Description Of Scoliotic Deformity Pattern By Harmonic Functions

NASA Astrophysics Data System (ADS)

Drerup, Burkhard; Hierholzer, Eberhard

1989-04-01

Frontal radiographs of scoliotic deformity of the spine reveal a characteristic pattern of lateral deviation, lateral tilt and axial rotation of vertebrae. In order to study interrelations between deformation parameters 478 radiographs of idiopathic scolioses, 23 of scolioses after Wilms-tumor treatment and 18 of scolioses following poliomyelitis were digitized. From these the curves of lateral deviation, tilt and rotation are calculated and fitted by Fourier series. By restriction to the first harmonic, analysis reduces to the analysis of a single phase and amplitude for each curve. Justification of this simplification will be discussed. Results provide a general geometric description of scoliotic deformity.

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging

NASA Astrophysics Data System (ADS)

Yang, Xinmai; Cleveland, Robin O.

2005-01-01

A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging. .

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging.

PubMed

Yang, Xinmai; Cleveland, Robin O

2005-01-01

A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging.

Static Aeroelastic Analysis with an Inviscid Cartesian Method

NASA Technical Reports Server (NTRS)

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.

2014-01-01

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation

NASA Astrophysics Data System (ADS)

Gallinato, Olivier; Poignard, Clair

2017-06-01

In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.

A decoupled recursive approach for constrained flexible multibody system dynamics

NASA Technical Reports Server (NTRS)

Lai, Hao-Jan; Kim, Sung-Soo; Haug, Edward J.; Bae, Dae-Sung

1989-01-01

A variational-vector calculus approach is employed to derive a recursive formulation for dynamic analysis of flexible multibody systems. Kinematic relationships for adjacent flexible bodies are derived in a companion paper, using a state vector notation that represents translational and rotational components simultaneously. Cartesian generalized coordinates are assigned for all body and joint reference frames, to explicitly formulate deformation kinematics under small deformation kinematics and an efficient flexible dynamics recursive algorithm is developed. Dynamic analysis of a closed loop robot is performed to illustrate efficiency of the algorithm.

Dip and anisotropy effects on flow using a vertically skewed model grid.

PubMed

Hoaglund, John R; Pollard, David

2003-01-01

Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.

Zero frequency modes of the Maclaurin spheroids

NASA Astrophysics Data System (ADS)

Baumgart, D.; Friedman, J. L.

1986-05-01

The location of all zero-frequency modes of oscillation along the Maclaurin sequence are found for modes corresponding to oblate spheroidal harmonics with indices (l,m) where l less than 6 (equivalently, for modes described by Lagrangian displacements whose components in Cartesian coordinates are polynomials of degree less than or equal to 5). These points of zero frequency mark the onset of instability in each mode in the context of general relativity, or when a gravitational radiation reaction term is adjointed to the Newtonian theory.

DAMQT: A package for the analysis of electron density in molecules

NASA Astrophysics Data System (ADS)

López, Rafael; Rico, Jaime Fernández; Ramírez, Guillermo; Ema, Ignacio; Zorrilla, David

2009-09-01

DAMQT is a package for the analysis of the electron density in molecules and the fast computation of the density, density deformations, electrostatic potential and field, and Hellmann-Feynman forces. The method is based on the partition of the electron density into atomic fragments by means of a least deformation criterion. Each atomic fragment of the density is expanded in regular spherical harmonics times radial factors, which are piecewise represented in terms of analytical functions. This representation is used for the fast evaluation of the electrostatic potential and field generated by the electron density and nuclei, as well as for the computation of the Hellmann-Feynman forces on the nuclei. An analysis of the atomic and molecular deformations of the density can be also carried out, yielding a picture that connects with several concepts of the empirical structural chemistry. Program summaryProgram title: DAMQT1.0 Catalogue identifier: AEDL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv3 No. of lines in distributed program, including test data, etc.: 278 356 No. of bytes in distributed program, including test data, etc.: 31 065 317 Distribution format: tar.gz Programming language: Fortran90 and C++ Computer: Any Operating system: Linux, Windows (Xp, Vista) RAM: 190 Mbytes Classification: 16.1 External routines: Trolltech's Qt (4.3 or higher) ( http://www.qtsoftware.com/products), OpenGL (1.1 or higher) ( http://www.opengl.org/), GLUT 3.7 ( http://www.opengl.org/resources/libraries/glut/). Nature of problem: Analysis of the molecular electron density and density deformations, including fast evaluation of electrostatic potential, electric field and Hellmann-Feynman forces on nuclei. Solution method: The method of Deformed Atoms in Molecules, reported elsewhere [1], is used for partitioning the molecular electron density into atomic fragments, which are further expanded in spherical harmonics times radial factors. The partition is used for defining molecular density deformations and for the fast calculation of several properties associated to density. Restrictions: The current version is limited to 120 atoms, 2000 contracted functions, and l=5 in basis functions. Density must come from a LCAO calculation (any level) with spherical (not Cartesian) Gaussian functions. Unusual features: The program contains an OPEN statement to binary files (stream) in file GOPENMOL.F90. This statement has not a standard syntax in Fortran 90. Two possibilities are considered in conditional compilation: Intel's ifort and Fortran2003 standard. This latter is applied to compilers other than ifort (gfortran uses this one, for instance). Additional comments: The distribution file for this program is over 30 Mbytes and therefore is not delivered directly when download or e-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: Largely dependent on the system size and the module run (from fractions of a second to hours). References: [1] J. Fernández Rico, R. López, I. Ema, G. Ramírez, J. Mol. Struct. (Theochem) 727 (2005) 115.

Trapped waves on the mid-latitude β-plane

NASA Astrophysics Data System (ADS)

Paldor, Nathan; Sigalov, Andrey

2008-08-01

A new type of approximate solutions of the Linearized Shallow Water Equations (LSWE) on the mid-latitude β-plane, zonally propagating trapped waves with Airy-like latitude-dependent amplitude, is constructed in this work, for sufficiently small radius of deformation. In contrast to harmonic Poincare and Rossby waves, these newly found trapped waves vanish fast in the positive half-axis, and their zonal phase speed is larger than that of the corresponding harmonic waves for sufficiently large meridional domains. Our analysis implies that due to the smaller radius of deformation in the ocean compared with that in the atmosphere, the trapped waves are relevant to observations in the ocean whereas harmonic waves typify atmospheric observations. The increase in the zonal phase speed of trapped Rossby waves compared with that of harmonic ones is consistent with recent observations that showed that Sea Surface Height features propagated westwards faster than the phase speed of harmonic Rossby waves.

Energy spectrum inverse problem of q-deformed harmonic oscillator and entanglement of composite bosons

NASA Astrophysics Data System (ADS)

Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

2017-06-01

Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.

The influence of a local wall deformation on the development of natural instabilities in a laminar boundary layer

NASA Technical Reports Server (NTRS)

Burnel, S.; Gougat, P.; Martin, F.

1981-01-01

The natural instabilities which propagate in the laminar boundary layer of a flat plate composed of intermittent wave trains are described. A spectral analysis determines the frequency range and gives a frequency and the harmonic 2 only if there is a wall deformation. This analysis provides the amplitude modulation spectrum of the instabilities. Plots of the evolution of power spectral density are compared with the numerical results obtained from the resolve of the Orr-Sommerfeld equation, while the harmonic is related to a micro-recirculating flow near the wall deformation.

Computational Methods for Configurational Entropy Using Internal and Cartesian Coordinates.

PubMed

Hikiri, Simon; Yoshidome, Takashi; Ikeguchi, Mitsunori

2016-12-13

The configurational entropy of solute molecules is a crucially important quantity to study various biophysical processes. Consequently, it is necessary to establish an efficient quantitative computational method to calculate configurational entropy as accurately as possible. In the present paper, we investigate the quantitative performance of the quasi-harmonic and related computational methods, including widely used methods implemented in popular molecular dynamics (MD) software packages, compared with the Clausius method, which is capable of accurately computing the change of the configurational entropy upon temperature change. Notably, we focused on the choice of the coordinate systems (i.e., internal or Cartesian coordinates). The Boltzmann-quasi-harmonic (BQH) method using internal coordinates outperformed all the six methods examined here. The introduction of improper torsions in the BQH method improves its performance, and anharmonicity of proper torsions in proteins is identified to be the origin of the superior performance of the BQH method. In contrast, widely used methods implemented in MD packages show rather poor performance. In addition, the enhanced sampling of replica-exchange MD simulations was found to be efficient for the convergent behavior of entropy calculations. Also in folding/unfolding transitions of a small protein, Chignolin, the BQH method was reasonably accurate. However, the independent term without the correlation term in the BQH method was most accurate for the folding entropy among the methods considered in this study, because the QH approximation of the correlation term in the BQH method was no longer valid for the divergent unfolded structures.

An optimal FFT-based anisotropic power spectrum estimator

NASA Astrophysics Data System (ADS)

Hand, Nick; Li, Yin; Slepian, Zachary; Seljak, Uroš

2017-07-01

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order l requires only 2l+1 FFTs rather than the (l+1)(l+2)/2 FFTs of the Cartesian approach. For the hexadecapole (l = 4), this translates to 40% fewer FFTs, with increased savings for higher l. The reduction in wall-clock time enables the calculation of finely-binned wedges in P(k,μ), obtained by computing multipoles up to a large lmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ simeq while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of lmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using lmax=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with lmax=4.

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

Hand, Nick; Seljak, Uroš; Li, Yin

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTsmore » of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k ,μ), obtained by computing multipoles up to a large ℓ{sub max} and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≅ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓ{sub max}, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓ{sub max}=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ{sub 8}, as compared to a 54% increase with ℓ{sub max}=4.« less

Essaying the mechanical hypothesis: Descartes, La Forge, and Malebranche on the formation of birthmarks.

PubMed

Wilkin, Rebecca M

2008-01-01

This essay examines the determination by Cartesians to explain the maternal imagination's alleged role in the formation of birthmarks and the changing notion of monstrosity. Cartesians saw the formation of birthmarks as a challenge through which to demonstrate the heuristic capacity of mechanism. Descartes claimed to be able to explain the transmission of a perception from the mother's imagination to the fetus' skin without having recourse to the little pictures postulated by his contemporaries. La Forge offered a detailed account stating that the failure to explain the maternal imagination's impressions would cast doubt on mechanism. Whereas both characterized the birthmark as a deformation or monstrosity in miniature, Malebranche attributed a role to the maternal imagination in fashioning family likenesses. However, he also charged the mother's imagination with the transmission of original sin.

The anharmonic quartic force field infrared spectra of three polycyclic aromatic hydrocarbons: Naphthalene, anthracene, and tetracene.

PubMed

Mackie, Cameron J; Candian, Alessandra; Huang, Xinchuan; Maltseva, Elena; Petrignani, Annemieke; Oomens, Jos; Buma, Wybren Jan; Lee, Timothy J; Tielens, Alexander G G M

2015-12-14

Current efforts to characterize and study interstellar polycyclic aromatic hydrocarbons (PAHs) rely heavily on theoretically predicted infrared (IR) spectra. Generally, such studies use the scaled harmonic frequencies for band positions and double harmonic approximation for intensities of species, and then compare these calculated spectra with experimental spectra obtained under matrix isolation conditions. High-resolution gas-phase experimental spectroscopic studies have recently revealed that the double harmonic approximation is not sufficient for reliable spectra prediction. In this paper, we present the anharmonic theoretical spectra of three PAHs: naphthalene, anthracene, and tetracene, computed with a locally modified version of the SPECTRO program using Cartesian derivatives transformed from Gaussian 09 normal coordinate force constants. Proper treatments of Fermi resonances lead to an impressive improvement on the agreement between the observed and theoretical spectra, especially in the C-H stretching region. All major IR absorption features in the full-scale matrix-isolated spectra, the high-temperature gas-phase spectra, and the most recent high-resolution gas-phase spectra obtained under supersonically cooled molecular beam conditions in the CH-stretching region are assigned.

Geodetic measurement of deformation in the Loma Prieta, California earthquake with very long baseline interferometry

NASA Technical Reports Server (NTRS)

Clark, T. A.; Ma, C.; Sauber, J. M.; Ryan, J. W.; Gordon, D.; Shaffer, D. B.; Carprette, D. S.; Vandenberg, N. R.

1990-01-01

VLBI measurements were conducted immediately after the Loma Prieta earthquake and compared with VLBI gathered at Monterey, San Francisco, and Point Reyes since 1983 to obtain preearthquake deformation rates with respect to a North American reference frame. The estimated displacements at Monterey and San Francisco are consistent with the static displacements predicted on the basis of a coseismic slip model in which slip on the southern segment is shallower than slip on the northern segment of the fault rupture. Cartesian positions are presented at epoch 1990.0 of a set of VLBI fiducial stations and the three mobile sites in the earthquake's vicinity.

A position-dependent mass harmonic oscillator and deformed space

NASA Astrophysics Data System (ADS)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Second Harmonic Generation of Unpolarized Light

NASA Astrophysics Data System (ADS)

Ding, Changqin; Ulcickas, James R. W.; Deng, Fengyuan; Simpson, Garth J.

2017-11-01

A Mueller tensor mathematical framework was applied for predicting and interpreting the second harmonic generation (SHG) produced with an unpolarized fundamental beam. In deep tissue imaging through SHG and multiphoton fluorescence, partial or complete depolarization of the incident light complicates polarization analysis. The proposed framework has the distinct advantage of seamlessly merging the purely polarized theory based on the Jones or Cartesian susceptibility tensors with a more general Mueller tensor framework capable of handling partial depolarized fundamental and/or SHG produced. The predictions of the model are in excellent agreement with experimental measurements of z -cut quartz and mouse tail tendon obtained with polarized and depolarized incident light. The polarization-dependent SHG produced with unpolarized fundamental allowed determination of collagen fiber orientation in agreement with orthogonal methods based on image analysis. This method has the distinct advantage of being immune to birefringence or depolarization of the fundamental beam for structural analysis of tissues.

Quantifying torso deformity in scoliosis

NASA Astrophysics Data System (ADS)

Ajemba, Peter O.; Kumar, Anish; Durdle, Nelson G.; Raso, V. James

2006-03-01

Scoliosis affects the alignment of the spine and the shape of the torso. Most scoliosis patients and their families are more concerned about the effect of scoliosis on the torso than its effect on the spine. There is a need to develop robust techniques for quantifying torso deformity based on full torso scans. In this paper, deformation indices obtained from orthogonal maps of full torso scans are used to quantify torso deformity in scoliosis. 'Orthogonal maps' are obtained by applying orthogonal transforms to 3D surface maps. (An 'orthogonal transform' maps a cylindrical coordinate system to a Cartesian coordinate system.) The technique was tested on 361 deformed computer models of the human torso and on 22 scans of volunteers (8 normal and 14 scoliosis). Deformation indices from the orthogonal maps correctly classified up to 95% of the volunteers with a specificity of 1.00 and a sensitivity of 0.91. In addition to classifying scoliosis, the system gives a visual representation of the entire torso in one view and is viable for use in a clinical environment for managing scoliosis.

Spheroidal models of the exterior gravitational field of Asteroids Bennu and Castalia

NASA Astrophysics Data System (ADS)

Sebera, Josef; Bezděk, Aleš; Pešek, Ivan; Henych, Tomáš

2016-07-01

Gravitational field of small bodies can be modeled e.g. with mascons, a polyhedral model or in terms of harmonic functions. If the shape of a body is close to the spheroid, it is advantageous to employ the spheroidal basis functions for expressing the gravitational field. Spheroidal harmonic models, similarly to the spherical ones, may be used in navigation and geophysical tasks. We focus on modeling the exterior gravitational field of oblate-like Asteroid (101955) Bennu and prolate-like Asteroid (4769) Castalia with spheroidal harmonics. Using the Gauss-Legendre quadrature and the spheroidal basis functions, we converted the gravitational potential of a particular polyhedral model of a constant density into the spheroidal harmonics. The results consist of (i) spheroidal harmonic coefficients of the exterior gravitational field for the Asteroids Bennu and Castalia, (ii) spherical harmonic coefficients for Bennu, and (iii) the first and second-order Cartesian derivatives in the local spheroidal South-East-Up frame for both bodies. The spheroidal harmonics offer biaxial flexibility (compared with spherical harmonics) and low computational costs that allow high-degree expansions (compared with ellipsoidal harmonics). The obtained spheroidal models for Bennu and Castalia represent the exterior gravitational field valid on and outside the Brillouin spheroid but they can be used even under this surface. For Bennu, 5 m above the surface the agreement with point-wise integration was 1% or less, while it was about 10% for Castalia due to its more irregular shape. As the shape models may produce very high frequencies, it was crucial to use higher maximum degree to reduce the aliasing. We have used the maximum degree 360 to achieve 9-10 common digits (in RMS) when reconstructing the input (the gravitational potential) from the spheroidal coefficients. The physically meaningful maximum degree may be lower (≪ 360) but its particular value depends on the distance and/or on the application (navigation, exploration, etc.).

An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations

NASA Astrophysics Data System (ADS)

Santhanam, Anand P.; Min, Yugang; Mudur, Sudhir P.; Rastogi, Abhinav; Ruddy, Bari H.; Shah, Amish; Divo, Eduardo; Kassab, Alain; Rolland, Jannick P.; Kupelian, Patrick

2010-07-01

A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2004-04-01

We describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX. Program summaryTitle of the program:HFODD (v2.08i) Catalogue number: ADTO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTO Reference in CPC for earlier version of program: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 131 (2000) 164 (v1.75r) Catalogue number of previous version: ADML Licensing provisions: none Does the new version supersede the previous one: yes Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems: UNIX, LINUX, Windows-2000 Programming language used: FORTRAN-77 and FORTRAN-90 Memory required to execute with typical data: 10 Mwords No. of bits in a word: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Has the code been vectorised?: Yes No. of bytes in distributed program, including test data, etc.: 265352 No. of lines in distributed program: 52656 Distribution format: tar gzip file Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Method of solution: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166. Summary of revisions:Two insignificant errors have been corrected. Breaking of all the three plane-reflection symmetries has been implemented. Breaking of all the three time-reversal×plane-reflection symmetries has been implemented. Conservation of parity with simultaneously broken simplex has been implemented. Tilted-axis cranking has been implemented. Cranking with isovector angular frequency has been implemented. Quadratic constraint on tilted angular momentum has been added. Constraint on the vector product of angular frequency and angular momentum has been added. Calculation of surface multipole moments has been added. Constraints on surface multipole moments have been added. Calculation of magnetic moments has been added. Calculation of multipole and surface multipole moments in the center-of-mass reference frame has been added. Calculation of multipole, surface multipole, and magnetic moments in the principal-axes (intrinsic) reference frame has been added. Calculation of angular momenta in the center-of-mass and principal-axes reference frames has been added. New single-particle observables for a diabatic blocking have been added. Solution of the Hartree-Fock-Bogolyubov equations has been implemented. Non-standard spin-orbit energy density has been implemented. Non-standard center-of-mass corrections have been implemented. Definition of the time-odd terms through the Landau parameters has been implemented. Definition of Skyrme forces taken from the literature now includes the force parameters as well as the value of the nucleon mass and the treatment of tensor, spin-orbit, and center-of-mass terms specific to the given force. Interface to the LAPACK subroutine ZHPEVX has been implemented. Computer memory management has been improved by implementing the memory-allocation features available within FORTRAN-90. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Typical running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy 86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J(2) can be obtained within forty minutes of CPU on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. Unusual features of the program: The user must have an access to the NAGLIB subroutine F02AXE, or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpevx.f respectively.

Solution of the Skyrme Hartree Fock Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2005-05-01

We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic-oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constrains are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [J. Dobaczewski, J. Dudek, Comput. Phys. Comm. 102 (1997) 166]. Summary of revisions: 1. Incorrect value of the " t" force parameter for SLY5 has been corrected. 2. Opening of an empty file "FILREC" for IWRIRE=-1 has been removed. 3. Call to subroutine "OLSTOR" has been moved before that to "SPZERO". In this way, correct data transferred to "FLISIG", "FLISIM", "FLISIQ" or "FLISIZ" allow for a correct determination of the candidate states for diabatic blocking. These corrections pertain to the user interface of the code and do not affect results performed for forces other than SLY5. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Unusual features: The user must have access to the NAGLIB subroutine F02AXE or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex Hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpevx.f, respectively. The code is written in single-precision for use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Typical running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy 86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In the case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J can be obtained within forty minutes of CPU on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. Additional comments: The actual output files obtained during user's test runs may differ from those provided in the distribution file. The differences may occur because various compilers may produce different results in the following aspects: The initial Nilsson spectrum (the starting point of each run) is Kramers degenerate, and thus the diagonalization routine may return the degenerate states in arbitrary order and in arbitrary mixture. For an odd number of particles, one of these states becomes occupied, and the other one is left empty. Therefore, starting points of such runs can widely vary from compiler to compiler, and these differences cannot be controlled. For axial shapes, two quadrupole moments (with respect to two different axes) become very small and their values reflect only a numerical noise. However, depending on which of these two moments is smaller, the intrinsic-frame Euler axes will differ, most often by 180 degrees. Hence, signs of some moments and angular momenta may vary from compiler to compiler, and these differences cannot be controlled. These differences are insignificant. The final energies do not depend on them, although the intermediate results can.

Calculation of steady and unsteady transonic flow using a Cartesian mesh and gridless boundary conditions with application to aeroelasticity

NASA Astrophysics Data System (ADS)

Kirshman, David

A numerical method for the solution of inviscid compressible flow using an array of embedded Cartesian meshes in conjunction with gridless surface boundary conditions is developed. The gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the surface geometry. The method allows for accurate treatment of the surface boundary conditions using a grid resolution an order of magnitude coarser than required of typical Cartesian approaches. Additionally, the method does not suffer from issues associated with thin body geometry or extremely fine cut cells near the body. Unlike some methods that consider a gridless (or "meshless") treatment throughout the entire domain, multi-grid acceleration can be effectively incorporated and issues associated with global conservation are alleviated. The "gridless" surface boundary condition provides for efficient and simple problem set up since definition of the body geometry is generated independently from the field mesh, and automatically incorporated into the field discretization of the domain. The applicability of the method is first demonstrated for steady flow of single and multi-element airfoil configurations. Using this method, comparisons with traditional body-fitted grid simulations reveal that steady flow solutions can be obtained accurately with minimal effort associated with grid generation. The method is then extended to unsteady flow predictions. In this application, flow field simulations for the prescribed oscillation of an airfoil indicate excellent agreement with experimental data. Furthermore, it is shown that the phase lag associated with shock oscillation is accurately predicted without the need for a deformable mesh. Lastly, the method is applied to the prediction of transonic flutter using a two-dimensional wing model, in which comparisons with moving mesh simulations yield nearly identical results. As a result, applicability of the method to transient and vibrating fluid-structure interaction problems is established in which the requirement for a deformable mesh is eliminated.

Implementation of a hybrid particle code with a PIC description in r–z and a gridless description in ϕ into OSIRIS

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

Davidson, A., E-mail: davidsoa@physics.ucla.edu; Tableman, A., E-mail: Tableman@physics.ucla.edu; An, W., E-mail: anweiming@ucla.edu

2015-01-15

For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [1] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r–z grid and a procedure for calculating the complexmore » current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r–z and a gridless description in ϕ. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.« less

Axially deformed solution of the Skyrme–Hartree–Fock–Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): A new version of the program

DOE PAGES

Perez, R. Navarro; Schunck, N.; Lasseri, R. -D.; ...

2017-07-05

Here, we describe the new version 3.00 of the code hfbtho that solves the nuclear Hartree–Fock (HF) or Hartree–Fock–Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle–hole and particle–particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scalemore » mass table calculations.« less

Quantifying cortical surface harmonic deformation with stereovision during open cranial neurosurgery

NASA Astrophysics Data System (ADS)

Ji, Songbai; Fan, Xiaoyao; Roberts, David W.; Paulsen, Keith D.

2012-02-01

Cortical surface harmonic motion during open cranial neurosurgery is well observed in image-guided neurosurgery. Recently, we quantified cortical surface deformation noninvasively with synchronized blood pressure pulsation (BPP) from a sequence of stereo image pairs using optical flow motion tracking. With three subjects, we found the average cortical surface displacement can reach more than 1 mm and in-plane principal strains of up to 7% relative to the first image pair. In addition, the temporal changes in deformation and strain were in concert with BPP and patient respiration [1]. However, because deformation was essentially computed relative to an arbitrary reference, comparing cortical surface deformation at different times was not possible. In this study, we extend the technique developed earlier by establishing a more reliable reference profile of the cortical surface for each sequence of stereo image acquisitions. Specifically, fast Fourier transform (FFT) was applied to the dynamic cortical surface deformation, and the fundamental frequencies corresponding to patient respiration and BPP were identified, which were used to determine the number of image acquisitions for use in averaging cortical surface images. This technique is important because it potentially allows in vivo characterization of soft tissue biomechanical properties using intraoperative stereovision and motion tracking.

Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates.

PubMed

Cerezo, Javier; Santoro, Fabrizio

2016-10-11

Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q 1 -frame, where Q 1 are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q 1 -frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal modes of initial and final states in adiabatic approaches. We highlight that such a dependence of G on s is also an issue in vertical models, due to the necessity to approximate the kinetic term in the Hamiltonian when setting up the so-called GF problem. When large structural differences exist between the initial and the final-state minima, the changes in the G matrix can become too large to be disregarded.

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Tooth-meshing-harmonic static-transmission-error amplitudes of helical gears

NASA Astrophysics Data System (ADS)

Mark, William D.

2018-01-01

The static transmission errors of meshing gear pairs arise from deviations of loaded tooth working surfaces from equispaced perfect involute surfaces. Such deviations consist of tooth-pair elastic deformations and geometric deviations (modifications) of tooth working surfaces. To a very good approximation, the static-transmission-error tooth-meshing-harmonic amplitudes of helical gears are herein expressed by superposition of Fourier transforms of the quantities: (1) the combination of tooth-pair elastic deformations and geometric tooth-pair modifications and (2) fractional mesh-stiffness fluctuations, each quantity (1) and (2) expressed as a function of involute "roll distance." Normalization of the total roll-distance single-tooth contact span to unity allows tooth-meshing-harmonic amplitudes to be computed for different shapes of the above-described quantities (1) and (2). Tooth-meshing harmonics p = 1, 2, … are shown to occur at Fourier-transform harmonic values of Qp, p = 1, 2, …, where Q is the actual (total) contact ratio, thereby verifying its importance in minimizing transmission-error tooth-meshing-harmonic amplitudes. Two individual shapes and two series of shapes of the quantities (1) and (2) are chosen to illustrate a wide variety of shapes. In most cases representative of helical gears, tooth-meshing-harmonic values p = 1, 2, … are shown to occur in Fourier-transform harmonic regions governed by discontinuities arising from tooth-pair-contact initiation and termination, thereby showing the importance of minimizing such discontinuities. Plots and analytical expressions for all such Fourier transforms are presented, thereby illustrating the effects of various types of tooth-working-surface modifications and tooth-pair stiffnesses on transmission-error generation.

Octave-spanning carrier-envelope phase stabilized visible pulse with sub-3-fs pulse duration.

PubMed

Okamura, Kotaro; Kobayashi, Takayoshi

2011-01-15

The visible second harmonic of the idler output from a noncollinear optical parametric amplifier was compressed using adaptive dispersion control with a deformable mirror. The amplifier was pumped by and seeded in the signal path by a common 400 nm second-harmonic pulse from a Ti:sapphire regenerative amplifier. Thus, both the idler output and the second harmonic of the idler were passively carrier-envelope phase stabilized. The shortest pulse duration achieved was below 3 fs.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Component mode synthesis and large deflection vibrations of complex structures. [beams and trusses

NASA Technical Reports Server (NTRS)

Mei, C.

1984-01-01

The accuracy of the NASTRAN modal synthesis analysis was assessed by comparing it with full structure NASTRAN and nine other modal synthesis results using a nine-bay truss. A NASTRAN component mode transient response analysis was also performed on the free-free truss structure. A finite element method was developed for nonlinear vibration of beam structures subjected to harmonic excitation. Longitudinal deformation and inertia are both included in the formula. Tables show the finite element free vibration results with and without considering the effects of longitudinal deformation and inertia as well as the frequency ratios for a simply supported and a clamped beam subjected to a uniform harmonic force.

Deformation of angle profiles in forward kinematics for nullifying end-point offset while preserving movement properties.

PubMed

Zhang, Xudong

2002-10-01

This work describes a new approach that allows an angle-domain human movement model to generate, via forward kinematics, Cartesian-space human movement representation with otherwise inevitable end-point offset nullified but much of the kinematic authenticity retained. The approach incorporates a rectification procedure that determines the minimum postural angle change at the final frame to correct the end-point offset, and a deformation procedure that deforms the angle profile accordingly to preserve maximum original kinematic authenticity. Two alternative deformation schemes, named amplitude-proportional (AP) and time-proportional (TP) schemes, are proposed and formulated. As an illustration and empirical evaluation, the proposed approach, along with two deformation schemes, was applied to a set of target-directed right-hand reaching movements that had been previously measured and modeled. The evaluation showed that both deformation schemes nullified the final frame end-point offset and significantly reduced time-averaged position errors for the end-point as well as the most distal intermediate joint while causing essentially no change in the remaining joints. A comparison between the two schemes based on time-averaged joint and end-point position errors indicated that overall the TP scheme outperformed the AP scheme. In addition, no statistically significant difference in time-averaged angle error was identified between the raw prediction and either of the deformation schemes, nor between the two schemes themselves, suggesting minimal angle-domain distortion incurred by the deformation.

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals.

PubMed

Golze, Dorothea; Benedikter, Niels; Iannuzzi, Marcella; Wilhelm, Jan; Hutter, Jürg

2017-01-21

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

NASA Astrophysics Data System (ADS)

Golze, Dorothea; Benedikter, Niels; Iannuzzi, Marcella; Wilhelm, Jan; Hutter, Jürg

2017-01-01

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VI) HFODD (v2.40h): A new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Satuła, W.; Carlsson, B. G.; Engel, J.; Olbratowski, P.; Powałowski, P.; Sadziak, M.; Sarich, J.; Schunck, N.; Staszczak, A.; Stoitsov, M.; Zalewski, M.; Zduńczuk, H.

2009-11-01

We describe the new version (v2.40h) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors. New version program summaryProgram title: HFODD (v2.40h) Catalogue identifier: ADFL_v2_2 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v2_2.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 618 No. of bytes in distributed program, including test data, etc.: 372 548 Distribution format: tar.gz Programming language: FORTRAN-77 and Fortran-90 Computer: Pentium-III, AMD-Athlon, AMD-Opteron Operating system: UNIX, LINUX, Windows XP Has the code been vectorised or parallelized?: Yes, vectorised RAM: 10 Mwords Word size: The code is written in single-precision for use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Classification: 17.22 Catalogue identifier of previous version: ADFL_v2_1 Journal reference of previous version: Comput. Phys. Commun. 167 (2005) 214 External routines: Lapack (http://www.netlib.org/lapack/), Blas (http://www.netlib.org), linpack (http://www.netlib/linpack/) Does the new version supersede the previous version?: Yes Nature of problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [1]. Summary of revisions: Projection on good angular momentum (for the Hartree-Fock states) has been implemented. Calculation of the GCM kernels has been implemented. Calculation of matrix elements of the Yukawa interaction has been implemented. The BCS solutions for state-dependent pairing gaps have been implemented. The HFB solutions for broken simplex symmetry have been implemented. Calculation of Bohr deformation parameters has been implemented. Constraints on the Schiff moments and scalar multipole moments have been implemented. The DT2h transformations and rotations of wave functions have been implemented. The quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei has been implemented. The Broyden method to accelerate the convergence has been implemented. The Lipkin-Nogami method to treat pairing correlations has been implemented. The exact Coulomb exchange term has been implemented. Several utility options have been implemented. Three insignificant errors have been corrected. Restrictions: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Unusual features: The user must have access to an implementation of the BLAS (Basic Linear Algebra Subroutines), the NAGLIB subroutine F02AXE, or LAPACK subroutines ZHPEV, ZHPEVX, or ZHEEVR, which diagonalize complex Hermitian matrices, and the LINPACK subroutines ZGEDI and ZGECO, which invert arbitrary complex matrices and calculate determinants or provide another set of subroutines that can perform such a tasks. The LAPACK and LINPACK subroutines and an unoptimized version of the BLAS can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://www.netlib.org/. Running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In the case where every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J (2) can be obtained in forty minutes of CPU time on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. References: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166.

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein-Gordon potentials

DOE PAGES

Baczewski, Andrew David; Vikram, Melapudi; Shanker, Balasubramaniam; ...

2010-08-27

Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(N s 2N t 2), where N s and N t are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The firstmore » scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(N sN tlog 2N t). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.« less

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

Park, G. Barratt, E-mail: barratt@mit.edu

Franck-Condon vibrational overlap integrals for the A{sup ~1}A{sub u}—X{sup ~1}Σ{sup +}{sub g} transition in acetylene have been calculated in full dimension in the harmonic normal mode basis. The calculation uses the method of generating functions first developed for polyatomic Franck-Condon factors by Sharp and Rosenstock [J. Chem. Phys. 41(11), 3453–3463 (1964)], and previously applied to acetylene by Watson [J. Mol. Spectrosc. 207(2), 276–284 (2001)] in a reduced-dimension calculation. Because the transition involves a large change in the equilibrium geometry of the electronic states, two different types of corrections to the coordinate transformation are considered to first order: corrections for axis-switchingmore » between the Cartesian molecular frames and corrections for the curvilinear nature of the normal modes at large amplitude. The angular factor in the wave function for the out-of-plane component of the trans bending mode, ν{sub 4}{sup ″}, is treated as a rotation, which results in an Eckart constraint on the polar coordinates of the bending modes. To simplify the calculation, the other degenerate bending mode, ν{sub 5}{sup ″}, is integrated in the Cartesian basis and later transformed to the constrained polar coordinate basis, restoring the conventional v and l quantum numbers. An updated A{sup ~}-state harmonic force field obtained recently in the R. W. Field research group is evaluated. The results for transitions involving the gerade vibrational modes are in qualitative agreement with experiment. Calculated results for transitions involving ungerade modes are presented in Paper II of this series [G. B. Park, J. H. Baraban, and R. W. Field, “Full dimensional Franck–Condon factors for the acetylene A{sup ~1}A{sub u}—X{sup ~1}Σ{sup +}{sub g} transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes,” J. Chem. Phys. 141, 134305 (2014)].« less

Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design

NASA Technical Reports Server (NTRS)

Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian

2012-01-01

We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools.

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

NASA Astrophysics Data System (ADS)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

Information measures of a deformed harmonic oscillator in a static electric field

NASA Astrophysics Data System (ADS)

Nascimento, J. P. G.; Ferreira, F. A. P.; Aguiar, V.; Guedes, I.; Costa Filho, Raimundo N.

2018-06-01

The Shannon entropy and the Fischer information are calculated for an harmonic oscillator in the presence of an applied electric field (ε) in a space with metrics given by gxx-1/2 = 1 + γx. For that metric the harmonic oscillator can be mapped into a Morse potential in an Euclidean space. For ε = 0, the ground state energy decreases when γ increases. However, for certain values of ε the energy decrease can be canceled out. The dependence of the uncertainties, the entropy, and the information on the parameters γ and ε are shown.

Quantification of focal adhesion dynamics of cell movement based on cell-induced collagen matrix deformation using second-harmonic generation microscopy.

PubMed

Kang, Yong Guk; Jang, Hwanseok; Yang, Taeseok Daniel; Notbohm, Jacob; Choi, Youngwoon; Park, Yongdoo; Kim, Beop-Min

2018-06-01

Mechanical interactions of living cells with the surrounding environment via focal adhesion (FA) in three dimensions (3-D) play a key role in dynamic biological events, such as tissue regeneration, wound healing, and cancer invasion. Recently, several methods for observing 3-D cell-extracellular matrix (ECM) interactions have been reported, lacking solid and quantitative analysis on the dynamics of the physical interaction between the cell and the ECM. We measured the submicron displacements of ECM deformation in 3-D due to protrusion-retraction dynamics during cell migration, using second-harmonic generation without labeling the matrix structures. We then quantitatively analyzed the mechanical deformation between the ECM and the cells based on spatiotemporal volumetric correlations. The greatest deformations within the collagen matrix were found to occur at sites of colocalization of the FA site-related proteins vinculin and actin, which confirms that FA sites play a critical role in living cells within the ECM as a point for adhesion, traction, and migration. We believe that this modality can be used in studies of cell-ECM interaction during angiogenesis, wound healing, and metastasis. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Non-Cartesian Parallel Imaging Reconstruction

PubMed Central

Wright, Katherine L.; Hamilton, Jesse I.; Griswold, Mark A.; Gulani, Vikas; Seiberlich, Nicole

2014-01-01

Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be employed to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the non-homogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian GRAPPA, and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. PMID:24408499

Ranking of stopping criteria for log domain diffeomorphic demons application in clinical radiation therapy.

PubMed

Peroni, M; Golland, P; Sharp, G C; Baroni, G

2011-01-01

Deformable Image Registration is a complex optimization algorithm with the goal of modeling a non-rigid transformation between two images. A crucial issue in this field is guaranteeing the user a robust but computationally reasonable algorithm. We rank the performances of four stopping criteria and six stopping value computation strategies for a log domain deformable registration. The stopping criteria we test are: (a) velocity field update magnitude, (b) vector field Jacobian, (c) mean squared error, and (d) harmonic energy. Experiments demonstrate that comparing the metric value over the last three iterations with the metric minimum of between four and six previous iterations is a robust and appropriate strategy. The harmonic energy and vector field update magnitude metrics give the best results in terms of robustness and speed of convergence.

Revisiting the factors which control the angle of shear bands in geodynamic numerical models of brittle deformation

NASA Astrophysics Data System (ADS)

Thieulot, Cedric

2017-04-01

In this work I present Finite Element numerical simulations of brittle deformation in two-dimensional Cartesian systems subjected to compressional or extensional kinematical boundary conditions with a basal velocity discontinuity. The rheology is visco-plastic and is characterised by a cohesion and an angle of internal friction (Drucker-Prager type). I will explore the influence of the following factors on the recovered shear band angles when the angle of internal friction is varied: a) element type (quadrilateral vs triangle), b) element order, c) continuous vs discontinous pressure, d) visco-plasticity model implementation, e) the nonlinear tolerance value, f) the use of markers, g) Picard vs Newton-Raphson, h) velocity discontinuity nature. I will present these results in the light of already published literature (e.g. Lemiale et al, PEPI 171, 2008; Kaus, Tectonophysics 484, 2010).

Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series

NASA Astrophysics Data System (ADS)

Chanard, Kristel; Fleitout, Luce; Calais, Eric; Rebischung, Paul; Avouac, Jean-Philippe

2018-04-01

We model surface displacements induced by variations in continental water, atmospheric pressure, and nontidal oceanic loading, derived from the Gravity Recovery and Climate Experiment (GRACE) for spherical harmonic degrees two and higher. As they are not observable by GRACE, we use at first the degree-1 spherical harmonic coefficients from Swenson et al. (2008, https://doi.org/10.1029/2007JB005338). We compare the predicted displacements with the position time series of 689 globally distributed continuous Global Navigation Satellite System (GNSS) stations. While GNSS vertical displacements are well explained by the model at a global scale, horizontal displacements are systematically underpredicted and out of phase with GNSS station position time series. We then reestimate the degree 1 deformation field from a comparison between our GRACE-derived model, with no a priori degree 1 loads, and the GNSS observations. We show that this approach reconciles GRACE-derived loading displacements and GNSS station position time series at a global scale, particularly in the horizontal components. Assuming that they reflect surface loading deformation only, our degree-1 estimates can be translated into geocenter motion time series. We also address and assess the impact of systematic errors in GNSS station position time series at the Global Positioning System (GPS) draconitic period and its harmonics on the comparison between GNSS and GRACE-derived annual displacements. Our results confirm that surface mass redistributions observed by GRACE, combined with an elastic spherical and layered Earth model, can be used to provide first-order corrections for loading deformation observed in both horizontal and vertical components of GNSS station position time series.

Optical Quantification of Harmonic Acoustic Radiation Force Excitation in a Tissue-Mimicking Phantom.

PubMed

Suomi, Visa; Edwards, David; Cleveland, Robin

2015-12-01

Optical tracking was used to characterize acoustic radiation force-induced displacements in a tissue-mimicking phantom. Amplitude-modulated 3.3-MHz ultrasound was used to induce acoustic radiation force in the phantom, which was embedded with 10-μm microspheres that were tracked using a microscope objective and high-speed camera. For sine and square amplitude modulation, the harmonic components of the fundamental and second and third harmonic frequencies were measured. The displacement amplitudes were found to increase linearly with acoustic radiation force up to 10 μm, with sine modulation having 19.5% lower peak-to-peak amplitude values than square modulation. Square modulation produced almost no second harmonic, but energy was present in the third harmonic. For the sine modulation, energy was present in the second harmonic and low energy in the third harmonic. A finite-element model was used to simulate the deformation and was both qualitatively and quantitatively in agreement with the measurements. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ormiston, R. A.

1975-01-01

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

Fast and accurate reference-free alignment of subtomograms.

PubMed

Chen, Yuxiang; Pfeffer, Stefan; Hrabe, Thomas; Schuller, Jan Michael; Förster, Friedrich

2013-06-01

In cryoelectron tomography alignment and averaging of subtomograms, each dnepicting the same macromolecule, improves the resolution compared to the individual subtomogram. Major challenges of subtomogram alignment are noise enhancement due to overfitting, the bias of an initial reference in the iterative alignment process, and the computational cost of processing increasingly large amounts of data. Here, we propose an efficient and accurate alignment algorithm via a generalized convolution theorem, which allows computation of a constrained correlation function using spherical harmonics. This formulation increases computational speed of rotational matching dramatically compared to rotation search in Cartesian space without sacrificing accuracy in contrast to other spherical harmonic based approaches. Using this sampling method, a reference-free alignment procedure is proposed to tackle reference bias and overfitting, which also includes contrast transfer function correction by Wiener filtering. Application of the method to simulated data allowed us to obtain resolutions near the ground truth. For two experimental datasets, ribosomes from yeast lysate and purified 20S proteasomes, we achieved reconstructions of approximately 20Å and 16Å, respectively. The software is ready-to-use and made public to the community. Copyright © 2013 Elsevier Inc. All rights reserved.

Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation.

PubMed

Timofeeva, Maria; Lang, Lukas; Timpu, Flavia; Renaut, Claude; Bouravleuv, Alexei; Shtrom, Igor; Cirlin, George; Grange, Rachel

2018-06-13

Nonradiating electromagnetic configurations in nanostructures open new horizons for applications due to two essential features: a lack of energy losses and invisibility to the propagating electromagnetic field. Such radiationless configurations form a basis for new types of nanophotonic devices, in which a strong electromagnetic field confinement can be achieved together with lossless interactions between nearby components. In our work, we present a new design of free-standing disk nanoantennas with nonradiating current distributions for the optical near-infrared range. We show a novel approach to creating nanoantennas by slicing III-V nanowires into standing disks using focused ion-beam milling. We experimentally demonstrate the suppression of the far-field radiation and the associated strong enhancement of the second-harmonic generation from the disk nanoantennas. With a theoretical analysis of the electromagnetic field distribution using multipole expansions in both spherical and Cartesian coordinates, we confirm that the demonstrated nonradiating configurations are anapoles. We expect that the presented procedure of designing and producing disk nanoantennas from nanowires becomes one of the standard approaches to fabricating controlled chains of standing nanodisks with different designs and configurations. These chains can be essential building blocks for new types of lasers and sensors with low power consumption.

3D full-field quantification of cell-induced large deformations in fibrillar biomaterials by combining non-rigid image registration with label-free second harmonic generation.

PubMed

Jorge-Peñas, Alvaro; Bové, Hannelore; Sanen, Kathleen; Vaeyens, Marie-Mo; Steuwe, Christian; Roeffaers, Maarten; Ameloot, Marcel; Van Oosterwyck, Hans

2017-08-01

To advance our current understanding of cell-matrix mechanics and its importance for biomaterials development, advanced three-dimensional (3D) measurement techniques are necessary. Cell-induced deformations of the surrounding matrix are commonly derived from the displacement of embedded fiducial markers, as part of traction force microscopy (TFM) procedures. However, these fluorescent markers may alter the mechanical properties of the matrix or can be taken up by the embedded cells, and therefore influence cellular behavior and fate. In addition, the currently developed methods for calculating cell-induced deformations are generally limited to relatively small deformations, with displacement magnitudes and strains typically of the order of a few microns and less than 10% respectively. Yet, large, complex deformation fields can be expected from cells exerting tractions in fibrillar biomaterials, like collagen. To circumvent these hurdles, we present a technique for the 3D full-field quantification of large cell-generated deformations in collagen, without the need of fiducial markers. We applied non-rigid, Free Form Deformation (FFD)-based image registration to compute full-field displacements induced by MRC-5 human lung fibroblasts in a collagen type I hydrogel by solely relying on second harmonic generation (SHG) from the collagen fibrils. By executing comparative experiments, we show that comparable displacement fields can be derived from both fibrils and fluorescent beads. SHG-based fibril imaging can circumvent all described disadvantages of using fiducial markers. This approach allows measuring 3D full-field deformations under large displacement (of the order of 10 μm) and strain regimes (up to 40%). As such, it holds great promise for the study of large cell-induced deformations as an inherent component of cell-biomaterial interactions and cell-mediated biomaterial remodeling. Copyright © 2017 Elsevier Ltd. All rights reserved.

GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows

NASA Technical Reports Server (NTRS)

2003-01-01

With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.

SPECIAL ISSUE DEVOTED TO THE 80TH BIRTHDAY OF S.A. AKHMANOV: Three-wave interactions of surface defect-deformation waves and their manifestations in the self-organisation of nano- and microstructures in solids exposed to laser radiation

NASA Astrophysics Data System (ADS)

Emel'yanov, Vladimir I.; Seval'nev, D. M.

2009-07-01

The self-organisation of the surface-relief nanostructures in solids under the action of energy and particle fluxes is interpreted as the instability of defect-deformation (DD) gratings produced by quasi-static Lamb and Rayleigh waves and defect-concentration waves. The allowance for the nonlocality in the defects—lattice atom interaction with a simultaneous account for both (normal and longitudinal) defect-induced forces bending the surface layer leads to the appearance of two maxima in the dependence of the instability growth rate of DD waves on the wave number. Three-wave interactions of quasi-static coupled DD waves (second harmonic generation and wave vector mixing) are considered for the first time, which are similar to three-wave interactions in nonlinear optics and acoustics and lead to the enrichment of the spectrum of surface-relief harmonics. Computer processing of experimental data on laser-induced generation of micro- and nanostructures of the surface relief reveals the presence of effects responsible for the second harmonic generation and wave vector mixing.

Characterization of microscopic deformation through two-point spatial correlation functions

NASA Astrophysics Data System (ADS)

Huang, Guan-Rong; Wu, Bin; Wang, Yangyang; Chen, Wei-Ren

2018-01-01

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

Characterization of microscopic deformation through two-point spatial correlation functions.

PubMed

Huang, Guan-Rong; Wu, Bin; Wang, Yangyang; Chen, Wei-Ren

2018-01-01

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

NASA Astrophysics Data System (ADS)

Byun, Do-Seong; Hart, Deirdre E.

2017-04-01

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world's coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical "boundaries" between 359° and 0° degrees (or 179° and 0°). In nature, such "boundaries" are in fact smooth transitions, but if these mathematical "boundaries" are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman's (1978) "northern semi-major axis convention" since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based "vector embodiment" solutions are employed.

Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow

NASA Astrophysics Data System (ADS)

Sugiyama, Kazuyasu; , Satoshi, II; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro

2010-03-01

For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full Eulerian finite difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy-Green deformation tensor are temporally updated on the Eulerian frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present Eulerian approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.

Two dimensional vernier

NASA Technical Reports Server (NTRS)

Juday, Richard D. (Inventor)

1992-01-01

A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.

Time-frequency analyses of fluid-solid interaction under sinusoidal translational shear deformation of the viscoelastic rat cerebrum

NASA Astrophysics Data System (ADS)

Leahy, Lauren N.; Haslach, Henry W.

2018-02-01

During normal extracellular fluid (ECF) flow in the brain glymphatic system or during pathological flow induced by trauma resulting from impacts and blast waves, ECF-solid matter interactions result from sinusoidal shear waves in the brain and cranial arterial tissue, both heterogeneous biological tissues with high fluid content. The flow in the glymphatic system is known to be forced by pulsations of the cranial arteries at about 1 Hz. The experimental shear stress response to sinusoidal translational shear deformation at 1 Hz and 25% strain amplitude and either 0% or 33% compression is compared for rat cerebrum and bovine aortic tissue. Time-frequency analyses aim to correlate the shear stress signal frequency components over time with the behavior of brain tissue constituents to identify the physical source of the shear nonlinear viscoelastic response. Discrete fast Fourier transformation analysis and the novel application to the shear stress signal of harmonic wavelet decomposition both show significant 1 Hz and 3 Hz components. The 3 Hz component in brain tissue, whose magnitude is much larger than in aortic tissue, may result from interstitial fluid induced drag forces. The harmonic wavelet decomposition locates 3 Hz harmonics whose magnitudes decrease on subsequent cycles perhaps because of bond breaking that results in easier fluid movement. Both tissues exhibit transient shear stress softening similar to the Mullins effect in rubber. The form of a new mathematical model for the drag force produced by ECF-solid matter interactions captures the third harmonic seen experimentally.

