantranont, Adisorn

2016-08-01

Recently, three-dimensional graphene interconnected network has attracted great interest as a scaffold structure for tissue engineering due to its high biocompatibility, high electrical conductivity, high specific surface area and high porosity. However, free-standing three-dimensional graphene exhibits poor flexibility and stability due to ease of disintegration during processing. In this work, three-dimensional graphene is composited with polydimethylsiloxane to improve the structural flexibility and stability by a new simple two-step process comprising dip coating of polydimethylsiloxane on chemical vapor deposited graphene/Ni foam and wet etching of nickel foam. Structural characterizations confirmed an interconnected three-dimensional multi-layer graphene structure with thin polydimethylsiloxane scaffold. The composite was employed as a substrate for culture of L929 fibroblast cells and its cytocompatibility was evaluated by cell viability (Alamar blue assay), reactive oxygen species production and vinculin immunofluorescence imaging. The result revealed that cell viability on three-dimensional graphene/polydimethylsiloxane composite increased with increasing culture time and was slightly different from a polystyrene substrate (control). Moreover, cells cultured on three-dimensional graphene/polydimethylsiloxane composite generated less ROS than the control at culture times of 3-6 h. The results of immunofluorescence staining demonstrated that fibroblast cells expressed adhesion protein (vinculin) and adhered well on three-dimensional graphene/polydimethylsiloxane surface. Good cell adhesion could be attributed to suitable surface properties of three-dimensional graphene/polydimethylsiloxane with moderate contact angle and small negative zeta potential in culture solution. The results of electrochemical study by cyclic voltammetry showed that an oxidation current signal with no apparent peak was induced by fibroblast cells and the oxidation current at an oxidation potential of +0.9 V increased linearly with increasing cell number. Therefore, the three-dimensional graphene/polydimethylsiloxane composite exhibits high cytocompatibility and can potentially be used as a conductive substrate for cell-based electrochemical sensing. © The Author(s) 2016.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R. K.

1985-01-01

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Approximate cluster analysis method and three-dimensional diagram of optical characteristics of lunar surface

NASA Astrophysics Data System (ADS)

Yevsyukov, N. N.

1985-09-01

An approximate isolation algorithm for the isolation of multidimensional clusters is developed and applied in the construction of a three-dimensional diagram of the optical characteristics of the lunar surface. The method is somewhat analogous to that of Koontz and Fukunaga (1972) and involves isolating two-dimensional clusters, adding a new characteristic, and linearizing, a cycle which is repeated a limited number of times. The lunar-surface parameters analyzed are the 620-nm albedo, the 620/380-nm color index, and the 950/620-nm index. The results are presented graphically; the reliability of the cluster-isolation process is discussed; and some correspondences between known lunar morphology and the cluster maps are indicated.

Modeling, Control and Simulation of Three-Dimensional Robotic Systems with Applications to Biped Locomotion.

NASA Astrophysics Data System (ADS)

Zheng, Yuan-Fang

A three-dimensional, five link biped system is established. Newton-Euler state space formulation is employed to derive the equations of the system. The constraint forces involved in the equations can be eliminated by projection onto a smaller state space system for deriving advanced control laws. A model-referenced adaptive control scheme is developed to control the system. Digital computer simulations of point to point movement are carried out to show that the model-referenced adaptive control increases the dynamic range and speeds up the response of the system in comparison with linear and nonlinear feedback control. Further, the implementation of the controller is simpler. Impact effects of biped contact with the environment are modeled and studied. The instant velocity change at the moment of impact is derived as a function of the biped state and contact speed. The effects of impact on the state, as well as constraints are studied in biped landing on heels and toes simultaneously or on toes first. Rate and nonlinear position feedback are employed for stability of the biped after the impact. The complex structure of the foot is properly modeled. A spring and dashpot pair is suggested to represent the action of plantar fascia during the impact. This action prevents the arch of the foot from collapsing. A mathematical model of the skeletal muscle is discussed. A direct relationship between the stimulus rate and the active state is established. A piecewise linear relation between the length of the contractile element and the isometric force is considered. Hill's characteristic equation is maintained for determining the actual output force during different shortening velocities. A physical threshold model is proposed for recruitment which encompasses the size principle, its manifestations and exceptions to the size principle. Finally the role of spindle feedback in stability of the model is demonstrated by study of a pair of muscles.

Direct Harmonic Linear Navier-Stokes Methods for Efficient Simulation of Wave Packets

NASA Technical Reports Server (NTRS)

Streett, C. L.

1998-01-01

Wave packets produced by localized disturbances play an important role in transition in three-dimensional boundary layers, such as that on a swept wing. Starting with the receptivity process, we show the effects of wave-space energy distribution on the development of packets and other three-dimensional disturbance patterns. Nonlinearity in the receptivity process is specifically addressed, including demonstration of an effect which can enhance receptivity of traveling crossflow disturbances. An efficient spatial numerical simulation method is allowing most of the simulations presented to be carried out on a workstation.

Three dimensional thermal stresses in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Griffin, O. Hayden, Jr.

1988-01-01

The room temperature stress distributions and shapes of a family of angle ply graphite/epoxy laminates have been obtained using a three-dimensional linear finite element analysis. The sensitivity of the corners to fiber angle variations is examined, in addition to the errors introduced by assuming planes of symmetry which do not exist in angle-ply laminates. The results show that angle ply laminates with 'clustered' plies will tend to delaminate at diagonally opposite corners, and that matrix cracks in this family of laminates will be initiated in the laminate interior.

Full High-definition three-dimensional gynaecological laparoscopy--clinical assessment of a new robot-assisted device.

PubMed

Tuschy, Benjamin; Berlit, Sebastian; Brade, Joachim; Sütterlin, Marc; Hornemann, Amadeus

2014-01-01

To investigate the clinical assessment of a full high-definition (HD) three-dimensional robot-assisted laparoscopic device in gynaecological surgery. This study included 70 women who underwent gynaecological laparoscopic procedures. Demographic parameters, type and duration of surgery and perioperative complications were analyzed. Fifteen surgeons were postoperatively interviewed regarding their assessment of this new system with a standardized questionnaire. The clinical assessment revealed that three-dimensional full-HD visualisation is comfortable and improves spatial orientation and hand-to-eye coordination. The majority of the surgeons stated they would prefer a three-dimensional system to a conventional two-dimensional device and stated that the robotic camera arm led to more relaxed working conditions. Three-dimensional laparoscopy is feasible, comfortable and well-accepted in daily routine. The three-dimensional visualisation improves surgeons' hand-to-eye coordination, intracorporeal suturing and fine dissection. The combination of full-HD three-dimensional visualisation with the robotic camera arm results in very high image quality and stability.

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.

Visual exploration of high-dimensional data through subspace analysis and dynamic projections

DOE PAGES

Liu, S.; Wang, B.; Thiagarajan, J. J.; ...

2015-06-01

Here, we introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that createmore » smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Visual Exploration of High-Dimensional Data through Subspace Analysis and Dynamic Projections

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

Liu, S.; Wang, B.; Thiagarajan, Jayaraman J.

2015-06-01

We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smoothmore » animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Repeatability of road pavement condition assessment based on three-dimensional analysis of linear accelerations of vehicles

NASA Astrophysics Data System (ADS)

Staniek, Marcin

2018-05-01

The article provides a discussion concerning a tool used for road pavement condition assessment based on signals of linear accelerations recorded with high sampling frequency for typical vehicles traversing the road network under real-life road traffic conditions. Specific relationships have been established for the sake of road pavement condition assessment, including identification of road sections of poor technical condition. The data thus acquired have been verified with regard to repeatability of estimated road pavement assessment indices. The data make it possible to describe the road network status against an area in which users of the system being developed move. What proves to be crucial in the assessment process is the scope of the data set based on multiple transfers within the road network.

Electron beam throughput from raster to imaging

NASA Astrophysics Data System (ADS)

Zywno, Marek

2016-12-01

Two architectures of electron beam tools are presented: single beam MEBES Exara designed and built by Etec Systems for mask writing, and the Reflected E-Beam Lithography tool (REBL), designed and built by KLA-Tencor under a DARPA Agreement No. HR0011-07-9-0007. Both tools have implemented technologies not used before to achieve their goals. The MEBES X, renamed Exara for marketing purposes, used an air bearing stage running in vacuum to achieve smooth continuous scanning. The REBL used 2 dimensional imaging to distribute charge to a 4k pixel swath to achieve writing times on the order of 1 wafer per hour, scalable to throughput approaching optical projection tools. Three stage architectures were designed for continuous scanning of wafers: linear maglev, rotary maglev, and dual linear maglev.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Deep linear autoencoder and patch clustering-based unified one-dimensional coding of image and video

NASA Astrophysics Data System (ADS)

Li, Honggui

2017-09-01

This paper proposes a unified one-dimensional (1-D) coding framework of image and video, which depends on deep learning neural network and image patch clustering. First, an improved K-means clustering algorithm for image patches is employed to obtain the compact inputs of deep artificial neural network. Second, for the purpose of best reconstructing original image patches, deep linear autoencoder (DLA), a linear version of the classical deep nonlinear autoencoder, is introduced to achieve the 1-D representation of image blocks. Under the circumstances of 1-D representation, DLA is capable of attaining zero reconstruction error, which is impossible for the classical nonlinear dimensionality reduction methods. Third, a unified 1-D coding infrastructure for image, intraframe, interframe, multiview video, three-dimensional (3-D) video, and multiview 3-D video is built by incorporating different categories of videos into the inputs of patch clustering algorithm. Finally, it is shown in the results of simulation experiments that the proposed methods can simultaneously gain higher compression ratio and peak signal-to-noise ratio than those of the state-of-the-art methods in the situation of low bitrate transmission.

Constructing Compact Takagi-Sugeno Rule Systems: Identification of Complex Interactions in Epidemiological Data

PubMed Central

Zhou, Shang-Ming; Lyons, Ronan A.; Brophy, Sinead; Gravenor, Mike B.

2012-01-01

The Takagi-Sugeno (TS) fuzzy rule system is a widely used data mining technique, and is of particular use in the identification of non-linear interactions between variables. However the number of rules increases dramatically when applied to high dimensional data sets (the curse of dimensionality). Few robust methods are available to identify important rules while removing redundant ones, and this results in limited applicability in fields such as epidemiology or bioinformatics where the interaction of many variables must be considered. Here, we develop a new parsimonious TS rule system. We propose three statistics: R, L, and ω-values, to rank the importance of each TS rule, and a forward selection procedure to construct a final model. We use our method to predict how key components of childhood deprivation combine to influence educational achievement outcome. We show that a parsimonious TS model can be constructed, based on a small subset of rules, that provides an accurate description of the relationship between deprivation indices and educational outcomes. The selected rules shed light on the synergistic relationships between the variables, and reveal that the effect of targeting specific domains of deprivation is crucially dependent on the state of the other domains. Policy decisions need to incorporate these interactions, and deprivation indices should not be considered in isolation. The TS rule system provides a basis for such decision making, and has wide applicability for the identification of non-linear interactions in complex biomedical data. PMID:23272108

Constructing compact Takagi-Sugeno rule systems: identification of complex interactions in epidemiological data.

PubMed

Zhou, Shang-Ming; Lyons, Ronan A; Brophy, Sinead; Gravenor, Mike B

2012-01-01

The Takagi-Sugeno (TS) fuzzy rule system is a widely used data mining technique, and is of particular use in the identification of non-linear interactions between variables. However the number of rules increases dramatically when applied to high dimensional data sets (the curse of dimensionality). Few robust methods are available to identify important rules while removing redundant ones, and this results in limited applicability in fields such as epidemiology or bioinformatics where the interaction of many variables must be considered. Here, we develop a new parsimonious TS rule system. We propose three statistics: R, L, and ω-values, to rank the importance of each TS rule, and a forward selection procedure to construct a final model. We use our method to predict how key components of childhood deprivation combine to influence educational achievement outcome. We show that a parsimonious TS model can be constructed, based on a small subset of rules, that provides an accurate description of the relationship between deprivation indices and educational outcomes. The selected rules shed light on the synergistic relationships between the variables, and reveal that the effect of targeting specific domains of deprivation is crucially dependent on the state of the other domains. Policy decisions need to incorporate these interactions, and deprivation indices should not be considered in isolation. The TS rule system provides a basis for such decision making, and has wide applicability for the identification of non-linear interactions in complex biomedical data.

SU-F-J-41: Experimental Validation of a Cascaded Linear System Model for MVCBCT with a Multi-Layer EPID

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

Hu, Y; Rottmann, J; Myronakis, M

2016-06-15

Purpose: The purpose of this study was to validate the use of a cascaded linear system model for MV cone-beam CT (CBCT) using a multi-layer (MLI) electronic portal imaging device (EPID) and provide experimental insight into image formation. A validated 3D model provides insight into salient factors affecting reconstructed image quality, allowing potential for optimizing detector design for CBCT applications. Methods: A cascaded linear system model was developed to investigate the potential improvement in reconstructed image quality for MV CBCT using an MLI EPID. Inputs to the three-dimensional (3D) model include projection space MTF and NPS. Experimental validation was performedmore » on a prototype MLI detector installed on the portal imaging arm of a Varian TrueBeam radiotherapy system. CBCT scans of up to 898 projections over 360 degrees were acquired at exposures of 16 and 64 MU. Image volumes were reconstructed using a Feldkamp-type (FDK) filtered backprojection (FBP) algorithm. Flat field images and scans of a Catphan model 604 phantom were acquired. The effect of 2×2 and 4×4 detector binning was also examined. Results: Using projection flat fields as an input, examination of the modeled and measured NPS in the axial plane exhibits good agreement. Binning projection images was shown to improve axial slice SDNR by a factor of approximately 1.4. This improvement is largely driven by a decrease in image noise of roughly 20%. However, this effect is accompanied by a subsequent loss in image resolution. Conclusion: The measured axial NPS shows good agreement with the theoretical calculation using a linear system model. Binning of projection images improves SNR of large objects on the Catphan phantom by decreasing noise. Specific imaging tasks will dictate the implementation image binning to two-dimensional projection images. The project was partially supported by a grant from Varian Medical Systems, Inc. and grant No. R01CA188446-01 from the National Cancer Institute.« less

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Three is much more than two in coarsening dynamics of cyclic competitions

NASA Astrophysics Data System (ADS)

Mitarai, Namiko; Gunnarson, Ivar; Pedersen, Buster Niels; Rosiek, Christian Anker; Sneppen, Kim

2016-04-01

The classical game of rock-paper-scissors has inspired experiments and spatial model systems that address the robustness of biological diversity. In particular, the game nicely illustrates that cyclic interactions allow multiple strategies to coexist for long-time intervals. When formulated in terms of a one-dimensional cellular automata, the spatial distribution of strategies exhibits coarsening with algebraically growing domain size over time, while the two-dimensional version allows domains to break and thereby opens the possibility for long-time coexistence. We consider a quasi-one-dimensional implementation of the cyclic competition, and study the long-term dynamics as a function of rare invasions between parallel linear ecosystems. We find that increasing the complexity from two to three parallel subsystems allows a transition from complete coarsening to an active steady state where the domain size stays finite. We further find that this transition happens irrespective of whether the update is done in parallel for all sites simultaneously or done randomly in sequential order. In both cases, the active state is characterized by localized bursts of dislocations, followed by longer periods of coarsening. In the case of the parallel dynamics, we find that there is another phase transition between the active steady state and the coarsening state within the three-line system when the invasion rate between the subsystems is varied. We identify the critical parameter for this transition and show that the density of active boundaries has critical exponents that are consistent with the directed percolation universality class. On the other hand, numerical simulations with the random sequential dynamics suggest that the system may exhibit an active steady state as long as the invasion rate is finite.