Mathematical Development and Computational Analysis of Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) Based on Bloch Nuclear Magnetic Resonance (NMR) Diffusion Model for Myocardial Motion.

PubMed

Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E

2017-09-13

Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.

2012-01-01

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

NASA Astrophysics Data System (ADS)

Sikora, Roman; Markiewicz, Przemysław; Pabjańczyk, Wiesława

2018-04-01

The power systems usually include a number of nonlinear receivers. Nonlinear receivers are the source of disturbances generated to the power system in the form of higher harmonics. The level of these disturbances describes the total harmonic distortion coefficient THD. Its value depends on many factors. One of them are the deformation and change in RMS value of supply voltage. A modern LED luminaire is a nonlinear receiver as well. The paper presents the results of the analysis of the influence of change in RMS value of supply voltage and the level of dimming of the tested luminaire on the value of the current THD. The analysis was made using a mathematical model based on multivariable polynomial fitting.

Simplification of the kinematic model of human movement

NASA Astrophysics Data System (ADS)

Dusza, Jacek J.; Wawrzyniak, Zbigniew M.; del Prado Martinez, David

2013-10-01

The paper presents a methods of simplification of the human gait model. The experimental data were obtained in the laboratory of the group SATI in the Electronics Engineering Department of the University of Valencia. As a result of the Mean Double Step (MDS) procedure, the human motion were described by a matrix containing the Cartesian coordinates of 26 markers placed on the human body recorded in the 100 time points. With these data it has been possible to develop an software application which performs a wide diversity of tasks like array simplification, mask calculation for the simplification, error calculation as well as tools for signals comparison and movement animation of the markers. Simplifications were made by the spectral analysis of signals and calculating the standard deviation of the differences between the signal and its approximation. Using this method the signals of displacement could be written as the time series limited to a small number of harmonic signals. This approach allows us for a high degree of data compression. The model presented in this work can be applied into the context of medical diagnostics or rehabilitation because for a given approximation error and a large number of harmonics may demonstrate some abnormalities (of orthopaedic symptoms) in the gait cycle analysis.

Confined active Brownian particles: theoretical description of propulsion-induced accumulation

NASA Astrophysics Data System (ADS)

Das, Shibananda; Gompper, Gerhard; Winkler, Roland G.

2018-01-01

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

Numerical Simulation of Shock Interaction with Deformable Particles Using a Constrained Interface Reinitialization Scheme

NASA Astrophysics Data System (ADS)

Jackson, Thomas L.; Sridharan, Prashanth; Zhang, Ju; Balachandar, S.

2015-11-01

In this work we present axisymmetric numerical simulations of shock propagating in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. The numerical method is a finite-volume based solver on a Cartesian grid, which allows for multi-material interfaces and shocks. To preserve particle mass and volume, a novel constraint reinitialization scheme is introduced. We compute the unsteady drag coefficient as a function of post-shock pressure, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. Using this information, we also present a simplified point-particle force model that can be used for mesoscale simulations.

Deformation of supersymmetric and conformal quantum mechanics through affine transformations

NASA Technical Reports Server (NTRS)

Spiridonov, Vyacheslav

1993-01-01

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

The Evolution of the "Cartesian Connection"

ERIC Educational Resources Information Center

Anderson, Gail M.

2008-01-01

Students often struggle with the connection between algebraic and graphical representations of functions. This overview of the history of the Cartesian coordinate system helps the classroom teacher consider new ways to aid students in making the "Cartesian connection." (Contains 7 figures.)

Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: Torsional anharmonicity and kinetic isotope effect

NASA Astrophysics Data System (ADS)

Wang, Wenji; Zhao, Yi

2012-12-01

Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.

Plate Like Convection with Viscous Strain Weakening and Corresponding Surface Deformation Pattern

NASA Astrophysics Data System (ADS)

Fuchs, L.; Becker, T. W.

2017-12-01

How plate tectonic surface motions are generated by mantle convection on Earth and possibly other terrestrial type planets has recently become more readily accessible with fully dynamic convection computations. However, it remains debated how plate-like the behavior in such models truly is, and in particular how the well plate boundary dynamics are captured in models which typically exclude the effects of deformation history and memory. Here, we analyze some of the effects of viscous strain weakening on plate behavior and the interactions between interior convection dynamics and surface deformation patterns. We use the finite element code CitcomCU to model convection in a 3D Cartesian model setup. The models are internally heated, with an Arrhenius-type temperature dependent viscosity including plastic yielding and viscous strain weakening (VSW) and healing (VSWH). VSW can mimic first order features of more complex damage mechanisms such as grain-size dependent rheology. Besides plate diagnostic parameters (Plateness, Mobility, and Toroidal: Poloidal ratio) to analyze the tectonic behavior our models, we also explore how "plate boundaries" link to convective patterns. In a first model series, we analyze general surface deformation patterns without VSW. In the early stages, deformation patterns are clearly co-located with up- and downwelling limbs of convection. Along downwellings strain-rates are high and localized, whereas upwellings tend to lead to broad zones of high deformation. At a more advanced stage, however, the plates' interior is highly deformed due to continuous strain accumulation and resurfaced inherited strain. Including only VSW leads to more localized deformation along downwellings. However, at a more advanced stage plate-like convection fails due an overall weakening of the material. This is prevented including strain healing. Deformation pattern at the surface more closely coincide with the internal convection patterns. The average surface deformation is reduced significantly and mainly governed by the location of the up- and downwellings. VSWH thereby affects plate dynamics due to two main properties: the intensity of weakening with increasing strain and the strain healing rate. As both increase, mobility increases as well and strain becomes more localized at the downwellings.

The 3D Euler solutions using automated Cartesian grid generation

NASA Technical Reports Server (NTRS)

Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.

1993-01-01

Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.

Zero-point energy conservation in classical trajectory simulations: Application to H2CO

NASA Astrophysics Data System (ADS)

Lee, Kin Long Kelvin; Quinn, Mitchell S.; Kolmann, Stephen J.; Kable, Scott H.; Jordan, Meredith J. T.

2018-05-01

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO "roaming" reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a "ZPE-corrected" potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol—chemical accuracy—for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of "projected" Cartesian coordinates and a global ZPE "surface" is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, Veff, at no additional computational cost to the PES itself. Both V and Veff are used to model product state distributions from the H + HCO → H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on Veff and classical simulations of kinetic energy release should therefore be viewed with caution.

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

2015-06-15

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformedmore » oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.« less

Application of the ASP3D Computer Program to Unsteady Aerodynamic and Aeroelastic Analyses

NASA Technical Reports Server (NTRS)

Batina, John T.

2006-01-01

A new computer program has been developed called ASP3D (Advanced Small Perturbation - 3D), which solves the small perturbation potential flow equation in an advanced form including mass-consistent surface and trailing wake boundary conditions, and entropy, vorticity, and viscous effects. The purpose of the program is for unsteady aerodynamic and aeroelastic analyses, especially in the nonlinear transonic flight regime. The program exploits the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The paper presents unsteady aerodynamic and aeroelastic applications of ASP3D to assess the time dependent capability and demonstrate various features of the code.

Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

NASA Technical Reports Server (NTRS)

Natarajan, R.; Brown, R. A.

1986-01-01

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

Rethinking the birthing body: Cartesian dualism and perinatal nursing.

PubMed

Goldberg, Lisa

2002-03-01

This paper highlights the pervasive influence of a Cartesian metaphysics on the medical paradigm and its profound impact on the practice of perinatal nursing in North America. Modern perinatal health care practices are founded on a Cartesian metaphysics that reduce birthing women to the status of object. Such practices deny the holistic aims of perinatal nursing. A philosophical inquiry informs the tenets of this metaphysical discussion regarding the foundations of perinatal nursing practices. Although perinatal health care is founded on a Cartesian metaphysics, an alternative paradigm of embodied practice is suggested as a way of viewing birthing women as embodied subjects. If the foundations of health care, which have been built on a Cartesian metaphysics, are not re-examined, perinatal nurses will be providing care that further reduce women to the status of object.

Quantification of turbulence and velocity in stenotic flow using spiral three-dimensional phase-contrast MRI.

PubMed

Petersson, Sven; Dyverfeldt, Petter; Sigfridsson, Andreas; Lantz, Jonas; Carlhäll, Carl-Johan; Ebbers, Tino

2016-03-01

Evaluate spiral three-dimensional (3D) phase contrast MRI for the assessment of turbulence and velocity in stenotic flow. A-stack-of-spirals 3D phase contrast MRI sequence was evaluated in vitro against a conventional Cartesian sequence. Measurements were made in a flow phantom with a 75% stenosis. Both spiral and Cartesian imaging were performed using different scan orientations and flow rates. Volume flow rate, maximum velocity and turbulent kinetic energy (TKE) were computed for both methods. Moreover, the estimated TKE was compared with computational fluid dynamics (CFD) data. There was good agreement between the turbulent kinetic energy from the spiral, Cartesian and CFD data. Flow rate and maximum velocity from the spiral data agreed well with Cartesian data. As expected, the short echo time of the spiral sequence resulted in less prominent displacement artifacts compared with the Cartesian sequence. However, both spiral and Cartesian flow rate estimates were sensitive to displacement when the flow was oblique to the encoding directions. Spiral 3D phase contrast MRI appears favorable for the assessment of stenotic flow. The spiral sequence was more than three times faster and less sensitive to displacement artifacts when compared with a conventional Cartesian sequence. © 2015 Wiley Periodicals, Inc.

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

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

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

2007-03-15

Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translatesmore » into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.« less

Gauged supergravities from M-theory reductions

NASA Astrophysics Data System (ADS)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

Improved genetic algorithm for the protein folding problem by use of a Cartesian combination operator.

PubMed Central

Rabow, A. A.; Scheraga, H. A.

1996-01-01

We have devised a Cartesian combination operator and coding scheme for improving the performance of genetic algorithms applied to the protein folding problem. The genetic coding consists of the C alpha Cartesian coordinates of the protein chain. The recombination of the genes of the parents is accomplished by: (1) a rigid superposition of one parent chain on the other, to make the relation of Cartesian coordinates meaningful, then, (2) the chains of the children are formed through a linear combination of the coordinates of their parents. The children produced with this Cartesian combination operator scheme have similar topology and retain the long-range contacts of their parents. The new scheme is significantly more efficient than the standard genetic algorithm methods for locating low-energy conformations of proteins. The considerable superiority of genetic algorithms over Monte Carlo optimization methods is also demonstrated. We have also devised a new dynamic programming lattice fitting procedure for use with the Cartesian combination operator method. The procedure finds excellent fits of real-space chains to the lattice while satisfying bond-length, bond-angle, and overlap constraints. PMID:8880904

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

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

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

Towards improved NDE and SHM methodologies incorporating nonlinear structural features

NASA Astrophysics Data System (ADS)

Chillara, Vamshi Krishna

Ultrasound is widely employed in Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM) applications to detect and characterize damage/defects in materials. In particular, ultrasonic guided waves are considered a foremost candidate for in-situ monitoring applications. Conventional ultrasonic techniques rely on changes/discontinuities in linear elastic material properties, namely the Young's modulus and shear modulus to detect damage. On the other hand, nonlinear ultrasonic techniques that rely on micro-scale nonlinear material/structural behavior are proven to be sensitive to damage induced microstructural changes that precede macro-scale damage and are hence capable of early damage detection. The goal of this thesis is to investigate the capabilities of nonlinear guided waves --- a fusion of nonlinear ultrasonic techniques with the guided wave methodologies for early damage detection. To that end, the thesis focuses on two important aspects of the problem: 1. Wavemechanics - deals with ultrasonic guided wave propagation in nonlinear waveguides; 2. Micromechanics - deals with correlating ultrasonic response with micro-scale nonlinear material behavior. For the development of efficient NDE and SHM methodologies that incorporate nonlinear structural features, a detailed understanding of the above aspects is indispensable. In this thesis, the wavemechanics aspect of the problem is dealt with from both theoretical and numerical standpoints. A generalized theoretical framework is developed to study higher harmonic guided waves in plates. This was employed to study second harmonic guided waves in pipes using a large-radius asymptotic approximation. Second harmonic guided waves in plates are studied from a numerical standpoint. Theoretical predictions are validated and some key aspects of higher harmonic generation in waveguides are outlined. Finally, second harmonic guided waves in plates with inhomogeneous and localized nonlinearities are studied and some important aspects of guided wave mode selection are addressed. The other part of the work focused on developing a micromechanics based understanding of ultrasonic higher harmonic generation. Three important aspects of micro-scale material behavior, namely tension-compression asymmetry, shearnormal coupling and deformation induced asymmetry are identified and their role in ultrasonic higher harmonic generation is discussed. Tension-compression asymmetry is identified to cause second (even) harmonic generation in materials. Then, shearnormal coupling is identified to cause generation of secondary waves of different polarity than the primary waves. In addition, deformation induced anisotropy due to the presence of residual stress/strain and its contribution to ultrasonic higher harmonic generation is qualitatively discussed. Also, the tension-compression asymmetry in the material is quantified using an energy based measure. The above measure is employed to develop a homogenization based approach amenable to multi-scale analysis to correlate microstructure with ultrasonic higher harmonic generation. Finally, experimental investigations concerning third harmonic SH wave generation in plates are carried out and the effect of load and temperature changes on nonlinear ultrasonic measurements are discussed in the context of SHM. It was found that while nonlinear ultrasound is sensitive to micro-scale damage, the relative nonlinearity parameter may not always be the best measure to quantify the nonlinearity as it is subject to spurious effects from changes in environmental factors such as loads and temperature.

Smoothly deformed light

NASA Technical Reports Server (NTRS)

Stenholm, Stig

1993-01-01

A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

NASA Astrophysics Data System (ADS)

Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

2012-01-01

We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution format: tar.gz Programming language: FORTRAN-90 Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT4, Cray XT5 Operating system: UNIX, LINUX, Windows XP Has the code been vectorized or parallelized?: Yes, parallelized using MPI RAM: 10 Mwords Word size: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Classification: 17.22 Catalogue identifier of previous version: ADFL_v2_2 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2361 External routines: The user must have access to the NAGLIB subroutine f02axe, or LAPACK subroutines zhpev, zhpevx, zheevr, or zheevd, which diagonalize complex hermitian matrices, the LAPACK subroutines dgetri and dgetrf which invert arbitrary real matrices, the LAPACK subroutines dsyevd, dsytrf and dsytri which compute eigenvalues and eigenfunctions of real symmetric matrices, the LINPACK subroutines zgedi and zgeco, which invert arbitrary complex matrices and calculate determinants, the BLAS routines dcopy, dscal, dgeem and dgemv for double-precision linear algebra and zcopy, zdscal, zgeem and zgemv for complex linear algebra, or provide another set of subroutines that can perform such tasks. The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/. Does the new version supersede the previous version?: Yes Nature of problem: The nuclear mean field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle- n-hole) configurations, deformations, excitation energies, or angular momenta. Similarly, Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: [J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166]. Reasons for new version: Version 2.49s of HFODD provides a number of new options such as the isospin mixing and projection of the Skyrme functional, the finite-temperature HF and HFB formalism and optimized methods to perform multi-constrained calculations. It is also the first version of HFODD to contain threading and parallel capabilities. Summary of revisions: Isospin mixing and projection of the HF states has been implemented. The finite-temperature formalism for the HFB equations has been implemented. The Lipkin translational energy correction method has been implemented. Calculation of the shell correction has been implemented. The two-basis method for the solution to the HFB equations has been implemented. The Augmented Lagrangian Method (ALM) for calculations with multiple constraints has been implemented. The linear constraint method based on the cranking approximation of the RPA matrix has been implemented. An interface between HFODD and the axially-symmetric and parity-conserving code HFBTHO has been implemented. The mixing of the matrix elements of the HF or HFB matrix has been implemented. A parallel interface using the MPI library has been implemented. A scalable model for reading input data has been implemented. OpenMP pragmas have been implemented in three subroutines. The diagonalization of the HFB matrix in the simplex-breaking case has been parallelized using the ScaLAPACK library. Several little significant errors of the previous published version were corrected. Running time: In serial mode, running 6 HFB iterations for 152Dy for conserved parity and signature symmetries in a full spherical basis of N=14 shells takes approximately 8 min on an AMD Opteron processor at 2.6 GHz, assuming standard BLAS and LAPACK libraries. As a rule of thumb, runtime for HFB calculations for parity and signature conserved symmetries roughly increases as N, where N is the number of full HO shells. Using custom-built optimized BLAS and LAPACK libraries (such as in the ATLAS implementation) can bring down the execution time by 60%. Using the threaded version of the code with 12 threads and threaded BLAS libraries can bring an additional factor 2 speed-up, so that the same 6 HFB iterations now take of the order of 2 min 30 s.

The adaptive, cut-cell Cartesian approach (warts and all)

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.

1995-01-01

Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.

An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies

NASA Technical Reports Server (NTRS)

Quirk, James J.

1992-01-01

In this paper we describe an approach for dealing with arbitrary complex, two dimensional geometries, the so-called cartesian boundary method. Conceptually, the cartesian boundary method is quite simple. Solid bodies blank out areas of a background, cartesian mesh, and the resultant cut cells are singled out for special attention. However, there are several obstacles that must be overcome in order to achieve a practical scheme. We present a general strategy that overcomes these obstacles, together with some details of our successful conversion of an adaptive mesh algorithm from a body-fitted code to a cartesian boundary code.

Determination of displacements and their derivatives from 3D fringe patterns via extended monogenic phasor method

NASA Astrophysics Data System (ADS)

Sciammarella, Cesar A.; Lamberti, Luciano

2018-05-01

For 1D signals, it is necessary to resort to a 2D abstract space because the concept of phase utilized in the retrieval of fringe pattern analysis information relies on the use of a vectorial function. Fourier and Hilbert transforms provide in-quadrature signals that lead to the very important basic concept of local phase. A 3D abstract space must hence be generated in order to analyze 2D signals. A 3D vector space in a Cartesian complex space is graphically represented by a Poincare sphere. In this study, the extension of the associated spaces is extended to 3D. A 4D hypersphere is defined for that purpose. The proposed approach is illustrated by determining the deformations of the heart left ventricle.

Shock-driven fluid-structure interaction for civil design

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

Wood, Stephen L; Deiterding, Ralf

The multiphysics fluid-structure interaction simulation of shock-loaded structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. The Virtual Test Facility combines a Cartesian embedded boundary approach with dynamic mesh adaptation in a generic software framework of flow solvers using hydrodynamic finite volume upwind schemes that are coupled to various explicit finite element solid dynamics solvers (Deiterding et al., 2006). This paper gives a brief overview of the computational approach and presents first simulations that utilize the general purpose solid dynamics code DYNA3D for complex 3D structures of interest in civil engineering.more » Results from simulations of a reinforced column, highway bridge, multistory building, and nuclear reactor building are presented.« less

A global estimate of the Earth's magnetic crustal thickness

NASA Astrophysics Data System (ADS)

Vervelidou, Foteini; Thébault, Erwan

2014-05-01

The Earth's lithosphere is considered to be magnetic only down to the Curie isotherm. Therefore the Curie isotherm can, in principle, be estimated by analysis of magnetic data. Here, we propose such an analysis in the spectral domain by means of a newly introduced regional spatial power spectrum. This spectrum is based on the Revised Spherical Cap Harmonic Analysis (R-SCHA) formalism (Thébault et al., 2006). We briefly discuss its properties and its relationship with the Spherical Harmonic spatial power spectrum. This relationship allows us to adapt any theoretical expression of the lithospheric field power spectrum expressed in Spherical Harmonic degrees to the regional formulation. We compared previously published statistical expressions (Jackson, 1994 ; Voorhies et al., 2002) to the recent lithospheric field models derived from the CHAMP and airborne measurements and we finally developed a new statistical form for the power spectrum of the Earth's magnetic lithosphere that we think provides more consistent results. This expression depends on the mean magnetization, the mean crustal thickness and a power law value that describes the amount of spatial correlation of the sources. In this study, we make a combine use of the R-SCHA surface power spectrum and this statistical form. We conduct a series of regional spectral analyses for the entire Earth. For each region, we estimate the R-SCHA surface power spectrum of the NGDC-720 Spherical Harmonic model (Maus, 2010). We then fit each of these observational spectra to the statistical expression of the power spectrum of the Earth's lithosphere. By doing so, we estimate the large wavelengths of the magnetic crustal thickness on a global scale that are not accessible directly from the magnetic measurements due to the masking core field. We then discuss these results and compare them to the results we obtained by conducting a similar spectral analysis, but this time in the cartesian coordinates, by means of a published statistical expression (Maus et al., 1997). We also compare our results to crustal thickness global maps derived by means of additional geophysical data (Purucker et al., 2002).

Radial Symmetry of p-Harmonic Minimizers

NASA Astrophysics Data System (ADS)

Koski, Aleksis; Onninen, Jani

2018-03-01

"It is still not known if the radial cavitating minimizers obtained by uc(Ball) (Philos Trans R Soc Lond A 306:557-611, 1982) (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy". This quotation is from uc(Sivaloganathan) and uc(Spector) (Ann Inst Henri Poincaré Anal Non Linéaire 25(1):201-213, 2008) and seems to be still accurate. The model case of the p-harmonic energy is considered here. We prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary. In the traction free setting, however, even the identity map need not be a global minimizer.

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

Zhang, He; Huang, He; Li, Rui; ...

2017-03-06

Here, the fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor-based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed.

Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

PubMed Central

Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri

2016-01-01

The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement. PMID:27917882

Analysis of higher order harmonics with holographic reflection gratings

NASA Astrophysics Data System (ADS)

Mas-Abellan, P.; Madrigal, R.; Fimia, A.

2017-05-01

Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.

Geopotential Field Anomaly Continuation with Multi-Altitude Observations

NASA Technical Reports Server (NTRS)

Kim, Jeong Woo; Kim, Hyung Rae; von Frese, Ralph; Taylor, Patrick; Rangelova, Elena

2012-01-01

Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.

Geopotential Field Anomaly Continuation with Multi-Altitude Observations

NASA Technical Reports Server (NTRS)

Kim, Jeong Woo; Kim, Hyung Rae; vonFrese, Ralph; Taylor, Patrick; Rangelova, Elena

2011-01-01

Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.

Freeze-out dynamics via charged kaon femtoscopy in sNN=200 GeV central Au + Au collisions

NASA Astrophysics Data System (ADS)

Adamczyk, L.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z.; Alekseev, I.; Alford, J.; Anson, C. D.; Aparin, A.; Arkhipkin, D.; Aschenauer, E.; Averichev, G. S.; Balewski, J.; Banerjee, A.; Barnovska, Z.; Beavis, D. R.; Bellwied, R.; Betancourt, M. J.; Betts, R. R.; Bhasin, A.; Bhati, A. K.; Bhattarai; Bichsel, H.; Bielcik, J.; Bielcikova, J.; Bland, L. C.; Bordyuzhin, I. G.; Borowski, W.; Bouchet, J.; Brandin, A. V.; Brovko, S. G.; Bruna, E.; Bültmann, S.; Bunzarov, I.; Burton, T. P.; Butterworth, J.; Caines, H.; Calderón de la Barca Sánchez, M.; Cebra, D.; Cendejas, R.; Cervantes, M. C.; Chaloupka, P.; Chang, Z.; Chattopadhyay, S.; Chen, H. F.; Chen, J. H.; Chen, J. Y.; Chen, L.; Cheng, J.; Cherney, M.; Chikanian, A.; Christie, W.; Chung, P.; Chwastowski, J.; Codrington, M. J. M.; Corliss, R.; Cramer, J. G.; Crawford, H. J.; Cui, X.; Das, S.; Davila Leyva, A.; De Silva, L. C.; Debbe, R. R.; Dedovich, T. G.; Deng, J.; Derradi de Souza, R.; Dhamija, S.; di Ruzza, B.; Didenko, L.; Dilks; Ding, F.; Dion, A.; Djawotho, P.; Dong, X.; Drachenberg, J. L.; Draper, J. E.; Du, C. M.; Dunkelberger, L. E.; Dunlop, J. C.; Efimov, L. G.; Elnimr, M.; Engelage, J.; Engle, K. S.; Eppley, G.; Eun, L.; Evdokimov, O.; Fatemi, R.; Fazio, S.; Fedorisin, J.; Fersch, R. G.; Filip, P.; Finch, E.; Fisyak, Y.; Flores, C. E.; Gagliardi, C. A.; Gangadharan, D. R.; Garand, D.; Geurts, F.; Gibson, A.; Gliske, S.; Grebenyuk, O. G.; Grosnick, D.; Guo, Y.; Gupta, A.; Gupta, S.; Guryn, W.; Haag, B.; Hajkova, O.; Hamed, A.; Han, L.-X.; Haque, R.; Harris, J. W.; Hays-Wehle, J. P.; Heppelmann, S.; Hirsch, A.; Hoffmann, G. W.; Hofman, D. J.; Horvat, S.; Huang, B.; Huang, H. Z.; Huck, P.; Humanic, T. J.; Igo, G.; Jacobs, W. W.; Jena, C.; Judd, E. G.; Kabana, S.; Kang, K.; Kauder, K.; Ke, H. W.; Keane, D.; Kechechyan, A.; Kesich, A.; Kikola, D. P.; Kiryluk, J.; Kisel, I.; Kisiel, A.; Koetke, D. D.; Kollegger, T.; Konzer, J.; Koralt, I.; Korsch, W.; Kotchenda, L.; Kravtsov, P.; Krueger, K.; Kulakov, I.; Kumar, L.; Kycia, R. A.; Lamont, M. A. C.; Landgraf, J. M.; Landry, K. D.; LaPointe, S.; Lauret, J.; Lebedev, A.; Lednicky, R.; Lee, J. H.; Leight, W.; LeVine, M. J.; Li, C.; Li, W.; Li, X.; Li, X.; Li, Y.; Li, Z. M.; Lima, L. M.; Lisa, M. A.; Liu, F.; Ljubicic, T.; Llope, W. J.; Longacre, R. S.; Luo, X.; Ma, G. L.; Ma, Y. G.; Madagodagettige Don, D. M. M. D.; Mahapatra, D. P.; Majka, R.; Margetis, S.; Markert, C.; Masui, H.; Matis, H. S.; McDonald, D.; McShane, T. S.; Mioduszewski, S.; Mitrovski, M. K.; Mohammed, Y.; Mohanty, B.; Mondal, M. M.; Munhoz, M. G.; Mustafa, M. K.; Naglis, M.; Nandi, B. K.; Nasim, Md.; Nayak, T. K.; Nelson, J. M.; Nogach, L. V.; Novak, J.; Odyniec, G.; Ogawa, A.; Oh, K.; Ohlson, A.; Okorokov, V.; Oldag, E. W.; Oliveira, R. A. N.; Olson, D.; Pachr, M.; Page, B. S.; Pal, S. K.; Pan, Y. X.; Pandit, Y.; Panebratsev, Y.; Pawlak, T.; Pawlik, B.; Pei, H.; Perkins, C.; Peryt, W.; Pile, P.; Planinic, M.; Pluta, J.; Plyku, D.; Poljak, N.; Porter, J.; Poskanzer, A. M.; Powell, C. B.; Pruneau, C.; Pruthi, N. K.; Przybycien, M.; Pujahari, P. R.; Putschke, J.; Qiu, H.; Ramachandran, S.; Raniwala, R.; Raniwala, S.; Ray, R. L.; Riley, C. K.; Ritter, H. G.; Roberts, J. B.; Rogachevskiy, O. V.; Romero, J. L.; Ross, J. F.; Roy, A.; Ruan, L.; Rusnak, J.; Sahoo, N. R.; Sahu, P. K.; Sakrejda, I.; Salur, S.; Sandacz, A.; Sandweiss, J.; Sangaline, E.; Sarkar, A.; Schambach, J.; Scharenberg, R. P.; Schmah, A. M.; Schmidke, B.; Schmitz, N.; Schuster, T. R.; Seger, J.; Seyboth, P.; Shah, N.; Shahaliev, E.; Shao, M.; Sharma, B.; Sharma, M.; Shen, W. Q.; Shi, S. S.; Shou, Q. Y.; Sichtermann, E. P.; Singaraju, R. N.; Skoby, M. J.; Smirnov, D.; Smirnov, N.; Solanki, D.; Sorensen, P.; deSouza, U. G.; Spinka, H. M.; Srivastava, B.; Stanislaus, T. D. S.; Stevens, J. R.; Stock, R.; Strikhanov, M.; Stringfellow, B.; Suaide, A. A. P.; Suarez, M. C.; Sumbera, M.; Sun, X. M.; Sun, Y.; Sun, Z.; Surrow, B.; Svirida, D. N.; Symons, T. J. M.; Szanto de Toledo, A.; Takahashi, J.; Tang, A. H.; Tang, Z.; Tarini, L. H.; Tarnowsky, T.; Thomas, J. H.; Timmins, A. R.; Tlusty, D.; Tokarev, M.; Trentalange, S.; Tribble, R. E.; Tribedy, P.; Trzeciak, B. A.; Tsai, O. D.; Turnau, J.; Ullrich, T.; Underwood, D. G.; Van Buren, G.; van Nieuwenhuizen, G.; Vanfossen, J. A., Jr.; Varma, R.; Vasconcelos, G. M. S.; Vertesi, R.; Videbæk, F.; Viyogi, Y. P.; Vokal, S.; Voloshin, S. A.; Vossen, A.; Wada, M.; Walker, M.; Wang, F.; Wang, G.; Wang, H.; Wang, J. S.; Wang, Q.; Wang, X. L.; Wang, Y.; Webb, G.; Webb, J. C.; Westfall, G. D.; Wieman, H.; Wissink, S. W.; Witt, R.; Wu, Y. F.; Xiao, Z.; Xie, W.; Xin, K.; Xu, H.; Xu, N.; Xu, Q. H.; Xu, W.; Xu, Y.; Xu, Z.; Yan; Yang, C.; Yang, Y.; Yang, Y.; Yepes, P.; Yi, L.; Yip, K.; Yoo, I.-K.; Zawisza, Y.; Zbroszczyk, H.; Zha, W.; Zhang, J. B.; Zhang, S.; Zhang, X. P.; Zhang, Y.; Zhang, Z. P.; Zhao, F.; Zhao, J.; Zhong, C.; Zhu, X.; Zhu, Y. H.; Zoulkarneeva, Y.; Zyzak, M.

2013-09-01

We present measurements of three-dimensional correlation functions of like-sign, low-transverse-momentum kaon pairs from sNN=200 GeV Au+Au collisions. A Cartesian surface-spherical harmonic decomposition technique was used to extract the kaon source function. The latter was found to have a three-dimensional Gaussian shape and can be adequately reproduced by Therminator event-generator simulations with resonance contributions taken into account. Compared to the pion one, the kaon source function is generally narrower and does not have the long tail along the pair transverse momentum direction. The kaon Gaussian radii display a monotonic decrease with increasing transverse mass mT over the interval of 0.55≤mT≤1.15 GeV/c2. While the kaon radii are adequately described by the mT -scaling in the outward and sideward directions, in the longitudinal direction the lowest mT value exceeds the expectations from a pure hydrodynamical model prediction.

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

Perez, R. Navarro; Schunck, N.; Lasseri, R. -D.

Here, we describe the new version 3.00 of the code hfbtho that solves the nuclear Hartree–Fock (HF) or Hartree–Fock–Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle–hole and particle–particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scalemore » mass table calculations.« less

Deformation analysis of the unified lunar control networks

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

3DNALandscapes: a database for exploring the conformational features of DNA.

PubMed

Zheng, Guohui; Colasanti, Andrew V; Lu, Xiang-Jun; Olson, Wilma K

2010-01-01

3DNALandscapes, located at: http://3DNAscapes.rutgers.edu, is a new database for exploring the conformational features of DNA. In contrast to most structural databases, which archive the Cartesian coordinates and/or derived parameters and images for individual structures, 3DNALandscapes enables searches of conformational information across multiple structures. The database contains a wide variety of structural parameters and molecular images, computed with the 3DNA software package and known to be useful for characterizing and understanding the sequence-dependent spatial arrangements of the DNA sugar-phosphate backbone, sugar-base side groups, base pairs, base-pair steps, groove structure, etc. The data comprise all DNA-containing structures--both free and bound to proteins, drugs and other ligands--currently available in the Protein Data Bank. The web interface allows the user to link, report, plot and analyze this information from numerous perspectives and thereby gain insight into DNA conformation, deformability and interactions in different sequence and structural contexts. The data accumulated from known, well-resolved DNA structures can serve as useful benchmarks for the analysis and simulation of new structures. The collective data can also help to understand how DNA deforms in response to proteins and other molecules and undergoes conformational rearrangements.

Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2014-02-01

Three-dimensional fluid-structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

NASA Technical Reports Server (NTRS)

Kim, Hyoungin; Liou, Meng-Sing

2011-01-01

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems

PubMed Central

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2013-01-01

Three-dimensional fluid–structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration. PMID:24415796

Hybrid Solution-Adaptive Unstructured Cartesian Method for Large-Eddy Simulation of Detonation in Multi-Phase Turbulent Reactive Mixtures

DTIC Science & Technology

2012-03-27

pulse- detonation engines ( PDE ), stage separation, supersonic cav- ity oscillations, hypersonic aerodynamics, detonation induced structural...ADAPTIVE UNSTRUCTURED CARTESIAN METHOD FOR LARGE-EDDY SIMULATION OF DETONATION IN MULTI-PHASE TURBULENT REACTIVE MIXTURES 5b. GRANT NUMBER FA9550...CCL Report TR-2012-03-03 Hybrid Solution-Adaptive Unstructured Cartesian Method for Large-Eddy Simulation of Detonation in Multi-Phase Turbulent

Working the kinks out of nucleosomal DNA

PubMed Central

Olson, Wilma K.; Zhurkin, Victor B.

2011-01-01

Condensation of DNA in the nucleosome takes advantage of its double-helical architecture. The DNA deforms at sites where the base pairs face the histone octamer. The largest so-called kink-and-slide deformations occur in the vicinity of arginines that penetrate the minor groove. Nucleosome structures formed from the 601 positioning sequence differ subtly from those incorporating an AT-rich human α-satellite DNA. Restraints imposed by the histone arginines on the displacement of base pairs can modulate the sequence-dependent deformability of DNA and potentially contribute to the unique features of the different nucleosomes. Steric barriers mimicking constraints found in the nucleosome induce the simulated large-scale rearrangement of canonical B-DNA to kink-and-slide states. The pathway to these states shows non-harmonic behavior consistent with bending profiles inferred from AFM measurements. PMID:21482100

Deformation of Fluid Column by Action of Axial Vibration and Some Aspects of High-Rate Thermocapillary Convection

NASA Technical Reports Server (NTRS)

Feonychev, Alexander I.; Kalachinskaya, Irina S.; Pokhilko, Victor I.

1996-01-01

The deformation of the fluid column by an action of a low-frequency vibration is considered. It is shown that behavior of the free fluid surface depends on the frequency of applied vibration and its amplitude. In the area of very low frequencies when fluid has time to comment on travel of bounding solid walls limiting column, the harmonical oscillations of free surface with given frequency are observed. With increase of vibration frequency the steady-state relief on free fluid surface is formed. If the amplitude of vibration is very small and the frequency corresponding to the first peak in the vibration spectrum on the Mir orbital station, the deformation of free surface tends to zero. Fluid flow induced thermocapillary effect on deformed free surface is more unstable as in the case of smooth cylindrical surface. It was shown that width of heating zone affects very essentially the flow pattern and transition to oscillatory regime of thermocapillary convection.

Sink or Swim: The Cartesian Diver.

ERIC Educational Resources Information Center

Pinkerton, K. David

2001-01-01

Presents the activity of Cartesian divers which demonstrates the relationship between pressure, temperature, volume, and buoyancy. Includes both instructor information and student activity sheet. (YDS)

Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions

NASA Astrophysics Data System (ADS)

Dmitrieva, Ksenia; Hotovec-Ellis, Alicia J.; Prejean, Stephanie; Dunham, Eric M.

2013-08-01

Seismic unrest, indicative of subsurface magma transport and pressure changes within fluid-filled cracks and conduits, often precedes volcanic eruptions. An intriguing form of volcano seismicity is harmonic tremor, that is, sustained vibrations in the range of 0.5-5Hz. Many source processes can generate harmonic tremor. Harmonic tremor in the 2009 eruption of Redoubt Volcano, Alaska, has been linked to repeating earthquakes of magnitudes around 0.5-1.5 that occur a few kilometres beneath the vent. Before many explosions in that eruption, these small earthquakes occurred in such rapid succession--up to 30 events per second--that distinct seismic wave arrivals blurred into continuous, high-frequency tremor. Tremor abruptly ceased about 30 s before the explosions. Here we introduce a frictional-faulting model to evaluate the credibility and implications of this tremor mechanism. We find that the fault stressing rates rise to values ten orders of magnitude higher than in typical tectonic settings. At that point, inertial effects stabilize fault sliding and the earthquakes cease. Our model of the Redoubt Volcano observations implies that the onset of volcanic explosions is preceded by active deformation and extreme stressing within a localized region of the volcano conduit, at a depth of several kilometres.

Parameterization of deformed nuclei for Glauber modeling in relativistic heavy ion collisions

DOE PAGES

Sorensen, P.; Tang, A. H.; Videbaek, F.; ...

2015-08-04

In this study, the density distributions of large nuclei are typically modeled with a Woods–Saxon distribution characterized by a radius R 0 and skin depth a. Deformation parameters β are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics R 0(1+β 2Y 2 0+β 4Y 4 0). But when a nucleus is non-spherical, the R 0 and a inferred from electron scattering experiments that integrate over all nuclear orientations cannot be used directly as the parameters in the Woods–Saxon distribution. In addition, the β 2 values typically derived from the reduced electric quadrupole transition probability B(E2)↑ aremore » not directly related to the β 2 values used in the spherical harmonic expansion. B(E2)↑ is more accurately related to the intrinsic quadrupole moment Q 0 than to β 2. One can however calculate Q 0 for a given β 2 and then derive B(E2)↑ from Q 0. In this paper we calculate and tabulate the R 0, a , and β 2 values that when used in a Woods–Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the second and third harmonic participant eccentricity (ε 2 and ε 3) with the new and old parameters. We demonstrate that ε 3 is particularly sensitive to a and argue that using the incorrect value of a has important implications for the extraction of viscosity to entropy ratio (η/s) from the QGP created in Heavy Ion collisions.« less

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

NASA Astrophysics Data System (ADS)

Saleh, Mohammad; Alice Collaboration

2017-11-01

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

Adaptive mesh refinement techniques for the immersed interface method applied to flow problems

PubMed Central

Li, Zhilin; Song, Peng

2013-01-01

In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515–527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of |φ(x, y, t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. PMID:23794763

Accelerating volumetric cine MRI (VC-MRI) using undersampling for real-time 3D target localization/tracking in radiation therapy: a feasibility study

NASA Astrophysics Data System (ADS)

Harris, Wendy; Yin, Fang-Fang; Wang, Chunhao; Zhang, You; Cai, Jing; Ren, Lei

2018-01-01

Purpose. To accelerate volumetric cine MRI (VC-MRI) using undersampled 2D-cine MRI to provide real-time 3D guidance for gating/target tracking in radiotherapy. Methods. 4D-MRI is acquired during patient simulation. One phase of the prior 4D-MRI is selected as the prior images, designated as MRIprior. The on-board VC-MRI at each time-step is considered a deformation of the MRIprior. The deformation field map is represented as a linear combination of the motion components extracted by principal component analysis from the prior 4D-MRI. The weighting coefficients of the motion components are solved by matching the corresponding 2D-slice of the VC-MRI with the on-board undersampled 2D-cine MRI acquired. Undersampled Cartesian and radial k-space acquisition strategies were investigated. The effects of k-space sampling percentage (SP) and distribution, tumor sizes and noise on the VC-MRI estimation were studied. The VC-MRI estimation was evaluated using XCAT simulation of lung cancer patients and data from liver cancer patients. Volume percent difference (VPD) and Center of Mass Shift (COMS) of the tumor volumes and tumor tracking errors were calculated. Results. For XCAT, VPD/COMS were 11.93  ±  2.37%/0.90  ±  0.27 mm and 11.53  ±  1.47%/0.85  ±  0.20 mm among all scenarios with Cartesian sampling (SP  =  10%) and radial sampling (21 spokes, SP  =  5.2%), respectively. When tumor size decreased, higher sampling rate achieved more accurate VC-MRI than lower sampling rate. VC-MRI was robust against noise levels up to SNR  =  20. For patient data, the tumor tracking errors in superior-inferior, anterior-posterior and lateral (LAT) directions were 0.46  ±  0.20 mm, 0.56  ±  0.17 mm and 0.23  ±  0.16 mm, respectively, for Cartesian-based sampling with SP  =  20% and 0.60  ±  0.19 mm, 0.56  ±  0.22 mm and 0.42  ±  0.15 mm, respectively, for radial-based sampling with SP  =  8% (32 spokes). Conclusions. It is feasible to estimate VC-MRI from a single undersampled on-board 2D cine MRI. Phantom and patient studies showed that the temporal resolution of VC-MRI can potentially be improved by 5-10 times using a 2D cine image acquired with 10-20% k-space sampling.

Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers

PubMed Central

Zanchi, Marta G.; Pauly, John M.; Scott, Greig C.

2010-01-01

A modified Cartesian feedback method called “frequency-offset Cartesian feedback” and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems. In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200–1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback. In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems. PMID:20814450

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

NASA Technical Reports Server (NTRS)

Myhill, Elizabeth A.; Boss, Alan P.

1993-01-01

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

Material souls and imagination in late Aristotelian embryology.

PubMed

Blank, Andreas

2010-04-01

This article explores some continuities between Late Aristotelian and Cartesian embryology. In particular, it argues that there is an interesting consilience between some accounts of the role of imagination in trait acquisition in Late Aristotelian and Cartesian embryology. Evidence for this thesis is presented using the extensive biological writings of the Padua-based philosopher and physician, Fortunio Liceti (1577-1657). Like the Cartesian physiologists, Liceti believed that animal souls are material beings and that acts of imagination result in material images that can be transmitted by means of medical spirits to the embryo. Moreover, while the Cartesian embryologists accepted such a view in a quite speculative way, one finds penetrating criticism of imagination theories of trait acquisition in the Late Aristotelian tradition. Evidence for this thesis is presented using the no less extensive biological writings of Liceti's contemporary, Emilio Parisano (1567-1643). In conclusion, the Late Aristotelian tradition itself provides the theoretical tools for excising immaterial formative forces from embryology and at the same time evinces a much more acute sense for the problems inherent in imagination theories of trait acquisition than the Cartesian tradition.

Efficient Unstructured Cartesian/Immersed-Boundary Method with Local Mesh Refinement to Simulate Flows in Complex 3D Geometries

NASA Astrophysics Data System (ADS)

de Zelicourt, Diane; Ge, Liang; Sotiropoulos, Fotis; Yoganathan, Ajit

2008-11-01

Image-guided computational fluid dynamics has recently gained attention as a tool for predicting the outcome of different surgical scenarios. Cartesian Immersed-Boundary methods constitute an attractive option to tackle the complexity of real-life anatomies. However, when such methods are applied to the branching, multi-vessel configurations typically encountered in cardiovascular anatomies the majority of the grid nodes of the background Cartesian mesh end up lying outside the computational domain, increasing the memory and computational overhead without enhancing the numerical resolution in the region of interest. To remedy this situation, the method presented here superimposes local mesh refinement onto an unstructured Cartesian grid formulation. A baseline unstructured Cartesian mesh is generated by eliminating all nodes that reside in the exterior of the flow domain from the grid structure, and is locally refined in the vicinity of the immersed-boundary. The potential of the method is demonstrated by carrying out systematic mesh refinement studies for internal flow problems ranging in complexity from a 90 deg pipe bend to an actual, patient-specific anatomy reconstructed from magnetic resonance.

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

Higher-Order Containers

NASA Astrophysics Data System (ADS)

Altenkirch, Thorsten; Levy, Paul; Staton, Sam

Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications in generic programming and representation of higher order abstract syntax. We also show that the category of containers has finite limits, but it is not locally cartesian closed.

RDM lifetime measurements in 107Cd

NASA Astrophysics Data System (ADS)

Andgren, K.; Ashley, S. F.; Regan, P. H.; McCutchan, E. A.; Zamfir, N. V.; Amon, L.; Cakirli, R. B.; Casten, R. F.; Clark, R. M.; Gürdal, G.; Keyes, K. L.; Meyer, D. A.; Erduran, M. N.; Papenberg, A.; Pietralla, N.; Plettner, C.; Rainovski, G.; Ribas, R. V.; Thomas, N. J.; Vinson, J.; Warner, D. D.; Werner, V.; Williams, E.

2005-10-01

Lifetimes for decays linking near-yrast states in 107Cd have been measured using the recoil distance method (RDM). The nucleus of interest was populated via the 98Mo(12C,3n)107Cd fusion-evaporation reaction at an incident beam energy of 60 MeV. From the measured lifetimes, transition probabilities have been deduced and compared with the theoretical B(E2) values for limiting cases of harmonic vibrational and axially deformed rotational systems. Our initial results suggest a rotor-like behaviour for the structure based on the unnatural-parity, h11/2 orbital in 107Cd, providing further evidence for the role of this 'shape-polarizing' orbital in stabilizing the nuclear deformation in the A ~ 100 transitional region.

A Cartesian parametrization for the numerical analysis of material instability

DOE PAGES

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

2016-02-25

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

A Cartesian parametrization for the numerical analysis of material instability

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

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

Mouse manipulation through single-switch scanning.

PubMed

Blackstien-Adler, Susie; Shein, Fraser; Quintal, Janet; Birch, Shae; Weiss, Patrice L Tamar

2004-01-01

Given the current extensive reliance on the graphical user interface, independent access to computer software requires that users be able to manipulate a pointing device of some type (e.g., mouse, trackball) or be able to emulate a mouse by some other means (e.g., scanning). The purpose of the present study was to identify one or more optimal single-switch scanning mouse emulation strategies. Four alternative scanning strategies (continuous Cartesian, discrete Cartesian, rotational, and hybrid quadrant/continuous Cartesian) were selected for testing based on current market availability as well as on theoretical considerations of their potential speed and accuracy. Each strategy was evaluated using a repeated measures study design by means of a test program that permitted mouse emulation via any one of four scanning strategies in a motivating environment; response speed and accuracy could be automatically recorded and considered in view of the motor, cognitive, and perceptual demands of each scanning strategy. Ten individuals whose disabilities required them to operate a computer via single-switch scanning participated in the study. Results indicated that Cartesian scanning was the preferred and most effective scanning strategy. There were no significant differences between results from the Continuous Cartesian and Discrete Cartesian scanning strategies. Rotational scanning was quite slow with respect to the other strategies, although it was equally accurate. Hybrid Quadrant scanning improved access time but at the cost of fewer correct selections. These results demonstrated the importance of testing and comparing alternate single-switch scanning strategies.

Complex deformation associated with anhydrite layers in the Tromsø Basin, SW Barents Sea.

NASA Astrophysics Data System (ADS)

Marfo, George; Olakunle Omosanya, Kamaldeen; Johansen, Ståle Emil; Zervas, Ioannis

2017-04-01

Internal and external deformation associated with salt structures is of prime interest due to their economic importance as hydrocarbon seals, reservoirs, repositories for chemical waste and their implication on drilling. Salt structures are often associated with anhydrites, which may 'cap' or are enclosed within the allochthonous salt structures. Despite their economic importance, the internal and external structures of evaporites remain poorly studied from field and seismic data due to the sparse outcrops of evaporites and poor seismic imaging. The zero-phased, normal polarity, high resolution multiple 2D seismic data, in combination with detailed interpretation of wireline logs provide an excellent study into the salt structures, and offers a good opportunity to investigate the dynamics, geometries and mechanisms driving deformation of internal and external salt layers associated with the Late Carboniferous to Early Permian Salt structures in the Tromsø Basin. The methods include seismic interpretation and the application of multiple seismic attributes to map stratigraphic units and discontinuities. Our results show that the anhydrite layers are marked by high amplitude reflections at the crests and flanks or fully enclosed within the salt diapirs. Crestal and lateral anhydrite caprocks represent external salt structures whilst the entrained anhydrites or stringers are intrasalt structures. Anhydrite caprocks generally show structural styles such as faults and large-scale folds which are harmonic to the top salt structure. In contrast, anhydrite stringers show folds of varying scale, which are harmonic to disharmonic to the top salt structure. Boudins and steeply dipping stringer fragments are also interpreted within the stringers. Caprock deformation is attributed to salt upwelling. Folding and boudinaging of originally horizontal and continuous stringer layers formed from a multiphase superimposed sequence of ductile and brittle deformation in response to complex multi-dimensional salt flow. Internal salt flow involves radial and tangential compression, which leads to dominant fold structures near the margins. Boudins on the lower flanks of the diapir formed due radial extension. Our study further demonstrates that differential geometries exhibited by the different anhydrite groups imply that the mechanisms deforming internal and external salt structures are different. The results from this study are comparable to observations from salt mines, field exposures, scaled physical and numerical models.

Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions

USGS Publications Warehouse

Dmitrieva, Ksenia; Hotovec-Ellis, Alicia J.; Prejean, Stephanie G.; Dunham, Eric M.