Evaluation of the osteogenic differentiation of gingiva-derived stem cells grown on culture plates or in stem cell spheroids: Comparison of two- and three-dimensional cultures.

PubMed

Lee, Sung-Il; Ko, Youngkyung; Park, Jun-Beom

2017-09-01

Three-dimensional cell culture systems provide a convenient in vitro model for the study of complex cell-cell and cell-matrix interactions in the absence of exogenous substrates. The current study aimed to evaluate the osteogenic differentiation potential of gingiva-derived stem cells cultured in two-dimensional or three-dimensional systems. To the best of our knowledge, the present study is the first to compare the growth of gingiva-derived stem cells in monolayer culture to a three-dimensional culture system with microwells. For three-dimensional culture, gingiva-derived stem cells were isolated and seeded into polydimethylsiloxane-based concave micromolds. Alkaline phosphatase activity and alizarin red S staining assays were then performed to evaluate osteogenesis and the degree of mineralization, respectively. Stem cell spheroids had a significantly increased level of alkaline phosphatase activity and mineralization compared with cells from the two-dimensional culture. In addition, an increase in mineralized deposits was observed with an increase in the loading cell number. The results of present study indicate that gingiva-derived stem cell spheroids exhibit an increased osteogenic potential compared with stem cells from two-dimensional culture. This highlights the potential of three-dimensional culture systems using gingiva-derived stem cells for regenerative medicine applications requiring stem cells with osteogenic potential.

Method of Individual Adjustment for 3D CT Analysis: Linear Measurement.

PubMed

Kim, Dong Kyu; Choi, Dong Hun; Lee, Jeong Woo; Yang, Jung Dug; Chung, Ho Yun; Cho, Byung Chae; Choi, Kang Young

2016-01-01

Introduction . We aim to regularize measurement values in three-dimensional (3D) computed tomography (CT) reconstructed images for higher-precision 3D analysis, focusing on length-based 3D cephalometric examinations. Methods . We measure the linear distances between points on different skull models using Vernier calipers (real values). We use 10 differently tilted CT scans for 3D CT reconstruction of the models and measure the same linear distances from the picture archiving and communication system (PACS). In both cases, each measurement is performed three times by three doctors, yielding nine measurements. The real values are compared with the PACS values. Each PACS measurement is revised based on the display field of view (DFOV) values and compared with the real values. Results . The real values and the PACS measurement changes according to tilt value have no significant correlations ( p > 0.05). However, significant correlations appear between the real values and DFOV-adjusted PACS measurements ( p < 0.001). Hence, we obtain a correlation expression that can yield real physical values from PACS measurements. The DFOV value intervals for various age groups are also verified. Conclusion . Precise confirmation of individual preoperative length and precise analysis of postoperative improvements through 3D analysis is possible, which is helpful for facial-bone-surgery symmetry correction.

Relating Linear and Volumetric Variables Through Body Scanning to Improve Human Interfaces in Space

NASA Technical Reports Server (NTRS)

Margerum, Sarah E.; Ferrer, Mike A.; Young, Karen S.; Rajulu, Sudhakar

2010-01-01

Designing space suits and vehicles for the diverse human population present unique challenges for the methods of traditional anthropometry. Space suits are bulky and allow the operator to shift position within the suit and inhibit the ability to identify body landmarks. Limited suit sizing options also cause variability in fit and performance between similarly sized individuals. Space vehicles are restrictive in volume in both the fit and the ability to collect data. NASA's Anthropometric and Biomechanics Facility (ABF) has utilized 3D scanning to shift from traditional linear anthropometry to explore and examine volumetric capabilities to provide anthropometric solutions for design. Overall, the key goals are to improve the human-system performance and develop new processes to aid in the design and evaluation of space systems. Four case studies are presented that illustrate the shift from purely linear analyses to an augmented volumetric toolset to predict and analyze the human within the space suit and vehicle. The first case study involves the calculation of maximal head volume to estimate total free volume in the helmet for proper air exchange. Traditional linear measurements resulted in an inaccurate representation of the head shape, yet limited data exists for the determination of a large head volume. Steps were first taken to identify and classify a maximum head volume and the resulting comparisons to the estimate are presented in this paper. This study illustrates the gap between linear components of anthropometry and the need for overall volume metrics in order to provide solutions. A second case study examines the overlay of the space suit scans and components onto scanned individuals to quantify fit and clearance to aid in sizing the suit to the individual. Restrictions in space suit size availability present unique challenges to optimally fit the individual within a limited sizing range while maintaining performance. Quantification of the clearance and fit between similarly sized individuals is critical in providing a greater understanding of the human body's function within the suit. The third case study presented in this paper explores the development of a conformal seat pan using scanning techniques, and details the challenges of volumetric analyses that were overcome in order to develop a universal seat pan that can be utilized across the entire user population. The final case study explores expanding volumetric capabilities through generation of boundary manikins. Boundary manikins are representative individuals from the population of interest that represent the extremes of the population spectrum. The ABF developed a technique to take three-dimensional scans of individuals and manipulate the scans to reflect the boundary manikins' anthropometry. In essence, this process generates a representative three-dimensional scan of an individual from anthropometry, using another individual's scanned image. The results from this process can be used in design process modeling and initial suit sizing work as a three dimensional, realistic example of individuals from the population, maintaining the variability between and correlation to the relevant dimensions of interest.

Three-dimensional organization of vestibular-related eye movements to off-vertical axis rotation and linear translation in pigeons

NASA Technical Reports Server (NTRS)

Dickman, J. D.; Angelaki, D. E.

1999-01-01

During linear accelerations, compensatory reflexes should continually occur in order to maintain objects of visual interest as stable images on the retina. In the present study, the three-dimensional organization of the vestibulo-ocular reflex in pigeons was quantitatively examined during linear accelerations produced by constant velocity off-vertical axis yaw rotations and translational motion in darkness. With off-vertical axis rotations, sinusoidally modulated eye-position and velocity responses were observed in all three components, with the vertical and torsional eye movements predominating the response. Peak torsional and vertical eye positions occurred when the head was oriented with the lateral visual axis of the right eye directed orthogonal to or aligned with the gravity vector, respectively. No steady-state horizontal nystagmus was obtained with any of the rotational velocities (8-58 degrees /s) tested. During translational motion, delivered along or perpendicular to the lateral visual axis, vertical and torsional eye movements were elicited. No significant horizontal eye movements were observed during lateral translation at frequencies up to 3 Hz. These responses suggest that, in pigeons, all linear accelerations generate eye movements that are compensatory to the direction of actual or perceived tilt of the head relative to gravity. In contrast, no translational horizontal eye movements, which are known to be compensatory to lateral translational motion in primates, were observed under the present experimental conditions.

Asymmetric Base-Bleed Effect on Aerospike Plume-Induced Base-Heating Environment

NASA Technical Reports Server (NTRS)

Wang, Ten-See; Droege, Alan; DAgostino, Mark; Lee, Young-Ching; Williams, Robert

2004-01-01

A computational heat transfer design methodology was developed to study the dual-engine linear aerospike plume-induced base-heating environment during one power-pack out, in ascent flight. It includes a three-dimensional, finite volume, viscous, chemically reacting, and pressure-based computational fluid dynamics formulation, a special base-bleed boundary condition, and a three-dimensional, finite volume, and spectral-line-based weighted-sum-of-gray-gases absorption computational radiation heat transfer formulation. A separate radiation model was used for diagnostic purposes. The computational methodology was systematically benchmarked. In this study, near-base radiative heat fluxes were computed, and they compared well with those measured during static linear aerospike engine tests. The base-heating environment of 18 trajectory points selected from three power-pack out scenarios was computed. The computed asymmetric base-heating physics were analyzed. The power-pack out condition has the most impact on convective base heating when it happens early in flight. The source of its impact comes from the asymmetric and reduced base bleed.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

The Stark Effect in Linear Potentials

ERIC Educational Resources Information Center

Robinett, R. W.

2010-01-01

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

Dusty plasma (Yukawa) rings

NASA Astrophysics Data System (ADS)

Sheridan, T. E.; Gallagher, James C.

2016-11-01

One-dimensional and quasi-one-dimensional strongly coupled dusty plasma rings have been created experimentally. Longitudinal (acoustic) and transverse (optical) dispersion relations for the one-ring are measured and found to be in excellent agreement with the theory for an unbounded straight chain of particles interacting through a Yukawa (i.e., screened Coulomb or Debye-Hückel) potential. These rings provide a new experimental system to directly study one-dimensional and quasi-one-dimensional linear and nonlinear phenomena.

Real-time in situ three-dimensional integral videography and surgical navigation using augmented reality: a pilot study

PubMed Central

Suenaga, Hideyuki; Hoang Tran, Huy; Liao, Hongen; Masamune, Ken; Dohi, Takeyoshi; Hoshi, Kazuto; Mori, Yoshiyuki; Takato, Tsuyoshi

2013-01-01

To evaluate the feasibility and accuracy of a three-dimensional augmented reality system incorporating integral videography for imaging oral and maxillofacial regions, based on preoperative computed tomography data. Three-dimensional surface models of the jawbones, based on the computed tomography data, were used to create the integral videography images of a subject's maxillofacial area. The three-dimensional augmented reality system (integral videography display, computed tomography, a position tracker and a computer) was used to generate a three-dimensional overlay that was projected on the surgical site via a half-silvered mirror. Thereafter, a feasibility study was performed on a volunteer. The accuracy of this system was verified on a solid model while simulating bone resection. Positional registration was attained by identifying and tracking the patient/surgical instrument's position. Thus, integral videography images of jawbones, teeth and the surgical tool were superimposed in the correct position. Stereoscopic images viewed from various angles were accurately displayed. Change in the viewing angle did not negatively affect the surgeon's ability to simultaneously observe the three-dimensional images and the patient, without special glasses. The difference in three-dimensional position of each measuring point on the solid model and augmented reality navigation was almost negligible (<1 mm); this indicates that the system was highly accurate. This augmented reality system was highly accurate and effective for surgical navigation and for overlaying a three-dimensional computed tomography image on a patient's surgical area, enabling the surgeon to understand the positional relationship between the preoperative image and the actual surgical site, with the naked eye. PMID:23703710

Evolution of lower hybrid turbulence in the ionosphere

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

Ganguli, G.; Crabtree, C.; Mithaiwala, M.

2015-11-15

Three-dimensional evolution of the lower hybrid turbulence driven by a spatially localized ion ring beam perpendicular to the ambient magnetic field in space plasmas is analyzed. It is shown that the quasi-linear saturation model breaks down when the nonlinear rate of scattering by thermal electron is larger than linear damping rates, which can occur even for low wave amplitudes. The evolution is found to be essentially a three-dimensional phenomenon, which cannot be accurately explained by two-dimensional simulations. An important feature missed in previous studies of this phenomenon is the nonlinear conversion of electrostatic lower hybrid waves into electromagnetic whistler andmore » magnetosonic waves and the consequent energy loss due to radiation from the source region. This can result in unique low-amplitude saturation with extended saturation time. It is shown that when the nonlinear effects are considered the net energy that can be permanently extracted from the ring beam is larger. The results are applied to anticipate the outcome of a planned experiment that will seed lower hybrid turbulence in the ionosphere and monitor its evolution.« less

Computational Optimization of a Natural Laminar Flow Experimental Wing Glove

NASA Technical Reports Server (NTRS)

Hartshom, Fletcher

2012-01-01

Computational optimization of a natural laminar flow experimental wing glove that is mounted on a business jet is presented and discussed. The process of designing a laminar flow wing glove starts with creating a two-dimensional optimized airfoil and then lofting it into a three-dimensional wing glove section. The airfoil design process does not consider the three dimensional flow effects such as cross flow due wing sweep as well as engine and body interference. Therefore, once an initial glove geometry is created from the airfoil, the three dimensional wing glove has to be optimized to ensure that the desired extent of laminar flow is maintained over the entire glove. TRANAIR, a non-linear full potential solver with a coupled boundary layer code was used as the main tool in the design and optimization process of the three-dimensional glove shape. The optimization process uses the Class-Shape-Transformation method to perturb the geometry with geometric constraints that allow for a 2-in clearance from the main wing. The three-dimensional glove shape was optimized with the objective of having a spanwise uniform pressure distribution that matches the optimized two-dimensional pressure distribution as closely as possible. Results show that with the appropriate inputs, the optimizer is able to match the two dimensional pressure distributions practically across the entire span of the wing glove. This allows for the experiment to have a much higher probability of having a large extent of natural laminar flow in flight.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Quantum Oscillations at Integer and Fractional Landau Level Indices in Single-Crystalline ZrTe 5

DOE PAGES

Yu, W.; Jiang, Y.; Yang, J.; ...

2016-10-14

A three-dimensional (3D) Dirac semimetal (DS) is an analogue of graphene, but with linear energy dispersion in all (three) momentum directions. 3D DSs have been a fertile playground in discovering novel quantum particles, for example Weyl fermions, in solid state systems. Many 3D DSs were theoretically predicted and experimentally confirmed. Here, we report here the results in exfoliated ZrTe 5 thin flakes from the studies of aberration-corrected scanning transmission electron microscopy and low temperature magneto-transport measurements. We observed several unique results. First, a π Berry phase was obtained from the Landau fan diagram of the Shubnikov-de Haas oscillations in themore » longitudinal conductivity σ xx. Second, the longitudinal resistivity ρ xx shows a linear magnetic field dependence in the quantum limit regime. Most surprisingly, quantum oscillations were also observed at fractional Landau level indices N = 5/3 and 7/5, demonstrating strong electron-electron interaction effects in ZrTe 5.« less

The development of global GRAPES 4DVAR

NASA Astrophysics Data System (ADS)