2013-01-01

Seismic unrest, indicative of subsurface magma transport and pressure changes within fluid-filled cracks and conduits, often precedes volcanic eruptions. An intriguing form of volcano seismicity is harmonic tremor, that is, sustained vibrations in the range of 0.5–5 Hz. Many source processes can generate harmonic tremor. Harmonic tremor in the 2009 eruption of Redoubt Volcano, Alaska, has been linked to repeating earthquakes of magnitudes around 0.5–1.5 that occur a few kilometres beneath the vent. Before many explosions in that eruption, these small earthquakes occurred in such rapid succession—up to 30 events per second—that distinct seismic wave arrivals blurred into continuous, high-frequency tremor. Tremor abruptly ceased about 30 s before the explosions. Here we introduce a frictional-faulting model to evaluate the credibility and implications of this tremor mechanism. We find that the fault stressing rates rise to values ten orders of magnitude higher than in typical tectonic settings. At that point, inertial effects stabilize fault sliding and the earthquakes cease. Our model of the Redoubt Volcano observations implies that the onset of volcanic explosions is preceded by active deformation and extreme stressing within a localized region of the volcano conduit, at a depth of several kilometres.

Self-sustained oscillations of a sinusoidally-deformed plate

NASA Astrophysics Data System (ADS)

Muriel, Diego F.; Cowen, Edwin A.

2015-11-01

Motivated by energy harvesting, the oscillatory motion of a deformed elastic material with aspect ratio Length/Width=2, immerse in an incompressible flow is studied experimentally. To induce the wave-like deformation a polycarbonate sheet is placed under longitudinal compression with external forcing provided by equispaced tension lines anchored in a frame. No additional constrains are placed in the material. Based on quantitative image-based edge detection, ADV, and PIV measurements, we document the existence of three natural states of motion. Bellow a critical velocity, a stable state presents a sinusoidal-like deformation with weak small perturbations. Above a critical velocity, instability appears in the form of a traveling wave with predictable dominant frequency accompanied by higher-order harmonics. As the flow velocity increases the instability converges faster to its limit cycle in the phase plane (e.g., vertical velocity and position), until the stable oscillatory mode transitions to chaos showing a broad energy spectrum and unstable limit cycle. The underlying objective is to induce the onset of the instability at lower critical velocities for higher bending rigidities, promoting possible energy extraction and increasing the range at which stable oscillations appear.

High-Reynolds Number Viscous Flow Simulations on Embedded-Boundary Cartesian Grids

DTIC Science & Technology

2016-05-05

d ) 2 χ ≥ 0 −cw1 ( ν̃d ) 2 otherwise (6) 2 DISTRIBUTION A: Distribution approved for public release. with νt = ν̃fv1 and the usual definitions of fw...1 The wall function is coupled to the underlying Cartesian grid through its endpoints. This is illustrated schematically in Fig. 2 . At the wall it is...by interpolation from the Cartesian grid . This eliminates the problem of uτ → 0 , since this works in physical coordinates and not plus coordinates. We

On automating domain connectivity for overset grids

NASA Technical Reports Server (NTRS)

Chiu, Ing-Tsau

1994-01-01

An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximated body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian Systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems.

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Parameter Studies, time-dependent simulations and design with automated Cartesian methods

NASA Technical Reports Server (NTRS)

Aftosmis, Michael

2005-01-01

Over the past decade, NASA has made a substantial investment in developing adaptive Cartesian grid methods for aerodynamic simulation. Cartesian-based methods played a key role in both the Space Shuttle Accident Investigation and in NASA's return to flight activities. The talk will provide an overview of recent technological developments focusing on the generation of large-scale aerodynamic databases, automated CAD-based design, and time-dependent simulations with of bodies in relative motion. Automation, scalability and robustness underly all of these applications and research in each of these topics will be presented.

Oceanic lithospheric magnetisation: Forward modelling and analysis using vector spherical harmonics (Invited)

NASA Astrophysics Data System (ADS)

Masterton, S. M.; Gubbins, D.; Müller, D.; Williams, S.

2013-12-01

The lithospheric contribution to the geomagnetic field arises from magnetised rocks that are cooler than the Curie temperature of their constituent minerals. Inversion of the magnetic field for this magnetisation is subject to inherent non-uniqueness, as many magnetisation distributions yield no potential field outside of the lithosphere. Such distributions are termed annihilators. We use a complete set of orthogonal vector spherical harmonics that separate the part of the magnetisation responsible for the magnetic field observed above the Earth's surface from the annihilators. A similar set of vector harmonics has been developed in Cartesian geometry suitable for small scale, industrial applications. In an attempt to quantify the significance of the annihilators, we first construct a global model of vertically integrated magnetisation (VIM) by combining a model of remanent magnetisation for the oceans with a previous model of induced magnetisation for the whole Earth. Remanence is computed by assigning magnetisations to the oceanic lithosphere acquired at the location and time of formation. The magnetising field is assumed to be an axial dipole that switches polarity with the reversal time scale. The magnetisation evolves with time by decay of thermal remanence and acquisition of chemical remanence. Remanence directions are calculated by implementing finite rotations of the original geomagnetic field direction with respect to an absolute reference frame. We then represent our estimated VIM in terms of vector spherical harmonics, to allow us to evaluate its relative contributions to a potential field that is observable outside of the lithosphere and to fields (both potential and non-potential) that are not observable. This analysis shows that our model of magnetisation is dominated by a part of the magnetisation that produces a potential field restricted to Earth's sub-lithospheric interior; it therefore contributes significantly to the huge null space in the inversion of lithospheric magnetic anomaly data for VIM. We calculate the observable potential field that arises from our magnetisation estimates and compare it with a model that is based upon satellite data (MF7); this allows us to evaluate our magnetisation estimates and suggest likely sources of error in areas with high misfit between our predictions and the observed magnetic field. For example, under-prediction of the observed magnetic field may be indicative of poorly-known magnetisation deep in the crust or upper mantle, locally underplated continental lithosphere or anomalous oceanic crust.

Vibrational entropy of a protein: large differences between distinct conformations.

PubMed

Goethe, Martin; Fita, Ignacio; Rubi, J Miguel

2015-01-13

In this article, it is investigated whether vibrational entropy (VE) is an important contribution to the free energy of globular proteins at ambient conditions. VE represents the major configurational-entropy contribution of these proteins. By definition, it is an average of the configurational entropies of the protein within single minima of the energy landscape, weighted by their occupation probabilities. Its large part originates from thermal motion of flexible torsion angles giving rise to the finite peak widths observed in torsion angle distributions. While VE may affect the equilibrium properties of proteins, it is usually neglected in numerical calculations as its consideration is difficult. Moreover, it is sometimes believed that all well-packed conformations of a globular protein have similar VE anyway. Here, we measure explicitly the VE for six different conformations from simulation data of a test protein. Estimates are obtained using the quasi-harmonic approximation for three coordinate sets, Cartesian, bond-angle-torsion (BAT), and a new set termed rotamer-degeneracy lifted BAT coordinates by us. The new set gives improved estimates as it overcomes a known shortcoming of the quasi-harmonic approximation caused by multiply populated rotamer states, and it may serve for VE estimation of macromolecules in a very general context. The obtained VE values depend considerably on the type of coordinates used. However, for all coordinate sets we find large entropy differences between the conformations, of the order of the overall stability of the protein. This result may have important implications on the choice of free energy expressions used in software for protein structure prediction, protein design, and NMR refinement.

A 2.5D Computational Method to Simulate Cylindrical Fluidized Beds

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

Li, Tingwen; Benyahia, Sofiane; Dietiker, Jeff

2015-02-17

In this paper, the limitations of axisymmetric and Cartesian two-dimensional (2D) simulations of cylindrical gas-solid fluidized beds are discussed. A new method has been proposed to carry out pseudo-two-dimensional (2.5D) simulations of a cylindrical fluidized bed by appropriately combining computational domains of Cartesian 2D and axisymmetric simulations. The proposed method was implemented in the open-source code MFIX and applied to the simulation of a lab-scale bubbling fluidized bed with necessary sensitivity study. After a careful grid study to ensure the numerical results are grid independent, detailed comparisons of the flow hydrodynamics were presented against axisymmetric and Cartesian 2D simulations. Furthermore,more » the 2.5D simulation results have been compared to the three-dimensional (3D) simulation for evaluation. This new approach yields better agreement with the 3D simulation results than with axisymmetric and Cartesian 2D simulations.« less

A climatically-derived global soil moisture data set for use in the GLAS atmospheric circulation model seasonal cycle experiment

NASA Technical Reports Server (NTRS)

Willmott, C. J.; Field, R. T.

1984-01-01

Algorithms for point interpolation and contouring on the surface of the sphere and in Cartesian two-space are developed from Shepard's (1968) well-known, local search method. These mapping procedures then are used to investigate the errors which appear on small-scale climate maps as a result of the all-too-common practice of of interpolating, from irregularly spaced data points to the nodes of a regular lattice, and contouring Cartesian two-space. Using mean annual air temperatures field over the western half of the northern hemisphere is estimated both on the sphere, assumed to be correct, and in Cartesian two-space. When the spherically- and Cartesian-approximted air temperature fields are mapped and compared, the magnitudes (as large as 5 C to 10 C) and distribution of the errors associated with the latter approach become apparent.

Efficient Fluid Dynamic Design Optimization Using Cartesian Grids

NASA Technical Reports Server (NTRS)

Dadone, A.; Grossman, B.; Sellers, Bill (Technical Monitor)

2004-01-01

This report is subdivided in three parts. The first one reviews a new approach to the computation of inviscid flows using Cartesian grid methods. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, which satisfies the normal momentum equation and the non-penetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we call the Ghost Body-Cell Method (GBCM). In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells which complicate other Cartesian mesh methods.

A Cartesian grid approach with hierarchical refinement for compressible flows

NASA Technical Reports Server (NTRS)

Quirk, James J.

1994-01-01

Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.

Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses.

PubMed

Ishii, Nobuhisa; Kaneshima, Keisuke; Kitano, Kenta; Kanai, Teruto; Watanabe, Shuntaro; Itatani, Jiro

2014-01-01

High harmonic generation (HHG) using waveform-controlled, few-cycle pulses from Ti:sapphire lasers has opened emerging researches in strong-field and attosecond physics. However, the maximum photon energy of attosecond pulses via HHG remains limited to the extreme ultraviolet region. Long-wavelength light sources with carrier-envelope phase stabilization are promising to extend the photon energy of attosecond pulses into the soft X-ray region. Here we demonstrate carrier-envelope phase-dependent HHG in the water window using sub-two-cycle optical pulses at 1,600 nm. Experimental and simulated results indicate the confinement of soft X-ray emission in a single recombination event with a bandwidth of 75 eV around the carbon K edge. Control of high harmonics by the waveform of few-cycle infrared pulses is a key milestone to generate soft X-ray attosecond pulses. We measure a dependence of half-cycle bursts on the gas pressure, which indicates subcycle deformation of the waveform of the infrared drive pulses in the HHG process.

Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses

PubMed Central

Ishii, Nobuhisa; Kaneshima, Keisuke; Kitano, Kenta; Kanai, Teruto; Watanabe, Shuntaro; Itatani, Jiro

2014-01-01

High harmonic generation (HHG) using waveform-controlled, few-cycle pulses from Ti:sapphire lasers has opened emerging researches in strong-field and attosecond physics. However, the maximum photon energy of attosecond pulses via HHG remains limited to the extreme ultraviolet region. Long-wavelength light sources with carrier-envelope phase stabilization are promising to extend the photon energy of attosecond pulses into the soft X-ray region. Here we demonstrate carrier-envelope phase-dependent HHG in the water window using sub-two-cycle optical pulses at 1,600 nm. Experimental and simulated results indicate the confinement of soft X-ray emission in a single recombination event with a bandwidth of 75 eV around the carbon K edge. Control of high harmonics by the waveform of few-cycle infrared pulses is a key milestone to generate soft X-ray attosecond pulses. We measure a dependence of half-cycle bursts on the gas pressure, which indicates subcycle deformation of the waveform of the infrared drive pulses in the HHG process. PMID:24535006

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

Pramanik, Souvik, E-mail: souvick.in@gmail.com; Moussa, Mohamed, E-mail: mohamed.ibrahim@fsc.bu.edu.eg; Faizal, Mir, E-mail: f2mir@uwaterloo.ca

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. Withmore » this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.« less

Exciting (and modulating) very-long-period seismic signals on White Island, New Zealand

NASA Astrophysics Data System (ADS)

Neuberg, Jurgen; Jolly, Art

2014-05-01

Very-long-period seismic signals (VLP) on volcanoes can be used to fill the gap between classic seismology and deformation studies. In this contribution we reiterate the principal processing steps to retrieve from a velocity seismogram 3D ground displacement with tiny amplitudes far beyond the resolution of GPS. As a case study we use several seismic and infrasonic signals of volcanic events from White Island, New Zealand. We apply particle motion analysis and deformation modelling tools to the resulting displacement signals and exam the potential link between ground displacement and the modulation of harmonic tremor, in turn linked to a hydrothermal system. In this way we want to demonstrate the full potential of VLPs in monitoring and modelling of volcanic processes.

Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces.

PubMed

Di Claudio, Elio D; Jacovitti, Giovanni; Laurenti, Alberto

2010-05-01

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

SACR ADVance 3-D Cartesian Cloud Cover (SACR-ADV-3D3C) product

DOE Data Explorer

Meng Wang, Tami Toto, Eugene Clothiaux, Katia Lamer, Mariko Oue

2017-03-08

SACR-ADV-3D3C remaps the outputs of SACRCORR for cross-wind range-height indicator (CW-RHI) scans to a Cartesian grid and reports reflectivity CFAD and best estimate domain averaged cloud fraction. The final output is a single NetCDF file containing all aforementioned corrected radar moments remapped on a 3-D Cartesian grid, the SACR reflectivity CFAD, a profile of best estimate cloud fraction, a profile of maximum observable x-domain size (xmax), a profile time to horizontal distance estimate and a profile of minimum observable reflectivity (dBZmin).

[Mental interiority in the early-modern age. The "Cartesian theater"].

PubMed

Gillot, Pascale

2010-01-01

This paper looks into the notion of mental interiority in the early-modern age and, more specifically, into the Cartesian conception of the mind as an "inner theater". The main claim emphasizes a close connexion at work between the representative theory of the mind, associated with internalism, on the one hand, and a "neuropsychological" view on the other hand. Cartesian mentalism, in so far as it is based upon a disjunction between representation and resemblance, can therefore not be separated from the general project, already at work in the Dioptrique, of an intra-cerebral localization of the mental.

Dual redundant arm system operational quality measures and their applications - Dynamic measures

NASA Technical Reports Server (NTRS)

Lee, Sukhan; Kim, Sungbok

1990-01-01

Dual-arm dynamic operation quality measures are presented which quantify the efficiency and capability of generating Cartesian accelerations by two cooperative arms based on the analysis of dual-arm dynamic interactions. Dual-arm dynamic manipulability is defined as the efficiency of generating Cartesian accelerations under the dynamic and kinematic interactions between individual arms and an object under manipulation. The analysis of dual-arm dynamic interactions is based on the so-called Cartesian space agent model of an arm, which represents an individual arm as a force source acting upon a point mass with the effective Cartesian space arm dynamics and an environment or an object under manipulation. The Cartesian space agent model of an arm makes it possible to derive the dynamic and kinematic constraints involved in the transport, assembly and grasping modes of dual-arm cooperation. A task-oriented operational quality measure, (TOQd) is defined by evaluating dual-arm dynamic manipulability in terms of given task requirements. TOQd is used in dual-arm joint configuration optimization. Simulation results are shown. A complete set of forward dynamic equations for a dual-arm system is derived, and dual-arm dynamic operational quality measures for various modes of dual-arm cooperation allowing sliding contacts are established.

Stopping Criteria for Log-Domain Diffeomorphic Demons Registration: An Experimental Survey for Radiotherapy Application.

PubMed

Peroni, M; Golland, P; Sharp, G C; Baroni, G

2016-02-01

A crucial issue in deformable image registration is achieving a robust registration algorithm at a reasonable computational cost. Given the iterative nature of the optimization procedure an algorithm must automatically detect convergence, and stop the iterative process when most appropriate. This paper ranks the performances of three stopping criteria and six stopping value computation strategies for a Log-Domain Demons Deformable registration method simulating both a coarse and a fine registration. The analyzed stopping criteria are: (a) velocity field update magnitude, (b) mean squared error, and (c) harmonic energy. Each stoping condition is formulated so that the user defines a threshold ∊, which quantifies the residual error that is acceptable for the particular problem and calculation strategy. In this work, we did not aim at assigning a value to e, but to give insights in how to evaluate and to set the threshold on a given exit strategy in a very popular registration scheme. Experiments on phantom and patient data demonstrate that comparing the optimization metric minimum over the most recent three iterations with the minimum over the fourth to sixth most recent iterations can be an appropriate algorithm stopping strategy. The harmonic energy was found to provide best trade-off between robustness and speed of convergence for the analyzed registration method at coarse registration, but was outperformed by mean squared error when all the original pixel information is used. This suggests the need of developing mathematically sound new convergence criteria in which both image and vector field information could be used to detect the actual convergence, which could be especially useful when considering multi-resolution registrations. Further work should be also dedicated to study same strategies performances in other deformable registration methods and body districts. © The Author(s) 2014.

CHIC - Coupling Habitability, Interior and Crust

NASA Astrophysics Data System (ADS)

Noack, Lena; Labbe, Francois; Boiveau, Thomas; Rivoldini, Attilio; Van Hoolst, Tim

2014-05-01

We present a new code developed for simulating convection in terrestrial planets and icy moons. The code CHIC is written in Fortran and employs the finite volume method and finite difference method for solving energy, mass and momentum equations in either silicate or icy mantles. The code uses either Cartesian (2D and 3D box) or spherical coordinates (2D cylinder or annulus). It furthermore contains a 1D parametrised model to obtain temperature profiles in specific regions, for example in the iron core or in the silicate mantle (solving only the energy equation). The 2D/3D convection model uses the same input parameters as the 1D model, which allows for comparison of the different models and adaptation of the 1D model, if needed. The code has already been benchmarked for the following aspects: - viscosity-dependent rheology (Blankenbach et al., 1989) - pseudo-plastic deformation (Tosi et al., in preparation phase) - subduction mechanism and plastic deformation (Quinquis et al., in preparation phase) New features that are currently developed and benchmarked include: - compressibility (following King et al., 2009 and Leng and Zhong, 2008) - different melt modules (Plesa et al., in preparation phase) - freezing of an inner core (comparison with GAIA code, Huettig and Stemmer, 2008) - build-up of oceanic and continental crust (Noack et al., in preparation phase) The code represents a useful tool to couple the interior with the surface of a planet (e.g. via build-up and erosion of crust) and it's atmosphere (via outgassing on the one hand and subduction of hydrated crust and carbonates back into the mantle). It will be applied to investigate several factors that might influence the habitability of a terrestrial planet, and will also be used to simulate icy bodies with high-pressure ice phases. References: Blankenbach et al. (1989). A benchmark comparison for mantle convection codes. GJI 98, 23-38. Huettig and Stemmer (2008). Finite volume discretization for dynamic viscosities on Voronoi grids. PEPI 171(1-4), 137-146. King et al. (2009). A Community Benchmark for 2D Cartesian Compressible Convection in the Earth's Mantle. GJI 179, 1-11. Leng and Zhong (2008). Viscous heating, adiabatic heating and energetic consistency in compressible mantle convection. GJI 173, 693-702.

Simulation of moving boundaries interacting with compressible reacting flows using a second-order adaptive Cartesian cut-cell method

NASA Astrophysics Data System (ADS)

Muralidharan, Balaji; Menon, Suresh

2018-03-01

A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [1] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge-Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen-oxygen-argon mixture is studied and a qualitative comparison of the results with the experimental data are made. Results indicate that the current method is able to correctly reproduce the different regimes of combustion observed in the experiments. Through the various examples it is demonstrated that our method is robust and accurate for simulation of compressible viscous reacting flow problems with moving/deforming boundaries.

Analysis, design, fabrication, and performance of three-dimensional braided composites

NASA Astrophysics Data System (ADS)

Kostar, Timothy D.

1998-11-01

Cartesian 3-D (track and column) braiding as a method of composite preforming has been investigated. A complete analysis of the process was conducted to understand the limitations and potentials of the process. Knowledge of the process was enhanced through development of a computer simulation, and it was discovered that individual control of each track and column and multiple-step braid cycles greatly increases possible braid architectures. Derived geometric constraints coupled with the fundamental principles of Cartesian braiding resulted in an algorithm to optimize preform geometry in relation to processing parameters. The design of complex and unusual 3-D braids was investigated in three parts: grouping of yarns to form hybrid composites via an iterative simulation; design of composite cross-sectional shape through implementation of the Universal Method; and a computer algorithm developed to determine the braid plan based on specified cross-sectional shape. Several 3-D braids, which are the result of variations or extensions to Cartesian braiding, are presented. An automated four-step braiding machine with axial yarn insertion has been constructed and used to fabricate two-step, double two-step, four-step, and four-step with axial and transverse yarn insertion braids. A working prototype of a multi-step braiding machine was used to fabricate four-step braids with surrogate material insertion, unique hybrid structures from multiple track and column displacement and multi-step cycles, and complex-shaped structures with constant or varying cross-sections. Braid materials include colored polyester yarn to study the yarn grouping phenomena, Kevlar, glass, and graphite for structural reinforcement, and polystyrene, silicone rubber, and fasteners for surrogate material insertion. A verification study for predicted yarn orientation and volume fraction was conducted, and a topological model of 3-D braids was developed. The solid model utilizes architectural parameters, generated from the process simulation, to determine the composite elastic properties. Methods of preform consolidation are investigated and the results documented. The extent of yarn deformation (packing) resulting from preform consolidation was investigated through cross-sectional micrographs. The fiber volume fraction of select hybrid composites was measured and representative unit cells are suggested. Finally, a comparison study of the elastic performance of Kevlar/epoxy and carbon/Kevlar hybrid composites was conducted.

An automated, quantitative, and case-specific evaluation of deformable image registration in computed tomography images

NASA Astrophysics Data System (ADS)

Kierkels, R. G. J.; den Otter, L. A.; Korevaar, E. W.; Langendijk, J. A.; van der Schaaf, A.; Knopf, A. C.; Sijtsema, N. M.

2018-02-01

A prerequisite for adaptive dose-tracking in radiotherapy is the assessment of the deformable image registration (DIR) quality. In this work, various metrics that quantify DIR uncertainties are investigated using realistic deformation fields of 26 head and neck and 12 lung cancer patients. Metrics related to the physiologically feasibility (the Jacobian determinant, harmonic energy (HE), and octahedral shear strain (OSS)) and numerically robustness of the deformation (the inverse consistency error (ICE), transitivity error (TE), and distance discordance metric (DDM)) were investigated. The deformable registrations were performed using a B-spline transformation model. The DIR error metrics were log-transformed and correlated (Pearson) against the log-transformed ground-truth error on a voxel level. Correlations of r  ⩾  0.5 were found for the DDM and HE. Given a DIR tolerance threshold of 2.0 mm and a negative predictive value of 0.90, the DDM and HE thresholds were 0.49 mm and 0.014, respectively. In conclusion, the log-transformed DDM and HE can be used to identify voxels at risk for large DIR errors with a large negative predictive value. The HE and/or DDM can therefore be used to perform automated quality assurance of each CT-based DIR for head and neck and lung cancer patients.

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

Khamzin, A. A., E-mail: airat.khamzin@rambler.ru; Sitdikov, A. S.; Nikitin, A. S.

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.

Data on processing of Ti-25Nb-25Zr β-titanium alloys via powder metallurgy route: Methodology, microstructure and mechanical properties.

PubMed

Ueda, D; Dirras, G; Hocini, A; Tingaud, D; Ameyama, K; Langlois, P; Vrel, D; Trzaska, Z

2018-04-01

The data presented in this article are related to the research article entitled "Cyclic Shear behavior of conventional and harmonic structure-designed Ti-25Nb-25Zr β-titanium alloy: Back-stress hardening and twinning inhibition" (Dirras et al., 2017) [1]. The datasheet describes the methods used to fabricate two β-titanium alloys having conventional microstructure and so-called harmonic structure (HS) design via a powder metallurgy route, namely the spark plasma sintering (SPS) route. The data show the as-processed unconsolidated powder microstructures as well as the post-SPS ones. The data illustrate the mechanical response under cyclic shear loading of consolidated alloy specimens. The data show how electron back scattering diffraction(EBSD) method is used to clearly identify induced deformation features in the case of the conventional alloy.

Acoustic Characteristics in Epiglottic Cyst.

PubMed

Lee, YeonWoo; Kim, GeunHyo; Wang, SooGeun; Jang, JeonYeob; Cha, Wonjae; Choi, HongSik; Kim, HyangHee

2018-05-03

The purpose of this study was to analyze the acoustic characteristics associated with alternation deformation of the vocal tract due to large epiglottic cyst, and to confirm the relation between the anatomical change and resonant function of the vocal tract. Eight men with epiglottic cyst were enrolled in this study. The jitter, shimmer, noise-to-harmonic ratio, and first two formants were analyzed in vowels /a:/, /e:/, /i:/, /o:/, and /u:/. These values were analyzed before and after laryngeal microsurgery. The F1 value of /a:/ was significantly raised after surgery. Significant differences of formant frequencies in other vowels, jitter, shimmer, and noise-to-harmonic ratio were not presented. The results of this study could be used to analyze changes in the resonance of vocal tracts due to the epiglottic cysts. Copyright © 2018 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Retrospectively gated intracardiac 4D flow MRI using spiral trajectories.

PubMed

Petersson, Sven; Sigfridsson, Andreas; Dyverfeldt, Petter; Carlhäll, Carl-Johan; Ebbers, Tino

2016-01-01

To develop and evaluate retrospectively gated spiral readout four-dimensional (4D) flow MRI for intracardiac flow analysis. Retrospectively gated spiral 4D flow MRI was implemented on a 1.5-tesla scanner. The spiral sequence was compared against conventional Cartesian 4D flow (SENSE [sensitivity encoding] 2) in seven healthy volunteers and three patients (only spiral). In addition to comparing flow values, linear regression was used to assess internal consistency of aortic versus pulmonary net volume flows and left ventricular inflow versus outflow using quantitative pathlines analysis. Total scan time with spiral 4D flow was 44% ± 6% of the Cartesian counterpart (13 ± 3 vs. 31 ± 7 min). Aortic versus pulmonary flow correlated strongly for the spiral sequence (P < 0.05, slope = 1.03, R(2) = 0.88, N = 10), whereas the linear relationship for the Cartesian sequence was not significant (P = 0.06, N = 7). Pathlines analysis indicated good data quality for the spiral (P < 0.05, slope = 1.02, R(2) = 0.90, N = 10) and Cartesian sequence (P < 0.05, slope = 1.10, R(2) = 0.93, N = 7). Spiral and Cartesian peak flow rate (P < 0.05, slope = 0.96, R(2) = 0.72, N = 14), peak velocity (P < 0.05, slope = 1.00, R(2) = 0.81, N = 14), and pathlines flow components (P < 0.05, slope = 1.04, R(2) = 0.87, N = 28) correlated well. Retrospectively gated spiral 4D flow MRI permits more than two-fold reduction in scan time compared to conventional Cartesian 4D flow MRI, while maintaining similar data quality. © 2015 Wiley Periodicals, Inc.

Application of overlay modeling and control with Zernike polynomials in an HVM environment

NASA Astrophysics Data System (ADS)

Ju, JaeWuk; Kim, MinGyu; Lee, JuHan; Nabeth, Jeremy; Jeon, Sanghuck; Heo, Hoyoung; Robinson, John C.; Pierson, Bill

2016-03-01

Shrinking technology nodes and smaller process margins require improved photolithography overlay control. Generally, overlay measurement results are modeled with Cartesian polynomial functions for both intra-field and inter-field models and the model coefficients are sent to an advanced process control (APC) system operating in an XY Cartesian basis. Dampened overlay corrections, typically via exponentially or linearly weighted moving average in time, are then retrieved from the APC system to apply on the scanner in XY Cartesian form for subsequent lot exposure. The goal of the above method is to process lots with corrections that target the least possible overlay misregistration in steady state as well as in change point situations. In this study, we model overlay errors on product using Zernike polynomials with same fitting capability as the process of reference (POR) to represent the wafer-level terms, and use the standard Cartesian polynomials to represent the field-level terms. APC calculations for wafer-level correction are performed in Zernike basis while field-level calculations use standard XY Cartesian basis. Finally, weighted wafer-level correction terms are converted to XY Cartesian space in order to be applied on the scanner, along with field-level corrections, for future wafer exposures. Since Zernike polynomials have the property of being orthogonal in the unit disk we are able to reduce the amount of collinearity between terms and improve overlay stability. Our real time Zernike modeling and feedback evaluation was performed on a 20-lot dataset in a high volume manufacturing (HVM) environment. The measured on-product results were compared to POR and showed a 7% reduction in overlay variation including a 22% terms variation. This led to an on-product raw overlay Mean + 3Sigma X&Y improvement of 5% and resulted in 0.1% yield improvement.

Neural coding of image structure and contrast polarity of Cartesian, hyperbolic, and polar gratings in the primary and secondary visual cortex of the tree shrew.

PubMed

Poirot, Jordan; De Luna, Paolo; Rainer, Gregor

2016-04-01

We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. Copyright © 2016 the American Physiological Society.

Optimization and validation of accelerated golden-angle radial sparse MRI reconstruction with self-calibrating GRAPPA operator gridding.

PubMed

Benkert, Thomas; Tian, Ye; Huang, Chenchan; DiBella, Edward V R; Chandarana, Hersh; Feng, Li

2018-07-01

Golden-angle radial sparse parallel (GRASP) MRI reconstruction requires gridding and regridding to transform data between radial and Cartesian k-space. These operations are repeatedly performed in each iteration, which makes the reconstruction computationally demanding. This work aimed to accelerate GRASP reconstruction using self-calibrating GRAPPA operator gridding (GROG) and to validate its performance in clinical imaging. GROG is an alternative gridding approach based on parallel imaging, in which k-space data acquired on a non-Cartesian grid are shifted onto a Cartesian k-space grid using information from multicoil arrays. For iterative non-Cartesian image reconstruction, GROG is performed only once as a preprocessing step. Therefore, the subsequent iterative reconstruction can be performed directly in Cartesian space, which significantly reduces computational burden. Here, a framework combining GROG with GRASP (GROG-GRASP) is first optimized and then compared with standard GRASP reconstruction in 22 prostate patients. GROG-GRASP achieved approximately 4.2-fold reduction in reconstruction time compared with GRASP (∼333 min versus ∼78 min) while maintaining image quality (structural similarity index ≈ 0.97 and root mean square error ≈ 0.007). Visual image quality assessment by two experienced radiologists did not show significant differences between the two reconstruction schemes. With a graphics processing unit implementation, image reconstruction time can be further reduced to approximately 14 min. The GRASP reconstruction can be substantially accelerated using GROG. This framework is promising toward broader clinical application of GRASP and other iterative non-Cartesian reconstruction methods. Magn Reson Med 80:286-293, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

PubMed Central

Kang, Chang-kwon; Shyy, Wei

2013-01-01

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots. PMID:23760300

XTRAN2L - A PROGRAM FOR SOLVING THE GENERAL-FREQUENCY UNSTEADY TWO-DIMENSIONAL TRANSONIC SMALL-DISTURBANCE EQUATIONS

NASA Technical Reports Server (NTRS)

Seidel, D. A.

1994-01-01

The Program for Solving the General-Frequency Unsteady Two-Dimensional Transonic Small-Disturbance Equation, XTRAN2L, is used to calculate time-accurate, finite-difference solutions of the nonlinear, small-disturbance potential equation for two- dimensional transonic flow about airfoils. The code can treat forced harmonic, pulse, or aeroelastic transient type motions. XTRAN2L uses a transonic small-disturbance equation that incorporates a time accurate finite-difference scheme. Airfoil flow tangency boundary conditions are defined to include airfoil contour, chord deformation, nondimensional plunge displacement, pitch, and trailing edge control surface deflection. Forced harmonic motion can be based on: 1) coefficients of harmonics based on information from each quarter period of the last cycle of harmonic motion; or 2) Fourier analyses of the last cycle of motion. Pulse motion (an alternate to forced harmonic motion) in which the airfoil is given a small prescribed pulse in a given mode of motion, and the aerodynamic transients are calculated. An aeroelastic transient capability is available within XTRAN2L, wherein the structural equations of motion are coupled with the aerodynamic solution procedure for simultaneous time-integration. The wake is represented as a slit downstream of the airfoil trailing edge. XTRAN2L includes nonreflecting farfield boundary conditions. XTRAN2L was developed on a CDC CYBER mainframe running under NOS 2.4. It is written in FORTRAN 5 and uses overlays to minimize storage requirements. The program requires 120K of memory in overlayed form. XTRAN2L was developed in 1987.

The Cartesian Heritage of Bloom's Taxonomy

ERIC Educational Resources Information Center

Bertucio, Brett

2017-01-01

This essay seeks to contribute to the critical reception of "Bloom's Taxonomy of Educational Objectives" by tracing the Taxonomy's underlying philosophical assumptions. Identifying Bloom's work as consistent with the legacy of Cartesian thought, I argue that its hierarchy of behavioral objectives provides a framework for certainty and…

Reduction of respiratory ghosting motion artifacts in conventional two-dimensional multi-slice Cartesian turbo spin-echo: which k-space filling order is the best?

PubMed

Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi

2018-06-01

The two-dimensional Cartesian turbo spin-echo (TSE) sequence is widely used in routine clinical studies, but it is sensitive to respiratory motion. We investigated the k-space orders in Cartesian TSE that can effectively reduce motion artifacts. The purpose of this study was to demonstrate the relationship between k-space order and degree of motion artifacts using a moving phantom. We compared the degree of motion artifacts between linear and asymmetric k-space orders. The actual spacing of ghost artifacts in the asymmetric order was doubled compared with that in the linear order in the free-breathing situation. The asymmetric order clearly showed less sensitivity to incomplete breath-hold at the latter half of the imaging period. Because of the actual number of partitions of the k-space and the temporal filling order, the asymmetric k-space order of Cartesian TSE was superior to the linear k-space order for reduction of ghosting motion artifacts.

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

NASA Technical Reports Server (NTRS)

Batina, John T.

2005-01-01

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

On differential transformations between Cartesian and curvilinear (geodetic) coordinates

NASA Technical Reports Server (NTRS)

Soler, T.

1976-01-01

Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.

Two-Liquid Cartesian Diver

ERIC Educational Resources Information Center

Planinsic, G.; Kos, M.; Jerman, R.

2004-01-01

It is quite easy to make a version of the well known Cartesian diver experiment that uses two immiscible liquids. This allows students to test their knowledge of density and pressure in explaining the diver's behaviour. Construction details are presented here together with a mathematical model to explain the observations.

Analysis of 3-D Tongue Motion From Tagged and Cine Magnetic Resonance Images

PubMed Central

Woo, Jonghye; Lee, Junghoon; Murano, Emi Z.; Stone, Maureen; Prince, Jerry L.

2016-01-01

Purpose Measuring tongue deformation and internal muscle motion during speech has been a challenging task because the tongue deforms in 3 dimensions, contains interdigitated muscles, and is largely hidden within the vocal tract. In this article, a new method is proposed to analyze tagged and cine magnetic resonance images of the tongue during speech in order to estimate 3-dimensional tissue displacement and deformation over time. Method The method involves computing 2-dimensional motion components using a standard tag-processing method called harmonic phase, constructing superresolution tongue volumes using cine magnetic resonance images, segmenting the tongue region using a random-walker algorithm, and estimating 3-dimensional tongue motion using an incompressible deformation estimation algorithm. Results Evaluation of the method is presented with a control group and a group of people who had received a glossectomy carrying out a speech task. A 2-step principal-components analysis is then used to reveal the unique motion patterns of the subjects. Azimuth motion angles and motion on the mirrored hemi-tongues are analyzed. Conclusion Tests of the method with a various collection of subjects show its capability of capturing patient motion patterns and indicate its potential value in future speech studies. PMID:27295428

Strain rate orientations near the Coso Geothermal Field

NASA Astrophysics Data System (ADS)

Ogasa, N. T.; Kaven, J. O.; Barbour, A. J.; von Huene, R.

2016-12-01

Many geothermal reservoirs derive their sustained capacity for heat exchange in large part due to continuous deformation of preexisting faults and fractures that permit permeability to be maintained. Similarly, enhanced geothermal systems rely on the creation of suitable permeability from fracture and faults networks to be viable. Stress measurements from boreholes or earthquake source mechanisms are commonly used to infer the tectonic conditions that drive deformation, but here we show that geodetic data can also be used. Specifically, we quantify variations in the horizontal strain rate tensor in the area surrounding the Coso Geothermal Field (CGF) by analyzing more than two decades of high accuracy differential GPS data from a network of 14 stations from the University of Nevada Reno Geodetic Laboratory. To handle offsets in the data, from equipment changes and coseismic deformation, we segment the data, perform a piecewise linear fit and take the average of each segment's strain rate to determine secular velocities at each station. With respect to North America, all stations tend to travel northwest at velocities ranging from 1 to 10 mm/yr. The nearest station to CGF shows anomalous motion compared to regional stations, which otherwise show a coherent increase in network velocity from the northeast to the southwest. We determine strain rates via linear approximation using GPS velocities in Cartesian reference frame due to the small area of our network. Principal strain rate components derived from this inversion show maximum extensional strain rates of 30 nanostrain/a occur at N87W with compressional strain rates of 37nanostrain/a at N3E. These results generally align with previous stress measurements from borehole breakouts, which indicate the least compressive horizontal principal stress is east-west oriented, and indicative of the basin and range tectonic setting. Our results suggest that the CGF represents an anomaly in the crustal deformation field, which may be influenced by the hydrothermal anomaly and possibly by the geothermal reservoir operations as well.

Study of the statistical physics bases on superstatistics from the β-fluctuated to the T-fluctuated form

NASA Astrophysics Data System (ADS)

Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-04-01

In this paper, we study the T -fluctuated form of superstatistics. In this form, some thermodynamic quantities such as the Helmholtz energy, the entropy and the internal energy, are expressed in terms of the T -fluctuated form for a canonical ensemble. In addition, the partition functions in the formalism for 2-level and 3-level distributions are derived. Then we make use of the T -fluctuated superstatistics for a quantum harmonic oscillator problem and the thermal properties of the system for three statistics of the Bose-Einstein, Maxwell-Boltzmann and Fermi-Dirac statistics are calculated. The effect of the deformation parameter on these properties is examined. All the results recover the well-known results by removing the deformation parameter.

Vapor Cartesian Diver

ERIC Educational Resources Information Center

Grebenev, Igor V.; Lebedeva, Olga V.; Polushkina, Svetlana V.

2018-01-01

The article proposes a new research object for a general physics course--the vapour Cartesian diver, designed to study the properties of saturated water vapour. Physics education puts great importance on the study of the saturated vapour state, as it is related to many fundamental laws and theories. For example, the temperature dependence of the…

Naturalistic Inquiry: Politics and Implications for Special Education.

ERIC Educational Resources Information Center

Lincoln, Yvonna S.

The revolution in hard sciences is explored, from the Cartesian-Newtonian worldview to the Heisenbergian universe, and consideration is given to whether the conventional, Cartesian model is a serviceable one for research in the social/applied sciences. Five axioms comprising the existing paradigm of logical positivism are outlined (reality,…

A Lot of Good Physics in the Cartesian Diver

ERIC Educational Resources Information Center

De Luca, Roberto; Ganci, Salvatore

2011-01-01

The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…

Migration Rate Of Tidal Meanders: Inferences From The Venice Lagoon

NASA Astrophysics Data System (ADS)

Finotello, A.; D'Alpaos, A.; Ghinassi, M.; Lanzoni, S.; Marani, M.; Rinaldo, A.

2015-12-01

Meandering channels are ubiquitous features of tidal landscapes. However, despite their fundamental role on the eco-morphodynamic evolution of these landscapes, tidal meanders have received less attention when compared to their fluvial counterparts. Improving current understanding of tidal meander migration, a largely-examined topic in fluvial landscapes, is a key step to highlight analogies and differences between tidal and fluvial cases. The migration of about 400 meander bends, belonging to 40 salt-marsh channels in the Northern Venice Lagoon (Italy), from 1968 to nowadays, has been investigated by means of both a classical method in fluvial frameworks and new procedure. Similarities with fluvial meanders occur, although important difference also emerge. Meanders cutting through the San Felice marsh follow the relationship between cartesian length and channel width, typical of meanders developed within different settings. However, meander migration rates proved to be smaller than those characterizing fluvial meanders. Indeed, the analysis of meander migration suggests a mean migration rate of about 0.10 m/year, consistent with the few data available in the literature. As for the fluvial case, the maximum-potential migration rate (i.e. the envelope curve of the relationship between migration rate and bend radius, both divided by channel width) reaches a maximum for radius-over-width ratio included between 2 and 3, regardless of the considered method. Nevertheless, the new-proposed method allows us to provide a more objective and continuous characterization. By using this new procedure, the channel curvature has finally been Fourier-analyzed, confirming the importance of even harmonics along the curvature spectrum. A correlation between migration rates and dominant harmonics seems to drive the evolution of tidal meanders and might represent a key-feature to distinguish them from their fluvial counterparts.

Simulations on Monitoring and Evaluation of Plasticity-Driven Material Damage Based on Second Harmonic of S0 Mode Lamb Waves in Metallic Plates

PubMed Central

Sun, Xiaoqiang; Liu, Xuyang; Liu, Yaolu; Hu, Ning; Zhao, Youxuan; Ding, Xiangyan; Qin, Shiwei; Zhang, Jianyu; Zhang, Jun; Liu, Feng; Fu, Shaoyun

2017-01-01

In this study, a numerical approach—the discontinuous Meshless Local Petrov-Galerkin-Eshelby Method (MLPGEM)—was adopted to simulate and measure material plasticity in an Al 7075-T651 plate. The plate was modeled in two dimensions by assemblies of small particles that interact with each other through bonding stiffness. The material plasticity of the model loaded to produce different levels of strain is evaluated with the Lamb waves of S0 mode. A tone burst at the center frequency of 200 kHz was used as excitation. Second-order nonlinear wave was extracted from the spectrogram of a signal receiving point. Tensile-driven plastic deformation and cumulative second harmonic generation of S0 mode were observed in the simulation. Simulated measurement of the acoustic nonlinearity increased monotonically with the level of tensile-driven plastic strain captured by MLPGEM, whereas achieving this state by other numerical methods is comparatively more difficult. This result indicates that the second harmonics of S0 mode can be employed to monitor and evaluate the material or structural early-stage damage induced by plasticity. PMID:28773188

A Cartesian cut cell method for rarefied flow simulations around moving obstacles

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

Dechristé, G., E-mail: Guillaume.Dechriste@math.u-bordeaux1.fr; CNRS, IMB, UMR 5251, F-33400 Talence; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux1.fr

2016-06-01

For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kinds of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including amore » 3D unsteady simulation of the Crookes radiometer.« less

On automating domain connectivity for overset grids

NASA Technical Reports Server (NTRS)

Chiu, Ing-Tsau; Meakin, Robert L.

1995-01-01

An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.

Acoustics of Idakkā: An Indian snare drum with definite pitch.

PubMed

Jose, Kevin; Chatterjee, Anindya; Gupta, Anurag

2018-05-01

The vibration of a homogeneous circular membrane backed by two taut strings is shown to yield several harmonic overtones for a wide range of physical and geometric parameters. Such a membrane is present at each end of the barrel of an idakkā, an Indian snare drum well known for its rich musicality. The audio recordings of the musical drum are analyzed and a case is made for the strong sense of pitch associated with the drum. A computationally inexpensive model of the string-membrane interaction is proposed assuming the strings to be without inertia. The interaction essentially entails wrapping/unwrapping of the string around a curve on the deforming membrane unlike the colliding strings in Western snare drums. The range of parameters for which harmonicity is achieved is examined and is found to be conforming with what is used in actual drum playing and construction.

The influence of rheological weakening and yield stress on the interaction of slabs with the 670 km discontinuity

NASA Astrophysics Data System (ADS)

Čížková, Hana; van Hunen, Jeroen; van den Berg, Arie P.; Vlaar, Nico J.

2002-06-01

Results of high resolution seismic tomography showing subducting slabs deflected in the transition zone and thickened in the lower mantle seem to call for slab material weaker than inferred from mineral physics deformation mechanisms. A possible mechanism suggested by several authors could be the weakening due to grain size reduction, which should occur in the cold portion of fast slabs after an exothermic phase transition at a depth of 400 km. Since the amount of weakening as well as the rate of subsequent strengthening due to the grain growth are not precisely known, we present here a parametric study of slab behavior in the transition zone and upper part of the lower mantle. We simulate a subducting slab in a two-dimensional (2-D) Cartesian box in the numerical model with composite rheology including diffusion creep, dislocation creep and a general stress limiting rheology approximating Peierl's creep. We concentrate on two rheologic effects: the dynamic effect of slab weakening due to grain size reduction at the phase boundary and the effect of yield stress of stress limiting rheology. The effect of trench migration on slab deformation is also included in our study. Results show that the slab ability to penetrate into the lower mantle is not significantly affected by a trench retreat in the absence of grain size weakening. However, in case of a 4 cm/yr trench retreat, grain size weakening provides a viable mechanism to deflect the slab in the transition zone, provided that stress limiting deformation mechanism would limit the effective viscosity outside the areas of grain size weakening to about 1024 Pa s.

Three-dimensional ultrasound strain imaging of skeletal muscles

NASA Astrophysics Data System (ADS)

Gijsbertse, K.; Sprengers, A. M. J.; Nillesen, M. M.; Hansen, H. H. G.; Lopata, R. G. P.; Verdonschot, N.; de Korte, C. L.

2017-01-01

In this study, a multi-dimensional strain estimation method is presented to assess local relative deformation in three orthogonal directions in 3D space of skeletal muscles during voluntary contractions. A rigid translation and compressive deformation of a block phantom, that mimics muscle contraction, is used as experimental validation of the 3D technique and to compare its performance with respect to a 2D based technique. Axial, lateral and (in case of 3D) elevational displacements are estimated using a cross-correlation based displacement estimation algorithm. After transformation of the displacements to a Cartesian coordinate system, strain is derived using a least-squares strain estimator. The performance of both methods is compared by calculating the root-mean-squared error of the estimated displacements with the calculated theoretical displacements of the phantom experiments. We observe that the 3D technique delivers more accurate displacement estimations compared to the 2D technique, especially in the translation experiment where out-of-plane motion hampers the 2D technique. In vivo application of the 3D technique in the musculus vastus intermedius shows good resemblance between measured strain and the force pattern. Similarity of the strain curves of repetitive measurements indicates the reproducibility of voluntary contractions. These results indicate that 3D ultrasound is a valuable imaging tool to quantify complex tissue motion, especially when there is motion in three directions, which results in out-of-plane errors for 2D techniques.

Submarine Periscope Depth Course Selection Tactical Decision Aid

DTIC Science & Technology

1997-12-01

are translated to Cartesian coordinates. Co is own ship’s course. 8 X0 = DMho. cos(Co) Yo = DAho . sin(Co) Xc = DMht- cos(Ct) Yc = DMhbt sin(Ct) These...Display Graph. The input parameters of DAho , Ct, and DMiht along with Co as generated by the simulation are used to determine the Cartesian

Supporting Generative Thinking about Number Lines, the Cartesian Plane, and Graphs of Linear Functions

ERIC Educational Resources Information Center

Earnest, Darrell Steven

2012-01-01

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

Sign(al)s: Living and Learning as Semiotic Engagement

ERIC Educational Resources Information Center

Stables, Andrew

2006-01-01

Cartesian mind-body dualism, while often explicitly denied, has left a legacy of conceptions that remain highly influential in education. I argue that trends in both analytic and continental philosophy of language point towards a post-Cartesian settlement in which the distinction between "signs" and "signals" is collapsed, and which thus construes…

An efficient gridding reconstruction method for multishot non-Cartesian imaging with correction of off-resonance artifacts.

PubMed

Meng, Yuguang; Lei, Hao

2010-06-01

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. (c) 2010 Wiley-Liss, Inc.

A Spiral Spin-Echo MR Imaging Technique for Improved Flow Artifact Suppression in T1-Weighted Postcontrast Brain Imaging: A Comparison with Cartesian Turbo Spin-Echo.

PubMed

Li, Z; Hu, H H; Miller, J H; Karis, J P; Cornejo, P; Wang, D; Pipe, J G

2016-04-01

A challenge with the T1-weighted postcontrast Cartesian spin-echo and turbo spin-echo brain MR imaging is the presence of flow artifacts. Our aim was to develop a rapid 2D spiral spin-echo sequence for T1-weighted MR imaging with minimal flow artifacts and to compare it with a conventional Cartesian 2D turbo spin-echo sequence. T1-weighted brain imaging was performed in 24 pediatric patients. After the administration of intravenous gadolinium contrast agent, a reference Cartesian TSE sequence with a scanning time of 2 minutes 30 seconds was performed, followed by the proposed spiral spin-echo sequence with a scanning time of 1 minutes 18 seconds, with similar spatial resolution and volumetric coverage. The results were reviewed independently and blindly by 3 neuroradiologists. Scores from a 3-point scale were assigned in 3 categories: flow artifact reduction, subjective preference, and lesion conspicuity, if any. The Wilcoxon signed rank test was performed to evaluate the reviewer scores. The t test was used to evaluate the SNR. The Fleiss κ coefficient was calculated to examine interreader agreement. In 23 cases, spiral spin-echo was scored over Cartesian TSE in flow artifact reduction (P < .001). In 21 cases, spiral spin-echo was rated superior in subjective preference (P < .001). Ten patients were identified with lesions, and no statistically significant difference in lesion conspicuity was observed between the 2 sequences. There was no statistically significant difference in SNR between the 2 techniques. The Fleiss κ coefficient was 0.79 (95% confidence interval, 0.65-0.93). The proposed spiral spin-echo pulse sequence provides postcontrast images with minimal flow artifacts at a faster scanning time than its Cartesian TSE counterpart. © 2016 by American Journal of Neuroradiology.

Motion-insensitive carotid intraplaque hemorrhage imaging using 3D inversion recovery preparation stack of stars (IR-prep SOS) technique.

PubMed

Kim, Seong-Eun; Roberts, John A; Eisenmenger, Laura B; Aldred, Booth W; Jamil, Osama; Bolster, Bradley D; Bi, Xiaoming; Parker, Dennis L; Treiman, Gerald S; McNally, J Scott

2017-02-01

Carotid artery imaging is important in the clinical management of patients at risk for stroke. Carotid intraplaque hemorrhage (IPH) presents an important diagnostic challenge. 3D magnetization prepared rapid acquisition gradient echo (MPRAGE) has been shown to accurately image carotid IPH; however, this sequence can be limited due to motion- and flow-related artifact. The purpose of this work was to develop and evaluate an improved 3D carotid MPRAGE sequence for IPH detection. We hypothesized that a radial-based k-space trajectory sequence such as "Stack of Stars" (SOS) incorporated with inversion recovery preparation would offer reduced motion sensitivity and more robust flow suppression by oversampling of central k-space. A total of 31 patients with carotid disease (62 carotid arteries) were imaged at 3T magnetic resonance imaging (MRI) with 3D IR-prep Cartesian and SOS sequences. Image quality was determined between SOS and Cartesian MPRAGE in 62 carotid arteries using t-tests and multivariable linear regression. Kappa analysis was used to determine interrater reliability. In all, 25 among 62 carotid plaques had carotid IPH by consensus from the reviewers on SOS compared to 24 on Cartesian sequence. Image quality was significantly higher with SOS compared to Cartesian (mean 3.74 vs. 3.11, P < 0.001). SOS acquisition yielded sharper image features with less motion (19.4% vs. 45.2%, P < 0.002) and flow artifact (27.4% vs. 41.9%, P < 0.089). There was also excellent interrater reliability with SOS (kappa = 0.89), higher than that of Cartesian (kappa = 0.84). By minimizing flow and motion artifacts and retaining high interrater reliability, the SOS MPRAGE has important advantages over Cartesian MPRAGE in carotid IPH detection. 1 J. Magn. Reson. Imaging 2017;45:410-417. © 2016 International Society for Magnetic Resonance in Medicine.

Terrain Correction on the moving equal area cylindrical map projection of the surface of a reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A.; Safari, A.; Grafarend, E.

2003-04-01

An operational algorithm for computing the ellipsoidal terrain correction based on application of closed form solution of the Newton integral in terms of Cartesian coordinates in the cylindrical equal area map projected surface of a reference ellipsoid has been developed. As the first step the mapping of the points on the surface of a reference ellipsoid onto the cylindrical equal area map projection of a cylinder tangent to a point on the surface of reference ellipsoid closely studied and the map projection formulas are computed. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid is considered and the gravitational potential and the vector of gravitational intensity of these mass elements has been computed via the solution of Newton integral in terms of ellipsoidal coordinates. The geographical cross section areas of the selected ellipsoidal mass elements are transferred into cylindrical equal area map projection and based on the transformed area elements Cartesian mass elements with the same height as that of the ellipsoidal mass elements are constructed. Using the close form solution of the Newton integral in terms of Cartesian coordinates the potential of the Cartesian mass elements are computed and compared with the same results based on the application of the ellipsoidal Newton integral over the ellipsoidal mass elements. The results of the numerical computations show that difference between computed gravitational potential of the ellipsoidal mass elements and Cartesian mass element in the cylindrical equal area map projection is of the order of 1.6 × 10-8m^2/s^2 for a mass element with the cross section size of 10 km × 10 km and the height of 1000 m. For a 1 km × 1 km mass element with the same height, this difference is less than 1.5 × 10-4 m^2}/s^2. The results of the numerical computations indicate that a new method for computing the terrain correction based on the closed form solution of the Newton integral in terms of Cartesian coordinates and with accuracy of ellipsoidal terrain correction has been achieved! In this way one can enjoy the simplicity of the solution of the Newton integral in terms of Cartesian coordinates and at the same time the accuracy of the ellipsoidal terrain correction, which is needed for the modern theory of geoid computations.

A breakthrough in neuroscience needs a "Nebulous Cartesian System" Oscillations, quantum dynamics and chaos in the brain and vegetative system.

PubMed

Başar, Erol; Güntekin, Bahar

2007-04-01

The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the metaphor of "finding the walking path in a cloudy or foggy day". This is meant by stating "The Nebulous Cartesian System" (NCS). Descartes, at his time undertaking his genius step, did not possess the knowledge of today's physiology and modern physics; we think that the time has come to consider such a New Cartesian System. To deal with this, we propose the utilization of the Heisenberg S-Matrix and a modified version of the Feynman Diagrams which we call "Brain Feynman Diagrams". Another metaphor to consider within the oscillatory approach of the NCS is the "string theory". We also emphasize that fundamental steps should be undertaken in order to create the own dynamical framework of the brain-body-mind incorporation; suggestions or metaphors from physics and mathematics are useful; however, the grammar of the brains intrinsic language must be understood with the help of a new biologically founded, adaptive-probabilistic Cartesian system. This new Cartesian System will undergo mutations and transcend to the philosophy of Henri Bergson in parallel to the Evolution theory of Charles Darwin to open gateways for approaching the brain-body-mind problem.

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

PubMed Central

Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2011-01-01

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009

Adaptive compensation of aberrations in ultrafast 3D microscopy using a deformable mirror

NASA Astrophysics Data System (ADS)

Sherman, Leah R.; Albert, O.; Schmidt, Christoph F.; Vdovin, Gleb V.; Mourou, Gerard A.; Norris, Theodore B.

2000-05-01

3D imaging using a multiphoton scanning confocal microscope is ultimately limited by aberrations of the system. We describe a system to adaptively compensate the aberrations with a deformable mirror. We have increased the transverse scanning range of the microscope by three with compensation of off-axis aberrations.We have also significantly increased the longitudinal scanning depth with compensation of spherical aberrations from the penetration into the sample. Our correction is based on a genetic algorithm that uses second harmonic or two-photon fluorescence signal excited by femtosecond pulses from the sample as the enhancement parameter. This allows us to globally optimize the wavefront without a wavefront measurement. To improve the speed of the optimization we use Zernike polynomials as the basis for correction. Corrections can be stored in a database for look-up with future samples.

A Computer Program To Increase Comprehension of the Cartesian Rectangular Coordinate System in High School Pre-Algebra Students.

ERIC Educational Resources Information Center

Exley, I. Sheck

The high percentage of high school pre-algebra students having difficulty learning the abstract concept of graphing ordered pairs on the Cartesian rectangular coordinate system was addressed by the creation and implementation of a computer-managed instructional program. Modules consisted of a pretest, instruction, two practice sessions, and a…

Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion

ERIC Educational Resources Information Center

Lelwica, Michelle Mary

2009-01-01

This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…

[Basic examination of an imagecharacteristic in Multivane].

PubMed

Ohshita, Tsuyoshi

2011-01-01

Deterioration in the image because of a patient's movement always becomes a problem in the MRI inspection. To solve this problem, the imaging procedure named Multivane was developed. The principle is similar to the periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) method. As for Multivane, the effect of the body motion correction is high. However, the filling method of k space is different than a past Cartesian method. A basic examination of the image characteristic of Multivane and Cartesian was utilized along with geostationary phantom. The examination items are SNR, CNR, and a spatial resolution. As a result, Multivane of SNR was high. Cartesian of the contrast and the spatial resolution was also high. It is important to recognize these features and to use Multivane.

On the Use of Parmetric-CAD Systems and Cartesian Methods for Aerodynamic Design

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.

2004-01-01

Automated, high-fidelity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry arid in permitting radical design changes. Success in these areas promises not only significantly shorter design- cycle times, but also superior and unconventional designs. To address these issues, we investigate the use of a parmetric-CAD system in conjunction with an embedded-boundary Cartesian method. Our goal is to combine the modeling capabilities of feature-based CAD with the robustness and flexibility of component-based Cartesian volume-mesh generation for complex geometry problems. We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.

PCTDSE: A parallel Cartesian-grid-based TDSE solver for modeling laser-atom interactions

NASA Astrophysics Data System (ADS)

Fu, Yongsheng; Zeng, Jiaolong; Yuan, Jianmin

2017-01-01

We present a parallel Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for modeling laser-atom interactions. It can simulate the single-electron dynamics of atoms in arbitrary time-dependent vector potentials. We use a split-operator method combined with fast Fourier transforms (FFT), on a three-dimensional (3D) Cartesian grid. Parallelization is realized using a 2D decomposition strategy based on the Message Passing Interface (MPI) library, which results in a good parallel scaling on modern supercomputers. We give simple applications for the hydrogen atom using the benchmark problems coming from the references and obtain repeatable results. The extensions to other laser-atom systems are straightforward with minimal modifications of the source code.

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

NASA Technical Reports Server (NTRS)

Simpson, David G.

1998-01-01

In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable on-board computer resources.

Dynamic MRI of Grid-Tagged Hyperpolarized Helium-3 for the Assessment of Lung Motion During Breathing

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

Cai Jing; Sheng Ke; Benedict, Stanley H.

2009-09-01

Purpose: To develop a dynamic magnetic resonance imaging (MRI) tagging technique using hyperpolarized helium-3 (HP He-3) to track lung motion. Methods and Materials: An accelerated non-Cartesian k-space trajectory was used to gain acquisition speed, at the cost of introducing image artifacts, providing a viable strategy for obtaining whole-lung coverage with adequate temporal resolution. Multiple-slice two-dimensional dynamic images of the lung were obtained in three healthy subjects after inhaling He-3 gas polarized to 35%-40%. Displacement, strain, and ventilation maps were computed from the observed motion of the grid peaks. Results: Both temporal and spatial variations of pulmonary mechanics were observed inmore » normal subjects, including shear motion between different lobes of the same lung. Conclusion: These initial results suggest that dynamic imaging of grid-tagged hyperpolarized magnetization may potentially be a powerful tool for observing and quantifying pulmonary biomechanics on a regional basis and for assessing, validating, and improving lung deformable image registration algorithms.« less

A VERSATILE SHARP INTERFACE IMMERSED BOUNDARY METHOD FOR INCOMPRESSIBLE FLOWS WITH COMPLEX BOUNDARIES

PubMed Central

Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F.M.; Vargas, A.; von Loebbecke, A.

2010-01-01

A sharp interface immersed boundary method for simulating incompressible viscous flow past three-dimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two- and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method. PMID:20216919

The 6-31B(d) basis set and the BMC-QCISD and BMC-CCSD multicoefficient correlation methods.

PubMed

Lynch, Benjamin J; Zhao, Yan; Truhlar, Donald G

2005-03-03

Three new multicoefficient correlation methods (MCCMs) called BMC-QCISD, BMC-CCSD, and BMC-CCSD-C are optimized against 274 data that include atomization energies, electron affinities, ionization potentials, and reaction barrier heights. A new basis set called 6-31B(d) is developed and used as part of the new methods. BMC-QCISD has mean unsigned errors in calculating atomization energies per bond and barrier heights of 0.49 and 0.80 kcal/mol, respectively. BMC-CCSD has mean unsigned errors of 0.42 and 0.71 kcal/mol for the same two quantities. BMC-CCSD-C is an equally effective variant of BMC-CCSD that employs Cartesian rather than spherical harmonic basis sets. The mean unsigned error of BMC-CCSD or BMC-CCSD-C for atomization energies, barrier heights, ionization potentials, and electron affinities is 22% lower than G3SX(MP2) at an order of magnitude less cost for gradients for molecules with 9-13 atoms, and it scales better (N6 vs N,7 where N is the number of atoms) when the size of the molecule is increased.

Uniform function constants of motion and their first-order perturbation

NASA Astrophysics Data System (ADS)

Prato, Domingo; Hamity, Victor H.

2005-05-01

The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

Static-transmission-error vibratory-excitation contributions from plastically deformed gear teeth caused by tooth bending-fatigue damage

NASA Astrophysics Data System (ADS)

Mark, W. D.; Reagor, C. P.

2007-02-01

To assess gear health and detect gear-tooth damage, the vibratory response from meshing gear-pair excitations is commonly monitored by accelerometers. In an earlier paper, strong evidence was presented suggesting that, in the case of tooth bending-fatigue damage, the principal source of detectable damage is whole-tooth plastic deformation; i.e. yielding, rather than changes in tooth stiffness caused by tooth-root cracks. Such plastic deformations are geometric deviation contributions to the "static-transmission-error" (STE) vibratory excitation caused by meshing gear pairs. The STE contributions caused by two likely occurring forms of such plastic deformations on a single tooth are derived, and displayed in the time domain as a function of involute "roll distance." Example calculations are provided for transverse contact ratios of Qt=1.4 and 1.8, for spur gears and for helical-gear axial contact ratios ranging from Qa=1.2 to Qa=3.6. Low-pass- and band-pass-filtered versions of these same STE contributions also are computed and displayed in the time domain. Several calculations, consisting of superposition of the computed STE tooth-meshing fundamental harmonic contribution and the band-pass STE contribution caused by a plastically deformed tooth, exhibit the amplitude and frequency or phase modulation character commonly observed in accelerometer-response waveforms caused by damaged teeth. General formulas are provided that enable computation of these STE vibratory-excitation contributions for any form of plastic deformation on any number of teeth for spur and helical gears with any contact ratios.

The Cartesian Diver as an Aid for Teaching Respiratory Physiology

ERIC Educational Resources Information Center

Fitch, Greg K.

2004-01-01

The mechanism by which air enters the mammalian lung is difficult for many students of physiology. In particular, some students have trouble seeing how pressure can be transmitted through a fluid such as the intrapleural fluid and how the magnitude of that pressure can change. A Cartesian diver, an old-time child's toy, may be used as a visual aid…

The Cartesian Diver, Surface Tension and the Cheerios Effect

ERIC Educational Resources Information Center

Chen, Chi-Tung; Lee, Wen-Tang; Kao, Sung-Kai

2014-01-01

A Cartesian diver can be used to measure the surface tension of a liquid to a certain extent. The surface tension measurement is related to the two critical pressures at which the diver is about to sink and about to emerge. After sinking because of increasing pressure, the diver is repulsed to the centre of the vessel. After the pressure is…

VAC: Versatile Advection Code

NASA Astrophysics Data System (ADS)

Tóth, Gábor; Keppens, Rony

2012-07-01

The Versatile Advection Code (VAC) is a freely available general hydrodynamic and magnetohydrodynamic simulation software that works in 1, 2 or 3 dimensions on Cartesian and logically Cartesian grids. VAC runs on any Unix/Linux system with a Fortran 90 (or 77) compiler and Perl interpreter. VAC can run on parallel machines using either the Message Passing Interface (MPI) library or a High Performance Fortran (HPF) compiler.

Real-time cartesian force feedback control of a teleoperated robot

NASA Technical Reports Server (NTRS)

Campbell, Perry

1989-01-01

Active cartesian force control of a teleoperated robot is investigated. An economical microcomputer based control method was tested. Limitations are discussed and methods of performance improvement suggested. To demonstrate the performance of this technique, a preliminary test was performed with success. A general purpose bilateral force reflecting hand controller is currently being constructed based on this control method.

[Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].

PubMed

Gysel, C

1979-01-01

In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1994-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Cartesian control of redundant robots

NASA Technical Reports Server (NTRS)

Colbaugh, R.; Glass, K.

1989-01-01

A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.

A weakly-compressible Cartesian grid approach for hydrodynamic flows

NASA Astrophysics Data System (ADS)

Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D.

2017-11-01

The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (> 3) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article.

Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.

PubMed

Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H

2013-05-01

In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction. Copyright © 2012 Wiley Periodicals, Inc.

Kalman Filter Techniques for Accelerated Cartesian Dynamic Cardiac Imaging

PubMed Central

Feng, Xue; Salerno, Michael; Kramer, Christopher M.; Meyer, Craig H.

2012-01-01

In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories, because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and SNR. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction. PMID:22926804

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1996-01-01

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Calculation of Water Entry Problem for Free-falling Bodies Using a Developed Cartesian Cut Cell Mesh

NASA Astrophysics Data System (ADS)

Wenhua, Wang; Yanying, Wang

2010-05-01

This paper describes the development of free surface capturing method on Cartesian cut cell mesh to water entry problem for free-falling bodies with body-fluid interaction. The incompressible Euler equations for a variable density fluid system are presented as governing equations and the free surface is treated as a contact discontinuity by using free surface capturing method. In order to be convenient for dealing with the problem with moving body boundary, the Cartesian cut cell technique is adopted for generating the boundary-fitted mesh around body edge by cutting solid regions out of a background Cartesian mesh. Based on this mesh system, governing equations are discretized by finite volume method, and at each cell edge inviscid flux is evaluated by means of Roe's approximate Riemann solver. Furthermore, for unsteady calculation in time domain, a time accurate solution is achieved by a dual time-stepping technique with artificial compressibility method. For the body-fluid interaction, the projection method of momentum equations and exact Riemann solution are applied in the calculation of fluid pressure on the solid boundary. Finally, the method is validated by test case of water entry for free-falling bodies.

Soul in the world: symbolic culture as the medium for psyche.

PubMed

Colman, Warren

2017-02-01

Whilst the loss of a sense of living connection with the material world is mainly associated with the scientific revolution in seventeenth century Europe, it can be traced back to Plato's introduction of a hierarchy between soul and body. Jung's attempted solution to this - esse in anima - is ingenious but maintains the Cartesian split by which the aliveness of the world is reduced to a projection of psychic forces (the archetypes). An alternative approach is proposed, rooted in the Aristotelean emphasis on practical activity that sees the soul as a function of our way of being in the world. Human cognition is extended and distributed by our social and material engagement with the world, especially via collective representations whose symbolic character is constitutive of the reality of the world in which we live. Despite the dominance of 'scientific Cartesian' representations in the modern Western world, there remain numerous instances of participation mystique that cannot be captured by the Cartesian notion of projection. These indicate an opening to ways of being in the world that may lead us out of the impasse of the Cartesian matrix. © 2017, The Society of Analytical Psychology.

On the completeness and the linear dependence of the Cartesian multipole series in representing the solution to the Helmholtz equation.

PubMed

Liu, Yangfan; Bolton, J Stuart

2016-08-01

The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis.

Grasp of Consciousness and Performance in Mathematics Making Explicit the Ways of Thinking in Solving Cartesian Product Problems

ERIC Educational Resources Information Center

Soares, Maria Tereza Carneiro; Moro, Maria Lucia Faria; Spinillo, Alina Galvao

2012-01-01

This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by…

3D automatic Cartesian grid generation for Euler flows

NASA Technical Reports Server (NTRS)

Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.

1993-01-01

We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.

"Mens Sana in Corpore Sano": Cartesian Dualism and the Marginalisation of Sex Education

ERIC Educational Resources Information Center

Paechter, Carrie

2004-01-01

Cartesian dualism has left a heavy legacy in terms of how we think about ourselves, so that we treat humans as minds within bodies rather than mind/body unities. This has far-reaching effects on our conceptualisation of the sex/gender distinction and on the relationship between bodies and identities. Related to this is a dualism that is embedded…

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei

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

Gulshani, P., E-mail: matlap@bell.net

We derive a microscopic version of the successful phenomenological hydrodynamic model of Bohr-Davydov-Faessler-Greiner for collective rotation-vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitude. The nuclear Schrodinger equation is canonically transformed to collective co-ordinates, which is then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. For harmonic oscillator mean-field potentials, these equations are solved in closed forms for excitation energy,more » cut-off angular momentum, and other nuclear properties for the ground-state rotational band in some deformed nuclei. The results are compared with measured data.« less

Theoretical study of large conformational transitions in DNA: the B↔A conformational change in water and ethanol/water

PubMed Central

Noy, Agnes; Pérez, Alberto; Laughton, Charles A.; Orozco, Modesto

2007-01-01

We explore here the possibility of determining theoretically the free energy change associated with large conformational transitions in DNA, like the solvent-induced B⇔A conformational change. We find that a combination of targeted molecular dynamics (tMD) and the weighted histogram analysis method (WHAM) can be used to trace this transition in both water and ethanol/water mixture. The pathway of the transition in the A→B direction mirrors the B→A pathway, and is dominated by two processes that occur somewhat independently: local changes in sugar puckering and global rearrangements (particularly twist and roll) in the structure. The B→A transition is found to be a quasi-harmonic process, which follows closely the first spontaneous deformation mode of B-DNA, showing that a physiologically-relevant deformation is in coded in the flexibility pattern of DNA. PMID:17459891

Do faults trigger folding in the lithosphere?

NASA Astrophysics Data System (ADS)

Gerbault, Muriel; Burov, Eugenii B.; Poliakov, Alexei N. B.; Daignières, Marc

A number of observations reveal large periodic undulations within the oceanic and continental lithospheres. The question if these observations are the result of large-scale compressive instabilities, i.e. buckling, remains open. In this study, we support the buckling hypothesis by direct numerical modeling. We compare our results with the data on three most proeminent cases of the oceanic and continental folding-like deformation (Indian Ocean, Western Gobi (Central Asia) and Central Australia). We demonstrate that under reasonable tectonic stresses, folds can develop from brittle faults cutting through the brittle parts of a lithosphere. The predicted wavelengths and finite growth rates are in agreement with observations. We also show that within a continental lithosphere with thermal age greater than 400 My, either a bi-harmonic mode (two superimposed wavelengths, crustal and mantle one) or a coupled mode (mono-layer deformation) of inelastic folding can develop, depending on the strength and thickness of the lower crust.

Reducing workpieces to their base geometry for multi-step incremental forming using manifold harmonics

NASA Astrophysics Data System (ADS)

Carette, Yannick; Vanhove, Hans; Duflou, Joost

2018-05-01

Single Point Incremental Forming is a flexible process that is well-suited for small batch production and rapid prototyping of complex sheet metal parts. The distributed nature of the deformation process and the unsupported sheet imply that controlling the final accuracy of the workpiece is challenging. To improve the process limits and the accuracy of SPIF, the use of multiple forming passes has been proposed and discussed by a number of authors. Most methods use multiple intermediate models, where the previous one is strictly smaller than the next one, while gradually increasing the workpieces' wall angles. Another method that can be used is the manufacture of a smoothed-out "base geometry" in the first pass, after which more detailed features can be added in subsequent passes. In both methods, the selection of these intermediate shapes is freely decided by the user. However, their practical implementation in the production of complex freeform parts is not straightforward. The original CAD model can be manually adjusted or completely new CAD models can be created. This paper discusses an automatic method that is able to extract the base geometry from a full STL-based CAD model in an analytical way. Harmonic decomposition is used to express the final geometry as the sum of individual surface harmonics. It is then possible to filter these harmonic contributions to obtain a new CAD model with a desired level of geometric detail. This paper explains the technique and its implementation, as well as its use in the automatic generation of multi-step geometries.

Internal Coordinate Molecular Dynamics: A Foundation for Multiscale Dynamics

PubMed Central

2015-01-01

Internal coordinates such as bond lengths, bond angles, and torsion angles (BAT) are natural coordinates for describing a bonded molecular system. However, the molecular dynamics (MD) simulation methods that are widely used for proteins, DNA, and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed with Cartesian MD simulations to enhance the conformational sampling. This makes the equations of motion in the Cartesian coordinates differential-algebraic, which adversely impacts the complexity and the robustness of the simulations. On the other hand, constraints can be easily placed in BAT coordinates by removing the degrees of freedom that need to be constrained. Thus, the internal coordinate MD (ICMD) offers an attractive alternative to Cartesian coordinate MD for developing multiscale MD method. The torsional MD method is a special adaptation of the ICMD method, where all the bond lengths and bond angles are kept rigid. The advantages of ICMD simulation methods are the longer time step size afforded by freezing high frequency degrees of freedom and performing a conformational search in the more important low frequency torsional degrees of freedom. However, the advancements in the ICMD simulations have been slow and stifled by long-standing mathematical bottlenecks. In this review, we summarize the recent mathematical advancements we have made based on spatial operator algebra, in developing a robust long time scale ICMD simulation toolkit useful for various applications. We also present the applications of ICMD simulations to study conformational changes in proteins and protein structure refinement. We review the advantages of the ICMD simulations over the Cartesian simulations when used with enhanced sampling methods and project the future use of ICMD simulations in protein dynamics. PMID:25517406

Geodetic measurement of deformation in the Loma Prieta, California earthquake with Very Long Baseline Interferometry (VLBI)

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

Clark, T.A.; Ma, C.; Sauber, J.M.

Following the Loma Prieta earthquake, two mobile Very Long Baseline Interferometry (VLBI) systems operated by the NASA Crustal Dynamics Project and the NOAA National Geodetic Survey were deployed at three previously established VLBI sites in the earthquake area: Fort Ord (near Monterey), the Presidio (in San Francisco) and Point Reyes. From repeated VLBI occupations of these sites since 1983, the pre-earthquake rates of deformation have been determined with respect to a North American reference frame with 1{sigma} formal standard errors of {approximately}1 mm/yr. The VLBI measurements immediately following the earthquake showed that the Fort Ord site was displaced 49 {plusmore » minus} 4 mm at an azimuth of 11 {plus minus} 4{degree} and that the Presidio site was displaced 12 {plus minus} 5 mm at an azimuth of 148 {plus minus} 13{degree}. No anomalous change was detected at Point Reyes with 1{sigma} uncertainty of 4 mm. The estimated displacements at Fort Ord and the Presidio are consistent with the static displacements predicted on the basis of a coseismic slip model in which slip on the southern segment is shallower than slip on the more northern segment is shallower than slip on the more northern segment of the fault rupture. The authors also give the Cartesian positions at epoch 1990.0 of a set of VLBI fiducial stations and the three mobile sites in the vicinity of the earthquake.« less

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

On the interpretations of Langevin stochastic equation in different coordinate systems

NASA Astrophysics Data System (ADS)

Martínez, E.; López-Díaz, L.; Torres, L.; Alejos, O.

2004-01-01

The stochastic Langevin Landau-Lifshitz equation is usually utilized in micromagnetics formalism to account for thermal effects. Commonly, two different interpretations of the stochastic integrals can be made: Ito and Stratonovich. In this work, the Langevin-Landau-Lifshitz (LLL) equation is written in both Cartesian and Spherical coordinates. If Spherical coordinates are employed, the noise is additive, and therefore, Ito and Stratonovich solutions are equal. This is not the case when (LLL) equation is written in Cartesian coordinates. In this case, the Langevin equation must be interpreted in the Stratonovich sense in order to reproduce correct statistical results. Nevertheless, the statistics of the numerical results obtained from Euler-Ito and Euler-Stratonovich schemes are equivalent due to the additional numerical constraint imposed in Cartesian system after each time step, which itself assures that the magnitude of the magnetization is preserved.

Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils.

PubMed

Mahajan, Virendra N

2010-12-20

The classical aberrations of an anamorphic optical imaging system, representing the terms of a power-series expansion of its aberration function, are separable in the Cartesian coordinates of a point on its pupil. We discuss the balancing of a classical aberration of a certain order with one or more such aberrations of lower order to minimize its variance across a rectangular pupil of such a system. We show that the balanced aberrations are the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point. The compound Legendre polynomials are orthogonal across a rectangular pupil and, like the classical aberrations, are inherently separable in the Cartesian coordinates of the pupil point. They are different from the balanced aberrations and the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil.

A Cartesian Adaptive Level Set Method for Two-Phase Flows

NASA Technical Reports Server (NTRS)

Ham, F.; Young, Y.-N.

2003-01-01

In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.

Vibration-synchronized magnetic resonance imaging for the detection of myocardial elasticity changes.

PubMed

Elgeti, Thomas; Tzschätzsch, Heiko; Hirsch, Sebastian; Krefting, Dagmar; Klatt, Dieter; Niendorf, Thoralf; Braun, Jürgen; Sack, Ingolf

2012-04-01

Vibration synchronized magnetic resonance imaging of harmonically oscillating tissue interfaces is proposed for cardiac magnetic resonance elastography. The new approach exploits cardiac triggered cine imaging synchronized with extrinsic harmonic stimulation (f = 22.83 Hz) to display oscillatory tissue deformations in magnitude images. Oscillations are analyzed by intensity threshold-based image processing to track wave amplitude variations over the cardiac cycle. In agreement to literature data, results in 10 volunteers showed that endocardial wave amplitudes during systole (0.13 ± 0.07 mm) were significantly lower than during diastole (0.34 ± 0.14 mm, P < 0.001). Wave amplitudes were found to decrease 117 ± 40 ms before myocardial contraction and to increase 75 ± 31 ms before myocardial relaxation. Vibration synchronized magnetic resonance imaging improves the temporal resolution of magnetic resonance elastography as it overcomes the use of extra motion encoding gradients, is less sensitive to susceptibility artifacts, and does not suffer from dynamic range constraints frequently encountered in phase-based magnetic resonance elastography. Copyright © 2012 Wiley Periodicals, Inc.

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

Ma, Kwan-Liu

In this project, we have developed techniques for visualizing large-scale time-varying multivariate particle and field data produced by the GPS_TTBP team. Our basic approach to particle data visualization is to provide the user with an intuitive interactive interface for exploring the data. We have designed a multivariate filtering interface for scientists to effortlessly isolate those particles of interest for revealing structures in densely packed particles as well as the temporal behaviors of selected particles. With such a visualization system, scientists on the GPS-TTBP project can validate known relationships and temporal trends, and possibly gain new insights in their simulations. Wemore » have tested the system using over several millions of particles on a single PC. We will also need to address the scalability of the system to handle billions of particles using a cluster of PCs. To visualize the field data, we choose to use direct volume rendering. Because the data provided by PPPL is on a curvilinear mesh, several processing steps have to be taken. The mesh is curvilinear in nature, following the shape of a deformed torus. Additionally, in order to properly interpolate between the given slices we cannot use simple linear interpolation in Cartesian space but instead have to interpolate along the magnetic field lines given to us by the scientists. With these limitations, building a system that can provide an accurate visualization of the dataset is quite a challenge to overcome. In the end we use a combination of deformation methods such as deformation textures in order to fit a normal torus into their deformed torus, allowing us to store the data in toroidal coordinates in order to take advantage of modern GPUs to perform the interpolation along the field lines for us. The resulting new rendering capability produces visualizations at a quality and detail level previously not available to the scientists at the PPPL. In summary, in this project we have successfully created new capabilities for the scientists to visualize their 3D data at higher accuracy and quality, enhancing their ability to evaluate the simulations and understand the modeled phenomena.« less

Early and Late Inhibitions Elicited by a Peripheral Visual Cue on Manual Response to a Visual Target: Are They Based on Cartesian Coordinates?

ERIC Educational Resources Information Center

Gawryszewski, Luiz G.; Carreiro, Luiz Renato R.; Magalhaes, Fabio V.

2005-01-01

A non-informative cue (C) elicits an inhibition of manual reaction time (MRT) to a visual target (T). We report an experiment to examine if the spatial distribution of this inhibitory effect follows Polar or Cartesian coordinate systems. C appeared at one out of 8 isoeccentric (7[degrees]) positions, the C-T angular distances (in polar…

Sliding-slab three-dimensional TSE imaging with a spiral-In/Out readout.

PubMed

Li, Zhiqiang; Wang, Dinghui; Robison, Ryan K; Zwart, Nicholas R; Schär, Michael; Karis, John P; Pipe, James G

2016-02-01

T2 -weighted imaging is of great diagnostic value in neuroimaging. Three-dimensional (3D) Cartesian turbo spin echo (TSE) scans provide high signal-to-noise ratio (SNR) and contiguous slice coverage. The purpose of this preliminary work is to implement a novel 3D spiral TSE technique with image quality comparable to 2D/3D Cartesian TSE. The proposed technique uses multislab 3D TSE imaging. To mitigate the slice boundary artifacts, a sliding-slab method is extended to spiral imaging. A spiral-in/out readout is adopted to minimize the artifacts that may be present with the conventional spiral-out readout. Phase errors induced by B0 eddy currents are measured and compensated to allow for the combination of the spiral-in and spiral-out images. A nonuniform slice encoding scheme is used to reduce the truncation artifacts while preserving the SNR performance. Preliminary results show that each of the individual measures contributes to the overall performance, and the image quality of the results obtained with the proposed technique is, in general, comparable to that of 2D or 3D Cartesian TSE. 3D sliding-slab TSE with a spiral-in/out readout provides good-quality T2 -weighted images, and, therefore, may become a promising alternative to Cartesian TSE. © 2015 Wiley Periodicals, Inc.

Fluid-Structure Interaction Study on a Pre-Buckled Deformable Flat Ribbon

NASA Astrophysics Data System (ADS)

Fovargue, Lauren; Shams, Ehsan; Watterson, Amy; Corson, Dave; Filardo, Benjamin; Zimmerman, Daniel; Shan, Bob; Oberai, Assad

2015-11-01

A Fluid-Structure Interaction study is conducted for the flow over a deformable flat ribbon. This mechanism, which is called ribbon frond, maybe used as a device for pumping water and/or harvesting energy in rivers. We use a lower dimensional mathematical model, which represents the ribbon as a pre-buckled structure. The surface forces from the fluid flow, dictate the deformation of the ribbon, and the ribbon in turn imposes boundary conditions for the incompressible Navier-Stokes equations. The mesh motion is handled using an Arbitrary Lagrangian-Eulerian (ALE) scheme and the fluid-structure coupling is handled by iterating over the staggered governing equations for the structure, the fluid and the mesh. Simulations are conducted at three different free stream velocities. The results, including the frequency of oscillations, show agreement with experimental data. The vortical structures near the surface of the ribbon and its deformation are highly correlated. It is observed that the ribbon motion exhibits deviation from a harmonic motion, especially at lower free stream velocities. The behavior of the ribbon is compared to swimming animals, such as eels, in order to better understand its performance. The authors acknowledge support from ONR SBIR Phase II, contract No. N0001412C0604 and USDA, NIFA SBIR Phase I, contract No. 2013-33610-20836 and NYSERDA PON 2569, contract No. 30364.

Reconciling GRACE and GPS estimates of long-term load deformation in southern Greenland

NASA Astrophysics Data System (ADS)

Wang, Song-Yun; Chen, J. L.; Wilson, Clark R.; Li, Jin; Hu, Xiaogong

2018-02-01

We examine vertical load deformation at four continuous Global Positioning System (GPS) sites in southern Greenland relative to Gravity Recovery and Climate Experiment (GRACE) predictions of vertical deformation over the period 2002-2016. With limited spatial resolution, GRACE predictions require adjustment before they can be compared with GPS height time series. Without adjustment, both GRACE spherical harmonic (SH) and mascon solutions predict significant vertical displacement rate differences relative to GPS. We use a scaling factor method to adjust GRACE results, based on a long-term mass rate model derived from GRACE measurements, glacial geography, and ice flow data. Adjusted GRACE estimates show significantly improved agreement with GPS, both in terms of long-term rates and interannual variations. A deceleration of mass loss is observed in southern Greenland since early 2013. The success at reconciling GPS and GRACE observations with a more detailed mass rate model demonstrates the high sensitivity to load distribution in regions surrounding GPS stations. Conversely, the value of GPS observations in constraining mass changes in surrounding regions is also demonstrated. In addition, our results are consistent with recent estimates of GIA uplift (˜4.4 mm yr-1) at the KULU site.

A new combined surface and volume registration

NASA Astrophysics Data System (ADS)

Lepore, Natasha; Joshi, Anand A.; Leahy, Richard M.; Brun, Caroline; Chou, Yi-Yu; Pennec, Xavier; Lee, Agatha D.; Barysheva, Marina; De Zubicaray, Greig I.; Wright, Margaret J.; McMahon, Katie L.; Toga, Arthur W.; Thompson, Paul M.

2010-03-01

3D registration of brain MRI data is vital for many medical imaging applications. However, purely intensitybased approaches for inter-subject matching of brain structure are generally inaccurate in cortical regions, due to the highly complex network of sulci and gyri, which vary widely across subjects. Here we combine a surfacebased cortical registration with a 3D fluid one for the first time, enabling precise matching of cortical folds, but allowing large deformations in the enclosed brain volume, which guarantee diffeomorphisms. This greatly improves the matching of anatomy in cortical areas. The cortices are segmented and registered with the software Freesurfer. The deformation field is initially extended to the full 3D brain volume using a 3D harmonic mapping that preserves the matching between cortical surfaces. Finally, these deformation fields are used to initialize a 3D Riemannian fluid registration algorithm, that improves the alignment of subcortical brain regions. We validate this method on an MRI dataset from 92 healthy adult twins. Results are compared to those based on volumetric registration without surface constraints; the resulting mean templates resolve consistent anatomical features both subcortically and at the cortex, suggesting that the approach is well-suited for cross-subject integration of functional and anatomic data.

Marshall N. Rosenbluth Outstanding Doctoral Thesis Award Talk: Control of Non-Axisymmetric Fields With Static and Dynamic Boundary Conditions

NASA Astrophysics Data System (ADS)

Paz-Soldan, C.

2013-10-01

Small deformations of the otherwise axisymmetric field, known as ``error fields'' (EFs), lead to large changes in global MHD stability. This talk will compare results from both 1) a line-tied screw-pinch with rotating conducting walls and 2) the DIII-D tokamak to illustrate that in both devices the EF has greatest effect where it overlaps with the spatial structure of its global kink mode. In both configurations the kink structure in the symmetry direction is well described by a single mode number (azimuthal m = 1 , toroidal n = 1 , respectively) and EF ordering is clear. In the asymmetric direction (axial and poloidal, respectively) the harmonics of the kink are coupled (by line-tying and toroidicity, respectively) and thus EF ordering is not straightforward. In the pinch, the kink is axially localized to the anode region and consequently the anode EF dominates the MHD stability. In DIII-D, the poloidal harmonics of the n = 1 EF whose pitch is smaller than the local field-line pitch are empirically shown to be dominant across a wide breadth of EF optimization experiments. In analogy with the pinch, these harmonics are also where overlap with the kink is greatest and thus where the largest plasma kink response is found. The robustness of the kink structure further enables vacuum-field cost-function minimization techniques to accurately predict optimal EF correction coil currents by strongly weighting the kink-like poloidal harmonics in the minimization. To test the limits of this paradigm recent experiments in DIII-D imposed field structures that lack kink-overlapping harmonics, yielding ~10X less sensitivity. The very different plasmas of the pinch and tokamak thus both demonstrate the dominance of the kink mode in determining optimal EF correction. Supported by US DOE under DE-AC05-06OR23100, DE-FG02-00ER54603, DE-FC02-04ER54698, and NSF 0903900.

Validation of 3D RANS-SA Calculations on Strand/Cartesian Meshes

DTIC Science & Technology

2014-01-07

a parallel environment. This allows for significant gains in efficiency and scalability of domain connectiv- ity, effectively eliminating inter... equation of state , p = ρRT is used to close the equations . 4 of 22 American Institute of Aeronautics and Astronautics 6 III.A. Discretization and...Utah State University 1415 Old Main Hill - Room 64 Logan, UT 84322 -1415 1 ABSTRACT Validation of 3D RANS-SA Calculations on Strand/Cartesian Meshes

Lattice Boltzmann and Navier-Stokes Cartesian CFD Approaches for Airframe Noise Predictions

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Kocheemoolayil, Joseph G.; Kiris, Cetin C.

2017-01-01

Lattice Boltzmann (LB) and compressible Navier-Stokes (NS) equations based computational fluid dynamics (CFD) approaches are compared for simulating airframe noise. Both LB and NS CFD approaches are implemented within the Launch Ascent and Vehicle Aerodynamics (LAVA) framework. Both schemes utilize the same underlying Cartesian structured mesh paradigm with provision for local adaptive grid refinement and sub-cycling in time. We choose a prototypical massively separated, wake-dominated flow ideally suited for Cartesian-grid based approaches in this study - The partially-dressed, cavity-closed nose landing gear (PDCC-NLG) noise problem from AIAA's Benchmark problems for Airframe Noise Computations (BANC) series of workshops. The relative accuracy and computational efficiency of the two approaches are systematically compared. Detailed comments are made on the potential held by LB to significantly reduce time-to-solution for a desired level of accuracy within the context of modeling airframes noise from first principles.

Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.

2003-01-01

The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.

Welcome home, Descartes! rethinking the anthropology of the body.

PubMed

Ecks, Stefan

2009-01-01

For many scholars, the Cartesian mind/body split is one of the fundamental mistakes of the Western scientific tradition. Anthropologists who study notions of the body in cultures around the world regularly take Descartes as their point of departure. Many also suggest that breaking free from Descartes is politically liberating: if the mindful body could be rediscovered, society could move away from its materialist, positivist, and commodity-fetishizing ways. Beyond the Body Proper is anthropology's best and most comprehensive anti-Cartesian manifesto to date. This volume brings together some of the finest studies on the cultural and historical diversity of bodies and minds. Yet anthropologists' blanket rejection of the mind/body dualism seems politically self-defeating. If anthropologists want to criticize racism, gender hierarchies, or discrimination against disabled people, they need to believe that the mind is independent from the body. In other words, they need to uphold the Cartesian split.

GESFIDE-PROPELLER approach for simultaneous R2 and R2* measurements in the abdomen.

PubMed

Jin, Ning; Guo, Yang; Zhang, Zhuoli; Zhang, Longjiang; Lu, Guangming; Larson, Andrew C

2013-12-01

To investigate the feasibility of combining GESFIDE with PROPELLER sampling approaches for simultaneous abdominal R2 and R2* mapping. R2 and R2* measurements were performed in 9 healthy volunteers and phantoms using the GESFIDE-PROPELLER and the conventional Cartesian-sampling GESFIDE approaches. Images acquired with the GESFIDE-PROPELLER sequence effectively mitigated the respiratory motion artifacts, which were clearly evident in the images acquired using the conventional GESFIDE approach. There was no significant difference between GESFIDE-PROPELLER and reference MGRE R2* measurements (p=0.162) whereas the Cartesian-sampling based GESFIDE methods significantly overestimated R2* values compared to MGRE measurements (p<0.001). The GESFIDE-PROPELLER sequence provided high quality images and accurate abdominal R2 and R2* maps while avoiding the motion artifacts common to the conventional Cartesian-sampling GESFIDE approaches. © 2013 Elsevier Inc. All rights reserved.

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy.

PubMed

Issack, Bilkiss B; Roy, Pierre-Nicholas

2005-08-22

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

GESFIDE-PROPELLER Approach for Simultaneous R2 and R2* Measurements in the Abdomen

PubMed Central

Jin, Ning; Guo, Yang; Zhang, Zhuoli; Zhang, Longjiang; Lu, Guangming; Larson, Andrew C.

2013-01-01

Purpose To investigate the feasibility of combining GESFIDE with PROPELLER sampling approaches for simultaneous abdominal R2 and R2* mapping. Materials and Methods R2 and R2* measurements were performed in 9 healthy volunteers and phantoms using the GESFIDE-PROPELLER and the conventional Cartesian-sampling GESFIDE approaches. Results Images acquired with the GESFIDE-PROPELLER sequence effectively mitigated the respiratory motion artifacts, which were clearly evident in the images acquired using the conventional GESFIDE approach. There were no significant difference between GESFIDE-PROPELLER and reference MGRE R2* measurements (p = 0.162) whereas the Cartesian-sampling based GESFIDE methods significantly overestimated R2* values compared to MGRE measurements (p < 0.001). Conclusion The GESFIDE-PROPELLER sequence provided high quality images and accurate abdominal R2 and R2* maps while avoiding the motion artifacts common to the conventional Cartesian-sampling GESFIDE approaches. PMID:24041478

Simulations of 6-DOF Motion with a Cartesian Method

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)

2003-01-01

Coupled 6-DOF/CFD trajectory predictions using an automated Cartesian method are demonstrated by simulating a GBU-32/JDAM store separating from an F-18C aircraft. Numerical simulations are performed at two Mach numbers near the sonic speed, and compared with flight-test telemetry and photographic-derived data. Simulation results obtained with a sequential-static series of flow solutions are contrasted with results using a time-dependent flow solver. Both numerical methods show good agreement with the flight-test data through the first half of the simulations. The sequential-static and time-dependent methods diverge over the last half of the trajectory prediction. after the store produces peak angular rates. A cost comparison for the Cartesian method is included, in terms of absolute cost and relative to computing uncoupled 6-DOF trajectories. A detailed description of the 6-DOF method, as well as a verification of its accuracy, is provided in an appendix.

Recommended coordinate systems for thin spherocylindrical lenses.

PubMed

Deal, F C; Toop, J

1993-05-01

Because the set of thin spherocylindrical lenses forms a vector space, any such lens can be expressed in terms of its cartesian coordinates with respect to whatever set of basis lenses we may choose. Two types of cartesian coordinate systems have become prominent, those having coordinates associated with the lens power matrix and those having coordinates associated with the Humphrey Vision Analyzer. This paper emphasizes the value of a particular cartesian coordinate system of the latter type, and the cylindrical coordinate system related to it, by showing how it can simplify the trigonometry of adding lenses and how it preserves symmetry in depicting the sets of all spherical lenses, all Jackson crossed-cylinders, and all cylindrical lenses. It also discusses appropriate coordinates for keeping statistics on lenses and shows that an easy extension of the lens vector space to include general optical systems is not possible.

Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation

NASA Technical Reports Server (NTRS)

Buning, Pieter G.; Pulliam, Thomas H.

2011-01-01

An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.

Reynolds stress and heat flux in spherical shell convection

NASA Astrophysics Data System (ADS)

Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg, A.; Chatterjee, P.

2011-07-01

Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims: Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods: We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results: For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong "banana cells". Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance. Movies and Appendix A are available in electronic form at http://www.aanda.org

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2004-01-01

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Acoustic Radiation Pressure

NASA Technical Reports Server (NTRS)

Cantrell, John H.

2018-01-01

The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.

Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment

DOE R&D Accomplishments Database

Marcus, R. A.

1964-01-01

In its usual form activated complex theory assumes a quasi-equilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced.

Seismic receiver function interpretation: Ps splitting or anisotropic underplating?

NASA Astrophysics Data System (ADS)

Liu, Z.; Park, J. J.

2016-12-01

Crustal anisotropy is crucial to understanding the evolutionary history of Earth's lithosphere. Shear-wave splitting of Moho P-to-s converted phases in receiver functions has often been used to infer crustal anisotropy. In addition to estimating birefringence directly, the harmonic variations of Moho Ps phases in delay times can be used to infer splitting parameters of averaged anisotropy in the crust. However, crustal anisotropy may localize at various levels within the crust due to complex deformational processes. Layered anisotropy requires careful investigation of the distribution of anisotropy before interpreting Moho Ps splitting. In this study, we show results from stations ARU in Russia, KIP in Hawaiian Islands and LSA in Tibetan Plateau, where layered anisotropy is well constrained by intra-crust Ps conversions at high frequencies using harmonic decomposition of multiple-taper correlation receiver functions. Anisotropic velocity models are inferred by forward-modeling decomposed RF waveforms. Our results of ARU and KIP show that the harmonic behavior of Moho Ps phases can be explained by a uniformly anisotropic crust model at lower cut-off frequencies, but higher-resolution RF-signals reveal a thin, highly anisotropic layer at the base of the crust. Station LSA tells a similar story with a twist: a modest Ps birefringence is revealed at high frequencies to stem from multiple thin (5-10-km) layers of localized anisotropy within the middle crust, but no strongly-sheared basal layer is inferred. We suggest that the harmonic variation of Moho Ps phases should always be investigated as a result of anisotropic layering using RFs with frequency content above 1Hz, rather than simply reporting averaged anisotropy of the whole crust.

Elastic continuum theory: towards understanding of the twist-bend nematic phases.

PubMed

Barbero, G; Evangelista, L R; Rosseto, M P; Zola, R S; Lelidis, I

2015-09-01

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

Ideal flow theory for the double - shearing model as a basis for metal forming design

NASA Astrophysics Data System (ADS)

Alexandrov, S.; Trung, N. T.

2018-02-01

In the case of Tresca’ solids (i.e. solids obeying the Tresca yield criterion and its associated flow rule) ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal stress (and strain rate) is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is often advantageous for metal forming processes. Therefore, the ideal flow theory is used as the basis of a procedure for the preliminary design of such processes. The present paper extends the theory of stationary planar ideal flow to pressure dependent materials obeying the double shearing model and the double slip and rotation model. It is shown that the original problem of plasticity reduces to a purely geometric problem. The corresponding system of equations is hyperbolic. The characteristic relations are integrated in elementary functions. In regions where one family of characteristics is straight, mapping between the principal lines and Cartesian coordinates is determined by linear ordinary differential equations. An illustrative example is provided.

Shock interaction with deformable particles using a constrained interface reinitialization scheme

NASA Astrophysics Data System (ADS)

Sridharan, P.; Jackson, T. L.; Zhang, J.; Balachandar, S.; Thakur, S.

2016-02-01

In this paper, we present axisymmetric numerical simulations of shock propagation in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. We use the Mie-Gruneisen equation of state to describe both the medium and the particle. The numerical method is a finite-volume based solver on a Cartesian grid, that allows for multi-material interfaces and shocks, and uses a novel constrained reinitialization scheme to precisely preserve particle mass and volume. We compute the unsteady inviscid drag coefficient as a function of time, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. We also compute the mass-averaged particle pressure and show that the observed oscillations inside the particle are on the particle-acoustic time scale. Finally, we present simplified point-particle models that can be used for macroscale simulations. In the Appendix, we extend the isothermal or isentropic assumption concerning the point-force models to non-ideal equations of state, thus justifying their use for the current problem.