Liu, Yongzhu

2017-04-01

Four-dimensional variation data assimilation (4DVAR) has given a great contribution to the improvement of NWP system over the past twenty years. Therefore, our strategy is to develop an operational global 4D-Var system from the outset. The aim at the paper is to introduce the development of the global GRAPES four-dimensional variation data assimilation (4DVAR) using incremental analysis schemes and to presents results of a comparison between 4DVAR using 6-hour assimilation window and simplified physics during the minimization with three-dimensional variation data assimilation (3DVAR). The dynamical cores of the tangent-linear and adjoint models are developed directly based on the non-hydrostatic forecast model. In addition, the standard correctness checks have been performed. As well as the development adjoint codes, most of our work is focused on improving the computational efficiency since the bulk of the computational cost of 4D-Var is in the integration of the tangent-linear and adjoint models. In terms of tangent-linear model, the wall-clock time is reduced to about 1.2 times as much as one of nonlinear model through the optimizing of the software framework. The significant computational cost savings on adjoint model result from the removing the redundant recompilations of model trajectories. It is encouraging that the wall-clock time of adjoint model is less than 1.5 times as much as one of nonlinear model. The current difficulty is that the numerical scheme used within the linear model is based on strategically on the numeric of the corresponding nonlinear model. Further computational acceleration should be expected from the improvement on nonlinear numerical algorithm. A series of linearized physical parameterization schemes has been developed to improve the representation of perturbed fields in the linear model. It consists of horizontal and vertical diffusion, sub-grid scale orographic gravity wave drag, large-scale condensation and cumulus convection schemes. We also found the straightforward linearization based on the nonlinear physical scheme might lead to significant growing of spurious unstable perturbations. It is essential to simplify the linear physics with respect to the non-linear schemes. The improvement on the perturbed fields in the tangent-linear model is visible with the linear physics included, especially at the low level. GRAPES variation data assimilation system adopts the incremental approach. The work is ongoing to develop a pre-operational 4DVAR suite with 0.25° outer loop resolution and multiple outer-loops configurations. One 4DVAR analysis using 6-hour assimilation windows can be finished within 40-minutes when using the available conventional and satellite data. In summary, it was found that the analysis over the northern, southern hemispheres, tropical region and East Asian area of GRAPES 4DVAR performed better than GRAPES 3DVAR for one month experiments. Moreover, the forecast results show that northern and southern extra-tropical scores for GRAPES 4DVAR are already better than GRAPES 3DVAR, but the tropical performance needs further investigations. Therefore, the subsequent main improvements will aim to enhance its computational efficiency and accuracy in 2017. The global GRAPES 4DVAR is planned for operation in 2018.

Three dimensional image correlation of CT, MR, and PET studies in radiotherapy treatment planning of brain tumors.

PubMed

Schad, L R; Boesecke, R; Schlegel, W; Hartmann, G H; Sturm, V; Strauss, L G; Lorenz, W J

1987-01-01

A treatment planning system for stereotactic convergent beam irradiation of deeply localized brain tumors is reported. The treatment technique consists of several moving field irradiations in noncoplanar planes at a linear accelerator facility. Using collimated narrow beams, a high concentration of dose within small volumes with a dose gradient of 10-15%/mm was obtained. The dose calculation was based on geometrical information of multiplanar CT or magnetic resonance (MR) imaging data. The patient's head was fixed in a stereotactic localization system, which is usable at CT, MR, and positron emission tomography (PET) installations. Special computer programs for correction of the geometrical MR distortions allowed a precise correlation of the different imaging modalities. The therapist can use combinations of CT, MR, and PET data for defining target volume. For instance, the superior soft tissue contrast of MR coupled with the metabolic features of PET may be a useful addition in the radiation treatment planning process. Furthermore, other features such as calculated dose distribution to critical structures can also be transferred from one set of imaging data to another and can be displayed as three-dimensional shaded structures.

A simple approach to quantitative analysis using three-dimensional spectra based on selected Zernike moments.

PubMed

Zhai, Hong Lin; Zhai, Yue Yuan; Li, Pei Zhen; Tian, Yue Li

2013-01-21

A very simple approach to quantitative analysis is proposed based on the technology of digital image processing using three-dimensional (3D) spectra obtained by high-performance liquid chromatography coupled with a diode array detector (HPLC-DAD). As the region-based shape features of a grayscale image, Zernike moments with inherently invariance property were employed to establish the linear quantitative models. This approach was applied to the quantitative analysis of three compounds in mixed samples using 3D HPLC-DAD spectra, and three linear models were obtained, respectively. The correlation coefficients (R(2)) for training and test sets were more than 0.999, and the statistical parameters and strict validation supported the reliability of established models. The analytical results suggest that the Zernike moment selected by stepwise regression can be used in the quantitative analysis of target compounds. Our study provides a new idea for quantitative analysis using 3D spectra, which can be extended to the analysis of other 3D spectra obtained by different methods or instruments.

Large-scale computation of incompressible viscous flow by least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol Concentration from Transdermal Biosensor Data.

PubMed

Rosen, I G; Luczak, Susan E; Weiss, Jordan

2014-03-15

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Powers, Robert K.

1987-01-01

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

Estimation of three-dimensional radar tracking using modified extended kalman filter

NASA Astrophysics Data System (ADS)

Aditya, Prima; Apriliani, Erna; Khusnul Arif, Didik; Baihaqi, Komar

2018-03-01

Kalman filter is an estimation method by combining data and mathematical models then developed be extended Kalman filter to handle nonlinear systems. Three-dimensional radar tracking is one of example of nonlinear system. In this paper developed a modification method of extended Kalman filter from the direct decline of the three-dimensional radar tracking case. The development of this filter algorithm can solve the three-dimensional radar measurements in the case proposed in this case the target measured by radar with distance r, azimuth angle θ, and the elevation angle ϕ. Artificial covariance and mean adjusted directly on the three-dimensional radar system. Simulations result show that the proposed formulation is effective in the calculation of nonlinear measurement compared with extended Kalman filter with the value error at 0.77% until 1.15%.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Modern control techniques in active flutter suppression using a control moment gyro

NASA Technical Reports Server (NTRS)

Buchek, P. M.

1974-01-01

Development of organized synthesis techniques, using concepts of modern control theory was studied for the design of active flutter suppression systems for two and three-dimensional lifting surfaces, utilizing a control moment gyro (CMG) to generate the required control torques. Incompressible flow theory is assumed, with the unsteady aerodynamic forces and moments for arbitrary airfoil motion obtained by using the convolution integral based on Wagner's indicial lift function. Linear optimal control theory is applied to find particular optimal sets of gain values which minimize a quadratic performance function. The closed loop system's response to impulsive gust disturbances and the resulting control power requirements are investigated, and the system eigenvalues necessary to minimize the maximum value of control power are determined.

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

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

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

Three-Dimensional Simulation of Liquid Drop Dynamics Within Unsaturated Vertical Hele-Shaw Cells

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

Hai Huang; Paul Meakin

A three-dimensional, multiphase fluid flow model with volume of fluid-interface tracking was developed and applied to study the multiphase dynamics of moving liquid drops of different sizes within vertical Hele-Shaw cells. The simulated moving velocities are significantly different from those obtained from a first-order analytical approximation, based on simple force-balance concepts. The simulation results also indicate that the moving drops can exhibit a variety of shapes and that the transition among these different shapes is largely determined by the moving velocities. More important, there is a transition from a linear moving regime at small capillary numbers, in which the capillarymore » number scales linearly with the Bond number, to a nonlinear moving regime at large capillary numbers, in which the moving drop releases a train of droplets from its trailing edge. The train of droplets forms a variety of patterns at different moving velocities.« less

Extension of non-linear beam models with deformable cross sections

NASA Astrophysics Data System (ADS)

Sokolov, I.; Krylov, S.; Harari, I.

2015-12-01

Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.

On solving three-dimensional open-dimension rectangular packing problems

NASA Astrophysics Data System (ADS)

Junqueira, Leonardo; Morabito, Reinaldo

2017-05-01

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.

Time-dependent analysis of the mixed-field orientation of molecules without rotational symmetry

NASA Astrophysics Data System (ADS)

Thesing, Linda V.; Küpper, Jochen; González-Férez, Rosario

2017-06-01

We present a theoretical study of the mixed-field orientation of molecules without rotational symmetry. The time-dependent one-dimensional and three-dimensional orientation of a thermal ensemble of 6-chloropyridazine-3-carbonitrile molecules in combined linearly or elliptically polarized laser fields and tilted dc electric fields is computed. The results are in good agreement with recent experimental results of one-dimensional orientation for weak dc electric fields [J. L. Hansen, J. Chem. Phys. 139, 234313 (2013)]. Moreover, they predict that using elliptically polarized laser fields or strong dc fields, three-dimensional orientation is obtained. The field-dressed dynamics of excited rotational states is characterized by highly non-adiabatic effects. We analyze the sources of these non-adiabatic effects and investigate their impact on the mixed-field orientation for different field configurations in mixed-field-orientation experiments.