Development of advanced control schemes for telerobot manipulators

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Zhou, Zhen-Lei

1991-01-01

To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed.

High accuracy binary black hole simulations with an extended wave zone

NASA Astrophysics Data System (ADS)

Pollney, Denis; Reisswig, Christian; Schnetter, Erik; Dorband, Nils; Diener, Peter

2011-02-01

We present results from a new code for binary black hole evolutions using the moving-puncture approach, implementing finite differences in generalized coordinates, and allowing the spacetime to be covered with multiple communicating nonsingular coordinate patches. Here we consider a regular Cartesian near-zone, with adapted spherical grids covering the wave zone. The efficiencies resulting from the use of adapted coordinates allow us to maintain sufficient grid resolution to an artificial outer boundary location which is causally disconnected from the measurement. For the well-studied test case of the inspiral of an equal-mass nonspinning binary (evolved for more than 8 orbits before merger), we determine the phase and amplitude to numerical accuracies better than 0.010% and 0.090% during inspiral, respectively, and 0.003% and 0.153% during merger. The waveforms, including the resolved higher harmonics, are convergent and can be consistently extrapolated to r→∞ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to (ℓ,m)=(6,6)) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass Mirr=0.884355±20×10-6 and spin Sf/Mf2=0.686923±10×10-6.

Uniform electron gases. III. Low-density gases on three-dimensional spheres.

PubMed

Agboola, Davids; Knol, Anneke L; Gill, Peter M W; Loos, Pierre-François

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

Using Quasi-3D OSIRIS simulations of LWFA to study generating high brightness electron beams using ionization and density downramp injection

NASA Astrophysics Data System (ADS)

Dalichaouch, Thamine; Davidson, Asher; Xu, Xinlu; Yu, Peicheng; Tsung, Frank; Mori, Warren; Li, Fei; Zhang, Chaojie; Lu, Wei; Vieira, Jorge; Fonseca, Ricardo

2016-10-01

In the past few decades, there has been much progress in theory, simulation, and experiment towards using Laser wakefield acceleration (LWFA) as the basis for designing and building compact x-ray free-electron-lasers (XFEL) as well as a next generation linear collider. Recently, ionization injection and density downramp injection have been proposed and demonstrated as a controllable injection scheme for creating higher quality and ultra-bright relativistic electron beams using LWFA. However, full-3D simulations of plasma-based accelerators are computationally intensive, sometimes taking 100 millions of core-hours on today's computers. A more efficient quasi-3D algorithm was developed and implemented into OSIRIS using a particle-in-cell description with a charge conserving current deposition scheme in r - z and a gridless Fourier expansion in ϕ. Due to the azimuthal symmetry in LWFA, quasi-3D simulations are computationally more efficient than 3D cartesian simulations since only the first few harmonics in are needed ϕ to capture the 3D physics of LWFA. Using the quasi-3D approach, we present preliminary results of ionization and down ramp triggered injection and compare the results against 3D LWFA simulations. This work was supported by DOE and NSF.

Effect of higher harmonic control on helicopter rotor blade-vortex interaction noise: Prediction and initial validation

NASA Technical Reports Server (NTRS)

Beaumier, P.; Prieur, J.; Rahier, G.; Spiegel, P.; Demargne, A.; Tung, C.; Gallman, J. M.; Yu, Y. H.; Kube, R.; Vanderwall, B. G.

1995-01-01

The paper presents a status of theoretical tools of AFDD, DLR, NASA and ONERA for prediction of the effect of HHC on helicopter main rotor BVI noise. Aeroacoustic predictions from the four research centers, concerning a wind tunnel simulation of a typical descent flight case without and with HHC are presented and compared. The results include blade deformation, geometry of interacting vortices, sectional loads and noise. Acoustic predictions are compared to experimental data. An analysis of the results provides a first insight of the mechanisms by which HHC may affect BVI noise.

Optimal approximation of harmonic growth clusters by orthogonal polynomials

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

Teodorescu, Razvan

2008-01-01

Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles

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

Sabitov, I Kh

We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.

Convection-driven tectonics on Venus

NASA Astrophysics Data System (ADS)

Phillips, R. J.

1990-02-01

An analysis is presented of convective stress coupling to an elastic lithosphere as applied to Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity, and a Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. An elastic-plastic analysis is carried out for the deformation of a model Venus lithosphere. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere.

Multishot cartesian turbo spin-echo diffusion imaging using iterative POCSMUSE Reconstruction.

PubMed

Zhang, Zhe; Zhang, Bing; Li, Ming; Liang, Xue; Chen, Xiaodong; Liu, Renyuan; Zhang, Xin; Guo, Hua

2017-07-01

To report a diffusion imaging technique insensitive to off-resonance artifacts and motion-induced ghost artifacts using multishot Cartesian turbo spin-echo (TSE) acquisition and iterative POCS-based reconstruction of multiplexed sensitivity encoded magnetic resonance imaging (MRI) (POCSMUSE) for phase correction. Phase insensitive diffusion preparation was used to deal with the violation of the Carr-Purcell-Meiboom-Gill (CPMG) conditions of TSE diffusion-weighted imaging (DWI), followed by a multishot Cartesian TSE readout for data acquisition. An iterative diffusion phase correction method, iterative POCSMUSE, was developed and implemented to eliminate the ghost artifacts in multishot TSE DWI. The in vivo human brain diffusion images (from one healthy volunteer and 10 patients) using multishot Cartesian TSE were acquired at 3T and reconstructed using iterative POCSMUSE, and compared with single-shot and multishot echo-planar imaging (EPI) results. These images were evaluated by two radiologists using visual scores (considering both image quality and distortion levels) from 1 to 5. The proposed iterative POCSMUSE reconstruction was able to correct the ghost artifacts in multishot DWI. The ghost-to-signal ratio of TSE DWI using iterative POCSMUSE (0.0174 ± 0.0024) was significantly (P < 0.0005) smaller than using POCSMUSE (0.0253 ± 0.0040). The image scores of multishot TSE DWI were significantly higher than single-shot (P = 0.004 and 0.006 from two reviewers) and multishot (P = 0.008 and 0.004 from two reviewers) EPI-based methods. The proposed multishot Cartesian TSE DWI using iterative POCSMUSE reconstruction can provide high-quality diffusion images insensitive to motion-induced ghost artifacts and off-resonance related artifacts such as chemical shifts and susceptibility-induced image distortions. 1 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2017;46:167-174. © 2016 International Society for Magnetic Resonance in Medicine.

Optimized respiratory-resolved motion-compensated 3D Cartesian coronary MR angiography.

PubMed

Correia, Teresa; Ginami, Giulia; Cruz, Gastão; Neji, Radhouene; Rashid, Imran; Botnar, René M; Prieto, Claudia

2018-04-22

To develop a robust and efficient reconstruction framework that provides high-quality motion-compensated respiratory-resolved images from free-breathing 3D whole-heart Cartesian coronary magnetic resonance angiography (CMRA) acquisitions. Recently, XD-GRASP (eXtra-Dimensional Golden-angle RAdial Sparse Parallel MRI) was proposed to achieve 100% scan efficiency and provide respiratory-resolved 3D radial CMRA images by exploiting sparsity in the respiratory dimension. Here, a reconstruction framework for Cartesian CMRA imaging is proposed, which provides respiratory-resolved motion-compensated images by incorporating 2D beat-to-beat translational motion information to increase sparsity in the respiratory dimension. The motion information is extracted from interleaved image navigators and is also used to compensate for 2D translational motion within each respiratory phase. The proposed Optimized Respiratory-resolved Cartesian Coronary MR Angiography (XD-ORCCA) method was tested on 10 healthy subjects and 2 patients with cardiovascular disease, and compared against XD-GRASP. The proposed XD-ORCCA provides high-quality respiratory-resolved images, allowing clear visualization of the right and left coronary arteries, even for irregular breathing patterns. Compared with XD-GRASP, the proposed method improves the visibility and sharpness of both coronaries. Significant differences (p < .05) in visible vessel length and proximal vessel sharpness were found between the 2 methods. The XD-GRASP method provides good-quality images in the absence of intraphase motion. However, motion blurring is observed in XD-GRASP images for respiratory phases with larger motion amplitudes and subjects with irregular breathing patterns. A robust respiratory-resolved motion-compensated framework for Cartesian CMRA has been proposed and tested in healthy subjects and patients. The proposed XD-ORCCA provides high-quality images for all respiratory phases, independently of the regularity of the breathing pattern. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

An ODE-Based Wall Model for Turbulent Flow Simulations

NASA Technical Reports Server (NTRS)

Berger, Marsha J.; Aftosmis, Michael J.

2017-01-01

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

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Aerodynamic Performance of Missile Configurations at Transonic Speeds Including the Effects of a Jet Plume

DTIC Science & Technology

1976-02-18

shows three different body-fixed Cartesian coordinate systems used in the present analysis . The Cartesian coordinate system with the axes x, y, and z... using the analysis of the previous section. A different situation exists when the base pressure is greater than the ambient value. Now it becomes... USED IN THE PRESENT ANALYSIS Figure 26. Computational model used in Section!!. D. 85 FIN BODY 00 C> Z t t Voa (b) FLOW FOR V oa z

Cartesian oval representation of freeform optics in illumination systems.

PubMed

Michaelis, D; Schreiber, P; Bräuer, A

2011-03-15

The geometrical method for constructing optical surfaces for illumination purpose developed by Oliker and co-workers [Trends in Nonlinear Analysis (Springer, 2003)] is generalized in order to obtain freeform designs in arbitrary optical systems. The freeform is created by a set of primitive surface elements, which are generalized Cartesian ovals adapted to the given optical system. Those primitives are determined by Hamiltonian theory of ray optics. The potential of this approach is demonstrated by some examples, e.g., freeform lenses with collimating front elements.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

2002-09-03

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

ψ -ontology result without the Cartesian product assumption

NASA Astrophysics Data System (ADS)

Myrvold, Wayne C.

2018-05-01

We introduce a weakening of the preparation independence postulate of Pusey et al. [Nat. Phys. 8, 475 (2012), 10.1038/nphys2309] that does not presuppose that the space of ontic states resulting from a product-state preparation can be represented by the Cartesian product of subsystem state spaces. On the basis of this weakened assumption, it is shown that, in any model that reproduces the quantum probabilities, any pair of pure quantum states |ψ >,|ϕ > with <ϕ |ψ > ≤1 /√{2 } must be ontologically distinct.

Mercury's Low-Degree Geoid and Topography from Insolation-Driven Elastic Deformation

NASA Astrophysics Data System (ADS)

Tosi, N.; Cadek, O.; Padovan, S.; Wieczorek, M. A.

2014-12-01

Because of Mercury's high eccentricity, nearly zero obliquity, and 3:2 spin-orbit resonance, the planet's surface is characterized by an average insolation pattern resulting in longitudinal and latitudinal temperature variations that can be expressed in terms of the (2,0), (2,2) and (4,0) harmonics [Vasavada et al., 1999]. We show that the temperature anomalies that propagate from the surface into the deep mantle can be used to interpret the above harmonics of the geoid and topography spectra in terms of the elastic response of the lithosphere and mantle. Using 3D numerical simulations of thermal evolution constrained by MESSENGER observations [Tosi et al., 2013], we first demonstrate that mantle convection either ceased in the past or, at most, is very weak at present, implying that the mantle is in a conductive or nearly-conductive state. As a consequence, the power spectra of the geoid and topography due to present-day mantle convection only are orders of magnitude smaller than the observed ones. We assume therefore that present-day heat transport in the mantle occurs primarily via thermal conduction and numerically solve the diffusion equation in a 3D spherical shell with variable surface temperature and internal heat sources partitioned between the mantle and a crust of variable thickness according to different enrichment factors. We obtain a set of temperature distributions that are employed to calculate the deformation of a compressible elastic layer overlying a quasi-hydrostatic mantle in which shear stresses are assumed to be relaxed and deformation solely induced by thermal and mechanical compressibility. The surface displacements calculated with this model are then compared against the observed topography, while the internal density anomalies and the displacements of the surface and core-mantle boundary are used to calculate Mercury's geoid. We thoroughly explore the parameter space by varying the thickness of the boundary between the elastic and quasi-hydrostatic layers, the lithosphere's elastic parameters and the coefficient of thermal expansion. Our model can reproduce more than 90% of the observed low-degree geoid and topography thereby allowing us to constrain the effective thickness of Mercury's elastic lithosphere.

A boundary element method for particle and droplet electrohydrodynamics in the Quincke regime

NASA Astrophysics Data System (ADS)

Das, Debasish; Saintillan, David

2014-11-01

Quincke electrorotation is the spontaneous rotation of dielectric particles suspended in a dielectric liquid of higher conductivity when placed in a sufficiently strong electric field. This phenomenon of Quincke rotation has interesting implications for the rheology of these suspensions, whose effective viscosity can be controlled and reduced by application of an external field. While spherical harmonics can be used to solve the governing equations for a spherical particle, they cannot be used to study the dynamics of particles of more complex shapes or deformable particles or droplets. Here, we develop a novel boundary element formulation to model the dynamics of a dielectric particle under Quincke rotation based on the Taylor-Melcher leaky dielectric model, and compare the numerical results to theoretical predictions. We then employ this boundary element method to analyze the dynamics of a two-dimensional drop under Quincke rotation, where we allow the drop to deform under the electric field. Extensions to three-dimensions and to the electrohydrodynamic interactions of multiple droplets are also discussed.

Energy harvesting with stacked dielectric elastomer transducers: Nonlinear theory, optimization, and linearized scaling law

NASA Astrophysics Data System (ADS)

Tutcuoglu, A.; Majidi, C.

2014-12-01

Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.

State-of-the-art of high-speed propeller noise prediction - A multidisciplinary approach and comparison with measured data

NASA Technical Reports Server (NTRS)

Dunn, Mark H.; Farassat, F.

1990-01-01

The results of NASA's Propeller Test Assessment program involving extensive flight tests of a large-scale advanced propeller are presented. This has provided the opportunity to evaluate the current capability of advanced propeller noise prediction utilizing principally the exterior acoustic measurements for the prediction of exterior noise. The principal object of this study was to evaluate the state-of-the-art of noise prediction for advanced propellers utilizing the best available codes of the disciplines involved. The effects of blade deformation on the aerodynamics and noise of advanced propellers were also studied. It is concluded that blade deformation can appreciably influence propeller noise and aerodynamics, and that, in general, centrifugal and blade forces must both be included in the calculation of blade forces. It is noted that the present capability for free-field noise prediction of the first three harmonics for advanced propellers is fairly good. Detailed data and diagrams of the test results are presented.

Shell Model Far From Stability: Island of Inversion Mergers

NASA Astrophysics Data System (ADS)

Nowacki, F.; Poves, A.

2018-02-01

In this study we propose a common mechanism for the disappearance of shell closures far from stabilty. With the use of Large Scale Shell Model calculations (SM-CI), we predict that the region of deformation which comprises the heaviest Chromium and Iron isotopes at and beyond N=40 will merge with a new one at N=50 in an astonishing parallel to the N=20 and N=28 case in the Neon and Magnesium isotopes. We propose a valence space including the full pf-shell for the protons and the full sdg shell for the neutrons, which represents a come-back of the the harmonic oscillator shells in the very neutron rich regime. Our calculations preserve the doubly magic nature of the ground state of 78Ni, which, however, exhibits a well deformed prolate band at low excitation energy, providing a striking example of shape coexistence far from stability. This new Island of Inversion (IoI) adds to the four well documented ones at N=8, 20, 28 and 40.

On the motion of a body whose dynamical structure is variable

NASA Astrophysics Data System (ADS)

Kolbut, V. R.

1982-02-01

Abul'naga and Barkin (1980) have considered the problem of the particular solutions for the translational-rotational motion of two rigid bodies, taking into account the third harmonics in the force function of their Newtonian interaction. Attention is given to the Hamiltonian of the problem, the distinctive motion of a body whose dynamical structure is variable, and the introduction of a known function of an independent variable. The solutions may be written in the form of a series. In the stationary case the solutions are the same as those provided by Abul'naga and Barkin. The variation in the dynamical structure of a constant-mass body may occur either because of changes in the density asymmetry or through redistribution of mass within the body. This last case is relevant to the analysis of effects arising from deformation of the body. One instance of a small distortion of this kind would be the tidal deformation of the earth.

Fission barriers at the end of the chart of the nuclides

NASA Astrophysics Data System (ADS)

Möller, Peter; Sierk, Arnold J.; Ichikawa, Takatoshi; Iwamoto, Akira; Mumpower, Matthew

2015-02-01

We present calculated fission-barrier heights for 5239 nuclides for all nuclei between the proton and neutron drip lines with 171 ≤A ≤330 . The barriers are calculated in the macroscopic-microscopic finite-range liquid-drop model with a 2002 set of macroscopic-model parameters. The saddle-point energies are determined from potential-energy surfaces based on more than 5 000 000 different shapes, defined by five deformation parameters in the three-quadratic-surface shape parametrization: elongation, neck diameter, left-fragment spheroidal deformation, right-fragment spheroidal deformation, and nascent-fragment mass asymmetry. The energy of the ground state is determined by calculating the lowest-energy configuration in both the Nilsson perturbed-spheroid (ɛ ) and the spherical-harmonic (β ) parametrizations, including axially asymmetric deformations. The lower of the two results (correcting for zero-point motion) is defined as the ground-state energy. The effect of axial asymmetry on the inner barrier peak is calculated in the (ɛ ,γ ) parametrization. We have earlier benchmarked our calculated barrier heights to experimentally extracted barrier parameters and found average agreement to about 1 MeV for known data across the nuclear chart. Here we do additional benchmarks and investigate the qualitative and, when possible, quantitative agreement and/or consistency with data on β -delayed fission, isotope generation along prompt-neutron-capture chains in nuclear-weapons tests, and superheavy-element stability. These studies all indicate that the model is realistic at considerable distances in Z and N from the region of nuclei where its parameters were determined.

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

Möller, Peter; Sierk, Arnold J.; Ichikawa, Takatoshi

We present calculated fission-barrier heights for 5239 nuclides for all nuclei between the proton and neutron drip lines with 171 ≤ A ≤ 330. The barriers are calculated in the macroscopic-microscopic finite-range liquid-drop (FRLDM) with a 2002 set of macroscopic-model parameters. The saddle-point energies are determined from potential-energy surfaces based on more than five million different shapes, defined by five deformation parameters in the three-quadratic-surface shape parametrization: elongation, neck diameter, left-fragment spheroidal deformation, right-fragment spheroidal deformation, and nascent-fragment mass asymmetry. The energy of the ground state is determined by calculating the lowest-energy configuration in both the Nilsson perturbed-spheroid (ϵ) andmore » the spherical-harmonic (β) parametrizations, including axially asymmetric deformations. The lower of the two results (correcting for zero-point motion) is defined as the ground-state energy. The effect of axial asymmetry on the inner barrier peak is calculated in the (ϵ,γ) parametrization. We have earlier benchmarked our calculated barrier heights to experimentally extracted barrier parameters and found average agreement to about one MeV for known data across the nuclear chart. Here we do additional benchmarks and investigate the qualitative and, when possible, quantitative agreement and/or consistency with data on β-delayed fission, isotope generation along prompt-neutron-capture chains in nuclear-weapons tests, and superheavy-element stability. In addition these studies all indicate that the model is realistic at considerable distances in Z and N from the region of nuclei where its parameters were determined.« less

Improving the detection of tectonic transients in Japan by accounting for Earth's deformation response to surface mass loading

NASA Astrophysics Data System (ADS)

Martens, H. R.; Simons, M.; Moore, A. W.; Owen, S. E.; Rivera, L. A.

2016-12-01

We explore the contributions of oceanic, atmospheric, and hydrologic mass loading to Global Navigation Satellite System (GNSS)-inferred observations of surface displacements in Japan. Surface mass loading (SML) generates mm- to cm-level deformation of the solid Earth on time scales of hours to years, which exceeds the measurement uncertainties of most GNSS position estimates. By improving the efficiency and accuracy of the prediction and empirical estimation of SML response, we aim to reduce the variance of GNSS time series and therefore enhance the ability to resolve subtle tectonic signals, such as aseismic transients associated with subduction zone processes. Using the GIPSY software in precise point positioning mode, we estimate time series of sub-daily receiver positions for the GNSS Earth Observation Network System (GEONET) in Japan. We also model the Earth's elastic deformation response to a variety of surface mass loads, including loads of atmospheric (e.g., ECMWF) and oceanic (e.g., TPXO8-Atlas, ECCO2) origin. We extract periodic signals, such as the ocean tides and seasonal variations in hydrological loading, using harmonic analysis. Deformation caused by non-periodic loads, such as non-tidal oceanic and atmospheric loads, can be predicted and removed to further reduce the variance. We seek to streamline the workflow for estimating SML-induced surface displacements from a variety of sources in order to account for loading signals in routine GNSS data processing, thereby improving the ability to assess the mechanics of plate boundaries.

On Statistical Analysis of Neuroimages with Imperfect Registration

PubMed Central

Kim, Won Hwa; Ravi, Sathya N.; Johnson, Sterling C.; Okonkwo, Ozioma C.; Singh, Vikas

2016-01-01

A variety of studies in neuroscience/neuroimaging seek to perform statistical inference on the acquired brain image scans for diagnosis as well as understanding the pathological manifestation of diseases. To do so, an important first step is to register (or co-register) all of the image data into a common coordinate system. This permits meaningful comparison of the intensities at each voxel across groups (e.g., diseased versus healthy) to evaluate the effects of the disease and/or use machine learning algorithms in a subsequent step. But errors in the underlying registration make this problematic, they either decrease the statistical power or make the follow-up inference tasks less effective/accurate. In this paper, we derive a novel algorithm which offers immunity to local errors in the underlying deformation field obtained from registration procedures. By deriving a deformation invariant representation of the image, the downstream analysis can be made more robust as if one had access to a (hypothetical) far superior registration procedure. Our algorithm is based on recent work on scattering transform. Using this as a starting point, we show how results from harmonic analysis (especially, non-Euclidean wavelets) yields strategies for designing deformation and additive noise invariant representations of large 3-D brain image volumes. We present a set of results on synthetic and real brain images where we achieve robust statistical analysis even in the presence of substantial deformation errors; here, standard analysis procedures significantly under-perform and fail to identify the true signal. PMID:27042168

Aligning Spinoza with Descartes: An informed Cartesian account of the truth bias.

PubMed

Street, Chris N H; Kingstone, Alan

2017-08-01

There is a bias towards believing information is true rather than false. The Spinozan account claims there is an early, automatic bias towards believing. Only afterwards can people engage in an effortful re-evaluation and disbelieve the information. Supporting this account, there is a greater bias towards believing information is true when under cognitive load. However, developing on the Adaptive Lie Detector (ALIED) theory, the informed Cartesian can equally explain this data. The account claims the bias under load is not evidence of automatic belief; rather, people are undecided, but if forced to guess they can rely on context information to make an informed judgement. The account predicts, and we found, that if people can explicitly indicate their uncertainty, there should be no bias towards believing because they are no longer required to guess. Thus, we conclude that belief formation can be better explained by an informed Cartesian account - an attempt to make an informed judgment under uncertainty. © 2016 The British Psychological Society.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Rapid Measurement and Correction of Phase Errors from B0 Eddy Currents: Impact on Image Quality for Non-Cartesian Imaging

PubMed Central

Brodsky, Ethan K.; Klaers, Jessica L.; Samsonov, Alexey A.; Kijowski, Richard; Block, Walter F.

2014-01-01

Non-Cartesian imaging sequences and navigational methods can be more sensitive to scanner imperfections that have little impact on conventional clinical sequences, an issue which has repeatedly complicated the commercialization of these techniques by frustrating transitions to multi-center evaluations. One such imperfection is phase errors caused by resonant frequency shifts from eddy currents induced in the cryostat by time-varying gradients, a phenomemon known as B0 eddy currents. These phase errors can have a substantial impact on sequences that use ramp sampling, bipolar gradients, and readouts at varying azimuthal angles. We present a method for measuring and correcting phase errors from B0 eddy currents and examine the results on two different scanner models. This technique yields significant improvements in image quality for high-resolution joint imaging on certain scanners. The results suggest that correction of short time B0 eddy currents in manufacturer provided service routines would simplify adoption of non-Cartesian sampling methods. PMID:22488532

Laser-induced nonlinear crystalline waveguide on glass fiber format and diode-pumped second harmonic generation

NASA Astrophysics Data System (ADS)

Shi, Jindan; Feng, Xian

2018-03-01

We report a diode pumped self-frequency-doubled nonlinear crystalline waveguide on glass fiber. A ribbon fiber has been drawn on the glass composition of 50GeO2-25B2O3-25(La,Yb)2O3. Surface channel waveguides have been written on the surface of the ribbon fiber, using space-selective laser heating method with the assistance of a 244 nm CW UV laser. The Raman spectrum of the written area indicates that the waveguide is composed of structure-deformed nonlinear (La,Yb)BGeO5 crystal. The laser-induced surface wavy cracks have also been observed and the forming mechanism of the wavy cracks has been discussed. Efficient second harmonic generation has been observed from the laser-induced crystalline waveguide, using a 976 nm diode pump. 13 μW of 488 nm output has been observed from a 17 mm long waveguide with 26.0 mW of launched diode pump power, corresponding to a normalized conversion efficiency of 4.4%W-1.

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

NASA Astrophysics Data System (ADS)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices

NASA Astrophysics Data System (ADS)

Wang, Yan-Feng; Wang, Yue-Sheng; Zhang, Chuanzeng

2014-12-01

In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

Anomalous tidal loading signals in South-West England and Brittany

NASA Astrophysics Data System (ADS)

Keshin, M.; Penna, N. T.; Clarke, P. J.; Bos, M. S.; Baker, T. F.

2010-05-01

The tidal deformation of the Earth, including ocean tide loading (OTL), sheds light on the Earth's internal structure. Uncertainties in the knowledge of this deformation may be a source of both direct and propagated periodic errors in GPS geodesy. The increasing number of global GPS stations with long histories of observations, as well as recent developments in precise GPS geodesy such as the availability of reprocessed satellite orbits, enables further study of these geophysical and geodetic phenomena. There are more than 10 worldwide regions where OTL displacement amplitudes exceed 25mm. In our work we considered one such region covering South-West England and stretching southward along the coasts of France, Spain and Portugal. Estimates of three-dimensional harmonic site motion at each of the principal diurnal (K1, O1, P1, Q1) and semi-diurnal (K2, M2, N2, S2) frequencies were obtained for 40 European stations with at least 2 year observation span, using the GIPSY-OASIS II software package with reprocessed precise satellite orbits from JPL. All GPS data available from 2002.0 to 2010.0 were considered. 34 stations were situated close to the Atlantic coast; a further 6 inland stations at similar latitudes were processed as a check on solid Earth tide models. Inter-model OTL displacement differences are small, especially for the inland sites; the problematic Bristol Channel area of South-West England was excluded. We validated the quality of our GPS estimates by using and comparing three different analysis strategies: (1) Harmonic estimation of total tidal displacement in 24-hour Precise Point Positioning (PPP) batch solutions: harmonic displacements are estimated per coordinate component for each of the eight principal tidal constituents. OTL is not modelled a priori, and nodal corrections are applied in post-processing after combination of the daily results; (2) Harmonic estimation of residual tidal displacement in 24-hour PPP batch solutions: OTL is modelled a priori using the FES2004 model in the reference frame of the whole Earth system (CM); the residual harmonic displacements are estimated per component per principal tidal constituent. Minor tidal harmonics are removed a priori using the routine "hardisp" by D. Agnew. Because of this, post-processing nodal corrections are not applied; (3) Amplitude and phase from kinematic PPP processing: kinematic GPS processing with a priori OTL modelling using FES2004 and hardisp as in (2); amplitude spectra are later estimated from the entire coordinate time series using the Lomb-Scargle periodogram method. We typically obtain excellent (0.3-0.7mm except for the K1 and K2 constituents) phasor agreement between all three strategies, comparable to the inter-model agreement between computed OTL displacements and suggesting that the GPS analysis strategy robustly detects actual tidal displacements. For sites in inland Europe where computed OTL displacements are less than 10mm with inter-model differences of less than 0.2mm, residual harmonic amplitudes are also at the 0.3-0.7mm level, confirming that solid Earth tides are modelled to at least this accuracy. For GPS stations located in South-West England and Brittany, onshore of the continental shelf, anomalous residual tidal signals were detected of about 2-3mm magnitude for the vertical M2 OTL constituent (10% of the expected signal). In contrast, sites in the Iberian Peninsula, with similar expected OTL magnitudes, have residuals at the expected 0.3-0.7mm level. Sites near to the Bay of Biscay show transitional behaviour between these regimes. Therefore at these locations, the different modern ocean tide models that agree very well must all either be systematically in error, or the difference in behaviour may be caused by errors in the displacement Green's functions applicable to loads on the nearby continental shelf.

Applications of Differential Operators in Geodetic Coordinates

NASA Astrophysics Data System (ADS)

Hallam, K. A. T.; Oliveira, V. C., Jr.

2016-12-01

The definition of coordinate systems and frames is an essential step to even start a problem in physical geodesy and geophysics. The commonly used coordinate systems when dealing with problems on (or close to) the surface of the Earth are the geocentric Cartesian coordinates, geocentric spherical coordinates and geodetic coordinates. Transformations between Cartesian and spherical coordinates are widely known and used for several problems. More complex, but not less important, are the transformations between Cartesian and geodetic coordinates. Although most of them utilize an ellipsoidal frame in which the three coordinates are geodetic longitude (λ), geodetic latitude (φ) and the scale factor (u), the latter being a combination of X and Y, not the geometric height (h), the data sets measured on (or close to) the surface of the Earth are given in geodetic coordinates which are usually transformed into Cartesian or spherical coordinates for mathematical developments. It would be useful, however, to preclude coordinate transformations for the subsequent operations. Thus, we derived expressions for the gradient and Laplacian operators in geodetic coordinates in order to make further use on mathematical developments. Results obtained analitically and from numerical simulations validate our expressions. We applied our operators to derive the gravitational field produced by a point mass and used it for representing the regional gravity field in geodetic coordinates. The results obtained with the numerical simulations show that our approach is potentially useful in solving a wide range of problems in physical geodesy and geophysics.

Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

NASA Astrophysics Data System (ADS)

Červený, Vlastislav; Pšenčík, Ivan

2017-08-01

Integral superposition of Gaussian beams is a useful generalization of the standard ray theory. It removes some of the deficiencies of the ray theory like its failure to describe properly behaviour of waves in caustic regions. It also leads to a more efficient computation of seismic wavefields since it does not require the time-consuming two-point ray tracing. We present the formula for a high-frequency elementary Green function expressed in terms of the integral superposition of Gaussian beams for inhomogeneous, isotropic or anisotropic, layered structures, based on the dynamic ray tracing (DRT) in Cartesian coordinates. For the evaluation of the superposition formula, it is sufficient to solve the DRT in Cartesian coordinates just for the point-source initial conditions. Moreover, instead of seeking 3 × 3 paraxial matrices in Cartesian coordinates, it is sufficient to seek just 3 × 2 parts of these matrices. The presented formulae can be used for the computation of the elementary Green function corresponding to an arbitrary direct, multiply reflected/transmitted, unconverted or converted, independently propagating elementary wave of any of the three modes, P, S1 and S2. Receivers distributed along or in a vicinity of a target surface may be situated at an arbitrary part of the medium, including ray-theory shadow regions. The elementary Green function formula can be used as a basis for the computation of wavefields generated by various types of point sources (explosive, moment tensor).

Autocalibrating motion-corrected wave-encoding for highly accelerated free-breathing abdominal MRI.

PubMed

Chen, Feiyu; Zhang, Tao; Cheng, Joseph Y; Shi, Xinwei; Pauly, John M; Vasanawala, Shreyas S

2017-11-01

To develop a motion-robust wave-encoding technique for highly accelerated free-breathing abdominal MRI. A comprehensive 3D wave-encoding-based method was developed to enable fast free-breathing abdominal imaging: (a) auto-calibration for wave-encoding was designed to avoid extra scan for coil sensitivity measurement; (b) intrinsic butterfly navigators were used to track respiratory motion; (c) variable-density sampling was included to enable compressed sensing; (d) golden-angle radial-Cartesian hybrid view-ordering was incorporated to improve motion robustness; and (e) localized rigid motion correction was combined with parallel imaging compressed sensing reconstruction to reconstruct the highly accelerated wave-encoded datasets. The proposed method was tested on six subjects and image quality was compared with standard accelerated Cartesian acquisition both with and without respiratory triggering. Inverse gradient entropy and normalized gradient squared metrics were calculated, testing whether image quality was improved using paired t-tests. For respiratory-triggered scans, wave-encoding significantly reduced residual aliasing and blurring compared with standard Cartesian acquisition (metrics suggesting P < 0.05). For non-respiratory-triggered scans, the proposed method yielded significantly better motion correction compared with standard motion-corrected Cartesian acquisition (metrics suggesting P < 0.01). The proposed methods can reduce motion artifacts and improve overall image quality of highly accelerated free-breathing abdominal MRI. Magn Reson Med 78:1757-1766, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Spinoza's error: memory for truth and falsity.

PubMed

Nadarevic, Lena; Erdfelder, Edgar

2013-02-01

Two theoretical frameworks have been proposed to account for the representation of truth and falsity in human memory: the Cartesian model and the Spinozan model. Both models presume that during information processing a mental representation of the information is stored along with a tag indicating its truth value. However, the two models disagree on the nature of these tags. According to the Cartesian model, true information receives a "true" tag and false information receives a "false" tag. In contrast, the Spinozan model claims that only false information receives a "false" tag, whereas untagged information is automatically accepted as true. To test the Cartesian and Spinozan models, we conducted two source memory experiments in which participants studied true and false trivia statements from three different sources differing in credibility (i.e., presenting 100% true, 50% true and 50% false, or 100% false statements). In Experiment 1, half of the participants were informed about the source credibility prior to the study phase. As compared to a control group, this precue group showed improved source memory for both true and false statements, but not for statements with an uncertain validity status. Moreover, memory did not differ for truth and falsity in the precue group. As Experiment 2 revealed, this finding is replicated even when using a 1-week rather than a 20-min retention interval between study and test phases. The results of both experiments clearly contradict the Spinozan model but can be explained in terms of the Cartesian model.

Application of ply level analysis to flexural wave propagation

NASA Astrophysics Data System (ADS)

Valisetty, R. R.; Rehfield, L. W.

1988-10-01

A brief survey is presented of the shear deformation theories of laminated plates. It indicates that there are certain non-classical influences that affect bending-related behavior in the same way as do the transverse shear stresses. They include bending- and stretching-related section warping and the concomitant non-classical surface parallel stress contributions and the transverse normal stress. A bending theory gives significantly improved performance if these non-classical affects are incorporated. The heterogeneous shear deformations that are characteristic of laminates with highly dissimilar materials, however, require that attention be paid to the modeling of local rotations. In this paper, it is shown that a ply level analysis can be used to model such disparate shear deformations. Here, equilibrium of each layer is analyzed separately. Earlier applications of this analysis include free-edge laminate stresses. It is now extended to the study of flexural wave propagation in laminates. A recently developed homogeneous plate theory is used as a ply level model. Due consideration is given to the non-classical influences and no shear correction factors are introduced extraneously in this theory. The results for the lowest flexural mode of travelling planar harmonic waves indicate that this approach is competitive and yields better results for certain laminates.

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Safari, A.

2004-09-01

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {λ,ϕ,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10-8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10-4m2/s2. Since 1.5× 10-4 m2/s2 is equivalent to 1.5×10-5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

DOE PAGES

Devendran, Dharshi; Graves, Daniel; Johansen, Hans; ...

2017-05-08

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

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

Devendran, Dharshi; Graves, Daniel; Johansen, Hans

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

Globally Optimal Path Planning with Anisotropic Running Costs

DTIC Science & Technology

2013-03-01

contours were generated on a 3852 Cartesian grid. . . . . . . . . . . . . . . . 33 A1 The N(i, j ) set shown mapped onto Ωh as large dots for the case...function NF(x) near front set as a function of x ∈ Ωh NF(i, j ) near front set as a function of (i, j ) ∈ ΩZh Υ(x) anisotropy function at x δ Cartesian...discriminant of the polynomial p, see Equation (26) argmin argument of the minimum of a function V yz(x, ζ) see Equation (28) T (i, j ) the triplet {(i, j ), V

Strain Localization and Weakening Processes in Viscously Deforming Rocks: Numerical Modeling Based on Laboratory Torsion Experiments

NASA Astrophysics Data System (ADS)

Doehmann, M.; Brune, S.; Nardini, L.; Rybacki, E.; Dresen, G.

2017-12-01

Strain localization is an ubiquitous process in earth materials observed over a broad range of scales in space and time. Localized deformation and the formation of shear zones and faults typically involves material softening by various processes, like shear heating and grain size reduction. Numerical modeling enables us to study the complex physical and chemical weakening processes by separating the effect of individual parameters and boundary conditions. Using simple piece-wise linear functions for the parametrization of weakening processes allows studying a system at a chosen (lower) level of complexity (e.g. Cyprych et al., 2016). In this study, we utilize a finite element model to test two weakening laws that reduce the strength of the material depending on either the I) amount of accumulated strain or II) deformational work. Our 2D Cartesian models are benchmarked to single inclusion torsion experiments performed at elevated temperatures of 900 °C and pressures of up to 400 MPa (Rybacki et al., 2014). The experiments were performed on Carrara marble samples containing a weak Solnhofen limestone inclusion at a maximum strain rate of 2.0*10-4 s-1. Our models are designed to reproduce shear deformation of a hollow cylinder equivalent to the laboratory setup, such that material leaving one side of the model in shear direction enters again on the opposite side using periodic boundary conditions. Similar to the laboratory tests, we applied constant strain rate and constant stress boundary conditions.We use our model to investigate the time-dependent distribution of stress and strain and the effect of different parameters. For instance, inclusion rotation is shown to be strongly dependent on the viscosity ratio between matrix and inclusion and stronger ductile weakening increases the localization rate while decreasing shear zone width. The most suitable weakening law for representation of ductile rock is determined by combining the results of parameter tests with the comparison of our numerical models to the torsion experiments. In the future, this law will be applied first to investigate shear zone formation and then study localization in larger scale rift models.Cyprych, D. et al. (2016). Geochem Geophys, 17(9), 3608-3628. Rybacki, E. (2014). Tectonophysics, 634, 182-197.

Phase lag deduced information in photo-thermal actuation for nano-mechanical systems characterization

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

Bijster, R. J. F., E-mail: roy.bijster@tno.nl; Vreugd, J. de; Sadeghian, H.

2014-08-18

In photo-thermal actuation, heat is added locally to a micro-cantilever by means of a laser. A fraction of the irradiation is absorbed, yielding thermal stresses and deformations in the structure. Harmonic modulation of the laser power causes the cantilever to oscillate. Moreover, a phase lag is introduced which is very sensitive to the spot location and the cantilever properties. This phase lag is theoretically predicted and experimentally verified. Combined with thermo-mechanical properties of the cantilever and its geometry, the location of the laser spot, the thermal diffusivity, and the layer thicknesses of the cantilever can be extracted.

Exact partition functions for gauge theories on Rλ3

NASA Astrophysics Data System (ADS)

Wallet, Jean-Christophe

2016-11-01

The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

Free-breathing quantification of hepatic fat in healthy children and children with nonalcoholic fatty liver disease using a multi-echo 3-D stack-of-radial MRI technique.

PubMed

Armstrong, Tess; Ly, Karrie V; Murthy, Smruthi; Ghahremani, Shahnaz; Kim, Grace Hyun J; Calkins, Kara L; Wu, Holden H

2018-05-04

In adults, noninvasive chemical shift encoded Cartesian magnetic resonance imaging (MRI) and single-voxel magnetic resonance (MR) spectroscopy (SVS) accurately quantify hepatic steatosis but require breath-holding. In children, especially young and sick children, breath-holding is often limited or not feasible. Sedation can facilitate breath-holding but is highly undesirable. For these reasons, there is a need to develop free-breathing MRI technology that accurately quantifies steatosis in all children. This study aimed to compare non-sedated free-breathing multi-echo 3-D stack-of-radial (radial) MRI versus standard breath-holding MRI and SVS techniques in a group of children for fat quantification with respect to image quality, accuracy and repeatability. Healthy children (n=10, median age [±interquartile range]: 10.9 [±3.3] years) and overweight children with nonalcoholic fatty liver disease (NAFLD) (n=9, median age: 15.2 [±3.2] years) were imaged at 3 Tesla using free-breathing radial MRI, breath-holding Cartesian MRI and breath-holding SVS. Acquisitions were performed twice to assess repeatability (within-subject mean difference, MD within ). Images and hepatic proton-density fat fraction (PDFF) maps were scored for image quality. Free-breathing and breath-holding PDFF were compared using linear regression (correlation coefficient, r and concordance correlation coefficient, ρ c ) and Bland-Altman analysis (mean difference). P<0.05 was considered significant. In patients with NAFLD, free-breathing radial MRI demonstrated significantly less motion artifacts compared to breath-holding Cartesian (P<0.05). Free-breathing radial PDFF demonstrated a linear relationship (P<0.001) versus breath-holding SVS PDFF and breath-holding Cartesian PDFF with r=0.996 and ρ c =0.994, and r=0.997 and ρ c =0.995, respectively. The mean difference in PDFF between free-breathing radial MRI, breath-holding Cartesian MRI and breath-holding SVS was <0.7%. Repeated free-breathing radial MRI had MD within =0.25% for PDFF. In this pediatric study, non-sedated free-breathing radial MRI provided accurate and repeatable hepatic PDFF measurements and improved image quality, compared to standard breath-holding MR techniques.

First-pass myocardial perfusion MRI with reduced subendocardial dark-rim artifact using optimized Cartesian sampling.

PubMed

Zhou, Zhengwei; Bi, Xiaoming; Wei, Janet; Yang, Hsin-Jung; Dharmakumar, Rohan; Arsanjani, Reza; Bairey Merz, C Noel; Li, Debiao; Sharif, Behzad

2017-02-01

The presence of subendocardial dark-rim artifact (DRA) remains an ongoing challenge in first-pass perfusion (FPP) cardiac magnetic resonance imaging (MRI). We propose a free-breathing FPP imaging scheme with Cartesian sampling that is optimized to minimize the DRA and readily enables near-instantaneous image reconstruction. The proposed FPP method suppresses Gibbs ringing effects-a major underlying factor for the DRA-by "shaping" the underlying point spread function through a two-step process: 1) an undersampled Cartesian sampling scheme that widens the k-space coverage compared to the conventional scheme; and 2) a modified parallel-imaging scheme that incorporates optimized apodization (k-space data filtering) to suppress Gibbs-ringing effects. Healthy volunteer studies (n = 10) were performed to compare the proposed method against the conventional Cartesian technique-both using a saturation-recovery gradient-echo sequence at 3T. Furthermore, FPP imaging studies using the proposed method were performed in infarcted canines (n = 3), and in two symptomatic patients with suspected coronary microvascular dysfunction for assessment of myocardial hypoperfusion. Width of the DRA and the number of DRA-affected myocardial segments were significantly reduced in the proposed method compared to the conventional approach (width: 1.3 vs. 2.9 mm, P < 0.001; number of segments: 2.6 vs. 8.7; P < 0.0001). The number of slices with severe DRA was markedly lower for the proposed method (by 10-fold). The reader-assigned image quality scores were similar (P = 0.2), although the quantified myocardial signal-to-noise ratio was lower for the proposed method (P < 0.05). Animal studies showed that the proposed method can detect subendocardial perfusion defects and patient results were consistent with the gold-standard invasive test. The proposed free-breathing Cartesian FPP imaging method significantly reduces the prevalence of severe DRAs compared to the conventional approach while maintaining similar resolution and image quality. 2 J. Magn. Reson. Imaging 2017;45:542-555. © 2016 International Society for Magnetic Resonance in Medicine.

Single-breath-hold abdominal [Formula: see text]  mapping using 3D Cartesian Look-Locker with spatiotemporal sparsity constraints.

PubMed

Lugauer, Felix; Wetzl, Jens; Forman, Christoph; Schneider, Manuel; Kiefer, Berthold; Hornegger, Joachim; Nickel, Dominik; Maier, Andreas

2018-06-01

Our aim was to develop and validate a 3D Cartesian Look-Locker [Formula: see text] mapping technique that achieves high accuracy and whole-liver coverage within a single breath-hold. The proposed method combines sparse Cartesian sampling based on a spatiotemporally incoherent Poisson pattern and k-space segmentation, dedicated for high-temporal-resolution imaging. This combination allows capturing tissue with short relaxation times with volumetric coverage. A joint reconstruction of the 3D + inversion time (TI) data via compressed sensing exploits the spatiotemporal sparsity and ensures consistent quality for the subsequent multistep [Formula: see text] mapping. Data from the National Institute of Standards and Technology (NIST) phantom and 11 volunteers, along with reference 2D Look-Locker acquisitions, are used for validation. 2D and 3D methods are compared based on [Formula: see text] values in different abdominal tissues at 1.5 and 3 T. [Formula: see text] maps obtained from the proposed 3D method compare favorably with those from the 2D reference and additionally allow for reformatting or volumetric analysis. Excellent agreement is shown in phantom [bias[Formula: see text] < 2%, bias[Formula: see text] < 5% for (120; 2000) ms] and volunteer data (3D and 2D deviation < 4% for liver, muscle, and spleen) for clinically acceptable scan (20 s) and reconstruction times (< 4 min). Whole-liver [Formula: see text] mapping with high accuracy and precision is feasible in one breath-hold using spatiotemporally incoherent, sparse 3D Cartesian sampling.

Accuracy and Reproducibility of Adipose Tissue Measurements in Young Infants by Whole Body Magnetic Resonance Imaging

PubMed Central

Bauer, Jan Stefan; Noël, Peter Benjamin; Vollhardt, Christiane; Much, Daniela; Degirmenci, Saliha; Brunner, Stefanie; Rummeny, Ernst Josef; Hauner, Hans

2015-01-01

Purpose MR might be well suited to obtain reproducible and accurate measures of fat tissues in infants. This study evaluates MR-measurements of adipose tissue in young infants in vitro and in vivo. Material and Methods MR images of ten phantoms simulating subcutaneous fat of an infant’s torso were obtained using a 1.5T MR scanner with and without simulated breathing. Scans consisted of a cartesian water-suppression turbo spin echo (wsTSE) sequence, and a PROPELLER wsTSE sequence. Fat volume was quantified directly and by MR imaging using k-means clustering and threshold-based segmentation procedures to calculate accuracy in vitro. Whole body MR was obtained in sleeping young infants (average age 67±30 days). This study was approved by the local review board. All parents gave written informed consent. To obtain reproducibility in vivo, cartesian and PROPELLER wsTSE sequences were repeated in seven and four young infants, respectively. Overall, 21 repetitions were performed for the cartesian sequence and 13 repetitions for the PROPELLER sequence. Results In vitro accuracy errors depended on the chosen segmentation procedure, ranging from 5.4% to 76%, while the sequence showed no significant influence. Artificial breathing increased the minimal accuracy error to 9.1%. In vivo reproducibility errors for total fat volume of the sleeping infants ranged from 2.6% to 3.4%. Neither segmentation nor sequence significantly influenced reproducibility. Conclusion With both cartesian and PROPELLER sequences an accurate and reproducible measure of body fat was achieved. Adequate segmentation was mandatory for high accuracy. PMID:25706876

Comparison of several maneuvering target tracking models

NASA Astrophysics Data System (ADS)

McIntyre, Gregory A.; Hintz, Kenneth J.

1998-07-01

The tracking of maneuvering targets is complicated by the fact that acceleration is not directly observable or measurable. Additionally, acceleration can be induced by a variety of sources including human input, autonomous guidance, or atmospheric disturbances. The approaches to tracking maneuvering targets can be divided into two categories both of which assume that the maneuver input command is unknown. One approach is to model the maneuver as a random process. The other approach assumes that the maneuver is not random and that it is either detected or estimated in real time. The random process models generally assume one of two statistical properties, either white noise or an autocorrelated noise. The multiple-model approach is generally used with the white noise model while a zero-mean, exponentially correlated acceleration approach is used with the autocorrelated noise model. The nonrandom approach uses maneuver detection to correct the state estimate or a variable dimension filter to augment the state estimate with an extra state component during a detected maneuver. Another issue with the tracking of maneuvering target is whether to perform the Kalman filter in Polar or Cartesian coordinates. This paper will examine and compare several exponentially correlated acceleration approaches in both Polar and Cartesian coordinates for accuracy and computational complexity. They include the Singer model in both Polar and Cartesian coordinates, the Singer model in Polar coordinates converted to Cartesian coordinates, Helferty's third order rational approximation of the Singer model and the Bar-Shalom and Fortmann model. This paper shows that these models all provide very accurate position estimates with only minor differences in velocity estimates and compares the computational complexity of the models.

Beyond the pineal gland assumption: a neuroanatomical appraisal of dualism in Descartes' philosophy.

PubMed

Berhouma, Moncef

2013-09-01

The problem of the substantial union of the soul and the body and therefore the mechanisms of interaction between them represents the core of the Cartesian dualistic philosophy. This philosophy is based upon a neuroanatomical obvious misconception, consisting mainly on a wrong intraventricular position of the pineal gland and its capacity of movement to act as a valve regulating the flow of animal spirits. Should we consider the Cartesian neurophysiology as a purely anatomical descriptive work and therefore totally incorrect, or rather as a theoretical conception supporting his dualistic philosophy? From the various pre-Cartesian theories on the pineal organ, we try to explain how Descartes used his original conception of neuroanatomy to serve his dualistic philosophy. Moreover, we present an appraisal of the Cartesian neuroanatomical corpus from an anatomical but also metaphysical and theological perspectives. A new interpretation of Descartes' writings and an analysis of the secondary related literature shed the light on the voluntary anatomical approximations aiming to build an ad hoc neurophysiology that allows Descartes' soul-body theory. By its central position within the brain mass and its particular shape, the pineal gland raised diverse metaphysical theories regarding its function, but the most original theory remains certainly its role as the seat of soul in René Descartes' philosophy and more precisely the organ where soul and body interact. The author emphasizes on the critics raised by Descartes' theories on the soul-body interaction through the role of the pineal gland. Copyright © 2013 Elsevier B.V. All rights reserved.

Accuracy and reproducibility of adipose tissue measurements in young infants by whole body magnetic resonance imaging.

PubMed

Bauer, Jan Stefan; Noël, Peter Benjamin; Vollhardt, Christiane; Much, Daniela; Degirmenci, Saliha; Brunner, Stefanie; Rummeny, Ernst Josef; Hauner, Hans

2015-01-01

MR might be well suited to obtain reproducible and accurate measures of fat tissues in infants. This study evaluates MR-measurements of adipose tissue in young infants in vitro and in vivo. MR images of ten phantoms simulating subcutaneous fat of an infant's torso were obtained using a 1.5T MR scanner with and without simulated breathing. Scans consisted of a cartesian water-suppression turbo spin echo (wsTSE) sequence, and a PROPELLER wsTSE sequence. Fat volume was quantified directly and by MR imaging using k-means clustering and threshold-based segmentation procedures to calculate accuracy in vitro. Whole body MR was obtained in sleeping young infants (average age 67±30 days). This study was approved by the local review board. All parents gave written informed consent. To obtain reproducibility in vivo, cartesian and PROPELLER wsTSE sequences were repeated in seven and four young infants, respectively. Overall, 21 repetitions were performed for the cartesian sequence and 13 repetitions for the PROPELLER sequence. In vitro accuracy errors depended on the chosen segmentation procedure, ranging from 5.4% to 76%, while the sequence showed no significant influence. Artificial breathing increased the minimal accuracy error to 9.1%. In vivo reproducibility errors for total fat volume of the sleeping infants ranged from 2.6% to 3.4%. Neither segmentation nor sequence significantly influenced reproducibility. With both cartesian and PROPELLER sequences an accurate and reproducible measure of body fat was achieved. Adequate segmentation was mandatory for high accuracy.

Blast and ballistic trajectories in combat casualties: a preliminary analysis using a cartesian positioning system with MDCT.

PubMed

Folio, Les R; Fischer, Tatjana; Shogan, Paul; Frew, Michael; Dwyer, Andrew; Provenzale, James M

2011-08-01

The purpose of this study is to determine the agreement with which radiologists identify wound paths in vivo on MDCT and calculate missile trajectories on the basis of Cartesian coordinates using a Cartesian positioning system (CPS). Three radiologists retrospectively identified 25 trajectories on MDCT in 19 casualties who sustained penetrating trauma in Iraq. Trajectories were described qualitatively in terms of directional path descriptors and quantitatively as trajectory vectors. Directional descriptors, trajectory angles, and angles between trajectories were calculated based on Cartesian coordinates of entrance and terminus or exit recorded in x, y image and table space (z) using a Trajectory Calculator created using spreadsheet software. The consistency of qualitative descriptor determinations was assessed in terms of frequency of observer agreement and multirater kappa statistics. Consistency of trajectory vectors was evaluated in terms of distribution of magnitude of the angles between vectors and the differences between their paraaxial and parasagittal angles. In 68% of trajectories, the observers' visual assessment of qualitative descriptors was congruent. Calculated descriptors agreed across observers in 60% of the trajectories. Estimated kappa also showed good agreement (0.65-0.79, p < 0.001); 70% of calculated paraaxial and parasagittal angles were within 20° across observers, and 61.3% of angles between trajectory vectors were within 20° across observers. Results show agreement of visually assessed and calculated qualitative descriptors and trajectory angles among observers. The Trajectory Calculator describes trajectories qualitatively similar to radiologists' visual assessment, showing the potential feasibility of automated trajectory analysis.

Effects on Chilean Vertical Reference Frame due to the Maule Earthquake co-seismic and post-seismic effects

NASA Astrophysics Data System (ADS)

Montecino, Henry D.; de Freitas, Silvio R. C.; Báez, Juan C.; Ferreira, Vagner G.

2017-12-01

The Maule Earthquake (Mw = 8.8) of February 27, 2010 is among the strongest earthquakes that occurred in recent years throughout the world. The crustal deformation caused by this earthquake has been widely studied using GNSS, InSAR and gravity observations. However, there is currently no estimation of the possible vertical deformations produced by co-seismic and post-seismic effects in segments of the Chilean Vertical Reference Frame (CHVRF). In this paper, we present an estimation of co-seismic and post-seismic deformations on the CHVRF using an indirect approach based on GNSS and Gravity Recovery and Climate Experiment (GRACE) data as well as by applying a trajectory model. GNSS time series were used from 10 continuous GNSS stations in the period from 2007 to 2015, as well as 28 GNSS temporary stations realized before and after the earthquake, and 34 vertical deformation vectors in the region most affected by the earthquake. We considered a set of 147 monthly solutions of spherical harmonic gravity field that were expanded up to degree, as well as order 96 of the GRACE mission provided by Center for Space Research, University of Texas at Austin (UT-CSR) process center. The magnitude of vertical deformation was estimated in part of the Chilean vertical network due to the co-seismic and post-seismic effects. Once we evaluated the hydrological effect, natural and artificial jumps, and the effect of glacial isostatic adjustment in GNSS and GRACE time series, the maximum values associated to co- and post-seismic deformations on orthometric height were found to be ∼-34 cm and 5 cm, respectively. Overall, the deformation caused by the Maule earthquake in orthometric heights is almost entirely explained by the variation in the ellipsoidal heights (over 85% in co-seismic jump); however, coseismic jump in the geoid reached -3.3 mm, and could influence the maintenance of a modern vertical reference network in a medium to long term. We evaluated the consistency for a segment of the CHVRF after the earthquake and recommended precautions for using the CHVRF in the region.

Weighted augmented Jacobian matrix with a variable coefficient method for kinematics mapping of space teleoperation based on human-robot motion similarity

NASA Astrophysics Data System (ADS)

Shi, Zhong; Huang, Xuexiang; Hu, Tianjian; Tan, Qian; Hou, Yuzhuo

2016-10-01

Space teleoperation is an important space technology, and human-robot motion similarity can improve the flexibility and intuition of space teleoperation. This paper aims to obtain an appropriate kinematics mapping method of coupled Cartesian-joint space for space teleoperation. First, the coupled Cartesian-joint similarity principles concerning kinematics differences are defined. Then, a novel weighted augmented Jacobian matrix with a variable coefficient (WAJM-VC) method for kinematics mapping is proposed. The Jacobian matrix is augmented to achieve a global similarity of human-robot motion. A clamping weighted least norm scheme is introduced to achieve local optimizations, and the operating ratio coefficient is variable to pursue similarity in the elbow joint. Similarity in Cartesian space and the property of joint constraint satisfaction is analysed to determine the damping factor and clamping velocity. Finally, a teleoperation system based on human motion capture is established, and the experimental results indicate that the proposed WAJM-VC method can improve the flexibility and intuition of space teleoperation to complete complex space tasks.

Euler Technology Assessment for Preliminary Aircraft Design: Compressibility Predictions by Employing the Cartesian Unstructured Grid SPLITFLOW Code

NASA Technical Reports Server (NTRS)

Finley, Dennis B.; Karman, Steve L., Jr.

1996-01-01

The objective of the second phase of the Euler Technology Assessment program was to evaluate the ability of Euler computational fluid dynamics codes to predict compressible flow effects over a generic fighter wind tunnel model. This portion of the study was conducted by Lockheed Martin Tactical Aircraft Systems, using an in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaption of the volume grid during the solution to resolve high-gradient regions. The SPLITFLOW code predictions of configuration forces and moments are shown to be adequate for preliminary design, including predictions of sideslip effects and the effects of geometry variations at low and high angles-of-attack. The transonic pressure prediction capabilities of SPLITFLOW are shown to be improved over subsonic comparisons. The time required to generate the results from initial surface data is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.

Material translations in the Cartesian brain.

PubMed

Bassiri, Nima

2012-03-01

This article reexamines the controversial doctrine of the pineal gland in Cartesian psychophysiology. It argues initially that Descartes' combined metaphysics and natural philosophy yield a distinctly human subject who is rational, willful, but also a living and embodied being in the world, formed in the union and through the dynamics of the interaction between the soul and the body. However, Descartes only identified one site at which this union was staged: the brain, and more precisely, the pineal gland, the small bulb of nervous tissue at the brain's center. The pineal gland was charged with the incredible task of ensuring the interactive mutuality between the soul and body, while also maintaining the necessary ontological incommensurability between them. This article reconsiders the theoretical obligations placed on the pineal gland as the site of the soul-body union, and looks at how the gland was consequently forced to adopt a very precarious ontological status. The article ultimately questions how successfully the Cartesian human could be localized in the pineal gland, while briefly considering the broader historical consequences of the ensuing equivalence of the self and brain. Copyright © 2011 Elsevier Ltd. All rights reserved.

Fission barriers at the end of the chart of the nuclides

DOE PAGES

Möller, Peter; Sierk, Arnold J.; Ichikawa, Takatoshi; ...

2015-02-12

We present calculated fission-barrier heights for 5239 nuclides for all nuclei between the proton and neutron drip lines with 171 ≤ A ≤ 330. The barriers are calculated in the macroscopic-microscopic finite-range liquid-drop (FRLDM) with a 2002 set of macroscopic-model parameters. The saddle-point energies are determined from potential-energy surfaces based on more than five million different shapes, defined by five deformation parameters in the three-quadratic-surface shape parametrization: elongation, neck diameter, left-fragment spheroidal deformation, right-fragment spheroidal deformation, and nascent-fragment mass asymmetry. The energy of the ground state is determined by calculating the lowest-energy configuration in both the Nilsson perturbed-spheroid (ϵ) andmore » the spherical-harmonic (β) parametrizations, including axially asymmetric deformations. The lower of the two results (correcting for zero-point motion) is defined as the ground-state energy. The effect of axial asymmetry on the inner barrier peak is calculated in the (ϵ,γ) parametrization. We have earlier benchmarked our calculated barrier heights to experimentally extracted barrier parameters and found average agreement to about one MeV for known data across the nuclear chart. Here we do additional benchmarks and investigate the qualitative and, when possible, quantitative agreement and/or consistency with data on β-delayed fission, isotope generation along prompt-neutron-capture chains in nuclear-weapons tests, and superheavy-element stability. In addition these studies all indicate that the model is realistic at considerable distances in Z and N from the region of nuclei where its parameters were determined.« less

Interaction between mantle and crustal detachments: A nonlinear system controlling lithospheric extension

NASA Astrophysics Data System (ADS)

Rosenbaum, Gideon; Regenauer-Lieb, Klaus; Weinberg, Roberto F.

2010-11-01

We use numerical modeling to investigate the development of crustal and mantle detachments during lithospheric extension. Our models simulate a wide range of extensional systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles as a response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation. Crustal detachments, here referred as low-angle normal decoupling horizons, are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW m-2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate heat flow (60-70 mW m-2). Results show a nonlinear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometimes unexpected switches in extension modes (e.g., from diffuse extensional deformation to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this nonlinearity to result from the interference of doming wavelengths in the presence of multiple necking instabilities. Disharmonic crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonic crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged history of extension prior to continental breakup.

Uniform electron gases. III. Low-density gases on three-dimensional spheres

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

Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W., E-mail: peter.gill@anu.edu.au

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGFmore » centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.« less

An immersed boundary method for fluid-structure interaction with compressible multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Li; Currao, Gaetano M. D.; Han, Feng; Neely, Andrew J.; Young, John; Tian, Fang-Bao

2017-10-01

This paper presents a two-dimensional immersed boundary method for fluid-structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid-structure interaction coupling. In the flow solver, the compressible multiphase Navier-Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge-Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.

Hydrodynamic water impact. [Apollo spacecraft waterlanding

NASA Technical Reports Server (NTRS)

Kettleborough, C. F.

1972-01-01

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

PubMed

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

Numerical tool development of fluid-structure interactions for investigation of obstructive sleep apnea

NASA Astrophysics Data System (ADS)

Huang, Chien-Jung; White, Susan; Huang, Shao-Ching; Mallya, Sanjay; Eldredge, Jeff

2016-11-01

Obstructive sleep apnea (OSA) is a medical condition characterized by repetitive partial or complete occlusion of the airway during sleep. The soft tissues in the upper airway of OSA patients are prone to collapse under the low pressure loads incurred during breathing. The ultimate goal of this research is the development of a versatile numerical tool for simulation of air-tissue interactions in the patient specific upper airway geometry. This tool is expected to capture several phenomena, including flow-induced vibration (snoring) and large deformations during airway collapse of the complex airway geometry in respiratory flow conditions. Here, we present our ongoing progress toward this goal. To avoid mesh regeneration, for flow model, a sharp-interface embedded boundary method is used on Cartesian grids for resolving the fluid-structure interface, while for the structural model, a cut-cell finite element method is used. Also, to properly resolve large displacements, non-linear elasticity model is used. The fluid and structure solvers are connected with the strongly coupled iterative algorithm. The parallel computation is achieved with the numerical library PETSc. Some two- and three- dimensional preliminary results are shown to demonstrate the ability of this tool.

Translation by anisotropic peeling or fracturing in elastic media

NASA Astrophysics Data System (ADS)

Zheng, Zhong; Lister, John; Neufeld, Jerome

2017-11-01

The influence of rock anisotropy on the direction of hydraulic fracturing is an important open question. Two canonical systems have been proposed to investigate the fundamental aspects of such fluid-structure interaction problems: (i) Fluid injection and fracturing into an infinite elastic matrix (e.g., solid gelatin) and (ii) Fluid invasion and peeling beneath a deforming elastic sheet (e.g., bending plate). We investigate the second system and impose a non-uniform prewetting film thickness beneath the elastic sheet. We notice that while the bulk of the elastic sheet retains the static blister shape, a non-uniform prewetting film thickness can cause a horizontal translation of the blister. In particular, for a step jump in prewetting film thickness, asymptotic analysis indicates that, under constant fluid injection, the horizontal translation follows a t 7 / 17 time dependence in cartesian coordinates, and the prefactor of power-law translation depends on the ratio of the distinct prewetting film thicknesses on either side. We also provide numerical and experimental evidence demonstrating anisotropic blister evolution. This can be thought of as a model system for fluid-driven fracturing where the non-uniform prewetting film thickness mimics heterogeneity in material toughness.

Polar exponential sensor arrays unify iconic and Hough space representation

NASA Technical Reports Server (NTRS)

Weiman, Carl F. R.

1990-01-01

The log-polar coordinate system, inherent in both polar exponential sensor arrays and log-polar remapped video imagery, is identical to the coordinate system of its corresponding Hough transform parameter space. The resulting unification of iconic and Hough domains simplifies computation for line recognition and eliminates the slope quantization problems inherent in the classical Cartesian Hough transform. The geometric organization of the algorithm is more amenable to massively parallel architectures than that of the Cartesian version. The neural architecture of the human visual cortex meets the geometric requirements to execute 'in-place' log-Hough algorithms of the kind described here.

Explicitly computing geodetic coordinates from Cartesian coordinates

NASA Astrophysics Data System (ADS)

Zeng, Huaien

2013-04-01

This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.

Mind and consciousness in yoga – Vedanta: A comparative analysis with western psychological concepts

PubMed Central

Prabhu, H. R. Aravinda; Bhat, P. S.

2013-01-01

Study of mind and consciousness through established scientific methods is often difficult due to the observed-observer dichotomy. Cartesian approach of dualism considering the mind and matter as two diverse and unconnected entities has been questioned by oriental schools of Yoga and Vedanta as well as the recent quantum theories of modern physics. Freudian and Neo-freudian schools based on the Cartesian model have been criticized by the humanistic schools which come much closer to the vedantic approach of unitariness. A comparative analysis of the two approaches is discussed. PMID:23858252

Dualism and its importance for medicine.

PubMed

Switankowsky, I

2000-11-01

Cartesian dualism has been viewed by medical theorists to be one of the chief causes of a reductionist/mechanistic treatment of the patient. Although I aver that Cartesian dualism is one culprit for the misapprehension of the genuine treatment of patients in terms of both mind and body, I argue that interactive dualism which stresses the interaction of mind and body is essential to treat patients with dignity and compassion. Thus, adequate medical care that is humanistic in nature is difficult (if not impossible) to achieve without physicians adhering to a dualistic framework in which the body and person is treated during illness.

Analytical treatment of the deformation behavior of EUVL masks during electrostatic chucking

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-03-01

A new analytical approach is presented to predict mask deformation during electro-static chucking in next generation extreme-ultraviolet-lithography (EUVL). Given an arbitrary profile measurement of the mask and chuck non-flatness, this method has been developed as an alternative to time-consuming finite element simulations for overlay error correction algorithms. We consider the feature transfer of each harmonic component in the profile shapes via linear elasticity theory and demonstrate analytically how high spatial frequencies are filtered. The method is compared to presumably more accurate finite element simulations and has been tested successfully in an overlay error compensation experiment, where the residual error y-component could be reduced by a factor 2. As a side outcome, the formulation provides a tool to estimate the critical pin-size and -pitch such that the distortion on the mask front-side remains within given tolerances. We find for a numerical example that pin-pitches of less than 5 mm will result in a mask pattern-distortion of less than 1 nm if the chucking pressure is below 30 kPa.

Analytical treatment of the deformation behavior of extreme-ultraviolet-lithography masks during electrostatic chucking

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-10-01

A new analytical approach is presented to predict mask deformation during electrostatic chucking in next-generation extreme-ultraviolet-lithography. Given an arbitrary profile measurement of the mask and chuck nonflatness, this method has been developed as an alternative to time-consuming finite element simulations for overlay error correction algorithms. We consider the feature transfer of each harmonic component in the profile shapes via linear elasticity theory and demonstrate analytically how high spatial frequencies are filtered. The method is compared to presumably more accurate finite element simulations and has been tested successfully in an overlay error compensation experiment, where the residual error y-component could be reduced by a factor of 2. As a side outcome, the formulation provides a tool to estimate the critical pin-size and -pitch such that the distortion on the mask front-side remains within given tolerances. We find for a numerical example that pin-pitches of less than 5 mm will result in a mask pattern distortion of less than 1 nm if the chucking pressure is below 30 kPa.

Functional Dynamics of PDZ Binding Domains: A Normal-Mode Analysis

PubMed Central

De Los Rios, Paolo; Cecconi, Fabio; Pretre, Anna; Dietler, Giovanni; Michielin, Olivier; Piazza, Francesco; Juanico, Brice

2005-01-01

Postsynaptic density-95/disks large/zonula occludens-1 (PDZ) domains are relatively small (80–120 residues) protein binding modules central in the organization of receptor clusters and in the association of cellular proteins. Their main function is to bind C-terminals of selected proteins that are recognized through specific amino acids in their carboxyl end. Binding is associated with a deformation of the PDZ native structure and is responsible for dynamical changes in regions not in direct contact with the target. We investigate how this deformation is related to the harmonic dynamics of the PDZ structure and show that one low-frequency collective normal mode, characterized by the concerted movements of different secondary structures, is involved in the binding process. Our results suggest that even minimal structural changes are responsible for communication between distant regions of the protein, in agreement with recent NMR experiments. Thus, PDZ domains are a very clear example of how collective normal modes are able to characterize the relation between function and dynamics of proteins, and to provide indications on the precursors of binding/unbinding events. PMID:15821164

A highly accurate boundary integral equation method for surfactant-laden drops in 3D

NASA Astrophysics Data System (ADS)

Sorgentone, Chiara; Tornberg, Anna-Karin

2018-05-01

The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of increased importance. At such small scales, viscous forces dominate and inertial effects are often negligible. Considering Stokes flow, a numerical method based on a boundary integral formulation is presented for simulating 3D drops covered by an insoluble surfactant. The method is able to simulate drops with different viscosities and close interactions, automatically controlling the time step size and maintaining high accuracy also when substantial drop deformation appears. To achieve this, the drop surfaces as well as the surfactant concentration on each surface are represented by spherical harmonics expansions. A novel reparameterization method is introduced to ensure a high-quality representation of the drops also under deformation, specialized quadrature methods for singular and nearly singular integrals that appear in the formulation are evoked and the adaptive time stepping scheme for the coupled drop and surfactant evolution is designed with a preconditioned implicit treatment of the surfactant diffusion.

The dynamics of folding instability in a constrained Cosserat medium

NASA Astrophysics Data System (ADS)

Gourgiotis, Panos A.; Bigoni, Davide

2017-04-01

Different from Cauchy elastic materials, generalized continua, and in particular constrained Cosserat materials, can be designed to possess extreme (near a failure of ellipticity) orthotropy properties and in this way to model folding in a three-dimensional solid. Following this approach, folding, which is a narrow zone of highly localized bending, spontaneously emerges as a deformation pattern occurring in a strongly anisotropic solid. How this peculiar pattern interacts with wave propagation in the time-harmonic domain is revealed through the derivation of an antiplane, infinite-body Green's function, which opens the way to integral techniques for anisotropic constrained Cosserat continua. Viewed as a perturbing agent, the Green's function shows that folding, emerging near a steadily pulsating source in the limit of failure of ellipticity, is transformed into a disturbance with wavefronts parallel to the folding itself. The results of the presented study introduce the possibility of exploiting constrained Cosserat solids for propagating waves in materials displaying origami patterns of deformation. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Acoustic impact on the laminated plates placed between barriers

NASA Astrophysics Data System (ADS)

Paimushin, V. N.; Gazizullin, R. K.; Fedotenkov, G. V.

2016-11-01

On the basis of previously derived equations, analytical solutions are established on the forced vibrations of two-layer and three-layers rectangular plates hinged in an opening of absolutely rigid walls during the transmission of monoharmonic sound waves. It is assumed that the partition wall is situated between two absolutely rigid barriers, one of them by harmonic oscillation with a given displacements amplitude on the plate forms the incident sound wave, and the other is stationary and has a coating of deformable energy absorbing material with high damping properties. The behavior of acoustic environments in the spaces between the deformable plate and the barriers described by classical wave equation based on the ideal compressible fluid model. To describe the process of dynamic deformation of the energy absorbing coating of fixed barrier, two-dimensional equations of motion based on the use of models transversely soft layer are derived with a linear approximation of the displacement field in the thickness direction of the coating and taking into account the damping properties of the material and the hysteresis model for it. The influence of the physical and mechanical properties of the concerned mechanical system and the frequency of the incident sound wave on the parameters of its insulation properties of the plate, as well as on the parameters of the stress-strain state of the plate has been analyzed.

Crustal displacements due to continental water loading

USGS Publications Warehouse

Van Dam, T.; Wahr, J.; Milly, P.C.D.; Shmakin, A.B.; Blewitt, G.; Lavallee, D.; Larson, K.M.

2001-01-01

The effects of long-wavelength (> 100 km), seasonal variability in continental water storage on vertical crustal motions are assessed. The modeled vertical displacements (??rM) have root-mean-square (RMS) values for 1994-1998 as large as 8 mm, with ranges up to 30 mm, and are predominantly annual in character. Regional strains are on the order of 20 nanostrain for tilt and 5 nanostrain for horizontal deformation. We compare ??rM with observed Global Positioning System (GPS) heights (??rO) (which include adjustments to remove estimated effects of atmospheric pressure and annual tidal and non-tidal ocean loading) for 147 globally distributed sites. When the ??rO time series are adjusted by ??rM, their variances are reduced, on average, by an amount equal to the variance of the ??rM. Of the ??rO time series exhibiting a strong annual signal, more than half are found to have an annual harmonic that is in phase and of comparable amplitude with the annual harmonic in the ??rM. The ??rM time series exhibit long-period variations that could be mistaken for secular tectonic trends or post-glacial rebound when observed over a time span of a few years.

Wake vortex properties and thrust production of a harmonically-pitching flexible airfoil at low Reynolds number

NASA Astrophysics Data System (ADS)

Olson, David; Naguib, Ahmed; Koochesfahani, Manoochehr

2017-11-01

Many of the natural flyers have deformable wing structures and exhibit complex kinematics in order to produce lift and thrust. Replicating all of these conditions in the laboratory (or in simulations) is extremely difficult, and drawing explicit connections to basic unsteady aerodynamics models and theories is even more complicated. Therefore, simplified wing structure and kinematics are typically used to facilitate drawing out these connections. In this work, measurements are conducted using a rigid and a chordwise-flexible NACA 0009 airfoils when harmonically pitched about the quarter chord point. Molecular tagging velocimetry is used to characterize the wake and estimate the thrust based on the momentum integral equation as function of the reduced frequency and the pitching amplitude. The results obtained using the two different airfoils are compared in order to examine the influence of structural flexibility. Consistent with the literature, chordwise flexibility is found to enhance thrust production and the circulation of the vortices shed into the wake, for a certain range of frequencies and amplitudes. Additional characterizations are undertaken of the wake vortex structure and its scaling. This work was supported by AFOSR Award Number FA9550-10-1-0342.

Aeroelastic simulation of higher harmonic control

NASA Technical Reports Server (NTRS)

Robinson, Lawson H.; Friedmann, Peretz P.

1994-01-01

This report describes the development of an aeroelastic analysis of a helicopter rotor and its application to the simulation of helicopter vibration reduction through higher harmonic control (HHC). An improved finite-state, time-domain model of unsteady aerodynamics is developed to capture high frequency aerodynamic effects. An improved trim procedure is implemented which accounts for flap, lead-lag, and torsional deformations of the blade. The effect of unsteady aerodynamics is studied and it is found that its impact on blade aeroelastic stability and low frequency response is small, but it has a significant influence on rotor hub vibrations. Several different HHC algorithms are implemented on a hingeless rotor and their effectiveness in reducing hub vibratory shears is compared. All the controllers are found to be quite effective, but very differing HHC inputs are required depending on the aerodynamic model used. Effects of HHC on rotor stability and power requirements are found to be quite small. Simulations of roughly equivalent articulated and hingeless rotors are carried out, and it is found that hingeless rotors can require considerably larger HHC inputs to reduce vibratory shears. This implies that the practical implementation of HHC on hingeless rotors might be considerably more difficult than on articulated rotors.

Modeling of Soft Poroelastic Tissue in Time-Harmonic MR Elastography

PubMed Central

Perriñez, Phillip R.; Kennedy, Francis E.; Van Houten, Elijah E. W.; Weaver, John B.; Paulsen, Keith D.

2010-01-01

Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz–1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases. PMID:19272864

Motion correction for functional MRI with three‐dimensional hybrid radial‐Cartesian EPI

PubMed Central

McNab, Jennifer A.; Chiew, Mark; Miller, Karla L.

2016-01-01

Purpose Subject motion is a major source of image degradation for functional MRI (fMRI), especially when using multishot sequences like three‐dimensional (3D EPI). We present a hybrid radial‐Cartesian 3D EPI trajectory enabling motion correction in k‐space for functional MRI. Methods The EPI “blades” of the 3D hybrid radial‐Cartesian EPI sequence, called TURBINE, are rotated about the phase‐encoding axis to fill out a cylinder in 3D k‐space. Angular blades are acquired over time using a golden‐angle rotation increment, allowing reconstruction at flexible temporal resolution. The self‐navigating properties of the sequence are used to determine motion parameters from a high temporal‐resolution navigator time series. The motion is corrected in k‐space as part of the image reconstruction, and evaluated for experiments with both cued and natural motion. Results We demonstrate that the motion correction works robustly and that we can achieve substantial artifact reduction as well as improvement in temporal signal‐to‐noise ratio and fMRI activation in the presence of both severe and subtle motion. Conclusion We show the potential for hybrid radial‐Cartesian 3D EPI to substantially reduce artifacts for application in fMRI, especially for subject groups with significant head motion. The motion correction approach does not prolong the scan, and no extra hardware is required. Magn Reson Med 78:527–540, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:27604503

Simultaneous auto-calibration and gradient delays estimation (SAGE) in non-Cartesian parallel MRI using low-rank constraints.

PubMed

Jiang, Wenwen; Larson, Peder E Z; Lustig, Michael

2018-03-09

To correct gradient timing delays in non-Cartesian MRI while simultaneously recovering corruption-free auto-calibration data for parallel imaging, without additional calibration scans. The calibration matrix constructed from multi-channel k-space data should be inherently low-rank. This property is used to construct reconstruction kernels or sensitivity maps. Delays between the gradient hardware across different axes and RF receive chain, which are relatively benign in Cartesian MRI (excluding EPI), lead to trajectory deviations and hence data inconsistencies for non-Cartesian trajectories. These in turn lead to higher rank and corrupted calibration information which hampers the reconstruction. Here, a method named Simultaneous Auto-calibration and Gradient delays Estimation (SAGE) is proposed that estimates the actual k-space trajectory while simultaneously recovering the uncorrupted auto-calibration data. This is done by estimating the gradient delays that result in the lowest rank of the calibration matrix. The Gauss-Newton method is used to solve the non-linear problem. The method is validated in simulations using center-out radial, projection reconstruction and spiral trajectories. Feasibility is demonstrated on phantom and in vivo scans with center-out radial and projection reconstruction trajectories. SAGE is able to estimate gradient timing delays with high accuracy at a signal to noise ratio level as low as 5. The method is able to effectively remove artifacts resulting from gradient timing delays and restore image quality in center-out radial, projection reconstruction, and spiral trajectories. The low-rank based method introduced simultaneously estimates gradient timing delays and provides accurate auto-calibration data for improved image quality, without any additional calibration scans. © 2018 International Society for Magnetic Resonance in Medicine.

A deformation analysis of flat flexible gear and its equation of original curved surfaces

NASA Technical Reports Server (NTRS)

Yunwen, S.

1985-01-01

The equation of the original curved surface of end harmonic gearing is determined by displacement analysis of flat flexible gear. The displacement analysis is also used to calculate the strength and rigidity of the gear. The latter is regarded as a circular plate with two concentrated loads, since its torsional rigidity is much larger than its bending rigidity. Small-deflection theory of thin plates is used to solve for the displacement of any point in the middle plane of the gear. New expressions are given for radial and tangential displacements of the middle plane under asymmetrical loading. A digital computer is used to obtain numerical values for the displacements.

Coolant side heat transfer with rotation: User manual for 3D-TEACH with rotation

NASA Technical Reports Server (NTRS)

Syed, S. A.; James, R. H.

1989-01-01

This program solves the governing transport equations in Reynolds average form for the flow of a 3-D, steady state, viscous, heat conducting, multiple species, single phase, Newtonian fluid with combustion. The governing partial differential equations are solved in physical variables in either a Cartesian or cylindrical coordinate system. The effects of rotation on the momentum and enthalpy calculations modeled in Cartesian coordinates are examined. The flow of the fluid should be confined and subsonic with a maximum Mach number no larger than 0.5. This manual describes the operating procedures and input details for executing a 3D-TEACH computation.

CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.; Pulliam, Thomas H.

2003-01-01

A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.

Fifth-order superintegrable quantum systems separating in Cartesian coordinates: Doubly exotic potentials

NASA Astrophysics Data System (ADS)

Abouamal, Ismail; Winternitz, Pavel

2018-02-01

We consider a two-dimensional quantum Hamiltonian separable in Cartesian coordinates and allowing a fifth-order integral of motion. We impose the superintegrablity condition and find all doubly exotic superintegrable potentials (i.e., potentials V(x, y) = V1(x) + V2(y), where neither V1(x) nor V2(y) satisfy a linear ordinary differential equation), allowing the existence of such an integral. All of these potentials are found to have the Painlevé property. Most of them are expressed in terms of known Painlevé transcendents or elliptic functions but some may represent new higher order Painlevé transcendents.

Unstructured Cartesian/prismatic grid generation for complex geometries

NASA Technical Reports Server (NTRS)

Karman, Steve L., Jr.

1995-01-01

The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.

Robust recognition of handwritten numerals based on dual cooperative network

NASA Technical Reports Server (NTRS)

Lee, Sukhan; Choi, Yeongwoo

1992-01-01

An approach to robust recognition of handwritten numerals using two operating parallel networks is presented. The first network uses inputs in Cartesian coordinates, and the second network uses the same inputs transformed into polar coordinates. How the proposed approach realizes the robustness to local and global variations of input numerals by handling inputs both in Cartesian coordinates and in its transformed Polar coordinates is described. The required network structures and its learning scheme are discussed. Experimental results show that by tracking only a small number of distinctive features for each teaching numeral in each coordinate, the proposed system can provide robust recognition of handwritten numerals.

Zernike Basis to Cartesian Transformations

NASA Astrophysics Data System (ADS)

Mathar, R. J.

2009-12-01

The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.

Natural Strain

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1995-01-01

The purpose of this paper is to present a consistent and thorough development of the strain and strain-rate measures affiliated with Hencky. Natural measures for strain and strain-rate, as I refer to them, are first expressed in terms of of the fundamental body-metric tensors of Lodge. These strain and strain-rate measures are mixed tensor fields. They are mapped from the body to space in both the Eulerian and Lagrangian configurations, and then transformed from general to Cartesian fields. There they are compared with the various strain and strain-rate measures found in the literature. A simple Cartesian description for Hencky strain-rate in the Lagrangian state is obtained.

A short note on the use of the red-black tree in Cartesian adaptive mesh refinement algorithms

NASA Astrophysics Data System (ADS)

Hasbestan, Jaber J.; Senocak, Inanc

2017-12-01

Mesh adaptivity is an indispensable capability to tackle multiphysics problems with large disparity in time and length scales. With the availability of powerful supercomputers, there is a pressing need to extend time-proven computational techniques to extreme-scale problems. Cartesian adaptive mesh refinement (AMR) is one such method that enables simulation of multiscale, multiphysics problems. AMR is based on construction of octrees. Originally, an explicit tree data structure was used to generate and manipulate an adaptive Cartesian mesh. At least eight pointers are required in an explicit approach to construct an octree. Parent-child relationships are then used to traverse the tree. An explicit octree, however, is expensive in terms of memory usage and the time it takes to traverse the tree to access a specific node. For these reasons, implicit pointerless methods have been pioneered within the computer graphics community, motivated by applications requiring interactivity and realistic three dimensional visualization. Lewiner et al. [1] provides a concise review of pointerless approaches to generate an octree. Use of a hash table and Z-order curve are two key concepts in pointerless methods that we briefly discuss next.

Studying the unfolding process of protein G and protein L under physical property space

PubMed Central

Zhao, Liling; Wang, Jihua; Dou, Xianghua; Cao, Zanxia

2009-01-01

Background The studies on protein folding/unfolding indicate that the native state topology is an important determinant of protein folding mechanism. The folding/unfolding behaviors of proteins which have similar topologies have been studied under Cartesian space and the results indicate that some proteins share the similar folding/unfolding characters. Results We construct physical property space with twelve different physical properties. By studying the unfolding process of the protein G and protein L under the property space, we find that the two proteins have the similar unfolding pathways that can be divided into three types and the one which with the umbrella-shape represents the preferred pathway. Moreover, the unfolding simulation time of the two proteins is different and protein L unfolding faster than protein G. Additionally, the distributing area of unfolded state ensemble of protein L is larger than that of protein G. Conclusion Under the physical property space, the protein G and protein L have the similar folding/unfolding behaviors, which agree with the previous results obtained from the studies under Cartesian coordinate space. At the same time, some different unfolding properties can be detected easily, which can not be analyzed under Cartesian coordinate space. PMID:19208146

Mind-body dualism and the biopsychosocial model of pain: what did Descartes really say?

PubMed

Duncan, G

2000-08-01

In the last two decades there have been many critics of western biomedicine's poor integration of social and psychological factors in questions of human health. Such critiques frequently begin with a rejection of Descartes' mind-body dualism, viewing this as the decisive philosophical moment, radically separating the two realms in both theory and practice. It is argued here, however, that many such readings of Descartes have been selective and misleading. Contrary to the assumptions of many recent authors, Descartes' dualism does attempt to explain the union of psyche and soma - with more depth than is often appreciated. Pain plays a key role in Cartesian as well as contemporary thinking about the problem of dualism. Theories of the psychological origins of pain symptoms persisted throughout the history of modern medicine and were not necessarily discouraged by Cartesian mental philosophy. Moreover, the recently developed biopsychosocial model of pain may have more in common with Cartesian dualism than it purports to have. This article presents a rereading of Descartes' mental philosophy and his views on pain. The intention is not to defend his theories, but to re-evaluate them and to ask in what respect contemporary theories represent any significant advance in philosophical terms.

Deblurring for spatial and temporal varying motion with optical computing

NASA Astrophysics Data System (ADS)

Xiao, Xiao; Xue, Dongfeng; Hui, Zhao

2016-05-01

A way to estimate and remove spatially and temporally varying motion blur is proposed, which is based on an optical computing system. The translation and rotation motion can be independently estimated from the joint transform correlator (JTC) system without iterative optimization. The inspiration comes from the fact that the JTC system is immune to rotation motion in a Cartesian coordinate system. The work scheme of the JTC system is designed to keep switching between the Cartesian coordinate system and polar coordinate system in different time intervals with the ping-pang handover. In the ping interval, the JTC system works in the Cartesian coordinate system to obtain a translation motion vector with optical computing speed. In the pang interval, the JTC system works in the polar coordinate system. The rotation motion is transformed to the translation motion through coordinate transformation. Then the rotation motion vector can also be obtained from JTC instantaneously. To deal with continuous spatially variant motion blur, submotion vectors based on the projective motion path blur model are proposed. The submotion vectors model is more effective and accurate at modeling spatially variant motion blur than conventional methods. The simulation and real experiment results demonstrate its overall effectiveness.

Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations.

PubMed

van de Streek, Jacco; Neumann, Marcus A

2010-10-01

This paper describes the validation of a dispersion-corrected density functional theory (d-DFT) method for the purpose of assessing the correctness of experimental organic crystal structures and enhancing the information content of purely experimental data. 241 experimental organic crystal structures from the August 2008 issue of Acta Cryst. Section E were energy-minimized in full, including unit-cell parameters. The differences between the experimental and the minimized crystal structures were subjected to statistical analysis. The r.m.s. Cartesian displacement excluding H atoms upon energy minimization with flexible unit-cell parameters is selected as a pertinent indicator of the correctness of a crystal structure. All 241 experimental crystal structures are reproduced very well: the average r.m.s. Cartesian displacement for the 241 crystal structures, including 16 disordered structures, is only 0.095 Å (0.084 Å for the 225 ordered structures). R.m.s. Cartesian displacements above 0.25 A either indicate incorrect experimental crystal structures or reveal interesting structural features such as exceptionally large temperature effects, incorrectly modelled disorder or symmetry breaking H atoms. After validation, the method is applied to nine examples that are known to be ambiguous or subtly incorrect.

Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis

NASA Technical Reports Server (NTRS)

Ghrist, Richard W.; Plakalovic, Dragan

2012-01-01

An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant.

Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles.

PubMed

Yang, Ping; Kattawar, George W; Liou, Kuo-Nan; Lu, Jun Q

2004-08-10

Two grid configurations can be employed to implement the finite-difference time-domain (FDTD) technique in a Cartesian system. One configuration defines the electric and magnetic field components at the cell edges and cell-face centers, respectively, whereas the other reverses these definitions. These two grid configurations differ in terms of implication on the electromagnetic boundary conditions if the scatterer in the FDTD computation is a dielectric particle. The permittivity has an abrupt transition at the cell interface if the dielectric properties of two adjacent cells are not identical. Similarly, the discontinuity of permittivity is also observed at the edges of neighboring cells that are different in terms of their dielectric constants. We present two FDTD schemes for light scattering by dielectric particles to overcome the above-mentioned discontinuity on the basis of the electromagnetic boundary conditions for the two Cartesian grid configurations. We also present an empirical approach to accelerate the convergence of the discrete Fourier transform to obtain the field values in the frequency domain. As a new application of the FDTD method, we investigate the scattering properties of multibranched bullet-rosette ice crystals at both visible and thermal infrared wavelengths.

Coil Compression for Accelerated Imaging with Cartesian Sampling

PubMed Central

Zhang, Tao; Pauly, John M.; Vasanawala, Shreyas S.; Lustig, Michael

2012-01-01

MRI using receiver arrays with many coil elements can provide high signal-to-noise ratio and increase parallel imaging acceleration. At the same time, the growing number of elements results in larger datasets and more computation in the reconstruction. This is of particular concern in 3D acquisitions and in iterative reconstructions. Coil compression algorithms are effective in mitigating this problem by compressing data from many channels into fewer virtual coils. In Cartesian sampling there often are fully sampled k-space dimensions. In this work, a new coil compression technique for Cartesian sampling is presented that exploits the spatially varying coil sensitivities in these non-subsampled dimensions for better compression and computation reduction. Instead of directly compressing in k-space, coil compression is performed separately for each spatial location along the fully-sampled directions, followed by an additional alignment process that guarantees the smoothness of the virtual coil sensitivities. This important step provides compatibility with autocalibrating parallel imaging techniques. Its performance is not susceptible to artifacts caused by a tight imaging fieldof-view. High quality compression of in-vivo 3D data from a 32 channel pediatric coil into 6 virtual coils is demonstrated. PMID:22488589

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis,Michael J.

2006-01-01

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Toward Immersed Boundary Simulation of High Reynolds Number Flows

NASA Technical Reports Server (NTRS)

Kalitzin, Georgi; Iaccarino, Gianluca

2003-01-01

In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries. The IB method is ideally suited for Cartesian flow solvers. The flow equations written in Cartesian coordinates appear in a very simple form and several numerical algorithms can be used for an efficient solution of the equations. In addition, the accuracy of numerical algorithms is dependent on the underlying grid and it usually deteriorates when the grid deviates from a Cartesian mesh. The challenge for the IB method lies in the representation of the wall boundaries and in providing an adequate near wall flow field resolution. The issue of enforcing no-slip boundary conditions at the immersed surface has been addressed by several authors by imposing a local reconstruction of the solution. Initial work by Verzicco et al. was based on a simple linear, one-dimensional operator and this approach proved to be accurate for boundaries largely aligned with the grid lines. Majumdar et al. used various multidimensional and high order polynomial interpolations schemes. These high order schemes, however, are keen to introduce wiggles and spurious extrema. Iaccarino & Verzicco and Kalitzin & Iaccarino proposed a tri-linear reconstruction for the velocity components and the turbulent scalars. A modified implementation that has proven to be more robust is reported in this paper. The issue of adequate near wall resolution in a Cartesian framework can initially be addressed by using a non-uniform mesh which is stretched near the surface. In this paper, we investigate an unstructured approach for local grid refinement that utilizes Cartesian mesh features. The computation of high Reynolds number wall bounded flows is particularly challenging as it requires the consideration of thin turbulent boundary layers, i.e. near wall regions with large gradients of the flow field variables. For such flows, the representation of the wall boundary has a large impact on the accuracy of the computation. It is also critical for the robustness and convergence of the flow solver.

Mapping From an Instrumented Glove to a Robot Hand

NASA Technical Reports Server (NTRS)

Goza, Michael

2005-01-01

An algorithm has been developed to solve the problem of mapping from (1) a glove instrumented with joint-angle sensors to (2) an anthropomorphic robot hand. Such a mapping is needed to generate control signals to make the robot hand mimic the configuration of the hand of a human attempting to control the robot. The mapping problem is complicated by uncertainties in sensor locations caused by variations in sizes and shapes of hands and variations in the fit of the glove. The present mapping algorithm is robust in the face of these uncertainties, largely because it includes a calibration sub-algorithm that inherently adapts the mapping to the specific hand and glove, without need for measuring the hand and without regard for goodness of fit. The algorithm utilizes a forward-kinematics model of the glove derived from documentation provided by the manufacturer of the glove. In this case, forward-kinematics model signifies a mathematical model of the glove fingertip positions as functions of the sensor readings. More specifically, given the sensor readings, the forward-kinematics model calculates the glove fingertip positions in a Cartesian reference frame nominally attached to the palm. The algorithm also utilizes an inverse-kinematics model of the robot hand. In this case, inverse-kinematics model signifies a mathematical model of the robot finger-joint angles as functions of the robot fingertip positions. Again, more specifically, the inverse-kinematics model calculates the finger-joint commands needed to place the fingertips at specified positions in a Cartesian reference frame that is attached to the palm of the robot hand and that nominally corresponds to the Cartesian reference frame attached to the palm of the glove. Initially, because of the aforementioned uncertainties, the glove fingertip positions calculated by the forwardkinematics model in the glove Cartesian reference frame cannot be expected to match the robot fingertip positions in the robot-hand Cartesian reference frame. A calibration must be performed to make the glove and robot-hand fingertip positions correspond more precisely. The calibration procedure involves a few simple hand poses designed to provide well-defined fingertip positions. One of the poses is a fist. In each of the other poses, a finger touches the thumb. The calibration subalgorithm uses the sensor readings from these poses to modify the kinematical models to make the two sets of fingertip positions agree more closely.

Global deformation of the Earth, surface mass anomalies, and the geodetic infrastructure required to study these processes

NASA Astrophysics Data System (ADS)

Kusche, J.; Rietbroek, R.; Gunter, B.; Mark-Willem, J.

2008-12-01

Global deformation of the Earth can be linked to loading caused by mass changes in the atmosphere, the ocean and the terrestrial hydrosphere. World-wide geodetic observation systems like GPS, e.g., the global IGS network, can be used to study the global deformation of the Earth directly and, when other effects are properly modeled, provide information regarding the surface loading mass (e.g., to derive geo-center motion estimates). Vice versa, other observing systems that monitor mass change, either through gravitational changes (GRACE) or through a combination of in-situ and modeled quantities (e.g., the atmosphere, ocean or hydrosphere), can provide indirect information on global deformation. In the framework of the German 'Mass transport and mass distribution' program, we estimate surface mass anomalies at spherical harmonic resolution up to degree and order 30 by linking three complementary data sets in a least squares approach. Our estimates include geo-center motion and the thickness of a spatially uniform layer on top of the ocean surface (that is otherwise estimated from surface fluxes, evaporation and precipitation, and river run-off) as a time-series. As with all current Earth observing systems, each dataset has its own limitations and do not realize homogeneous coverage over the globe. To assess the impact that these limitations might have on current and future deformation and loading mass solutions, a sensitivity study was conducted. Simulated real-case and idealized solutions were explored in which the spatial distribution and quality of GPS, GRACE and OBP data sets were varied. The results show that significant improvements, e.g., over the current GRACE monthly gravity fields, in particular at the low degrees, can be achieved when these solutions are combined with present day GPS and OBP products. Our idealized scenarios also provide quantitative implications on how much surface mass change estimates may improve in the future when improved observing systems become available.

Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates

NASA Technical Reports Server (NTRS)

Deane, Anil E.

1996-01-01

Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.

System Wide Joint Position Sensor Fault Tolerance in Robot Systems Using Cartesian Accelerometers

NASA Technical Reports Server (NTRS)

Aldridge, Hal A.; Juang, Jer-Nan

1997-01-01

Joint position sensors are necessary for most robot control systems. A single position sensor failure in a normal robot system can greatly degrade performance. This paper presents a method to obtain position information from Cartesian accelerometers without integration. Depending on the number and location of the accelerometers. the proposed system can tolerate the loss of multiple position sensors. A solution technique suitable for real-time implementation is presented. Simulations were conducted using 5 triaxial accelerometers to recover from the loss of up to 4 joint position sensors on a 7 degree of freedom robot moving in general three dimensional space. The simulations show good estimation performance using non-ideal accelerometer measurements.

An Efficient Means of Adaptive Refinement Within Systems of Overset Grids

NASA Technical Reports Server (NTRS)

Meakin, Robert L.

1996-01-01

An efficient means of adaptive refinement within systems of overset grids is presented. Problem domains are segregated into near-body and off-body fields. Near-body fields are discretized via overlapping body-fitted grids that extend only a short distance from body surfaces. Off-body fields are discretized via systems of overlapping uniform Cartesian grids of varying levels of refinement. a novel off-body grid generation and management scheme provides the mechanism for carrying out adaptive refinement of off-body flow dynamics and solid body motion. The scheme allows for very efficient use of memory resources, and flow solvers and domain connectivity routines that can exploit the structure inherent to uniform Cartesian grids.

Ancient Ethical Practices of Dualism and Ethical Implications for Future Paradigms in Nursing.

PubMed

Milton, Constance L

2016-07-01

Paradigms contain theoretical structures to guide scientific disciplines. Since ancient times, Cartesian dualism has been a prominent philosophy incorporated in the practice of medicine. The discipline of nursing has continued the body-mind emphasis with similar paradigmatic thinking and theories of nursing that separate body and mind. Future trends for paradigm and nursing theory development are harkening to former ways of thinking. In this article the author discusses the origins of Cartesian dualism and implications for its current usage. The author shall illuminate what it potentially means to engage in dualism in nursing and discuss possible ethical implications for future paradigm and theory development in nursing. © The Author(s) 2016.

Development of a Finite-Difference Time Domain (FDTD) Model for Propagation of Transient Sounds in Very Shallow Water.

PubMed

Sprague, Mark W; Luczkovich, Joseph J

2016-01-01

This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.