A Two-Dimensional Linear Bicharacteristic FDTD Method

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics. The LBS has previously been extended to treat lossy materials for one-dimensional problems. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to include the Perfectly Matched Layer boundary condition with no added storage or complexity. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional free-space electromagnetic propagation and scattering problems. This paper extends the LBS to the two-dimensional case. Results are presented for point source radiation problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

NASA Technical Reports Server (NTRS)

Antar, B. N.; Fowlis, W. W.

1983-01-01

For the case of a baroclinic flow whose Richardson number, Ri, is of order unity, a three-dimensional linear stability analysis is conducted on the basis of a model for a thin, horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The Hadley cell basic state and stability analysis are both based on the Navier-Stokes and energy equations, and perturbations possessing zonal, meridional, and vertical structures are considered. An attempt is made to extend the previous theoretical work on three-dimensional baroclinic instability for small Ri to a more realistic model involving the Prandtl and Ekman numbers, as well as to finite growth rates and a wider range of the zonal wavenumber. In general, it is found that the symmetric modes of maximum growth are not purely symmetric, but have a weak zonal structure.

Three-dimensional anthropometry of the adult face.

DOT National Transportation Integrated Search

1978-03-01

This study describes a new three-dimensional anatomical axis system based on four conventional anthropometrical face landmarks. Coincident as a coordinate (orthogonal) axis system, this reference system was developed to provide convenient orientation...

[The clinical advantage of using three dimensional visualization technology in hepatic surgery].

PubMed

Lau, Y Y; Lau, X X

2016-09-01

The three-dimensional body visible system is a further development of the three-dimensional CT reconstruction system. It has a lot of merits over the latter system. Clinical application of the three-dimensional body visible system in liver surgery showed the system to have the following merits: (1) The system can support the Couinaud classification of liver anatomy into two hemilivers, four sectors and eight segments. As the system can rotate the liver to any angle and it has the ability to make part or whole of the liver transparent thus making the internal blood vessels and bile ducts visible. Learning liver anatomy and liver surgery becomes easier. (2)The system can clearly localize liver tumors within the liver segment(s). (3)It can help clinicians to decide and to plan different operations on an individual. (4)By carrying out simulation partial hepatectomy using this system, it can help clinicians to estimate the difficulty and the risks involved in different options of liver resection and finally.(5)The system helps clinicians to identify anomalies in hepatic artery, portal vein, hepatic vein and bile duct, thus making the operation safer. In conclusion, this system significantly improves on the conventional three-dimensional CT reconstruction system. It is especially useful for inexperienced liver surgeons.

Linearization instability for generic gravity in AdS spacetime

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Direct solution of the H(1s)-H + long-range interaction problem in momentum space

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu

1985-02-01

Perturbation equations for the H(1s)-H+ long-range interaction are solved directly in momentum space up to the fourth order with respect to the reciprocal of the internuclear distance. As in the hydrogen atom problem, the Fock transformation is used which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere. Solutions are given as linear combinations of several four-dimensional spherical harmonics. The present results add an example to the momentum-space solution of the nonspherical potential problem.

Two-dimensional models for the optical response of thin films

NASA Astrophysics Data System (ADS)

Li, Yilei; Heinz, Tony F.

2018-04-01

In this work, we present a systematic study of 2D optical models for the response of thin layers of material under excitation by normally incident light. The treatment, within the framework of classical optics, analyzes a thin film supported by a semi-infinite substrate, with both the thin layer and the substrate assumed to exhibit local, isotropic linear response. Starting from the conventional three-dimensional (3D) slab model of the system, we derive a two-dimensional (2D) sheet model for the thin film in which the optical response is described by a sheet optical conductivity. We develop criteria for the applicability of this 2D sheet model for a layer with an optical thickness far smaller than the wavelength of the light. We examine in detail atomically thin semi-metallic and semiconductor van-der-Waals layers and ultrathin metal films as representative examples. Excellent agreement of the 2D sheet model with the 3D slab model is demonstrated over a broad spectral range from the radio frequency limit to the near ultraviolet. A linearized version of system response for the 2D model is also presented for the case where the influence of the optically thin layer is sufficiently weak. Analytical expressions for the applicability and accuracy of the different optical models are derived, and the appropriateness of the linearized treatment for the materials is considered. We discuss the advantages, as well as limitations, of these models for the purpose of deducing the optical response function of the thin layer from experiment. We generalize the theory to take into account in-plane anisotropy, layered thin film structures, and more general substrates. Implications of the 2D model for the transmission of light by the thin film and for the implementation of half- and totally absorbing layers are discussed.

Active Response Gravity Offload and Method

NASA Technical Reports Server (NTRS)

Dungan, Larry K. (Inventor); Lieberman, Asher P. (Inventor); Shy, Cecil (Inventor); Bankieris, Derek R. (Inventor); Valle, Paul S. (Inventor); Redden, Lee (Inventor)

2015-01-01

A variable gravity field simulator can be utilized to provide three dimensional simulations for simulated gravity fields selectively ranging from Moon, Mars, and micro-gravity environments and/or other selectable gravity fields. The gravity field simulator utilizes a horizontally moveable carriage with a cable extending from a hoist. The cable can be attached to a load which experiences the effects of the simulated gravity environment. The load can be a human being or robot that makes movements that induce swinging of the cable whereby a horizontal control system reduces swinging energy. A vertical control system uses a non-linear feedback filter to remove noise from a load sensor that is in the same frequency range as signals from the load sensor.

Recursive inverse factorization.

PubMed

Rubensson, Emanuel H; Bock, Nicolas; Holmström, Erik; Niklasson, Anders M N

2008-03-14

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

PubMed

Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos

2003-07-01

To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Experimental and numerical characterization of the water flow in spacer-filled channels of spiral-wound membranes.

PubMed

Bucs, Szilard S; Linares, Rodrigo Valladares; Marston, Jeremy O; Radu, Andrea I; Vrouwenvelder, Johannes S; Picioreanu, Cristian

2015-12-15

Micro-scale flow distribution in spacer-filled flow channels of spiral-wound membrane modules was determined with a particle image velocimetry system (PIV), aiming to elucidate the flow behaviour in spacer-filled flow channels. Two-dimensional water velocity fields were measured in a flow cell (representing the feed spacer-filled flow channel of a spiral wound reverse osmosis membrane module without permeate production) at several planes throughout the channel height. At linear flow velocities (volumetric flow rate per cross-section of the flow channel considering the channel porosity, also described as crossflow velocities) used in practice (0.074 and 0.163 m·s(-1)) the recorded flow was laminar with only slight unsteadiness in the upper velocity limit. At higher linear flow velocity (0.3 m·s(-1)) the flow was observed to be unsteady and with recirculation zones. Measurements made at different locations in the flow cell exhibited very similar flow patterns within all feed spacer mesh elements, thus revealing the same hydrodynamic conditions along the length of the flow channel. Three-dimensional (3-D) computational fluid dynamics simulations were performed using the same geometries and flow parameters as the experiments, based on steady laminar flow assumption. The numerical results were in good agreement (0.85-0.95 Bray-Curtis similarity) with the measured flow fields at linear velocities of 0.074 and 0.163 m·s(-1), thus supporting the use of model-based studies in the optimization of feed spacer geometries and operational conditions of spiral wound membrane systems. Copyright © 2015 Elsevier Ltd. All rights reserved.

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

The method of approximate cluster analysis and the three-dimensional diagram of optical characteristics of the lunar surface

NASA Astrophysics Data System (ADS)

Evsyukov, N. N.