Estimating network effect in geocenter motion: Theory

NASA Astrophysics Data System (ADS)

Zannat, Umma Jamila; Tregoning, Paul

2017-10-01

Geophysical models and their interpretations of several processes of interest, such as sea level rise, postseismic relaxation, and glacial isostatic adjustment, are intertwined with the need to realize the International Terrestrial Reference Frame. However, this realization needs to take into account the geocenter motion, that is, the motion of the center of figure of the Earth surface, due to, for example, deformation of the surface by earthquakes or hydrological loading effects. Usually, there is also a discrepancy, known as the network effect, between the theoretically convenient center of figure and the physically accessible center of network frames, because of unavoidable factors such as uneven station distribution, lack of stations in the oceans, disparity in the coverage between the two hemispheres, and the existence of tectonically deforming zones. Here we develop a method to estimate the magnitude of the network effect, that is, the error introduced by the incomplete sampling of the Earth surface, in measuring the geocenter motion, for a network of space geodetic stations of a fixed size N. For this purpose, we use, as our proposed estimate, the standard deviations of the changes in Helmert parameters measured by a random network of the same size N. We show that our estimate scales as 1/√N and give an explicit formula for it in terms of the vector spherical harmonics expansion of the displacement field. In a complementary paper we apply this formalism to coseismic displacements and elastic deformations due to surface water movements.

Characterization of an improved 1-3 piezoelectric composite by simulation and experiment.

PubMed

Zhong, Chao; Wang, Likun; Qin, Lei; Zhang, Yanjun

2017-06-16

To increase electromechanical coupling factor of 1-3 piezoelectric composite and reduce its bending deformation under external stress, an improved 1-3 piezoelectric composite is developed. In the improved structure, both epoxy resin and silicone rubber are used as polymer material. The simulation model of the improved 1-3 piezoelectric composite was established using the finite element software ANSYS. The relationship of the performance of the improved composite to the volume percentage of silicone rubber was determined by harmonic response analysis and the bending deformation under external stress was simulated by static analysis. The improved composite samples were prepared by cutting and filling methods, and the performance was tested. The feasibility of the improved structure was verified by finite element simulation and experiment. The electromechanical coupling factor of the improved composite can reach 0.67 and meanwhile the characteristic impedance can decline to 13 MRayl. The electromechanical coupling factor of the improved composite is higher than that of the composite with only epoxy resin as the polymer and the improved composite can reduce bending deformation. Comparison of simulation and experiment, the results of the experiment are in general agreement with those from the simulation. However, most experimental values were higher than the simulation results, and the abnormality of the test results was also more obvious than that of the simulation. These findings may be attributed to slight difference in the material parameters of simulation and experiment.

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

NASA Technical Reports Server (NTRS)

Clark, William S.; Hall, Kenneth C.

1994-01-01

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces.

PubMed

Ban, Ehsan; Franklin, J Matthew; Nam, Sungmin; Smith, Lucas R; Wang, Hailong; Wells, Rebecca G; Chaudhuri, Ovijit; Liphardt, Jan T; Shenoy, Vivek B

2018-01-23

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

ShapeRotator: An R tool for standardized rigid rotations of articulated three-dimensional structures with application for geometric morphometrics.

PubMed

Vidal-García, Marta; Bandara, Lashi; Keogh, J Scott

2018-05-01

The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.

Selected Gravity Models in Terms of the fit to the GOCE Kinematic Orbit in the Dynamic Orbit Determination Process

NASA Astrophysics Data System (ADS)

Bobojć, Andrzej; Drożyner, Andrzej; Rzepecka, Zofia

2017-04-01

The work includes the comparison of performance of selected geopotential models in the dynamic orbit estimation of the satellite of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. This was realized by fitting estimated orbital arcs to the official centimeter-accuracy GOCE kinematic orbit which is provided by the European Space Agency. The Cartesian coordinates of kinematic orbit were treated as observations in the orbit estimation. The initial satellite state vector components were corrected in an iterative process with respect to the J2000.0 inertial reference frame using the given geopotential model, the models describing the remaining gravitational perturbations and the solar radiation pressure. Taking the obtained solutions into account, the RMS values of orbital residuals were computed. These residuals result from the difference between the determined orbit and the reference one - the GOCE kinematic orbit. The performance of selected gravity models was also determined using various orbital arc lengths. Additionally, the RMS fit values were obtained for some gravity models truncated at given degree and order of spherical harmonic coefficients. The advantage of using the kinematic orbit is its independence from any a priori dynamical models. For the research such GOCE-independent gravity models as HUST-Grace2016s, ITU_GRACE16, ITSG-Grace2014s, ITSG-Grace2014k, GGM05S, Tongji-GRACE01, ULUX_CHAMP2013S, ITG-GRACE2010S, EIGEN-51C, EIGEN5S, EGM2008 and EGM96 were adopted.

Shell Corrections Stabilizing Superheavy Nuclei and Semi-spheroidal Atomic Clusters

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

Poenaru, Dorin N.

2008-01-24

The macroscopic-microscopic method is used to illustrate the shell effect stabilizing superheavy nuclei and to study the stability of semi-spheroidal clusters deposited on planar surfaces. The alpha decay of superheavy nuclei is calculated using three models: the analytical superasymmetric fission model; the universal curve, and the semiempirical formula taking into account the shell effects. Analytical relationships are obtained for the energy levels of the new semi-spheroidal harmonic oscillator (SSHO) single-particle model and for the surface and curvature energies of the semi-spheroidal clusters. The maximum degeneracy of the SSHO is reached at a super-deformed prolate shape for which the minimum ofmore » the liquid drop model energy is also attained.« less

Consideration of permanent tidal deformation in the orbit determination and data analysis for the Topex/Poseidon mission

NASA Technical Reports Server (NTRS)

Rapp, Richard H.; Nerem, R. Steven; Shum, C. K.; Klosko, Steven M.; Williamson, Ronald G.

1991-01-01

The effects of the permanent tidal effects of the Sun and Moon with specific applications to satellite altimeter data reduction are reviewed in the context of a consistent definition of geoid undulations. Three situations are applicable not only for altimeter reduction and geoid definition, but also for the second degree zonal harmonic of the geopotential and the equatorial radius. A recommendation is made that sea surface heights and geoid undulations placed on the Topex/Poseidon geophysical data record should be referred to the mean Earth case (i.e., with the permanent effects of the Sun and Moon included). Numerical constants for a number of parameters, including a flattening and geoid geopotential, are included.

Parallel Cartesian grid refinement for 3D complex flow simulations

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2013-11-01

A second order accurate method for discretizing the Navier-Stokes equations on 3D unstructured Cartesian grids is presented. Although the grid generator is based on the oct-tree hierarchical method, fully unstructured data-structure is adopted enabling robust calculations for incompressible flows, avoiding both the need of synchronization of the solution between different levels of refinement and usage of prolongation/restriction operators. The current solver implements a hybrid staggered/non-staggered grid layout, employing the implicit fractional step method to satisfy the continuity equation. The pressure-Poisson equation is discretized by using a novel second order fully implicit scheme for unstructured Cartesian grids and solved using an efficient Krylov subspace solver. The momentum equation is also discretized with second order accuracy and the high performance Newton-Krylov method is used for integrating them in time. Neumann and Dirichlet conditions are used to validate the Poisson solver against analytical functions and grid refinement results to a significant reduction of the solution error. The effectiveness of the fractional step method results in the stability of the overall algorithm and enables the performance of accurate multi-resolution real life simulations. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482.

Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates

NASA Astrophysics Data System (ADS)

Sittel, Florian; Jain, Abhinav; Stock, Gerhard

2014-07-01

Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional free energy landscape. Using Cartesian coordinates, first the translation and overall rotation need to be removed from the trajectory. Since the rotation depends via the moment of inertia on the molecule's structure, this separation is only straightforward for relatively rigid systems. Adopting millisecond molecular dynamics simulations of the folding of villin headpiece and the functional dynamics of BPTI provided by D. E. Shaw Research, it is demonstrated via a comparison of local and global rotational fitting that the structural dynamics of flexible molecules necessarily results in a mixing of overall and internal motion. Even for the small-amplitude functional motion of BPTI, the conformational distribution obtained from a Cartesian principal component analysis therefore reflects to some extend the dominant overall motion rather than the much smaller internal motion of the protein. Internal coordinates such as backbone dihedral angles, on the other hand, are found to yield correct and well-resolved energy landscapes for both examples. The virtues and shortcomings of the choice of various fitting schemes and coordinate sets as well as the generality of these results are discussed in some detail.

Principal component analysis of molecular dynamics: on the use of Cartesian vs. internal coordinates.

PubMed

Sittel, Florian; Jain, Abhinav; Stock, Gerhard

2014-07-07

Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional free energy landscape. Using Cartesian coordinates, first the translation and overall rotation need to be removed from the trajectory. Since the rotation depends via the moment of inertia on the molecule's structure, this separation is only straightforward for relatively rigid systems. Adopting millisecond molecular dynamics simulations of the folding of villin headpiece and the functional dynamics of BPTI provided by D. E. Shaw Research, it is demonstrated via a comparison of local and global rotational fitting that the structural dynamics of flexible molecules necessarily results in a mixing of overall and internal motion. Even for the small-amplitude functional motion of BPTI, the conformational distribution obtained from a Cartesian principal component analysis therefore reflects to some extend the dominant overall motion rather than the much smaller internal motion of the protein. Internal coordinates such as backbone dihedral angles, on the other hand, are found to yield correct and well-resolved energy landscapes for both examples. The virtues and shortcomings of the choice of various fitting schemes and coordinate sets as well as the generality of these results are discussed in some detail.

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.

2003-01-01

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

Numerical relativity in spherical coordinates with the Einstein Toolkit

NASA Astrophysics Data System (ADS)

Mewes, Vassilios; Zlochower, Yosef; Campanelli, Manuela; Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

2018-04-01

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.

Euler Technology Assessment program for preliminary aircraft design employing SPLITFLOW code with Cartesian unstructured grid method

NASA Technical Reports Server (NTRS)

Finley, Dennis B.

1995-01-01

This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.

Strategies to overcome photobleaching in algorithm-based adaptive optics for nonlinear in-vivo imaging.

PubMed

Caroline Müllenbroich, M; McGhee, Ewan J; Wright, Amanda J; Anderson, Kurt I; Mathieson, Keith

2014-01-01

We have developed a nonlinear adaptive optics microscope utilizing a deformable membrane mirror (DMM) and demonstrated its use in compensating for system- and sample-induced aberrations. The optimum shape of the DMM was determined with a random search algorithm optimizing on either two photon fluorescence or second harmonic signals as merit factors. We present here several strategies to overcome photobleaching issues associated with lengthy optimization routines by adapting the search algorithm and the experimental methodology. Optimizations were performed on extrinsic fluorescent dyes, fluorescent beads loaded into organotypic tissue cultures and the intrinsic second harmonic signal of these cultures. We validate the approach of using these preoptimized mirror shapes to compile a robust look-up table that can be applied for imaging over several days and through a variety of tissues. In this way, the photon exposure to the fluorescent cells under investigation is limited to imaging. Using our look-up table approach, we show signal intensity improvement factors ranging from 1.7 to 4.1 in organotypic tissue cultures and freshly excised mouse tissue. Imaging zebrafish in vivo, we demonstrate signal improvement by a factor of 2. This methodology is easily reproducible and could be applied to many photon starved experiments, for example fluorescent life time imaging, or when photobleaching is a concern.

Crustal Displacements Due to Continental Water Loading

NASA Technical Reports Server (NTRS)

vanDam, T.; Wahr, J.; Milly, P. C. D.; Shmakin, A. B.; Blewitt, G.; Lavallee, D.; Larson, K. M.

2001-01-01

The effects of long-wavelength (> 100 km), seasonal variability in continental water storage on vertical crustal motions are assessed. The modeled vertical displacements (delta-r(sub M)) have root-mean-square (RMS) values for 1994-1998 as large as 8 mm with ranges up to 30 mm, and are predominantly annual in character. Regional strains are on the order of 20 nanostrain for tilt and 5 nanostrain for horizontal deformation. We compare delta-r(sub M) with observed Global Positioning System (GPS) heights (delta-r(sub O)) (which include adjustments to remove estimated effects of atmospheric pressure and annual tidal and non-tidal ocean loading) for 147 globally distributed sites. When the delta-r(sub O) time series are adjusted by delta-r(sub M), their variances are reduced, on average, by an amount equal to the variance of the delta-r(sub M). Of the delta-r(sub O) time series exhibiting a strong annual signal, more than half are found to have an annual harmonic that is in phase and of comparable amplitude with the annual harmonic in the delta-r(sub M). The delta-r(sub M) time series exhibit long-period variations that could be mistaken for secular tectonic trends or post-glacial rebound when observed over a time span of a few years.

On the unique structure of the magnetic fields of Uranus and Neptune

NASA Technical Reports Server (NTRS)

Dolginov, Sh. SH.

1993-01-01

The magnetic fields of Uranus and Neptune, which have comparable dipole, quadrupole, and octupole harmonics, are unique in the present-day solar system, but they resemble the geomagnetic field at the epochs of excursions and reversals known from paleomagnetic data. The precession dynamo model, in which the dominant role in the generation of the planetary magnetic fields is played by external gravitational forces, allows us to propose two scenarios for the formation of the unique topology of the magnetic fields of Uranus and Neptune. In the first case, tidal flows in the 'oceans' of these two planets extend down to the depths where the matter has a noticeable electric conductivity and velocity. A hydromagnetic interaction of the moving conducting fluid with the planetary magnetic field outside the generation region results in the deformation of the field and the deceleration of the motion under the action of the radial magnetic field. In the second case, the deformation of the field facilitates drastic changes in cyclonic cells within the generation region causing instabilities that result in a multi-polar field structure, excursions, and inversions. This paper considers this problem in greater detail by using the Neptune-Triton system as an example.

The dynamic deformation of a layered viscoelastic medium under surface excitation

NASA Astrophysics Data System (ADS)

Aglyamov, Salavat R.; Wang, Shang; Karpiouk, Andrei B.; Li, Jiasong; Twa, Michael; Emelianov, Stanislav Y.; Larin, Kirill V.

2015-06-01

In this study the dynamic behavior of a layered viscoelastic medium in response to the harmonic and impulsive acoustic radiation force applied to its surface was investigated both theoretically and experimentally. An analytical solution for a layered viscoelastic compressible medium in frequency and time domains was obtained using the Hankel transform. A special incompressible case was considered to model soft biological tissues. To verify our theoretical model, experiments were performed using tissue-like gel-based phantoms with varying mechanical properties. A 3.5 MHz single-element focused ultrasound transducer was used to apply the radiation force at the surface of the phantoms. A phase-sensitive optical coherence tomography system was used to track the displacements of the phantom surface. Theoretically predicted displacements were compared with experimental measurements. The role of the depth dependence of the elastic properties of a medium in its response to an acoustic pulse at the surface was studied. It was shown that the low-frequency vibrations at the surface are more sensitive to the deep layers than high-frequency ones. Therefore, the proposed model in combination with spectral analysis can be used to evaluate depth-dependent distribution of the mechanical properties based on the measurements of the surface deformation.

Texture and elastic anisotropy of a mylonitic anorthosite from the Morin Shear Zone (Quebec, Canada)

NASA Astrophysics Data System (ADS)

Gómez Barreiro, Juan; Wenk, Hans-Rudolf; Vogel, Sven

2015-02-01

A sample of anorthosite from the granulite facies Morin Shear Zone (Quebec, Canada) was investigated for crystal preferred orientation and elastic anisotropy. Time-of-flight neutron diffraction data obtained with the HIPPO diffractometer at LANSCE were analyzed with the Rietveld method to obtain orientation distribution functions of the principal phases (plagioclase, clinopyroxene and orthopyroxene). Texture and microstructures are compatible with the plastic deformation of the aggregate under high-T conditions. All mineral phases depict a significant preferred orientation that could be related to the general top-to-the north shearing history of the Morin Shear Zone. Texture patterns suggest that (010)[001] in plagioclase and (110)[001] in clinopyroxene are likely dominant slip systems. Using preferred orientation data P- and S-waves velocities and elastic anisotropy were calculated and compared with previous studies to explore elastic properties of rocks with different pyroxene-plagioclase mixtures. P-wave velocity, S-wave splitting and anisotropy increase with clinopyroxene content. Seismic anisotropy is linked to the texture symmetry which can lead to large deviations between actual anisotropy and that measured along Cartesian XYZ sample directions (lineation/foliation reference frame). This is significant for the prediction and interpretation of seismic data, particularly for monoclinic or triclinic texture symmetries.

Tsunami hazard assessment in the Colombian Caribbean Coast with a deterministic approach

NASA Astrophysics Data System (ADS)

Otero Diaz, L.; Correa, R.; Ortiz R, J. C.; Restrepo L, J. C.

2014-12-01

For the Caribbean Sea, we propose six potential tectonic sources of tsunami, defining for each source the worst credible earthquake from the analysis of historical seismicity, tectonics, pasts tsunami, and review of IRIS, PDE, NOAA, and CMT catalogs. The generation and propagation of tsunami waves in the selected sources were simulated with COMCOT 1.7, which is a numerical model that solves the linear and nonlinear long wave equations in finite differences in both Cartesian, and spherical coordinates. The results of the modeling are presented in maps of maximum displacement of the free surface for the Colombian Caribbean coast and the island areas, and they show that the event would produce greater impact is generated in the source of North Panama Deformed Belt (NPDB), where the first wave train reaches the central Colombian coast in 40 minutes, generating wave heights up to 3.7 m. In San Andrés and Providencia island, tsunami waves reach more than 4.5 m due effects of edge waves caused by interactions between waves and a barrier coral reef around of each island. The results obtained in this work are useful for planning systems and future regional and local warning systems and to identify priority areas to conduct detailed research to the tsunami threat.

Temporal behavior of a ventilated claystone at the Tournemire URL: Cross-spectral analyses focused on daily harmonics

NASA Astrophysics Data System (ADS)

Bailly, David; Matray, Jean-Michel; Ababou, Rachid

2014-12-01

The main topic of this communication is the presentation of study, auscultation and supervision procedures of deep geological radioactive waste storage repositories using natural harmonic forcings. In this paper, the effects of natural ventilation on the macroscopic behavior of a clayrock are investigated by means of time series recorded underground over a period of two years in the eastern part of Gallery 1996 at the Tournemire Underground Research Laboratory (URL). This study is based on time series acquired in theatmosphere, at the gallery wall surface, and inside the rock mass. It includes measured signals from 6 thermo-hygrometers, 5 crack-meters (measuring the displacement of 2 shrinkage cracks and 3 tectonic fractures), and a 1 meter-FDR (Frequency Domain Reflectometry) profile probe equipped with 6 sensors for measuring the volumetric pore-water content into the rock mass. Auto-spectral and cross-spectral analyses using the concept of Singular Spectrum Harmonics (SSHs and cross-SSHs) are developed. Our analyses and interpretations focus here mainly on the solar diurnal atmospheric tide (denoted S1 ). This tide corresponds to the insolation cycle of the Earth atmosphere during a mean Solar Day (24 h 00 min). This component is tracked throughout the various measured signals ("Spectral Tracking" of tide fluctuations across signals). This is equivalent, in a way, to analyzing the temporal behavior of the URL during a "Mean Solar Day on Earth". Results indicate that the daily natural forcing caused mainly by a combination of barometric and temperature related fluctuations, is the most important effect overall on our various signals. The daily harmonic induces the fluctuations of gallery air temperature, relative and absolute air humidity and it leads to desaturation of the claystone, which in turn leads to the claystone deformation and damage. The effects of the annual harmonic SA may also be significant (it was fully analyzed in the more complete version of this work); however the SA results are not presented here because the spectral resolution on the annual harmonic is insufficient at this stage with only 2 years and 2 months of clean recorded data. Focusing the present study on daily fluctuations, the cross-spectral time shifts were obtained from the phase spectrum, for the daily component S1, for various pairs of pore-water content sensors located at different distances from the gallery wall. These time shifts were then used to quantify a "spectral velocity" which is found to be on the same order than the hydraulic conductivities deduced previously from pneumatic tests performed in the Excavation Damaged Zone of Gallery 1996.

String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems.

PubMed

Branduardi, Davide; Faraldo-Gómez, José D

2013-09-10

The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β -D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.

String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems

PubMed Central

Branduardi, Davide; Faraldo-Gómez, José D.

2014-01-01

The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID:24729762

Feasibility of 4D flow MR imaging of the brain with either Cartesian y-z radial sampling or k-t SENSE: comparison with 4D Flow MR imaging using SENSE.

PubMed

Sekine, Tetsuro; Amano, Yasuo; Takagi, Ryo; Matsumura, Yoshio; Murai, Yasuo; Kumita, Shinichiro

2014-01-01

A drawback of time-resolved 3-dimensional phase contrast magnetic resonance (4D Flow MR) imaging is its lengthy scan time for clinical application in the brain. We assessed the feasibility for flow measurement and visualization of 4D Flow MR imaging using Cartesian y-z radial sampling and that using k-t sensitivity encoding (k-t SENSE) by comparison with the standard scan using SENSE. Sixteen volunteers underwent 3 types of 4D Flow MR imaging of the brain using a 3.0-tesla scanner. As the standard scan, 4D Flow MR imaging with SENSE was performed first and then followed by 2 types of acceleration scan-with Cartesian y-z radial sampling and with k-t SENSE. We measured peak systolic velocity (PSV) and blood flow volume (BFV) in 9 arteries, and the percentage of particles arriving from the emitter plane at the target plane in 3 arteries, visually graded image quality in 9 arteries, and compared these quantitative and visual data between the standard scan and each acceleration scan. 4D Flow MR imaging examinations were completed in all but one volunteer, who did not undergo the last examination because of headache. Each acceleration scan reduced scan time by 50% compared with the standard scan. The k-t SENSE imaging underestimated PSV and BFV (P < 0.05). There were significant correlations for PSV and BFV between the standard scan and each acceleration scan (P < 0.01). The percentage of particles reaching the target plane did not differ between the standard scan and each acceleration scan. For visual assessment, y-z radial sampling deteriorated the image quality of the 3 arteries. Cartesian y-z radial sampling is feasible for measuring flow, and k-t SENSE offers sufficient flow visualization; both allow acquisition of 4D Flow MR imaging with shorter scan time.

The combined geodetic network adjusted on the reference ellipsoid - a comparison of three functional models for GNSS observations

NASA Astrophysics Data System (ADS)

Kadaj, Roman

2016-12-01

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

Motion correction for functional MRI with three-dimensional hybrid radial-Cartesian EPI.

PubMed

Graedel, Nadine N; McNab, Jennifer A; Chiew, Mark; Miller, Karla L

2017-08-01

Subject motion is a major source of image degradation for functional MRI (fMRI), especially when using multishot sequences like three-dimensional (3D EPI). We present a hybrid radial-Cartesian 3D EPI trajectory enabling motion correction in k-space for functional MRI. The EPI "blades" of the 3D hybrid radial-Cartesian EPI sequence, called TURBINE, are rotated about the phase-encoding axis to fill out a cylinder in 3D k-space. Angular blades are acquired over time using a golden-angle rotation increment, allowing reconstruction at flexible temporal resolution. The self-navigating properties of the sequence are used to determine motion parameters from a high temporal-resolution navigator time series. The motion is corrected in k-space as part of the image reconstruction, and evaluated for experiments with both cued and natural motion. We demonstrate that the motion correction works robustly and that we can achieve substantial artifact reduction as well as improvement in temporal signal-to-noise ratio and fMRI activation in the presence of both severe and subtle motion. We show the potential for hybrid radial-Cartesian 3D EPI to substantially reduce artifacts for application in fMRI, especially for subject groups with significant head motion. The motion correction approach does not prolong the scan, and no extra hardware is required. Magn Reson Med 78:527-540, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

NASA Technical Reports Server (NTRS)

Pandya, Shishir; Murman, Scott; Aftosmis, Michael

2003-01-01

Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

NASA Astrophysics Data System (ADS)

Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

2017-11-01

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of HFBTHO, the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree-Fock-Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592-1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Additional comments: The user must have access to (i) the LAPACK subroutines DSYEEVR, DSYEVD, DSYTRF and DSYTRI, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices, (ii) the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and (iii) the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

Characterization of Space Shuttle Ascent Debris Aerodynamics Using CFD Methods

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosmis, Michael J.; Rogers, Stuart E.

2005-01-01

An automated Computational Fluid Dynamics process for determining the aerodynamic Characteristics of debris shedding from the Space Shuttle Launch Vehicle during ascent is presented. This process uses Cartesian fully-coupled, six-degree-of-freedom simulations of isolated debris pieces in a Monte Carlo fashion to produce models for the drag and crossrange behavior over a range of debris shapes and shedding scenarios. A validation of the Cartesian methods against ballistic range data for insulating foam debris shapes at flight conditions, as well as validation of the resulting models, are both contained. These models are integrated with the existing shuttle debris transport analysis software to provide an accurate and efficient engineering tool for analyzing debris sources and their potential for damage.

Parallelization of PANDA discrete ordinates code using spatial decomposition

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

Humbert, P.

2006-07-01

We present the parallel method, based on spatial domain decomposition, implemented in the 2D and 3D versions of the discrete Ordinates code PANDA. The spatial mesh is orthogonal and the spatial domain decomposition is Cartesian. For 3D problems a 3D Cartesian domain topology is created and the parallel method is based on a domain diagonal plane ordered sweep algorithm. The parallel efficiency of the method is improved by directions and octants pipelining. The implementation of the algorithm is straightforward using MPI blocking point to point communications. The efficiency of the method is illustrated by an application to the 3D-Ext C5G7more » benchmark of the OECD/NEA. (authors)« less

Dual redundant arm system operational quality measures and their applications - Static measures

NASA Technical Reports Server (NTRS)

Lee, Sukhan; Kim, Sungbok

1990-01-01

The authors present dual-arm system static operational quality measures which quantify the efficiency and capability of a dual-arm system in generating Cartesian velocities and static forces. First, they define and analyze the kinematic interactions between the two arms incurred by the various modes of dual-arm cooperation, such as transport, assembly, and grasping modes of cooperation, and specify the kinematic constraints imposed on individual arms in Cartesian space due to the kinematic interactions. Dual-arm static manipulability is presented. Finally, dual-arm operational quality is scaled by a task-oriented operational quality measure (TOQs) obtained by the comparison between the desired and actual static manipulabilities. TOQs is used in the optimization of dual-arm joint configurations. Simulation results are shown.

A projection method for coupling two-phase VOF and fluid structure interaction simulations

NASA Astrophysics Data System (ADS)

Cerroni, Daniele; Da Vià, Roberto; Manservisi, Sandro

2018-02-01

The study of Multiphase Fluid Structure Interaction (MFSI) is becoming of great interest in many engineering applications. In this work we propose a new algorithm for coupling a FSI problem to a multiphase interface advection problem. An unstructured computational grid and a Cartesian mesh are used for the FSI and the VOF problem, respectively. The coupling between these two different grids is obtained by interpolating the velocity field into the Cartesian grid through a projection operator that can take into account the natural movement of the FSI domain. The piecewise color function is interpolated back on the unstructured grid with a Galerkin interpolation to obtain a point-wise function which allows the direct computation of the surface tension forces.

Experimental Characterization of Electron-Beam-Driven Wakefield Modes in a Dielectric-Woodpile Cartesian Symmetric Structure

NASA Astrophysics Data System (ADS)

Hoang, P. D.; Andonian, G.; Gadjev, I.; Naranjo, B.; Sakai, Y.; Sudar, N.; Williams, O.; Fedurin, M.; Kusche, K.; Swinson, C.; Zhang, P.; Rosenzweig, J. B.

2018-04-01

Photonic structures operating in the terahertz (THz) spectral region enable the essential characteristics of confinement, modal control, and electric field shielding for very high gradient accelerators based on wakefields in dielectrics. We report here an experimental investigation of THz wakefield modes in a three-dimensional photonic woodpile structure. Selective control in exciting or suppressing of wakefield modes with a nonzero transverse wave vector is demonstrated by using drive beams of varying transverse ellipticity. Additionally, we show that the wakefield spectrum is insensitive to the offset position of strongly elliptical beams. These results are consistent with analytic theory and three-dimensional simulations and illustrate a key advantage of wakefield systems with Cartesian symmetry: the suppression of transverse wakes by elliptical beams.

Cartesian-Grid Simulations of a Canard-Controlled Missile with a Free-Spinning Tail

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosmis, Michael J.; Kwak, Dochan (Technical Monitor)

2002-01-01

The proposed paper presents a series of simulations of a geometrically complex, canard-controlled, supersonic missile with free-spinning tail fins. Time-dependent simulations were performed using an inviscid Cartesian-grid-based method with results compared to both experimental data and high-resolution Navier-Stokes computations. At fixed free stream conditions and canard deflections, the tail spin rate was iteratively determined such that the net rolling moment on the empennage is zero. This rate corresponds to the time-asymptotic rate of the free-to-spin fin system. After obtaining spin-averaged aerodynamic coefficients for the missile, the investigation seeks a fixed-tail approximation to the spin-averaged aerodynamic coefficients, and examines the validity of this approximation over a variety of freestream conditions.

The renewal of humanism in psychoanalytic therapy.

PubMed

Stolorow, Robert D

2012-12-01

The renewal of humanistic values and practices in contemporary psychoanalytic therapy is exemplified vividly by the impact of Heidegger's existential philosophy on a psychoanalytic perspective called post-Cartesian psychoanalysis. This perspective is a phenomenological-contextualist one in which the focus of psychoanalytic inquiry is shifted from Cartesian isolated minds to ways of being-in-the-world, and from endogenously arising drive derivatives to relationally constituted emotional experiences. A phenomenological-contextualist approach is shown to be especially fruitful in the understanding of, and therapeutic approach to, emotional trauma. The establishment of a hospitable relational home in which traumatic emotional pain and excruciating existential vulnerability can find a context of human understanding in which they can be held is crucial for therapeutic transformation. (c) 2012 APA, all rights reserved.

Methods for performing fast discrete curvelet transforms of data

DOEpatents

Candes, Emmanuel; Donoho, David; Demanet, Laurent

2010-11-23

Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while another is based on the wrapping of specially selected Fourier samples. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Both implementations are fast in the sense that they run in about O(n.sup.2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n.sup.3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.

An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

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

Kamm, James Russell

2015-03-05

This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equationmore » of state and for the JWL equation of state.« less

Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

NASA Astrophysics Data System (ADS)

Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

2013-06-01

We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the transformed harmonic oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single- particle basis to expand quasi-particle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogoliubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions until a self-consistent solution is found. A previous version of the program was presented in: M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Reasons for new version: Version 2.00d of HFBTHO provides a number of new options such as the optional breaking of reflection symmetry, the calculation of axial multipole moments, the finite temperature formalism for the HFB method, optimized multi-constraint calculations, the treatment of odd-even and odd-odd nuclei in the blocking approximation, and the framework for generalized energy density with arbitrary density-dependences. It is also the first version of HFBTHO to contain threading capabilities. Summary of revisions: The modified Broyden method has been implemented, Optional breaking of reflection symmetry has been implemented, The calculation of all axial multipole moments up to λ=8 has been implemented, The finite temperature formalism for the HFB method has been implemented, The linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations has been implemented, The blocking of quasi-particles in the Equal Filling Approximation (EFA) has been implemented, The framework for generalized energy density functionals with arbitrary density-dependence has been implemented, Shared memory parallelism via OpenMP pragmas has been implemented. Restrictions: Axial- and time-reversal symmetries are assumed. Unusual features: The user must have access to the LAPACK subroutines DSYEVD, DSYTRF and DSYTRI, and their dependences, which compute eigenvalues and eigenfunctions of real symmetric matrices, the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/. Running time: Highly variable, as it depends on the nucleus, size of the basis, requested accuracy, requested configuration, compiler and libraries, and hardware architecture. An order of magnitude would be a few seconds for ground-state configurations in small bases N≈8-12, to a few minutes in very deformed configuration of a heavy nucleus with a large basis N>20.

Monitoring microstructural evolution of alloy 617 with non-linear acoustics for remaining useful life prediction; multiaxial creep-fatigue and creep-ratcheting

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

Lissenden, Cliff; Hassan, Tasnin; Rangari, Vijaya

The research built upon a prior investigation to develop a unified constitutive model for design-­by-­analysis of the intermediate heat exchanger (IHX) for a very high temperature reactor (VHTR) design of next generation nuclear plants (NGNPs). Model development requires a set of failure data from complex mechanical experiments to characterize the material behavior. Therefore uniaxial and multiaxial creep-­fatigue and creep-­ratcheting tests were conducted on the nickel-­base Alloy 617 at 850 and 950°C. The time dependence of material behavior, and the interaction of time dependent behavior (e.g., creep) with ratcheting, which is an increase in the cyclic mean strain under load-­controlled cycling,more » are major concerns for NGNP design. This research project aimed at characterizing the microstructure evolution mechanisms activated in Alloy 617 by mechanical loading and dwell times at elevated temperature. The acoustic harmonic generation method was researched for microstructural characterization. It is a nonlinear acoustics method with excellent potential for nondestructive evaluation, and even online continuous monitoring once high temperature sensors become available. It is unique because it has the ability to quantitatively characterize microstructural features well before macroscale defects (e.g., cracks) form. The nonlinear acoustics beta parameter was shown to correlate with microstructural evolution using a systematic approach to handle the complexity of multiaxial creep-­fatigue and creep-­ratcheting deformation. Mechanical testing was conducted to provide a full spectrum of data for: thermal aging, tensile creep, uniaxial fatigue, uniaxial creep-­fatigue, uniaxial creep-ratcheting, multiaxial creep-fatigue, and multiaxial creep-­ratcheting. Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), and Optical Microscopy were conducted to correlate the beta parameter with individual microstructure mechanisms. We researched application of the harmonic generation method to tubular mechanical test specimens and pipes for nondestructive evaluation. Tubular specimens and pipes act as waveguides, thus we applied the acoustic harmonic generation method to guided waves in both plates and shells. Magnetostrictive transducers were used to generate and receive guided wave modes in the shell sample and the received signals were processed to show the sensitivity of higher harmonic generation to microstructure evolution. Modeling was initiated to correlate higher harmonic generation with the microstructure that will lead to development of a life prediction model that is informed by the nonlinear acoustics measurements.« less

Geodesic active fields--a geometric framework for image registration.

PubMed

Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe

2011-05-01

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

The analysis of the distribution of unitary stresses for the universal plowshare in tiller seeder combos (UPTSC)

NASA Astrophysics Data System (ADS)

Chiorescu, D.; Chiorescu, E.; Dodun, O.; Crăciun, V.

2016-11-01

The sustainable development of agriculture is an important component of economic and social progress of the mankind aiming especially at promoting environmentally friendly systems and technologies. Thus, the implementation of sustainable agriculture also requires some high performance farming aggregates such as tiller seeder combos. Their most stressed active working part is the plowshare which has an important part in cutting the soil. For this reason, we consider that theoretical and experimental research is needed for the tear to which this working part is subjected to. This paper analyses the behavior of the universal plowshare, component part of UPTSC, using the Finite Element Method (FEM) and the Ansys software program. With the help of FEM, we analyzed the universal plowshare in the material structure during the soil cutting process, highlighting the deformation degree and the stress field in the working part. In the first stage, we identified a representative set of problems concerning the soil cutting process, for which we designed the solutions through numerical simulations. In the processing stage, we designed a 3D model which respects entirely the geometric shape of the active element in Cartesian coordinates. In order to simulate the soil cutting process in accordance with the real conditions, the compilations are done for various refinement degrees of the discretization network in finite elements. In the same stage we introduced the constraints represented by: the fixation of the plowshare support, direction, as well as the action of the cohesion and shear strength. Using the Explicit Dynamics module of the Ansys software, which allows studying the plowshare behavior, we analyzed in real conditions, the normal and the shear stresses as well as the deformation, for various soil types and various soil states. Considering the data on the existent stresses, following the FEM analysis of the working part, we determined the wear and suggested the safety coefficients for this case.

Large-eddy simulation of wind turbine wake interactions on locally refined Cartesian grids

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2014-11-01

Performing high-fidelity numerical simulations of turbulent flow in wind farms remains a challenging issue mainly because of the large computational resources required to accurately simulate the turbine wakes and turbine/turbine interactions. The discretization of the governing equations on structured grids for mesoscale calculations may not be the most efficient approach for resolving the large disparity of spatial scales. A 3D Cartesian grid refinement method enabling the efficient coupling of the Actuator Line Model (ALM) with locally refined unstructured Cartesian grids adapted to accurately resolve tip vortices and multi-turbine interactions, is presented. Second order schemes are employed for the discretization of the incompressible Navier-Stokes equations in a hybrid staggered/non-staggered formulation coupled with a fractional step method that ensures the satisfaction of local mass conservation to machine zero. The current approach enables multi-resolution LES of turbulent flow in multi-turbine wind farms. The numerical simulations are in good agreement with experimental measurements and are able to resolve the rich dynamics of turbine wakes on grids containing only a small fraction of the grid nodes that would be required in simulations without local mesh refinement. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the National Science Foundation under Award number NSF PFI:BIC 1318201.

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

DOE PAGES

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

2018-06-07

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ku, Hwar-Ching; Popel, Aleksander S.

1996-01-01

A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.

Effects of using two- versus three-dimensional computational modeling of fluidized beds Part I, hydrodynamics

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

Xie, Nan; Battaglia, Francine; Pannala, Sreekanth

2008-01-01

Simulations of fluidized beds are performed to study and determine the effect on the use of coordinate systems and geometrical configurations to model fluidized bed reactors. Computational fluid dynamics is employed for an Eulerian-Eulerian model, which represents each phase as an interspersed continuum. The transport equation for granular temperature is solved and a hyperbolic tangent function is used to provide a smooth transition between the plastic and viscous regimes for the solid phase. The aim of the present work is to show the range of validity for employing simulations based on a 2D Cartesian coordinate system to approximate both cylindricalmore » and rectangular fluidized beds. Three different fluidization regimes, bubbling, slugging and turbulent regimes, are investigated and the results of 2D and 3D simulations are presented for both cylindrical and rectangular domains. The results demonstrate that a 2D Cartesian system can be used to successfully simulate and predict a bubbling regime. However, caution must be exercised when using 2D Cartesian coordinates for other fluidized regimes. A budget analysis that explains all the differences in detail is presented in Part II [N. Xie, F. Battaglia, S. Pannala, Effects of Using Two-Versus Three-Dimensional Computational Modeling of Fluidized Beds: Part II, budget analysis, 182 (1) (2007) 14] to complement the hydrodynamic theory of this paper.« less

[Cartesian misunderstanding as a cause of therapeutic failure].

PubMed

Isler, H

1986-01-01

Headache patients disassociate themselves from their own automatic responses, relying on the traditional separation of body and mind. On the other hand, patients who obtain voluntary control of automatic functions by biofeedback training modify not only vegetative but also voluntary behaviour patterns, losing "neurotic" traits. The basic misconception of the separation of body and mind, Cartesian dualism, is now ingrained in our culture. In the 17th century Descartes asserted that concepts applied to the soul must be entirely different from those used for the body in order to improve comprehension of the immortality of the soul. This dualism also led to "enlightenment" and to many later social and philosophical developments. But his basic neurophysiology was obsolete when he wrote it down. Other models from mainstream natural philosophy were better compatible with observation and experiments. Gassendi assumed a "body soul" consisting of energy as the functional principle of the nervous system, and Willis accommodated a series of anticipations of 19th century discoveries within this model. No comparable progress resulted from Descartes' own medieval model. Cartesian dualism has become untenable in view of recent neuropsychology but it still obstructs our management of functional patients. Instead of reinforcing the delusion of separation of psyche and soma, we ought to encourage patients to understand that their malfunctioning organs are on-line with their emotions, and with their mind.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Murman, S. M.; Berger, M. J.

2003-01-01

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

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

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

Improving the Long-Term Stability of Atmospheric Surface Deformation Predictions by Mitigating the Effects of Orography Updates in Operational Weather Forecast Models

NASA Astrophysics Data System (ADS)

Dill, Robert; Bergmann-Wolf, Inga; Thomas, Maik; Dobslaw, Henryk

2016-04-01

The global numerical weather prediction model routinely operated at the European Centre for Medium-Range Weather Forecasts (ECMWF) is typically updated about two times a year to incorporate the most recent improvements in the numerical scheme, the physical model or the data assimilation procedures into the system for steadily improving daily weather forecasting quality. Even though such changes frequently affect the long-term stability of meteorological quantities, data from the ECMWF deterministic model is often preferred over alternatively available atmospheric re-analyses due to both the availability of the data in near real-time and the substantially higher spatial resolution. However, global surface pressure time-series, which are crucial for the interpretation of geodetic observables, such as Earth rotation, surface deformation, and the Earth's gravity field, are in particular affected by changes in the surface orography of the model associated with every major change in horizontal resolution happened, e.g., in February 2006, January 2010, and May 2015 in case of the ECMWF operational model. In this contribution, we present an algorithm to harmonize surface pressure time-series from the operational ECMWF model by projecting them onto a time-invariant reference topography under consideration of the time-variable atmospheric density structure. The effectiveness of the method will be assessed globally in terms of pressure anomalies. In addition, we will discuss the impact of the method on predictions of crustal deformations based on ECMWF input, which have been recently made available by GFZ Potsdam.

Architecture of the crust and uppermost mantle in the northern Canadian Cordillera from receiver functions

NASA Astrophysics Data System (ADS)

Tarayoun, Alizia; Audet, Pascal; Mazzotti, Stéphane; Ashoori, Azadeh

2017-07-01

The northern Canadian Cordillera (NCC) is an active orogenic belt in northwestern Canada characterized by deformed autochtonous and allochtonous structures that were emplaced in successive episodes of convergence since the Late Cretaceous. Seismicity and crustal deformation are concentrated along corridors located far (>200 to 800 km) from the convergent plate margin. Proposed geodynamic models require information on crust and mantle structure and strain history, which are poorly constrained. We calculate receiver functions using 66 broadband seismic stations within and around the NCC and process them to estimate Moho depth and P-to-S velocity ratio (Vp/Vs) of the Cordilleran crust. We also perform a harmonic decomposition to determine the anisotropy of the subsurface layers. From these results, we construct simple seismic velocity models at selected stations and simulate receiver function data to constrain crust and uppermost mantle structure and anisotropy. Our results indicate a relatively flat and sharp Moho at 32 ± 2 km depth and crustal Vp/Vs of 1.75 ± 0.05. Seismic anisotropy is pervasive in the upper crust and within a thin ( 10-15 km thick) sub-Moho layer. The modeled plunging slow axis of hexagonal symmetry of the upper crustal anisotropic layer may reflect the presence of fractures or mica-rich mylonites. The subhorizontal fast axis of hexagonal anisotropy within the sub-Moho layer is generally consistent with the SE-NW orientation of large-scale tectonic structures. These results allow us to revise the geodynamic models proposed to explain active deformation within the NCC.

Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability

NASA Astrophysics Data System (ADS)

Barker, Adrian J.; Braviner, Harry J.; Ogilvie, Gordon I.

2016-06-01

We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders ℓ ≤ 5, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when n/Ω ≲ -1, where n and Ω are the orbital and spin angular frequencies, respectively) if the tidal amplitude is sufficiently large. We also explore the instability in a rigid ellipsoidal container, which is found to be quantitatively similar to that with a realistic free surface. Finally, we study the effect of rotation and tidal deformation on mode frequencies. We find that larger rotation rates and larger tidal deformations both decrease the frequencies of the prograde sectoral surface gravity modes. This increases the prospect of their tidal excitation, potentially enhancing the tidal response over expectations from linear theory. In a companion paper, we use our results to interpret global simulations of the elliptical instability.

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Study of dynamic fluid-structure coupling with application to human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Faber, Justin; Bodony, Daniel

2013-11-01

Two-dimensional direct numerical simulations of a compressible, viscous fluid interacting with a non-linear, viscoelastic solid are used to study the generation of the human voice. The vocal fold (VF) tissues are modeled using a finite-strain fractional derivative constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The viscoelastic solver is validated through in-house experiments using Agarose Gel, a human tissue simulant, undergoing static and harmonic deformation measured with load cell and optical diagnostics. The phonation simulations highlight the role tissue nonlinearity and viscosity play in the glottal jet dynamics and in the radiated sound. Supported by the National Science Foundation (CAREER award number 1150439).

Spheroidal and Toroidal Modes for Tidal Kinetic Energy in Spherical Elastic Bodies

NASA Astrophysics Data System (ADS)

Getino, Juan; Escapa, Alberto; Garcia, Amelia

In this work, the total expression of the perturbation of the kinetic energy of rotation, when an elastic spherical solid is deformed due to the gravitational attraction of external bodies, is studied. We do not limit this study to any order in the expansion of the perturbing potential in spherical harmonics, and we consider in the expression of the displacement vector the complete solution, composed by spheroidal and toroidal modes. We show in a very simple way, by using the properties of the Legendre polynomials, that the toroidal modes have no contribution at all under the hypothesis of spherical body, and, among the spheroidal modes, only the term n=2 acts, therefore the perturbation produced by the spheroidal component for n=2 gathers the total perturbation.

On superintegrable monopole systems

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2018-02-01

Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Kepler-type symmetries and provide non-trivial generalizations of the usual Kepler problems. In this paper, we overview new families of superintegrable Kepler, MIC-harmonic oscillator and deformed Kepler systems interacting with Yang-Coulomb monopoles in the flat and curved Taub-NUT spaces. We present their higher-order, algebraically independent integrals of motion via the direct and constructive approaches which prove the superintegrability of the models. The integrals form symmetry polynomial algebras of the systems with structure constants involving Casimir operators of certain Lie algebras. Such algebraic approaches provide a deeper understanding to the degeneracies of the energy spectra and connection between wave functions and differential equations and geometry.

The behaviour of stacking fault energy upon interstitial alloying.

PubMed

Lee, Jee-Yong; Koo, Yang Mo; Lu, Song; Vitos, Levente; Kwon, Se Kyun

2017-09-11

Stacking fault energy is one of key parameters for understanding the mechanical properties of face-centered cubic materials. It is well known that the plastic deformation mechanism is closely related to the size of stacking fault energy. Although alloying is a conventional method to modify the physical parameter, the underlying microscopic mechanisms are not yet clearly established. Here, we propose a simple model for determining the effect of interstitial alloying on the stacking fault energy. We derive a volumetric behaviour of stacking fault energy from the harmonic approximation to the energy-lattice curve and relate it to the contents of interstitials. The stacking fault energy is found to change linearly with the interstitial content in the usual low concentration domain. This is in good agreement with previously reported experimental and theoretical data.

Piezoelectric monolayers as nonlinear energy harvesters.

PubMed

López-Suárez, Miquel; Pruneda, Miguel; Abadal, Gabriel; Rurali, Riccardo

2014-05-02

We study the dynamics of h-BN monolayers by first performing ab-initio calculations of the deformation potential energy and then solving numerically a Langevine-type equation to explore their use in nonlinear vibration energy harvesting devices. An applied compressive strain is used to drive the system into a nonlinear bistable regime, where quasi-harmonic vibrations are combined with low-frequency swings between the minima of a double-well potential. Due to its intrinsic piezoelectric response, the nonlinear mechanical harvester naturally provides an electrical power that is readily available or can be stored by simply contacting the monolayer at its ends. Engineering the induced nonlinearity, a 20 nm2 device is predicted to harvest an electrical power of up to 0.18 pW for a noisy vibration of 5 pN.

Dynamic magnetic resonance imaging method based on golden-ratio cartesian sampling and compressed sensing.

PubMed

Li, Shuo; Zhu, Yanchun; Xie, Yaoqin; Gao, Song

2018-01-01

Dynamic magnetic resonance imaging (DMRI) is used to noninvasively trace the movements of organs and the process of drug delivery. The results can provide quantitative or semiquantitative pathology-related parameters, thus giving DMRI great potential for clinical applications. However, conventional DMRI techniques suffer from low temporal resolution and long scan time owing to the limitations of the k-space sampling scheme and image reconstruction algorithm. In this paper, we propose a novel DMRI sampling scheme based on a golden-ratio Cartesian trajectory in combination with a compressed sensing reconstruction algorithm. The results of two simulation experiments, designed according to the two major DMRI techniques, showed that the proposed method can improve the temporal resolution and shorten the scan time and provide high-quality reconstructed images.

Interpolation schemes for peptide rearrangements.

PubMed

Bauer, Marianne S; Strodel, Birgit; Fejer, Szilard N; Koslover, Elena F; Wales, David J

2010-02-07

A variety of methods (in total seven) comprising different combinations of internal and Cartesian coordinates are tested for interpolation and alignment in connection attempts for polypeptide rearrangements. We consider Cartesian coordinates, the internal coordinates used in CHARMM, and natural internal coordinates, each of which has been interfaced to the OPTIM code and compared with the corresponding results for united-atom force fields. We show that aligning the methylene hydrogens to preserve the sign of a local dihedral angle, rather than minimizing a distance metric, provides significant improvements with respect to connection times and failures. We also demonstrate the superiority of natural coordinate methods in conjunction with internal alignment. Checking the potential energy of the interpolated structures can act as a criterion for the choice of the interpolation coordinate system, which reduces failures and connection times significantly.

Reverse Kinematic Analysis and Uncertainty Analysis of the Space Shuttle AFT Propulsion System (APS) POD Lifting Fixture

NASA Technical Reports Server (NTRS)

Brink, Jeffrey S.

2005-01-01

The space shuttle Aft Propulsion System (APS) pod requires precision alignment to be installed onto the orbiter deck. The Ground Support Equipment (GSE) used to perform this task cannot be manipulated along a single Cartesian axis without causing motion along the other Cartesian axes. As a result, manipulations required to achieve a desired motion are not intuitive. My study calculated the joint angles required to align the APS pod, using reverse kinematic analysis techniques. Knowledge of these joint angles will allow the ground support team to align the APS pod more safely and efficiently. An uncertainty analysis was also performed to estimate the accuracy associated with this approach and to determine whether any inexpensive modifications can be made to further improve accuracy.

Multipole analysis in the radiation field for linearized f (R ) gravity with irreducible Cartesian tensors

NASA Astrophysics Data System (ADS)

Wu, Bofeng; Huang, Chao-Guang

2018-04-01

The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.

Calculation of radiation therapy dose using all particle Monte Carlo transport

DOEpatents

Chandler, William P.; Hartmann-Siantar, Christine L.; Rathkopf, James A.

1999-01-01

The actual radiation dose absorbed in the body is calculated using three-dimensional Monte Carlo transport. Neutrons, protons, deuterons, tritons, helium-3, alpha particles, photons, electrons, and positrons are transported in a completely coupled manner, using this Monte Carlo All-Particle Method (MCAPM). The major elements of the invention include: computer hardware, user description of the patient, description of the radiation source, physical databases, Monte Carlo transport, and output of dose distributions. This facilitated the estimation of dose distributions on a Cartesian grid for neutrons, photons, electrons, positrons, and heavy charged-particles incident on any biological target, with resolutions ranging from microns to centimeters. Calculations can be extended to estimate dose distributions on general-geometry (non-Cartesian) grids for biological and/or non-biological media.

Numerical Simulation of Rolling-Airframes Using a Multi-Level Cartesian Method

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)

2002-01-01

A supersonic rolling missile with two synchronous canard control surfaces is analyzed using an automated, inviscid, Cartesian method. Sequential-static and time-dependent dynamic simulations of the complete motion are computed for canard dither schedules for level flight, pitch, and yaw maneuver. The dynamic simulations are compared directly against both high-resolution viscous simulations and relevant experimental data, and are also utilized to compute dynamic stability derivatives. The results show that both the body roll rate and canard dither motion influence the roll-averaged forces and moments on the body. At the relatively, low roll rates analyzed in the current work these dynamic effects are modest, however the dynamic computations are effective in predicting the dynamic stability derivatives which can be significant for highly-maneuverable missiles.

Calculation of radiation therapy dose using all particle Monte Carlo transport

DOEpatents

Chandler, W.P.; Hartmann-Siantar, C.L.; Rathkopf, J.A.

1999-02-09

The actual radiation dose absorbed in the body is calculated using three-dimensional Monte Carlo transport. Neutrons, protons, deuterons, tritons, helium-3, alpha particles, photons, electrons, and positrons are transported in a completely coupled manner, using this Monte Carlo All-Particle Method (MCAPM). The major elements of the invention include: computer hardware, user description of the patient, description of the radiation source, physical databases, Monte Carlo transport, and output of dose distributions. This facilitated the estimation of dose distributions on a Cartesian grid for neutrons, photons, electrons, positrons, and heavy charged-particles incident on any biological target, with resolutions ranging from microns to centimeters. Calculations can be extended to estimate dose distributions on general-geometry (non-Cartesian) grids for biological and/or non-biological media. 57 figs.

An adaptive Cartesian control scheme for manipulators

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.

Quantitative assessment of corneal vibrations during intraocular pressure measurement with the air-puff method in patients with keratoconus.

PubMed

Koprowski, Robert; Ambrósio, Renato

2015-11-01

One of the current methods for measuring intraocular pressure is the air-puff method. A tonometer which uses this method is the Corvis device. With the ultra-high-speed (UHS) Scheimpflug camera, it is also possible to observe corneal deformation during measurement. The use of modern image analysis and processing methods allows for analysis of higher harmonics of corneal deflection above 100 Hz. 493 eyes of healthy subjects and 279 eyes of patients with keratoconus were used in the measurements. For each eye, 140 corneal deformation images were recorded during intraocular pressure measurement. Each image was recorded every 230 µs and had a resolution of 200 × 576 pixels. A new, original algorithm for image analysis and processing has been proposed. It enables to separate the eyeball reaction as well as low-frequency and high-frequency corneal deformations from the eye response to an air puff. Furthermore, a method for classification of healthy subjects and patients with keratoconus based on decision trees has been proposed. The obtained results confirm the possibility to distinguish between patients with keratoconus and healthy subjects. The features used in this classification are directly related to corneal vibrations. They are only available in the proposed software and provide specificity of 98%, sensitivity-85%, and accuracy-92%. This confirms the usefulness of the proposed method in this type of classification that uses corneal vibrations during intraocular pressure measurement with the Corvis tonometer. With the new proposed algorithm for image analysis and processing allowing for the separation of individual features from a corneal deformation image, it is possible to: automatically measure corneal vibrations in a few characteristic points of the cornea, obtain fully repeatable measurement of vibrations for the same registered sequence of images and measure vibration parameters for large inter-individual variability in patients. Copyright © 2015 Elsevier Ltd. All rights reserved.

Seismic anisotropy in central North Anatolian Fault Zone and its implications on crustal deformation

NASA Astrophysics Data System (ADS)

Licciardi, A.; Eken, T.; Taymaz, T.; Piana Agostinetti, N.; Yolsal-Çevikbilen, S.

2018-04-01

We investigate the crustal seismic structure and anisotropy around the central portion of the North Anatolian Fault Zone, a major plate boundary, using receiver function analysis. The characterization of crustal seismic anisotropy plays a key role in our understanding of present and past deformation processes at plate boundaries. The development of seismic anisotropy in the crust arises from the response of the rocks to complicated deformation regimes induced by plate interaction. Through the analysis of azimuthally-varying signals of teleseismic receiver functions, we map the anisotropic properties of the crust as a function of depth, by employing the harmonic decomposition technique. Although the Moho is located at a depth of about 40 km, with no major offset across the area, our results show a clear asymmetric distribution of crustal properties between the northern and southern blocks, divided by the North Anatolian Fault Zone. Heterogeneous and strongly anisotropic crust is present in the southern block, where complex intra-crustal signals are the results of strong deformation. In the north, a simpler and weakly anisotropic crust is typically observed. The strongest anisotropic signal is located in the first 15 km of the crust and is widespread in the southern block. Stations located on top of the main active faults in the area indicate the highest amplitudes, together with fault-parallel strikes of the fast plane of anisotropy. We interpret the origin of this signal as due to structure-induced anisotropy, and roughly determine its depth extent up to 15-20 km for these stations. Away from the faults, we suggest the contribution of previously documented uplifted basement blocks to explain the observed anisotropy at upper and middle crustal depths. Finally, we interpret coherent NE-SW orientations below the Moho as a result of frozen-in anisotropy in the upper mantle, as suggested by previous studies.

TH-EF-BRA-08: A Novel Technique for Estimating Volumetric Cine MRI (VC-MRI) From Multi-Slice Sparsely Sampled Cine Images Using Motion Modeling and Free Form Deformation

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

Harris, W; Yin, F; Wang, C

Purpose: To develop a technique to estimate on-board VC-MRI using multi-slice sparsely-sampled cine images, patient prior 4D-MRI, motion-modeling and free-form deformation for real-time 3D target verification of lung radiotherapy. Methods: A previous method has been developed to generate on-board VC-MRI by deforming prior MRI images based on a motion model(MM) extracted from prior 4D-MRI and a single-slice on-board 2D-cine image. In this study, free-form deformation(FD) was introduced to correct for errors in the MM when large anatomical changes exist. Multiple-slice sparsely-sampled on-board 2D-cine images located within the target are used to improve both the estimation accuracy and temporal resolution ofmore » VC-MRI. The on-board 2D-cine MRIs are acquired at 20–30frames/s by sampling only 10% of the k-space on Cartesian grid, with 85% of that taken at the central k-space. The method was evaluated using XCAT(computerized patient model) simulation of lung cancer patients with various anatomical and respirational changes from prior 4D-MRI to onboard volume. The accuracy was evaluated using Volume-Percent-Difference(VPD) and Center-of-Mass-Shift(COMS) of the estimated tumor volume. Effects of region-of-interest(ROI) selection, 2D-cine slice orientation, slice number and slice location on the estimation accuracy were evaluated. Results: VCMRI estimated using 10 sparsely-sampled sagittal 2D-cine MRIs achieved VPD/COMS of 9.07±3.54%/0.45±0.53mm among all scenarios based on estimation with ROI-MM-ROI-FD. The FD optimization improved estimation significantly for scenarios with anatomical changes. Using ROI-FD achieved better estimation than global-FD. Changing the multi-slice orientation to axial, coronal, and axial/sagittal orthogonal reduced the accuracy of VCMRI to VPD/COMS of 19.47±15.74%/1.57±2.54mm, 20.70±9.97%/2.34±0.92mm, and 16.02±13.79%/0.60±0.82mm, respectively. Reducing the number of cines to 8 enhanced temporal resolution of VC-MRI by 25% while maintaining the estimation accuracy. Estimation using slices sampled uniformly through the tumor achieved better accuracy than slices sampled non-uniformly. Conclusions: Preliminary studies showed that it is feasible to generate VC-MRI from multi-slice sparsely-sampled 2D-cine images for real-time 3D-target verification. This work was supported by the National Institutes of Health under Grant No. R01-CA184173 and a research grant from Varian Medical Systems.« less

Electronic Absolute Cartesian Autocollimator

NASA Technical Reports Server (NTRS)

Leviton, Douglas B.

2006-01-01

An electronic absolute Cartesian autocollimator performs the same basic optical function as does a conventional all-optical or a conventional electronic autocollimator but differs in the nature of its optical target and the manner in which the position of the image of the target is measured. The term absolute in the name of this apparatus reflects the nature of the position measurement, which, unlike in a conventional electronic autocollimator, is based absolutely on the position of the image rather than on an assumed proportionality between the position and the levels of processed analog electronic signals. The term Cartesian in the name of this apparatus reflects the nature of its optical target. Figure 1 depicts the electronic functional blocks of an electronic absolute Cartesian autocollimator along with its basic optical layout, which is the same as that of a conventional autocollimator. Referring first to the optical layout and functions only, this or any autocollimator is used to measure the compound angular deviation of a flat datum mirror with respect to the optical axis of the autocollimator itself. The optical components include an illuminated target, a beam splitter, an objective or collimating lens, and a viewer or detector (described in more detail below) at a viewing plane. The target and the viewing planes are focal planes of the lens. Target light reflected by the datum mirror is imaged on the viewing plane at unit magnification by the collimating lens. If the normal to the datum mirror is parallel to the optical axis of the autocollimator, then the target image is centered on the viewing plane. Any angular deviation of the normal from the optical axis manifests itself as a lateral displacement of the target image from the center. The magnitude of the displacement is proportional to the focal length and to the magnitude (assumed to be small) of the angular deviation. The direction of the displacement is perpendicular to the axis about which the mirror is slightly tilted. Hence, one can determine the amount and direction of tilt from the coordinates of the target image on the viewing plane.

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

2016-11-01

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved.

The representation of visual depth perception based on the plenoptic function in the retina and its neural computation in visual cortex V1.

PubMed

Songnian, Zhao; Qi, Zou; Chang, Liu; Xuemin, Liu; Shousi, Sun; Jun, Qiu

2014-04-23

How it is possible to "faithfully" represent a three-dimensional stereoscopic scene using Cartesian coordinates on a plane, and how three-dimensional perceptions differ between an actual scene and an image of the same scene are questions that have not yet been explored in depth. They seem like commonplace phenomena, but in fact, they are important and difficult issues for visual information processing, neural computation, physics, psychology, cognitive psychology, and neuroscience. The results of this study show that the use of plenoptic (or all-optical) functions and their dual plane parameterizations can not only explain the nature of information processing from the retina to the primary visual cortex and, in particular, the characteristics of the visual pathway's optical system and its affine transformation, but they can also clarify the reason why the vanishing point and line exist in a visual image. In addition, they can better explain the reasons why a three-dimensional Cartesian coordinate system can be introduced into the two-dimensional plane to express a real three-dimensional scene. 1. We introduce two different mathematical expressions of the plenoptic functions, Pw and Pv that can describe the objective world. We also analyze the differences between these two functions when describing visual depth perception, that is, the difference between how these two functions obtain the depth information of an external scene.2. The main results include a basic method for introducing a three-dimensional Cartesian coordinate system into a two-dimensional plane to express the depth of a scene, its constraints, and algorithmic implementation. In particular, we include a method to separate the plenoptic function and proceed with the corresponding transformation in the retina and visual cortex.3. We propose that size constancy, the vanishing point, and vanishing line form the basis of visual perception of the outside world, and that the introduction of a three-dimensional Cartesian coordinate system into a two dimensional plane reveals a corresponding mapping between a retinal image and the vanishing point and line.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Coirier, William John

1994-01-01

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors

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

Lin, Dejun, E-mail: dejun.lin@gmail.com

2015-09-21

Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between themore » kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A software library based on this algorithm has been implemented in C++11 and has been released.« less

The representation of visual depth perception based on the plenoptic function in the retina and its neural computation in visual cortex V1

PubMed Central

2014-01-01

Background How it is possible to “faithfully” represent a three-dimensional stereoscopic scene using Cartesian coordinates on a plane, and how three-dimensional perceptions differ between an actual scene and an image of the same scene are questions that have not yet been explored in depth. They seem like commonplace phenomena, but in fact, they are important and difficult issues for visual information processing, neural computation, physics, psychology, cognitive psychology, and neuroscience. Results The results of this study show that the use of plenoptic (or all-optical) functions and their dual plane parameterizations can not only explain the nature of information processing from the retina to the primary visual cortex and, in particular, the characteristics of the visual pathway’s optical system and its affine transformation, but they can also clarify the reason why the vanishing point and line exist in a visual image. In addition, they can better explain the reasons why a three-dimensional Cartesian coordinate system can be introduced into the two-dimensional plane to express a real three-dimensional scene. Conclusions 1. We introduce two different mathematical expressions of the plenoptic functions, P w and P v that can describe the objective world. We also analyze the differences between these two functions when describing visual depth perception, that is, the difference between how these two functions obtain the depth information of an external scene. 2. The main results include a basic method for introducing a three-dimensional Cartesian coordinate system into a two-dimensional plane to express the depth of a scene, its constraints, and algorithmic implementation. In particular, we include a method to separate the plenoptic function and proceed with the corresponding transformation in the retina and visual cortex. 3. We propose that size constancy, the vanishing point, and vanishing line form the basis of visual perception of the outside world, and that the introduction of a three-dimensional Cartesian coordinate system into a two dimensional plane reveals a corresponding mapping between a retinal image and the vanishing point and line. PMID:24755246

A Lorentz model for weak magnetic field bioeffects: part I--thermal noise is an essential component of AC/DC effects on bound ion trajectory.

PubMed

Muehsam, David J; Pilla, Arthur A

2009-09-01

We have previously employed the Lorentz-Langevin model to describe the effects of weak exogenous magnetic fields via the classical Lorentz force on a charged ion bound in a harmonic oscillator potential, in the presence of thermal noise forces. Previous analyses predicted that microT-range fields give rise to a rotation of the oscillator orientation at the Larmor frequency and bioeffects were based upon the assumption that the classical trajectory of the bound charge itself could modulate a biochemical process. Here, it is shown that the thermal component of the motion follows the Larmor trajectory. The results show that the Larmor frequency is independent of the thermal noise strength, and the motion retains the form of a coherent oscillator throughout the binding lifetime, rather than devolving into a random walk. Thermal equilibration results in a continual increase in the vibrational amplitude of the rotating oscillator towards the steady-state amplitude, but does not affect the Larmor orbit. Thus, thermal noise contributes to, rather than inhibits, the effect of the magnetic field upon reactivity. Expressions are derived for the ensemble average of position and the velocity of the thermal component of the oscillator motion. The projection of position and velocity onto a Cartesian axis measures the nonuniformity of the Larmor trajectory and is illustrated for AC and combined AC/DC magnetic fields, suggesting a means of interpreting resonance phenomena. It is noted that the specific location and height of resonances are dependent upon binding lifetime and initial AC phase.

Nonlinear interaction and wave breaking with a submerged porous structure

NASA Astrophysics Data System (ADS)

Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.

2016-12-01

Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.

Programmable Self-Locking Origami Mechanical Metamaterials.

PubMed

Fang, Hongbin; Chu, Shih-Cheng A; Xia, Yutong; Wang, Kon-Well

2018-04-01

Developing mechanical metamaterials with programmable properties is an emerging topic receiving wide attention. While the programmability mainly originates from structural multistability in previously designed metamaterials, here it is shown that nonflat-foldable origami provides a new platform to achieve programmability via its intrinsic self-locking and reconfiguration capabilities. Working with the single-collinear degree-4 vertex origami tessellation, it is found that each unit cell can self-lock at a nonflat configuration and, therefore, possesses wide design space to program its foldability and relative density. Experiments and numerical analyses are combined to demonstrate that by switching the deformation modes of the constituent cell from prelocking folding to postlocking pressing, its stiffness experiences a sudden jump, implying a limiting-stopper effect. Such a stiffness jump is generalized to a multisegment piecewise stiffness profile in a multilayer model. Furthermore, it is revealed that via strategically switching the constituent cells' deformation modes through passive or active means, the n-layer metamaterial's stiffness is controllable among 2 n target stiffness values. Additionally, the piecewise stiffness can also trigger bistable responses dynamically under harmonic excitations, highlighting the metamaterial's rich dynamic performance. These unique characteristics of self-locking origami present new paths for creating programmable mechanical metamaterials with in situ controllable mechanical properties. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Relationship of Three-Dimensional Human Skull Motion to Brain Tissue Deformation in Magnetic Resonance Elastography Studies

PubMed Central

Badachhape, Andrew A.; Okamoto, Ruth J.; Durham, Ramona S.; Efron, Brent D.; Nadell, Sam J.; Johnson, Curtis L.; Bayly, Philip V.

2017-01-01

In traumatic brain injury (TBI), membranes such as the dura mater, arachnoid mater, and pia mater play a vital role in transmitting motion from the skull to brain tissue. Magnetic resonance elastography (MRE) is an imaging technique developed for noninvasive estimation of soft tissue material parameters. In MRE, dynamic deformation of brain tissue is induced by skull vibrations during magnetic resonance imaging (MRI); however, skull motion and its mode of transmission to the brain remain largely uncharacterized. In this study, displacements of points in the skull, reconstructed using data from an array of MRI-safe accelerometers, were compared to displacements of neighboring material points in brain tissue, estimated from MRE measurements. Comparison of the relative amplitudes, directions, and temporal phases of harmonic motion in the skulls and brains of six human subjects shows that the skull–brain interface significantly attenuates and delays transmission of motion from skull to brain. In contrast, in a cylindrical gelatin “phantom,” displacements of the rigid case (reconstructed from accelerometer data) were transmitted to the gelatin inside (estimated from MRE data) with little attenuation or phase lag. This quantitative characterization of the skull–brain interface will be valuable in the parameterization and validation of computer models of TBI. PMID:28267188

The Relationship of Three-Dimensional Human Skull Motion to Brain Tissue Deformation in Magnetic Resonance Elastography Studies.

PubMed

Badachhape, Andrew A; Okamoto, Ruth J; Durham, Ramona S; Efron, Brent D; Nadell, Sam J; Johnson, Curtis L; Bayly, Philip V

2017-05-01

In traumatic brain injury (TBI), membranes such as the dura mater, arachnoid mater, and pia mater play a vital role in transmitting motion from the skull to brain tissue. Magnetic resonance elastography (MRE) is an imaging technique developed for noninvasive estimation of soft tissue material parameters. In MRE, dynamic deformation of brain tissue is induced by skull vibrations during magnetic resonance imaging (MRI); however, skull motion and its mode of transmission to the brain remain largely uncharacterized. In this study, displacements of points in the skull, reconstructed using data from an array of MRI-safe accelerometers, were compared to displacements of neighboring material points in brain tissue, estimated from MRE measurements. Comparison of the relative amplitudes, directions, and temporal phases of harmonic motion in the skulls and brains of six human subjects shows that the skull-brain interface significantly attenuates and delays transmission of motion from skull to brain. In contrast, in a cylindrical gelatin "phantom," displacements of the rigid case (reconstructed from accelerometer data) were transmitted to the gelatin inside (estimated from MRE data) with little attenuation or phase lag. This quantitative characterization of the skull-brain interface will be valuable in the parameterization and validation of computer models of TBI.

Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group

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

Gibbons, G.W., E-mail: gwg1@amtp.cam.ac.uk; Pope, C.N.; George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A and M University, College Station, TX 77843-4242

2011-07-15

Highlights: > We show that non-relativistic electrons moving in a magnetic field with trapping potential admits as relativity group the Newton-Hooke group. > We use this fact to give a group theoretic interpretation of Kohn's theorem and to obtain the spectrum. > We obtain the lightlike lift of the system exhibiting showing it coincides with the Nappi-Witten spacetime. - Abstract: We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the systemmore » admits a 'relativity group' which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inoenue contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the 'Eisenhart' or 'lightlike' lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.« less

LAVA Applications to Open Rotors

NASA Technical Reports Server (NTRS)

Kiris, Cetin C.; Housman, Jeff; Barad, Mike; Brehm, Christoph

2015-01-01

Outline: LAVA (Launch Ascent Vehicle Aerodynamics); Introduction; Acoustics Related Applications; LAVA Applications to Open Rotor; Structured Overset Grids; Cartesian Grid with Immersed Boundary; High Speed Case; High Speed Case with Plate Low Speed Case.

Experiments and Calculations.

ERIC Educational Resources Information Center

Siddons, J. C.

1982-01-01

Discusses several science experiments/activities and their associated measurements. These include a simple projectile activity, cartesian diver (used to measure altitude and atmospheric pressure), experiment demonstrating atmospheric pressure, and activities using a stroboscope, and electrometer. (JN)

Venusian Applications of 3D Convection Modeling

NASA Technical Reports Server (NTRS)

Bonaccorso, Timary Annie

2011-01-01

This study models mantle convection on Venus using the 'cubed sphere' code OEDIPUS, which models one-sixth of the planet in spherical geometry. We are attempting to balance internal heating, bottom mantle viscosity, and temperature difference across Venus' mantle, in order to create a realistic model that matches with current planetary observations. We also have begun to run both lower and upper mantle simulations to determine whether layered (as opposed to whole-mantle) convection might produce more efficient heat transfer, as well as to model coronae formation in the upper mantle. Upper mantle simulations are completed using OEDIPUS' Cartesian counterpart, JOCASTA. This summer's central question has been how to define a mantle plume. Traditionally, we have defined a hot plume the region with temperature at or above 40% of the difference between the maximum and horizontally averaged temperature, and a cold plume as the region with 40% of the difference between the minimum and average temperature. For less viscous cases (1020 Pa?s), the plumes generated by that definition lacked vigor, displaying buoyancies 1/100th of those found in previous, higher viscosity simulations (1021 Pa?s). As the mantle plumes with large buoyancy flux are most likely to produce topographic uplift and volcanism, the low viscosity cases' plumes may not produce observable deformation. In an effort to eliminate the smallest plumes, we experimented with different lower bound parameters and temperature percentages.

Cartesian contrivances

NASA Astrophysics Data System (ADS)

Kemp, Martin

1998-08-01

If matter fills the Universe, making everything happen by its interactions, what does it all look like? René Descartes may have been over-mechanistic in his view, but his efforts to visualize the invisible created striking images.

Idea Bank

ERIC Educational Resources Information Center

Science Teacher, 1978

1978-01-01

Described are methods for making Cartesian divers for explaining atomic models utilizing a city planning analogy, a game for reviewing subject matter, the construction of a cell model, an improved diffusion demonstration, and uses of inexpensive glass cutters. (SL)

Violation of the entanglement area law in bosonic systems with Bose surfaces: possible application to Bose metals.

PubMed

Lai, Hsin-Hua; Yang, Kun; Bonesteel, N E

2013-11-22

We show the violation of the entanglement area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on an N(d) Cartesian lattice in d dimensions, e.g., the exciton Bose liquid in two dimensions, we explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N(d-1)/3)lnL. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary, we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.

Field Mapping System for Solenoid Magnet

NASA Astrophysics Data System (ADS)

Park, K. H.; Jung, Y. K.; Kim, D. E.; Lee, H. G.; Park, S. J.; Chung, C. W.; Kang, B. K.

2007-01-01

A three-dimensional Hall probe mapping system for measuring the solenoid magnet of PLS photo-cathode RF e-gun has been developed. It can map the solenoid field either in Cartesian or in cylindrical coordinate system with a measurement reproducibility better than 5 × 10-5 T. The system has three axis motors: one for the azimuthal direction and the other two for the x and z direction. This architecture makes the measuring system simple in fabrication. The magnetic center was calculated using the measured axial component of magnetic field Bz in Cartesian coordinate system because the accuracy of magnetic axis measurement could be improved significantly by using Bz, instead of the radial component of magnetic field Br. This paper describes the measurement system and summarizes the measurement results for the solenoid magnetic of PLS photo-cathode RF e-gun.

Structured background grids for generation of unstructured grids by advancing front method

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar

1991-01-01

A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.

An atlas of monthly mean distributions of SSMI surface wind speed, ARGOS buoy drift, AVHRR/2 sea surface temperature, and ECMWF surface wind components during 1990

NASA Technical Reports Server (NTRS)

Halpern, D.; Knauss, W.; Brown, O.; Wentz, F.

1993-01-01

The following monthly mean global distributions for 1990 are proposed with a common color scale and geographical map: 10-m height wind speed estimated from the Special Sensor Microwave Imager (SSMI) on a United States (US) Air Force Defense Meteorological Satellite Program (DMSP) spacecraft; sea surface temperature estimated from the advanced very high resolution radiometer (AVHRR/2) on a U.S. National Oceanic and Atmospheric Administration (NOAA) spacecraft; Cartesian components of free drifting buoys which are tracked by the ARGOS navigation system on NOAA satellites; and Cartesian components on the 10-m height wind vector computed by the European Center for Medium-Range Weather Forecasting (ECMWF). Charts of monthly mean value, sampling distribution, and standard deviation values are displayed. Annual mean distributions are displayed.

An atlas of monthly mean distributions of SSMI surface wind speed, ARGOS buoy drift, AVHRR/2 sea surface temperature, and ECMWF surface wind components during 1991

NASA Technical Reports Server (NTRS)

Halpern, D.; Knauss, W.; Brown, O.; Wentz, F.

1993-01-01

The following monthly mean global distributions for 1991 are presented with a common color scale and geographical map: 10-m height wind speed estimated from the Special Sensor Microwave Imager (SSMI) on a United States Air Force Defense Meteorological Satellite Program (DMSP) spacecraft; sea surface temperature estimated from the advanced very high resolution radiometer (AVHRR/2) on a U.S. National Oceanic and Atmospheric Administration (NOAA) spacecraft; Cartesian components of free-drifting buoys which are tracked by the ARGOS navigation system on NOAA satellites; and Cartesian components of the 10-m height wind vector computed by the European Center for Medium-Range Weather Forecasting (ECMWF). Charts of monthly mean value, sampling distribution, and standard deviation value are displayed. Annual mean distributions are displayed.

Computationally efficient algorithm for Gaussian Process regression in case of structured samples

NASA Astrophysics Data System (ADS)

Belyaev, M.; Burnaev, E.; Kapushev, Y.

2016-04-01

Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation-Gaussian Process regression-can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.

Estimation of two-dimensional motion velocity using ultrasonic signals beamformed in Cartesian coordinate for measurement of cardiac dynamics

NASA Astrophysics Data System (ADS)

Kaburaki, Kaori; Mozumi, Michiya; Hasegawa, Hideyuki

2018-07-01

Methods for the estimation of two-dimensional (2D) velocity and displacement of physiological tissues are necessary for quantitative diagnosis. In echocardiography with a phased array probe, the accuracy in the estimation of the lateral motion is lower than that of the axial motion. To improve the accuracy in the estimation of the lateral motion, in the present study, the coordinate system for ultrasonic beamforming was changed from the conventional polar coordinate to the Cartesian coordinate. In a basic experiment, the motion velocity of a phantom, which was moved at a constant speed, was estimated by the conventional and proposed methods. The proposed method reduced the bias error and standard deviation in the estimated motion velocities. In an in vivo measurement, intracardiac blood flow was analyzed by the proposed method.

Computer coordination of limb motion for a three-legged walking robot

NASA Technical Reports Server (NTRS)

Klein, C. A.; Patterson, M. R.

1980-01-01

Coordination of the limb motion of a vehicle which could perform assembly and maintenance operations on large structures in space is described. Manipulator kinematics and walking robots are described. The basic control scheme of the robot is described. The control of the individual arms are described. Arm velocities are generally described in Cartesian coordinates. Cartesian velocities are converted to joint velocities using the Jacobian matrix. The calculation of a trajectory for an arm given a sequence of points through which it is to pass is described. The free gait algorithm which controls the lifting and placing of legs for the robot is described. The generation of commanded velocities for the robot, and the implementation of those velocities by the algorithm are discussed. Suggestions for further work in the area of robot legged locomotion are presented.

PARAMESH: A Parallel Adaptive Mesh Refinement Community Toolkit

NASA Technical Reports Server (NTRS)

MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; deFainchtein, Rosalinda; Packer, Charles

1999-01-01

In this paper, we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes. The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement. Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.

Pain and dualism: Which dualism?

PubMed

Arnaudo, Elisa

2017-10-01

In the literature, the allegation to pursue approaches grounded on Cartesian dualism in medicine is widespread. In this paper, I argue that dualism informing biomedicine has not only to do with a Cartesian view of mind and body, but that multiple dualisms are at play in biomedical approach to disease, especially regarding complex pain conditions. A form of epistemological dualism entailing the primacy of the physician's model of knowledge on the patient's direct experience of suffering is pointed out as the source of the inadequate medical attitude towards pain, particularly in relation to its complex forms such as fibromyalgic syndrome. The analysis, in particular, pays attention to the way in which dualism underlies and reinforces the delegitimization of chronic pain patients and suggests that solutions have to be found in the material organization of the health care service. © 2017 John Wiley & Sons, Ltd.

Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems

DOE PAGES

Baczewski, Andrew David; Dault, Daniel L.; Shanker, Balasubramaniam

2012-07-03

We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within themore » context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.« less

Whole-heart coronary MRA with 3D affine motion correction using 3D image-based navigation.

PubMed

Henningsson, Markus; Prieto, Claudia; Chiribiri, Amedeo; Vaillant, Ghislain; Razavi, Reza; Botnar, René M

2014-01-01

Robust motion correction is necessary to minimize respiratory motion artefacts in coronary MR angiography (CMRA). The state-of-the-art method uses a 1D feet-head translational motion correction approach, and data acquisition is limited to a small window in the respiratory cycle, which prolongs the scan by a factor of 2-3. The purpose of this work was to implement 3D affine motion correction for Cartesian whole-heart CMRA using a 3D navigator (3D-NAV) to allow for data acquisition throughout the whole respiratory cycle. 3D affine transformations for different respiratory states (bins) were estimated by using 3D-NAV image acquisitions which were acquired during the startup profiles of a steady-state free precession sequence. The calculated 3D affine transformations were applied to the corresponding high-resolution Cartesian image acquisition which had been similarly binned, to correct for respiratory motion between bins. Quantitative and qualitative comparisons showed no statistical difference between images acquired with the proposed method and the reference method using a diaphragmatic navigator with a narrow gating window. We demonstrate that 3D-NAV and 3D affine correction can be used to acquire Cartesian whole-heart 3D coronary artery images with 100% scan efficiency with similar image quality as with the state-of-the-art gated and corrected method with approximately 50% scan efficiency. Copyright © 2013 Wiley Periodicals, Inc.

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2001-01-01

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne E.

2013-01-01

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

Stability of horizontal viscous fluid layers in a vertical arbitrary time periodic electric field

NASA Astrophysics Data System (ADS)

Bandopadhyay, Aditya; Hardt, Steffen

2017-12-01

The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered theoretically. The two fluids are bounded by electrodes separated by a finite distance. For an applied ac electric field, the unstable interface deforms in a time periodic manner, owing to the time dependent Maxwell stress, and is characterized by the oscillation frequency which may or may not be the same as the frequency of the ac electric field. The stability curve, which relates the critical voltage, manifested through the Mason number—the ratio of normal electric stress and viscous stress, and the instability wavenumber at the onset of the instability, is obtained by means of the Floquet theory for a general arbitrary time periodic electric field. The limit of vanishing viscosities is shown to be in excellent agreement with the marginal stability curves predicted by means of a Mathieu equation. The influence of finite viscosity and electrode separation is discussed in relation to the ideal case of inviscid fluids. The methodology to obtain the marginal stability curves developed here is applicable to any arbitrary but time periodic signal, as demonstrated for the case of a signal with two different frequencies, and four different frequencies with a dc offset. The mode coupling in the interfacial normal stress leads to appearance of harmonic and subharmonic modes, characterized by the frequency of the oscillating interface at an integral or half-integral multiple of the applied frequency, respectively. This is in contrast to the application of a voltage with a single frequency which always leads to a harmonic mode oscillation of the interface. Whether a harmonic or subharmonic mode is the most unstable one depends on details of the excitation signal.

The Size of Mars' Fluid Core From Mars k2 Love Number Obtained From Analysis of MGS Doppler Tracking.

NASA Astrophysics Data System (ADS)

Yoder, C. F.; Konopliv, A. S.; Yuan, D. N.; Standish, E. M.; Folkner, W. M.

2002-12-01

The solar tidal deformation of Mars, measured by its k2 potential Love number, has been obtained from analysis of MGS radio tracking. The observed k2 =0.164+-0.016 is large enough to rule out a solid iron core. The inferred core radius Rc (1600km

Fluid core size of Mars from detection of the solar tide

NASA Technical Reports Server (NTRS)

Yoder, C. F.; Konopliv, A. S.; Yuan, D. N.; Standish, E. M.; Folkner, W. M.

2003-01-01

The solar tidal deformation of Mars, measured by its k2 potential Love number, has been obtained from an analysis of Mars Global Surveyor radio tracking. The observed k2 of 0.153 +/- 0.017 is large enough to rule out a solid iron core and so indicates that at least the outer part of the core is liquid. The inferred core radius is between 1520 and 1840 kilometers and is independent of many interior properties, although partial melt of the mantle is one factor that could reduce core size. Ice-cap mass changes can be deduced from the seasonal variations in air pressure and the odd gravity harmonic J3, given knowledge of cap mass distribution with latitude. The south cap seasonal mass change is about 30 to 40% larger than that of the north cap.

Reduction of Helicopter Blade-Vortex Interaction Noise by Active Rotor Control Technology

NASA Technical Reports Server (NTRS)

Yu, Yung H.; Gmelin, Bernd; Splettstoesser, Wolf; Brooks, Thomas F.; Philippe, Jean J.; Prieur, Jean

1997-01-01

Helicopter blade-vortex interaction noise is one of the most severe noise sources and is very important both in community annoyance and military detection. Research over the decades has substantially improved basic physical understanding of the mechanisms generating rotor blade-vortex interaction noise and also of controlling techniques, particularly using active rotor control technology. This paper reviews active rotor control techniques currently available for rotor blade vortex interaction noise reduction, including higher harmonic pitch control, individual blade control, and on-blade control technologies. Basic physical mechanisms of each active control technique are reviewed in terms of noise reduction mechanism and controlling aerodynamic or structural parameters of a blade. Active rotor control techniques using smart structures/materials are discussed, including distributed smart actuators to induce local torsional or flapping deformations, Published by Elsevier Science Ltd.

Characterization of mechanical properties of pseudoelastic shape memory alloys under harmonic excitation

NASA Astrophysics Data System (ADS)

Böttcher, J.; Jahn, M.; Tatzko, S.

2017-12-01

Pseudoelastic shape memory alloys exhibit a stress-induced phase transformation which leads to high strains during deformation of the material. The stress-strain characteristic during this thermomechanical process is hysteretic and results in the conversion of mechanical energy into thermal energy. This energy conversion allows for the use of shape memory alloys in vibration reduction. For the application of shape memory alloys as vibration damping devices a dynamic modeling of the material behavior is necessary. In this context experimentally determined material parameters which accurately represent the material behavior are essential for a reliable material model. Subject of this publication is the declaration of suitable material parameters for pseudoelastic shape memory alloys and the methodology of their identification from experimental investigations. The used test rig was specifically designed for the characterization of pseudoelastic shape memory alloys.

Fluid Core Size of Mars from Detection of the Solar Tide

NASA Astrophysics Data System (ADS)

Yoder, C. F.; Konopliv, A. S.; Yuan, D. N.; Standish, E. M.; Folkner, W. M.

2003-04-01

The solar tidal deformation of Mars, measured by its k2 potential Love number, has been obtained from an analysis of Mars Global Surveyor radio tracking. The observed k2 of 0.153 +/- 0.017 is large enough to rule out a solid iron core and so indicates that at least the outer part of the core is liquid. The inferred core radius is between 1520 and 1840 kilometers and is independent of many interior properties, although partial melt of the mantle is one factor that could reduce core size. Ice-cap mass changes can be deduced from the seasonal variations in air pressure and the odd gravity harmonic J3, given knowledge of cap mass distribution with latitude. The south cap seasonal mass change is about 30 to 40% larger than that of the north cap.

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

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

Generalized uncertainty principle and quantum gravity phenomenology

NASA Astrophysics Data System (ADS)

Bosso, Pasquale

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canonical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.

Study of five-dimensional potential-energy surfaces for actinide isotopes by the macroscopic-microscopic method

NASA Astrophysics Data System (ADS)

Fan, T. S.; Wang, Z. M.; Zhu, X.; Zhu, W. J.; Zhong, C. L.

2017-09-01

In this work, the nuclear potential-energy of the deformed nuclei as a function of shape coordinates is calculated in a five-dimensional (5D) parameter space of the axially symmetric generalized Lawrence shapes, on the basis of the macroscopic-microscopic method. The liquid-drop part of the nuclear energy is calculated according to the Myers-Swiatecki model and the Lublin-Strasbourg-drop (LSD) formula. The Woods-Saxon and the folded-Yukawa potentials for deformed nuclei are used for the shell and pairing corrections of the Strutinsky-type. The pairing corrections are calculated at zero temperature, T, related to the excitation energy. The eigenvalues of Hamiltonians for protons and neutrons are found by expanding the eigen-functions in terms of harmonic-oscillator wave functions of a spheroid. Then the BCS pair is applied on the smeared-out single-particle spectrum. By comparing the results obtained by different models, the most favorable combination of the macroscopic-microscopic model is known as the LSD formula with the folded-Yukawa potential. Potential-energy landscapes for actinide isotopes are investigated based on a grid of more than 4,000,000 deformation points and the heights of static fission barriers are obtained in terms of a double-humped structure on the full 5D parameter space. In order to locate the ground state shapes, saddle points, scission points and optimal fission path on the calculated 5D potential-energy surface, the falling rain algorithm and immersion method are designed and implemented. The comparison of our results with available experimental data and others' theoretical results confirms the reliability of our calculations.

On Lateral Viscosity Contrast in the Mantle and the Rheology of Low-Frequency Geodynamics

NASA Technical Reports Server (NTRS)

Ivins, Erik R.; Sammis, Charles G.

1995-01-01

Mantle-wide heterogeneity is largely controlled by deeply penetrating thermal convective currents. These thermal currents are likely to produce significant lateral variation in rheology, and this can profoundly influence overall material behaviour. How thermally related lateral viscosity variations impact models of glacio-isostatic and tidal deformation is largely unknown. An important step towards model improvement is to quantify, or bound, the actual viscosity variations that characterize the mantle. Simple scaling of viscosity to shear-wave velocity fluctuations yields map-views of long- wavelength viscosity variation. These give a general quantitative description and aid in estimating the depth dependence of rheological heterogeneity throughout the mantle. The upper mantle is probably characterized by two to four orders of magnitude variation (peak-to-peak). Discrepant time-scales for rebounding Holocene shorelines of Hudson Bay and southern Iceland are consistent with this characterization. Results are given in terms of a local average viscosity ratio, (Delta)eta(bar)(sub i), of volumetric concentration, phi(sub i). For the upper mantle deeper than 340 km the following reasonable limits are estimated for (delta)eta(bar) approx. equal 10(exp -2): 0.01 less than or equal to phi less than or equal to 0.15. A spectrum of ratios (Delta)eta(bar)(sub i) less than 0.1 at concentration level eta(sub i) approx. equal 10(exp -6) - 10(exp -1) in the lower mantle implies a spectrum of shorter time-scale deformational response modes for second-degree spherical harmonic deformations of the Earth. Although highly uncertain, this spectrum of spatial variation allows a purely Maxwellian viscoelastic rheology simultaneously to explain all solid tidal dispersion phenomena and long-term rebound-related mantle viscosity. Composite theory of multiphase viscoelastic media is used to demonstrate this effect.

DNA algorithms of implementing biomolecular databases on a biological computer.

PubMed

Chang, Weng-Long; Vasilakos, Athanasios V

2015-01-01

In this paper, DNA algorithms are proposed to perform eight operations of relational algebra (calculus), which include Cartesian product, union, set difference, selection, projection, intersection, join, and division, on biomolecular relational databases.

A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate

NASA Astrophysics Data System (ADS)

Lin, Ruixing; Xu, Lin; Zheng, Xian

2018-03-01

Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.

Balancing Vibrations at Harmonic Frequencies by Injecting Harmonic Balancing Signals into the Armature of a Linear Motor/Alternator Coupled to a Stirling Machine

NASA Technical Reports Server (NTRS)

Holliday, Ezekiel S. (Inventor)

2014-01-01

Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.

Polyphase deformation history and strain analyses of the post-amalgamation depositional basins in the Arabian-Nubian Shield: Evidence from Fatima, Ablah and Hammamat Basins

NASA Astrophysics Data System (ADS)

Hamimi, Zakaria; El-Fakharani, Abdelhamid; Abdeen, Mamdouh M.

2014-11-01

Post-amalgamation depositional basins <650 Ma (PADBs), dominated by volcano-sedimentary assemblages, unconformably overlying Neoproterozoic juvenile (mantle-derived) arcs, represent one of the main collage in the Arabian-Nubian Shield (ANS). In this work, three distinguished PADBs; namely Fatima, Ablah and Hammamat PADBs, are the subject matter of detailed field investigations and quantitative strain analysis in an attempt to highlight the polyphase deformation history of these PADBs and to discern whether the ANS's PADBs were deformed at the same time or not. The Fatima PADB is studied in its type locality along the northwestern flank of Wadi Fatima; between Jabal Abu Ghurrah and Jabal Daf, in Jeddah tectonic terrane. The Ablah PADB is examined around Wadi Yiba, further south of its type locality near Jabal Ablah in Al-Aqiq Quadrangle, in Asir tectonic terrane. The Hammamat PADB is investigated in Wadi Umm Gheig, Wadi Allaqi and Wadi Hodein in the Egyptian Eastern Desert tectonic terrane. It is supposed that the Fatima is a basin controlled by dextral transcurrent shearing occurred along the NE-oriented Wadi Fatima Shear Zone and the Ablah is a strike-slip pull-apart basin, and both basins were believed to be deposited during and soon after the Nabitah Orogeny (680-640 Ma) that marked suturing of the Afif terrane with the oceanic ANS terranes to the west. They were affected by at least three Neoproterozoic deformation phases and show geometric and kinematic relationships between folding and thrusting. The Hammamat PADB is a fault-bounded basin affected by a NW-SE- to NNW-SSE-oriented shortening phase just after the deposition of the molasse sediments, proved by NW- to NNW-verging folds and SE- to SSE-dipping thrusts that were refolded and thrusted in the same direction. The shortening phase in the Hammamat was followed by a transpressional wrenching phase related to the Najd Shear System, which resulted in the formation of NW-SE sinistral-slip faults associated with positive flower structures that comprise NE-verging folds and SW-dipping thrusts. Strain results in the three studied PADBs are nearly consistent, indicating that they are correlated and underwent the same history of deformation. The ANOVA test indicates that there is no significant difference for the Vector mean and ISYM for the three PADBs. There is only a significant difference for the Harmonic mean (P-value < 0.05). A Post Hoc test (Shefee) shows that the difference exists between the Allaqi and the Umm Gheig's deformed polymictic conglomeratic pebbles of the Hammamat PADB.

Influence of vein fabric on strain distribution and fold kinematics

NASA Astrophysics Data System (ADS)

Torremans, Koen; Muchez, Philippe; Sintubin, Manuel

2014-05-01

Abundant pre-folding, bedding-parallel fibrous dolomite veins in shale are found associated with the Nkana-Mindola stratiform Cu-Co deposit in the Central African Copperbelt, Zambia. These monomineralic veins extend for several meters along strike, with a fibrous infill orthogonal to low-tortuosity vein walls. Growth morphologies vary from antitaxial with a pronounced median surface to asymmetric syntaxial, always with small but quantifiable growth competition. Subsequently, these veins were folded. In this study, we aim to constrain the kinematic fold mechanism by which strain is accommodated in these veins, estimate paleorheology at time of deformation and investigate the influence of vein fabric on deformation during folding. Finally, the influence of the deformation on known metallogenetic stages is assessed. Various deformation styles are observed, ultimately related to vein attitude across tight to close lower-order, hectometre-scale folds. In fold hinges, at low to average dips, veins are (poly-)harmonically to disharmonically folded as parasitic folds in single or multilayer systems. With increasing distance from the fold hinge, parasitic fold amplitude decreases and asymmetry increases. At high dips in the limbs, low-displacement duplication thrusts of veins at low angles to bedding are abundant. Slickenfibres and slickenlines are sub-perpendicular to fold hinges and shallow-dipping slickenfibre-step lineations are parallel to local fold hinge lines. A dip isogon analysis of reconstructed fold geometries prior to homogeneous shortening reveals type 1B parallel folds for the veins and type 1C for the matrix. Two main deformation mechanisms are identified in folded veins. Firstly, undulatory extinction, subgrains and fluid inclusions planes parallel the fibre long axis, with deformation intensity increasing away from the fold hinges, indicate intracrystalline strain accumulation. Secondly, intergranular deformation through bookshelf rotation of fibres, via collective parallel rotation of fibres and shearing along fibre grain boundaries, is clearly observed under cathodoluminescence. We analysed the internal strain distribution by quantifying simple shear strain caused by deflection of the initially orthogonal fibres relative to layer inclination at a given position across the fold. Shear angle, and thus shear strain, steadily increases towards the limbs away from the fold hinge. Comparison of observed shear strain to theoretical distribution for kinematic mechanisms, amongst other lines of evidence, clearly points to pure flexural flow followed by homogeneous shortening. As flexural flow is not the expected kinematic folding mechanism for competent layers in an incompetent shale matrix, our analysis shows that the internal vein fabric in these dolomite veins can exhibit a first-order influence on folding mechanisms. In addition, quantitative analysis shows that these veins acted as rigid objects with high viscosity contrast relative to the incompetent carbonaceous shale, rather than as semi-passive markers. Later folding-related syn-orogenic veins, intensely mineralised with Cu-Co sulphides, are strongly related to deformation of these pre-folding veins. The high viscosity contrast created by the pre-folding fibrous dolomite veins was therefore essential in creating transient permeability for subsequent mineralising stages in the veining history.

Research in Parallel Algorithms and Software for Computational Aerosciences

DOT National Transportation Integrated Search

1996-04-01

Phase I is complete for the development of a Computational Fluid Dynamics : with automatic grid generation and adaptation for the Euler : analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian : grid code developed at Lockheed...

Some Geometric Aspects of the Ternary Diagram.

ERIC Educational Resources Information Center

Philip, G. M.; Watson, D. F.

1989-01-01

Uses the process of normalization in the Cartesian coordinate system which entails radial projection onto a transect to compare different compositions of minerals. Warns that the ternary diagram should not be used as a framework for calculations. (MVL)

An Application of Cartesian Graphing to Seismic Exploration.

ERIC Educational Resources Information Center

Robertson, Douglas Frederick

1992-01-01

Describes how college students enrolled in a course in elementary algebra apply graphing and algebra to data collected from a seismic profile to uncover the structure of a subterranean rock formation. Includes steps guiding the activity. (MDH)

High-order continuum kinetic method for modeling plasma dynamics in phase space

DOE PAGES

Vogman, G. V.; Colella, P.; Shumlak, U.

2014-12-15

Continuum methods offer a high-fidelity means of simulating plasma kinetics. While computationally intensive, these methods are advantageous because they can be cast in conservation-law form, are not susceptible to noise, and can be implemented using high-order numerical methods. Advances in continuum method capabilities for modeling kinetic phenomena in plasmas require the development of validation tools in higher dimensional phase space and an ability to handle non-cartesian geometries. To that end, a new benchmark for validating Vlasov-Poisson simulations in 3D (x,v x,v y) is presented. The benchmark is based on the Dory-Guest-Harris instability and is successfully used to validate a continuummore » finite volume algorithm. To address challenges associated with non-cartesian geometries, unique features of cylindrical phase space coordinates are described. Preliminary results of continuum kinetic simulations in 4D (r,z,v r,v z) phase space are presented.« less

Efficient Transition State Optimization of Periodic Structures through Automated Relaxed Potential Energy Surface Scans.

PubMed

Plessow, Philipp N

2018-02-13

This work explores how constrained linear combinations of bond lengths can be used to optimize transition states in periodic structures. Scanning of constrained coordinates is a standard approach for molecular codes with localized basis functions, where a full set of internal coordinates is used for optimization. Common plane wave-codes for periodic boundary conditions almost exlusively rely on Cartesian coordinates. An implementation of constrained linear combinations of bond lengths with Cartesian coordinates is described. Along with an optimization of the value of the constrained coordinate toward the transition states, this allows transition optimization within a single calculation. The approach is suitable for transition states that can be well described in terms of broken and formed bonds. In particular, the implementation is shown to be effective and efficient in the optimization of transition states in zeolite-catalyzed reactions, which have high relevance in industrial processes.