1984-12-01

An approximate isolation algorithm for the isolation of multidimensional clusters is developed and applied in the construction of a three-dimensional diagram of the optical characteristics of the lunar surface. The method is somewhat analogous to that of Koontz and Fukunaga (1972) and involves isolating two-dimensional clusters, adding a new characteristic, and linearizing, a cycle which is repeated a limited number of times. The lunar-surface parameters analyzed are the 620-nm albedo, the 620/380-nm color index, and the 950/620-nm index. The results are presented graphically; the reliability of the cluster-isolation process is discussed; and some correspondences between known lunar morphology and the cluster maps are indicated.

[Development and evaluation of a novel three-dimensional adjustable confocal laser-induced fluorescence detector].

PubMed

Liu, Fan; Yu, Shuxin; Tang, Tao; Sun, Yuanshe; Zhang, Weibing; Li, Tong

2011-09-01

Laser-induced fluorescence detector (LIFD) is one of the most sensitive detectors in analytical chemical files. Confocal optical configuration is widely used in LIFDs. Two effective approaches used to achieve the best signal to noise ratio (S/N) are increasing the confocal precision and minimizing the background noise. A novel three-dimensional adjustable confocal LIFD was developed, using a new three-dimensional adjustable supporter of reflector and modularized optical system. A detection limit (S/N = 3) of 1 x 10(-12) mol/L and a linear dynamic range of 3 orders of magnitude were obtained using fluorescein isothiocyanate (FITC) standard as the test sample. The noise level and drift levels were 8.0 x 10(-3) mV and 1.4 x 10(-3) mV/h, respectively, which were almost 10 times lower than before. And the stability of the LIFD was evaluated by five replicate injections of 5 x 10(-9) mol/L FITC, and the relative standard deviations (RSDs) of peak height and peak area were 0.38% and 0.41%, respectively. Further more, three biogenic amines, which were derivatized by FITC, were separated by high performance liquid chromatography (HPLC) and then detected by the novel LIFD. And the detection limits (S/N = 3) ranged 0.01 to 0.02 nmol/L, which were better than other methods. Therefore, the LIFD is highly sensitive, as well as shows a real low noise level and good reproducibility.

From Two- to Three-Dimensional Structures of a Supertetrahedral Boran Using Density Functional Calculations.

PubMed

Getmanskii, Iliya V; Minyaev, Ruslan M; Steglenko, Dmitrii V; Koval, Vitaliy V; Zaitsev, Stanislav A; Minkin, Vladimir I

2017-08-14

With help of the DFT calculations and imposing of periodic boundary conditions the geometrical and electronic structures were investigated of two- and three-dimensional boron systems designed on the basis of graphane and diamond lattices in which carbons were replaced with boron tetrahedrons. The consequent studies of two- and three-layer systems resulted in the construction of a three-dimensional supertetrahedral borane crystal structure. The two-dimensional supertetrahedral borane structures with less than seven layers are dynamically unstable. At the same time the three-dimensional superborane systems were found to be dynamically stable. Lack of the forbidden electronic zone for the studied boron systems testifies that these structures can behave as good conductors. The low density of the supertetrahedral borane crystal structures (0.9 g cm -3 ) is close to that of water, which offers the perspective for their application as aerospace and cosmic materials. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space

NASA Astrophysics Data System (ADS)

Khadjiev, Djavvat; Ören, Idri˙s; Pekşen, Ömer

Let E2 be the 2-dimensional Euclidean space, LSim(2) be the group of all linear similarities of E2 and LSim+(2) be the group of all orientation-preserving linear similarities of E2. The present paper is devoted to solutions of problems of global G-equivalence of paths and curves in E2 for the groups G = LSim(2),LSim+(2). Complete systems of global G-invariants of a path and a curve in E2 are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given global invariants are obtained.

ANGIOCARE: an automated system for fast three-dimensional coronary reconstruction by integrating angiographic and intracoronary ultrasound data.

PubMed

Bourantas, Christos V; Kalatzis, Fanis G; Papafaklis, Michail I; Fotiadis, Dimitrios I; Tweddel, Ann C; Kourtis, Iraklis C; Katsouras, Christos S; Michalis, Lampros K

2008-08-01

The development of an automated, user-friendly system (ANGIOCARE), for rapid three-dimensional (3D) coronary reconstruction, integrating angiographic and, intracoronary ultrasound (ICUS) data. Biplane angiographic and ICUS sequence images are imported into the system where a prevalidated method is used for coronary reconstruction. This incorporates extraction of the catheter path from two end-diastolic X-ray images and detection of regions of interest (lumen, outer vessel wall) in the ICUS sequence by an automated border detection algorithm. The detected borders are placed perpendicular to the catheter path and established algorithms used to estimate their absolute orientation. The resulting 3D object is imported into an advanced visualization module with which the operator can interact, examine plaque distribution (depicted as a color coded map) and assess plaque burden by virtual endoscopy. Data from 19 patients (27 vessels) undergoing biplane angiography and ICUS were examined. The reconstructed vessels were 21.3-80.2 mm long. The mean difference was 0.9 +/- 2.9% between the plaque volumes measured using linear 3D ICUS analysis and the volumes, estimated by taking into account the curvature of the vessel. The time required to reconstruct a luminal narrowing of 25 mm was approximately 10 min. The ANGIOCARE system provides rapid coronary reconstruction allowing the operator accurately to estimate the length of the lesion and determine plaque distribution and volume. (c) 2008 Wiley-Liss, Inc.

Impact of Wall Shear Stress and Pressure Variation on the Stability of Atherosclerotic Plaque

NASA Astrophysics Data System (ADS)

Taviani, V.; Li, Z. Y.; Sutcliffe, M.; Gillard, J.

Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The mechanism of blood flow and plaque rupture in stenotic arteries is still not fully understood. A three dimensional rigid wall model was solved under steady and unsteady conditions assuming a time-varying inlet velocity profile to investigate the relative importance of axial forces and pressure drops in arteries with asymmetric stenosis. Flow-structure interactions were investigated for the same geometry and the results were compared with those retrieved with the corresponding one dimensional models. The Navier-Stokes equations were used as the governing equations for the fluid. The tube wall was assumed linearly elastic, homogeneous isotropic. The analysis showed that wall shear stress is small (less than 3.5%) with respect to pressure drop throughout the cycle even for severe stenosis. On the contrary, the three dimensional behavior of velocity, pressure and wall shear stress is in general very different from that predicted by one dimensional models. This suggests that the primary source of mistakes in one dimensional studies comes from neglecting the three dimensional geometry of the plaque. Neglecting axial forces only involves minor errors.

Spectral embedding finds meaningful (relevant) structure in image and microarray data

PubMed Central

Higgs, Brandon W; Weller, Jennifer; Solka, Jeffrey L

2006-01-01

Background Accurate methods for extraction of meaningful patterns in high dimensional data have become increasingly important with the recent generation of data types containing measurements across thousands of variables. Principal components analysis (PCA) is a linear dimensionality reduction (DR) method that is unsupervised in that it relies only on the data; projections are calculated in Euclidean or a similar linear space and do not use tuning parameters for optimizing the fit to the data. However, relationships within sets of nonlinear data types, such as biological networks or images, are frequently mis-rendered into a low dimensional space by linear methods. Nonlinear methods, in contrast, attempt to model important aspects of the underlying data structure, often requiring parameter(s) fitting to the data type of interest. In many cases, the optimal parameter values vary when different classification algorithms are applied on the same rendered subspace, making the results of such methods highly dependent upon the type of classifier implemented. Results We present the results of applying the spectral method of Lafon, a nonlinear DR method based on the weighted graph Laplacian, that minimizes the requirements for such parameter optimization for two biological data types. We demonstrate that it is successful in determining implicit ordering of brain slice image data and in classifying separate species in microarray data, as compared to two conventional linear methods and three nonlinear methods (one of which is an alternative spectral method). This spectral implementation is shown to provide more meaningful information, by preserving important relationships, than the methods of DR presented for comparison. Tuning parameter fitting is simple and is a general, rather than data type or experiment specific approach, for the two datasets analyzed here. Tuning parameter optimization is minimized in the DR step to each subsequent classification method, enabling the possibility of valid cross-experiment comparisons. Conclusion Results from the spectral method presented here exhibit the desirable properties of preserving meaningful nonlinear relationships in lower dimensional space and requiring minimal parameter fitting, providing a useful algorithm for purposes of visualization and classification across diverse datasets, a common challenge in systems biology. PMID:16483359

Spatial geometry of the human pelvis.

DOT National Transportation Integrated Search

1982-03-01

This report presents a three-dimensional description of adult female and male pelvis from the Hamann-Todd skeletal collection, Cleveland Museum of Natural History. Based on a linear height/weight matching strategy and the 1961- 1964 U.S. Health and E...

Let's Do It: Patterns and Geometry with Logo.

ERIC Educational Resources Information Center

Thompson, Charles S.; Van de Walle, John

1985-01-01

Described are: how teachers can use the computer language Logo, along with noncomputer activities, for teaching about linear and two-dimensional patterns and about combining shapes to create more complex shapes. Three computer program listings are included. (MNS)

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

Wigner tomography of multispin quantum states

NASA Astrophysics Data System (ADS)

Leiner, David; Zeier, Robert; Glaser, Steffen J.

2017-12-01

We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015), 10.1103/PhysRevA.91.042122]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.

Hysteretic magnetoresistance and unconventional anomalous Hall effect in the frustrated magnet TmB 4

DOE PAGES

Sunku, Sai Swaroop; Kong, Tai; Ito, Toshimitsu; ...

2016-05-11

We study TmB 4, a frustrated magnet on the Archimedean Shastry-Sutherland lattice, through magnetization and transport experiments. The lack of anisotropy in resistivity shows that TmB4 is an electronically three-dimensional system. The magnetoresistance (MR) is hysteretic at low temperature even though a corresponding hysteresis in magnetization is absent. The Hall resistivity shows unconventional anomalous Hall effect (AHE) and is linear above saturation despite a large MR. In conclusion, we propose that complex structures at magnetic domain walls may be responsible for the hysteretic MR and may also lead to the AHE.

Numerical study for melting heat transfer and homogeneous-heterogeneous reactions in flow involving carbon nanotubes

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Muhammad, Khursheed; Alsaedi, Ahmed; Asghar, Saleem

2018-03-01

Present work concentrates on melting heat transfer in three-dimensional flow of nanofluid over an impermeable stretchable surface. Analysis is made in presence of porous medium and homogeneous-heterogeneous reactions. Single and multi-wall CNTs (carbon nanotubes) are considered. Water is chosen as basefluid. Adequate transformations yield the non-linear ordinary differential systems. Solution of emerging problems is obtained using shooting method. Impacts of influential variables on velocity and temperature are discussed graphically. Skin friction coefficient and Nusselt number are numerically discussed. The results for MWCNTs and SWCNTs are compared and examined.

System for generating two-dimensional masks from a three-dimensional model using topological analysis

DOEpatents

Schiek, Richard [Albuquerque, NM

2006-06-20

A method of generating two-dimensional masks from a three-dimensional model comprises providing a three-dimensional model representing a micro-electro-mechanical structure for manufacture and a description of process mask requirements, reducing the three-dimensional model to a topological description of unique cross sections, and selecting candidate masks from the unique cross sections and the cross section topology. The method further can comprise reconciling the candidate masks based on the process mask requirements description to produce two-dimensional process masks.

Optimizing the physical ergonomics indices for the use of partial pressure suits.

PubMed

Ding, Li; Li, Xianxue; Hedge, Alan; Hu, Huimin; Feathers, David; Qin, Zhifeng; Xiao, Huajun; Xue, Lihao; Zhou, Qianxiang

2015-03-01

This study developed an ergonomic evaluation system for the design of high-altitude partial pressure suits (PPSs). A total of twenty-one Chinese males participated in the experiment which tested three types of ergonomics indices (manipulative mission, operational reach and operational strength) were studied using a three-dimensional video-based motion capture system, a target-pointing board, a hand dynamometer, and a step-tread apparatus. In total, 36 ergonomics indices were evaluated and optimized using regression and fitting analysis. Some indices that were found to be linearly related and redundant were removed from the study. An optimal ergonomics index system was established that can be used to conveniently and quickly evaluate the performance of different pressurized/non-pressurized suit designs. The resulting ergonomics index system will provide a theoretical basis and practical guidance for mission planners, suit designers and engineers to design equipment for human use, and to aid in assessing partial pressure suits. Copyright © 2014 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas

2015-04-01

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.

Algebraic multigrid methods applied to problems in computational structural mechanics

NASA Technical Reports Server (NTRS)

Mccormick, Steve; Ruge, John

1989-01-01

The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.

Q-balls in flat potentials

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

Copeland, Edmund J.; Tsumagari, Mitsuo I.

2009-07-15

We study the classical and absolute stability of Q-balls in scalar field theories with flat potentials arising in both gravity-mediated and gauge-mediated models. We show that the associated Q-matter formed in gravity-mediated potentials can be stable against decay into their own free particles as long as the coupling constant of the nonrenormalizable term is small, and that all of the possible three-dimensional Q-ball configurations are classically stable against linear fluctuations. Three-dimensional gauge-mediated Q-balls can be absolutely stable in the thin-wall limit, but are completely unstable in the thick-wall limit.

Three-dimensional nitrogen-doped graphene as an ultrasensitive electrochemical sensor for the detection of dopamine

NASA Astrophysics Data System (ADS)

Feng, Xiaomiao; Zhang, Yu; Zhou, Jinhua; Li, Yi; Chen, Shufen; Zhang, Lei; Ma, Yanwen; Wang, Lianhui; Yan, Xiaohong

2015-01-01

Three-dimensional nitrogen-doped graphene (3D N-doped graphene) was prepared through chemical vapor deposition (CVD) by using porous nickel foam as a substrate. As a model, a dopamine biosensor was constructed based on the 3D N-doped graphene porous foam. Electrochemical experiments exhibited that this biosensor had a remarkable detection ability with a wide linear detection range from 3 × 10-6 M to 1 × 10-4 M and a low detection limit of 1 nM. Moreover, the fabricated biosensor also showed an excellent anti-interference ability, reproducibility, and stability.

Three-dimensional nitrogen-doped graphene as an ultrasensitive electrochemical sensor for the detection of dopamine.

PubMed

Feng, Xiaomiao; Zhang, Yu; Zhou, Jinhua; Li, Yi; Chen, Shufen; Zhang, Lei; Ma, Yanwen; Wang, Lianhui; Yan, Xiaohong

2015-02-14

Three-dimensional nitrogen-doped graphene (3D N-doped graphene) was prepared through chemical vapor deposition (CVD) by using porous nickel foam as a substrate. As a model, a dopamine biosensor was constructed based on the 3D N-doped graphene porous foam. Electrochemical experiments exhibited that this biosensor had a remarkable detection ability with a wide linear detection range from 3 × 10(-6) M to 1 × 10(-4) M and a low detection limit of 1 nM. Moreover, the fabricated biosensor also showed an excellent anti-interference ability, reproducibility, and stability.

Calculus of nonrigid surfaces for geometry and texture manipulation.

PubMed

Bronstein, Alexander; Bronstein, Michael; Kimmel, Ron

2007-01-01

We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting.