Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Global collocation methods for approximation and the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Solomonoff, A.; Turkel, E.

1986-01-01

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

PubMed Central

Chen, Weitian; Sica, Christopher T.; Meyer, Craig H.

2008-01-01

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method. PMID:18956462

A study on Marangoni convection by the variational iteration method

NASA Astrophysics Data System (ADS)

Karaoǧlu, Onur; Oturanç, Galip

2012-09-01

In this paper, we will consider the use of the variational iteration method and Padé approximant for finding approximate solutions for a Marangoni convection induced flow over a free surface due to an imposed temperature gradient. The solutions are compared with the numerical (fourth-order Runge Kutta) solutions.

Retention prediction and separation optimization under multilinear gradient elution in liquid chromatography with Microsoft Excel macros.

PubMed

Fasoula, S; Zisi, Ch; Gika, H; Pappa-Louisi, A; Nikitas, P

2015-05-22

A package of Excel VBA macros have been developed for modeling multilinear gradient retention data obtained in single or double gradient elution mode by changing organic modifier(s) content and/or eluent pH. For this purpose, ten chromatographic models were used and four methods were adopted for their application. The methods were based on (a) the analytical expression of the retention time, provided that this expression is available, (b) the retention times estimated using the Nikitas-Pappa approach, (c) the stepwise approximation, and (d) a simple numerical approximation involving the trapezoid rule for integration of the fundamental equation for gradient elution. For all these methods, Excel VBA macros have been written and implemented using two different platforms; the fitting and the optimization platform. The fitting platform calculates not only the adjustable parameters of the chromatographic models, but also the significance of these parameters and furthermore predicts the analyte elution times. The optimization platform determines the gradient conditions that lead to the optimum separation of a mixture of analytes by using the Solver evolutionary mode, provided that proper constraints are set in order to obtain the optimum gradient profile in the minimum gradient time. The performance of the two platforms was tested using experimental and artificial data. It was found that using the proposed spreadsheets, fitting, prediction, and optimization can be performed easily and effectively under all conditions. Overall, the best performance is exhibited by the analytical and Nikitas-Pappa's methods, although the former cannot be used under all circumstances. Copyright © 2015 Elsevier B.V. All rights reserved.

A result about scale transformation families in approximation

NASA Astrophysics Data System (ADS)

Apprato, Dominique; Gout, Christian

2000-06-01

Scale transformations are common in approximation. In surface approximation from rapidly varying data, one wants to suppress, or at least dampen the oscillations of the approximation near steep gradients implied by the data. In that case, scale transformations can be used to give some control over overshoot when the surface has large variations of its gradient. Conversely, in image analysis, scale transformations are used in preprocessing to enhance some features present on the image or to increase jumps of grey levels before segmentation of the image. In this paper, we establish the convergence of an approximation method which allows some control over the behavior of the approximation. More precisely, we study the convergence of an approximation from a data set of , while using scale transformations on the values before and after classical approximation. In addition, the construction of scale transformations is also given. The algorithm is presented with some numerical examples.

Hybrid DFP-CG method for solving unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Osman, Wan Farah Hanan Wan; Asrul Hery Ibrahim, Mohd; Mamat, Mustafa

2017-09-01

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

Geometrical-optics approximation of forward scattering by gradient-index spheres.

PubMed

Li, Xiangzhen; Han, Xiang'e; Li, Renxian; Jiang, Huifen

2007-08-01

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

$L_{0}$ Gradient Projection.

PubMed

Ono, Shunsuke

2017-04-01

Minimizing L 0 gradient, the number of the non-zero gradients of an image, together with a quadratic data-fidelity to an input image has been recognized as a powerful edge-preserving filtering method. However, the L 0 gradient minimization has an inherent difficulty: a user-given parameter controlling the degree of flatness does not have a physical meaning since the parameter just balances the relative importance of the L 0 gradient term to the quadratic data-fidelity term. As a result, the setting of the parameter is a troublesome work in the L 0 gradient minimization. To circumvent the difficulty, we propose a new edge-preserving filtering method with a novel use of the L 0 gradient. Our method is formulated as the minimization of the quadratic data-fidelity subject to the hard constraint that the L 0 gradient is less than a user-given parameter α . This strategy is much more intuitive than the L 0 gradient minimization because the parameter α has a clear meaning: the L 0 gradient value of the output image itself, so that one can directly impose a desired degree of flatness by α . We also provide an efficient algorithm based on the so-called alternating direction method of multipliers for computing an approximate solution of the nonconvex problem, where we decompose it into two subproblems and derive closed-form solutions to them. The advantages of our method are demonstrated through extensive experiments.

A weighted variational gradient-based fusion method for high-fidelity thin cloud removal of Landsat images

NASA Astrophysics Data System (ADS)

Huang, Wei; Chen, Xiu; Wang, Yueyun

2018-03-01

Landsat data are widely used in various earth observations, but the clouds interfere with the applications of the images. This paper proposes a weighted variational gradient-based fusion method (WVGBF) for high-fidelity thin cloud removal of Landsat images, which is an improvement of the variational gradient-based fusion (VGBF) method. The VGBF method integrates the gradient information from the reference band into visible bands of cloudy image to enable spatial details and remove thin clouds. The VGBF method utilizes the same gradient constraints to the entire image, which causes the color distortion in cloudless areas. In our method, a weight coefficient is introduced into the gradient approximation term to ensure the fidelity of image. The distribution of weight coefficient is related to the cloud thickness map. The map is built on Independence Component Analysis (ICA) by using multi-temporal Landsat images. Quantitatively, we use R value to evaluate the fidelity in the cloudless regions and metric Q to evaluate the clarity in the cloud areas. The experimental results indicate that the proposed method has the better ability to remove thin cloud and achieve high fidelity.

On the application of the partition of unity method for nonlocal response of low-dimensional structures

NASA Astrophysics Data System (ADS)

Natarajan, Sundararajan

2014-12-01

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

NASA Astrophysics Data System (ADS)

Muldoon, F. H.

2018-04-01

Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

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

Bozkaya, Uğur, E-mail: ugur.bozkaya@hacettepe.edu.tr; Department of Chemistry, Atatürk University, Erzurum 25240; Sherrill, C. David

2016-05-07

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbitalmore » (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C{sub 10}H{sub 22}), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.« less

Cosmological collapse and the improved Zel'dovich approximation.

NASA Astrophysics Data System (ADS)

Salopek, D. S.; Stewart, J. M.; Croudace, K. M.; Parry, J.

Using a general relativistic formulation, the authors show how to compute the higher order terms in the Zel'dovich approximation which describes cosmological collapse. They evolve the 3-metric in a spatial gradient expansion. Their method is an advance over earlier work because it is local at each order. Using the improved Zel'dovich approximation, they compute the epoch of collapse.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

PubMed Central

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

On the relation between phase-field crack approximation and gradient damage modelling

NASA Astrophysics Data System (ADS)

Steinke, Christian; Zreid, Imadeddin; Kaliske, Michael

2017-05-01

The finite element implementation of a gradient enhanced microplane damage model is compared to a phase-field model for brittle fracture. Phase-field models and implicit gradient damage models share many similarities despite being conceived from very different standpoints. In both approaches, an additional differential equation and a length scale are introduced. However, while the phase-field method is formulated starting from the description of a crack in fracture mechanics, the gradient method starts from a continuum mechanics point of view. At first, the scope of application for both models is discussed to point out intersections. Then, the analysis of the employed mathematical methods and their rigorous comparison are presented. Finally, numerical examples are introduced to illustrate the findings of the comparison which are summarized in a conclusion at the end of the paper.

Seafloor Topography Estimation from Gravity Gradient Using Simulated Annealing

NASA Astrophysics Data System (ADS)

Yang, J.; Jekeli, C.; Liu, L.

2017-12-01

Inferring seafloor topography from gravimetry is an indirect yet proven and efficient means to map the ocean floor. Standard techniques rely on an approximate, linear relationship (Parker's formula) between topography and gravity. It has been reported that in the very rugged areas the discrepancies between prediction and ship soundings are very large, partly because the linear term of Parker's infinite series is dominant only in areas where the local topography is small compared with the regional topography. The validity of the linear approximation is therefore in need of analysis. In this study the nonlinear effects caused by terrain are quantified by both numerical tests and an algorithmic approach called coherency. It is shown that the nonlinear effects are more significant at higher frequencies, which suggests that estimation algorithms with nonlinear approximation in the modeled relationship between gravity gradient and topography should be developed in preparation for future high-resolution gravity gradient missions. The simulated annealing (SA) method is such an optimization technique that can process nonlinear inverse problems, and is used to estimate the seafloor topography parameters in a forward model by minimizing the difference between the observed and forward-computed vertical gravity gradients. Careful treatments like choosing suitable truncation distance, padding the vicinity of the study area with a known topography model, and using the relative cost function, are considered to improve the estimation accuracy. This study uses the gravity gradient, which is more sensitive to topography at short wavelengths than gravity anomaly. The gravity gradient data are derived from satellite altimetry, but the SA has no restrictions on data distribution, as required in Parker's infinite series model, thus enabling the use of airborne gravity gradient data, whose survey trajectories are irregular. The SA method is tested in an area of Guyots (E 156°-158° in longitude, N 20°-22° in latitude). Comparison between the estimation and ship sounding shows that half of the discrepancy is within 110 m, which improves the result from standard techniques by 32%.

First-row diatomics: Calculation of the geometry and energetics using self-consistent gradient-functional approximations

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

Kutzler, F.W.; Painter, G.S.

1992-02-15

A fully self-consistent series of nonlocal (gradient) density-functional calculations has been carried out using the augmented-Gaussian-orbital method to determine the magnitude of gradient corrections to the potential-energy curves of the first-row diatomics, Li{sub 2} through F{sub 2}. Both the Langreth-Mehl-Hu and the Perdew-Wang gradient-density functionals were used in calculations of the binding energy, bond length, and vibrational frequency for each dimer. Comparison with results obtained in the local-spin-density approximation (LSDA) using the Vosko-Wilk-Nusair functional, and with experiment, reveals that bond lengths and vibrational frequencies are rather insensitive to details of the gradient functionals, including self-consistency effects, but the gradient correctionsmore » reduce the overbinding commonly observed in the LSDA calculations of first-row diatomics (with the exception of Li{sub 2}, the gradient-functional binding-energy error is only 50--12 % of the LSDA error). The improved binding energies result from a large differential energy lowering, which occurs in open-shell atoms relative to the diatomics. The stabilization of the atom arises from the use of nonspherical charge and spin densities in the gradient-functional calculations. This stabilization is negligibly small in LSDA calculations performed with nonspherical densities.« less

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

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

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less

Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation.

PubMed

Bozkaya, Uğur

2018-03-15

Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

PubMed

Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

2015-04-21

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning; Wang, Ding; Lewis, Frank L

2017-10-01

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

Distribution of thermal neutrons in a temperature gradient

NASA Astrophysics Data System (ADS)

Molinari, V. G.; Pollachini, L.

A method to determine the spatial distribution of the thermal spectrum of neutrons in heterogeneous systems is presented. The method is based on diffusion concepts and has a simple mathematical structure which increases computing efficiency. The application of this theory to the neutron thermal diffusion induced by a temperature gradient, as found in nuclear reactors, is described. After introducing approximations, a nonlinear equation system representing the neutron temperature is given. Values of the equation parameters and its dependence on geometrical factors and media characteristics are discussed.

Bidirectional composition on lie groups for gradient-based image alignment.

PubMed

Mégret, Rémi; Authesserre, Jean-Baptiste; Berthoumieu, Yannick

2010-09-01

In this paper, a new formulation based on bidirectional composition on Lie groups (BCL) for parametric gradient-based image alignment is presented. Contrary to the conventional approaches, the BCL method takes advantage of the gradients of both template and current image without combining them a priori. Based on this bidirectional formulation, two methods are proposed and their relationship with state-of-the-art gradient based approaches is fully discussed. The first one, i.e., the BCL method, relies on the compositional framework to provide the minimization of the compensated error with respect to an augmented parameter vector. The second one, the projected BCL (PBCL), corresponds to a close approximation of the BCL approach. A comparative study is carried out dealing with computational complexity, convergence rate and frequence of convergence. Numerical experiments using a conventional benchmark show the performance improvement especially for asymmetric levels of noise, which is also discussed from a theoretical point of view.

Detection, localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data

NASA Astrophysics Data System (ADS)

Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li; Guoquan, Ren

2016-05-01

We have developed a method for automatic detection, localization and classification (DLC) of multiple dipole sources using magnetic gradient tensor data. First, we define modified tilt angles to estimate the approximate horizontal locations of the multiple dipole-like magnetic sources simultaneously and detect the number of magnetic sources using a fixed threshold. Secondly, based on the isotropy of the normalized source strength (NSS) response of a dipole, we obtain accurate horizontal locations of the dipoles. Then the vertical locations are calculated using magnitude magnetic transforms of magnetic gradient tensor data. Finally, we invert for the magnetic moments of the sources using the measured magnetic gradient tensor data and forward model. Synthetic and field data sets demonstrate effectiveness and practicality of the proposed method.

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics.

PubMed

Sokoloski, Sacha

2017-09-01

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

Subpixel edge estimation with lens aberrations compensation based on the iterative image approximation for high-precision thermal expansion measurements of solids

NASA Astrophysics Data System (ADS)

Inochkin, F. M.; Kruglov, S. K.; Bronshtein, I. G.; Kompan, T. A.; Kondratjev, S. V.; Korenev, A. S.; Pukhov, N. F.

2017-06-01

A new method for precise subpixel edge estimation is presented. The principle of the method is the iterative image approximation in 2D with subpixel accuracy until the appropriate simulated is found, matching the simulated and acquired images. A numerical image model is presented consisting of three parts: an edge model, object and background brightness distribution model, lens aberrations model including diffraction. The optimal values of model parameters are determined by means of conjugate-gradient numerical optimization of a merit function corresponding to the L2 distance between acquired and simulated images. Computationally-effective procedure for the merit function calculation along with sufficient gradient approximation is described. Subpixel-accuracy image simulation is performed in a Fourier domain with theoretically unlimited precision of edge points location. The method is capable of compensating lens aberrations and obtaining the edge information with increased resolution. Experimental method verification with digital micromirror device applied to physically simulate an object with known edge geometry is shown. Experimental results for various high-temperature materials within the temperature range of 1000°C..2400°C are presented.

Application of Conjugate Gradient methods to tidal simulation

USGS Publications Warehouse

Barragy, E.; Carey, G.F.; Walters, R.A.

1993-01-01

A harmonic decomposition technique is applied to the shallow water equations to yield a complex, nonsymmetric, nonlinear, Helmholtz type problem for the sea surface and an accompanying complex, nonlinear diagonal problem for the velocities. The equation for the sea surface is linearized using successive approximation and then discretized with linear, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparative evaluation includes both standard iterative methods for the real subsystems and complex versions of the well known Bi-Conjugate Gradient and Bi-Conjugate Gradient Squared methods. Several Incomplete LU type preconditioners are discussed, and the effects of node ordering, rejection strategy, domain geometry and Coriolis parameter (affecting asymmetry) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made with a frontal solver. ?? 1993.

Gradient Pre-Emphasis to Counteract First-Order Concomitant Fields on Asymmetric MRI Gradient Systems

PubMed Central

Tao, Shengzhen; Weavers, Paul T.; Trzasko, Joshua D.; Shu, Yunhong; Huston, John; Lee, Seung-Kyun; Frigo, Louis M.; Bernstein, Matt A.

2016-01-01

PURPOSE To develop a gradient pre-emphasis scheme that prospectively counteracts the effects of the first-order concomitant fields for any arbitrary gradient waveform played on asymmetric gradient systems, and to demonstrate the effectiveness of this approach using a real-time implementation on a compact gradient system. METHODS After reviewing the first-order concomitant fields that are present on asymmetric gradients, a generalized gradient pre-emphasis model assuming arbitrary gradient waveforms is developed to counteract their effects. A numerically straightforward, simple to implement approximate solution to this pre-emphasis problem is derived, which is compatible with the current hardware infrastructure used on conventional MRI scanners for eddy current compensation. The proposed method was implemented on the gradient driver sub-system, and its real-time use was tested using a series of phantom and in vivo data acquired from 2D Cartesian phase-difference, echo-planar imaging (EPI) and spiral acquisitions. RESULTS The phantom and in vivo results demonstrate that unless accounted for, first-order concomitant fields introduce considerable phase estimation error into the measured data and result in images exhibiting spatially dependent blurring/distortion. The resulting artifacts are effectively prevented using the proposed gradient pre-emphasis. CONCLUSION An efficient and effective gradient pre-emphasis framework is developed to counteract the effects of first-order concomitant fields of asymmetric gradient systems. PMID:27373901

UNAERO: A package of FORTRAN subroutines for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1985-01-01

This report serves as an instruction and maintenance manual for a collection of CDC CYBER FORTRAN IV subroutines for approximating the unsteady aerodynamic forces in the time domain. The result is a set of constant-coefficient first-order differential equations that approximate the dynamics of the vehicle. Provisions are included for adjusting the number of modes used for calculating the approximations so that an accurate approximation is generated. The number of data points at different values of reduced frequency can also be varied to adjust the accuracy of the approximation over the reduced-frequency range. The denominator coefficients of the approximation may be calculated by means of a gradient method or a least-squares approximation technique. Both the approximation methods use weights on the residual error. A new set of system equations, at a different dynamic pressure, can be generated without the approximations being recalculated.

Charts and Tables for Estimating the Stability of the Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient

NASA Technical Reports Server (NTRS)

Tetervin, Neal

1959-01-01

The minimum critical Reynolds numbers for the similar solutions of the compressible laminar boundary layer computed by Cohen and Reshotko and also for the Falkner and Skan solutions as recomputed by Smith have been calculated by Lin's rapid approximate method for two-dimensional disturbances. These results enable the stability of the compressible laminar boundary layer with heat transfer and pressure gradient to be easily estimated after the behavior of the boundary layer has been computed by the approximate method of Cohen and Reshotko. The previously reported unusual result (NACA Technical Note 4037) that a highly cooled stagnation point flow is more unstable than a highly cooled flat-plate flow is again encountered. Moreover, this result is found to be part of the more general result that a favorable pressure gradient is destabilizing for very cool walls when the Mach number is less than that for complete stability. The minimum critical Reynolds numbers for these wall temperature ratios are, however, all larger than any value of the laminar-boundary-layer Reynolds number likely to be encountered. For Mach numbers greater than those for which complete stability occurs a favorable pressure gradient is stabilizing, even for very cool walls.

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization.

PubMed

Petrenko, Taras; Kossmann, Simone; Neese, Frank

2011-02-07

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.

Airship stresses due to vertical velocity gradients and atmospheric turbulence

NASA Technical Reports Server (NTRS)

Sheldon, D.

1975-01-01

Munk's potential flow method is used to calculate the resultant moment experienced by an ellipsoidal airship. This method is first used to calculate the moment arising from basic maneuvers considered by early designers, and then expended to calculate the moment arising from vertical velocity gradients and atmospheric turbulence. This resultant moment must be neutralized by the transverse force of the fins. The results show that vertical velocity gradients at a height of 6000 feet in thunderstorms produce a resultant moment approximately three to four times greater than the moment produced in still air by realistic values of pitch angle or steady turning. Realistic values of atmospheric turbulence produce a moment which is significantly less than the moment produced by maneuvers in still air.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients.

PubMed

Łazarski, Roman; Burow, Asbjörn Manfred; Grajciar, Lukáš; Sierka, Marek

2016-10-30

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

A fast pulse design for parallel excitation with gridding conjugate gradient.

PubMed

Feng, Shuo; Ji, Jim

2013-01-01

Parallel excitation (pTx) is recognized as a crucial technique in high field MRI to address the transmit field inhomogeneity problem. However, it can be time consuming to design pTx pulses which is not desirable. In this work, we propose a pulse design with gridding conjugate gradient (CG) based on the small-tip-angle approximation. The two major time consuming matrix-vector multiplications are substituted by two operators which involves with FFT and gridding only. Simulation results have shown that the proposed method is 3 times faster than conventional method and the memory cost is reduced by 1000 times.

Dimensional Representation and Gradient Boosting for Seismic Event Classification

NASA Astrophysics Data System (ADS)

Semmelmayer, F. C.; Kappedal, R. D.; Magana-Zook, S. A.

2017-12-01

In this research, we conducted experiments of representational structures on 5009 seismic signals with the intent of finding a method to classify signals as either an explosion or an earthquake in an automated fashion. We also applied a gradient boosted classifier. While perfect classification was not attained (approximately 88% was our best model), some cases demonstrate that many events can be filtered out as very high probability being explosions or earthquakes, diminishing subject-matter experts'(SME) workload for first stage analysis. It is our hope that these methods can be refined, further increasing the classification probability.

Analysis and correction of gradient nonlinearity bias in ADC measurements

PubMed Central

Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.

2013-01-01

Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2).

PubMed

Schütz, Martin

2015-06-07

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Conjugate gradient and cross-correlation based least-square reverse time migration and its application

NASA Astrophysics Data System (ADS)

Sun, Xiao-Dong; Ge, Zhong-Hui; Li, Zhen-Chun

2017-09-01

Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

Algorithms for accelerated convergence of adaptive PCA.

PubMed

Chatterjee, C; Kang, Z; Roychowdhury, V P

2000-01-01

We derive and discuss new adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja, Sanger, and Xu. It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: 1) gradient descent; 2) steepest descent; 3) conjugate direction; and 4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods.We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids.

PubMed

Chowdhary, J; Keyes, T

2002-02-01

Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.

On thermal conditions and properties of thallium bromide single crystals grown by the Electro Dynamic Gradient method

NASA Astrophysics Data System (ADS)

Zheng, Zhiping; Yu, Yongtao; Gong, Shuping; Fu, Qiuyun; Zhou, Dongxiang

2013-05-01

The Electro Dynamic Gradient (EDG) method has been proved to be a feasible way to grow TlBr crystals in our previous work. In this research, the influence of thermal conditions such as cooling rate during growth process on the crystal performance was investigated. Crystals of approximately 12 mm diameter were obtained by the EDG method at different cooling rates during the growth process, and the quality of the crystals was routinely evaluated by X-ray diffraction (XRD), infrared (IR) and ultraviolet (UV) transmission, I-V measurement and energy response spectrum. The results proved that thermal conditions during growth had a profound influence on the characteristics of the crystals.

Maximum Power Point Tracking with Dichotomy and Gradient Method for Automobile Exhaust Thermoelectric Generators

NASA Astrophysics Data System (ADS)

Fang, W.; Quan, S. H.; Xie, C. J.; Tang, X. F.; Wang, L. L.; Huang, L.

2016-03-01

In this study, a direct-current/direct-current (DC/DC) converter with maximum power point tracking (MPPT) is developed to down-convert the high voltage DC output from a thermoelectric generator to the lower voltage required to charge batteries. To improve the tracking accuracy and speed of the converter, a novel MPPT control scheme characterized by an aggregated dichotomy and gradient (ADG) method is proposed. In the first stage, the dichotomy algorithm is used as a fast search method to find the approximate region of the maximum power point. The gradient method is then applied for rapid and accurate tracking of the maximum power point. To validate the proposed MPPT method, a test bench composed of an automobile exhaust thermoelectric generator was constructed for harvesting the automotive exhaust heat energy. Steady-state and transient tracking experiments under five different load conditions were carried out using a DC/DC converter with the proposed ADG and with three traditional methods. The experimental results show that the ADG method can track the maximum power within 140 ms with a 1.1% error rate when the engine operates at 3300 rpm@71 NM, which is superior to the performance of the single dichotomy method, the single gradient method and the perturbation and observation method from the viewpoint of improved tracking accuracy and speed.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Conjugate-gradient optimization method for orbital-free density functional calculations.

PubMed

Jiang, Hong; Yang, Weitao

2004-08-01

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. (c) 2004 American Institute of Physics.

Numerical simulation of groundwater flow in strongly anisotropic aquifers using multiple-point flux approximation method

NASA Astrophysics Data System (ADS)

Lin, S. T.; Liou, T. S.

2017-12-01

Numerical simulation of groundwater flow in anisotropic aquifers usually suffers from the lack of accuracy of calculating groundwater flux across grid blocks. Conventional two-point flux approximation (TPFA) can only obtain the flux normal to the grid interface but completely neglects the one parallel to it. Furthermore, the hydraulic gradient in a grid block estimated from TPFA can only poorly represent the hydraulic condition near the intersection of grid blocks. These disadvantages are further exacerbated when the principal axes of hydraulic conductivity, global coordinate system, and grid boundary are not parallel to one another. In order to refine the estimation the in-grid hydraulic gradient, several multiple-point flux approximation (MPFA) methods have been developed for two-dimensional groundwater flow simulations. For example, the MPFA-O method uses the hydraulic head at the junction node as an auxiliary variable which is then eliminated using the head and flux continuity conditions. In this study, a three-dimensional MPFA method will be developed for numerical simulation of groundwater flow in three-dimensional and strongly anisotropic aquifers. This new MPFA method first discretizes the simulation domain into hexahedrons. Each hexahedron is further decomposed into a certain number of tetrahedrons. The 2D MPFA-O method is then extended to these tetrahedrons, using the unknown head at the intersection of hexahedrons as an auxiliary variable along with the head and flux continuity conditions to solve for the head at the center of each hexahedron. Numerical simulations using this new MPFA method have been successfully compared with those obtained from a modified version of TOUGH2.

Finding Dantzig Selectors with a Proximity Operator based Fixed-point Algorithm

DTIC Science & Technology

2014-11-01

experiments showed that this method usually outperforms the method in [2] in terms of CPU time while producing solutions of comparable quality. The... method proposed in [19]. To alleviate the difficulty caused by the subprob- lem without a closed form solution , a linearized ADM was proposed for the...a closed form solution , but the β-related subproblem does not and is solved approximately by using the nonmonotone gradient method in [18]. The

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

Thermal Management Techniques for Oil-Free Turbomachinery Systems

NASA Technical Reports Server (NTRS)

Radil, Kevin; DellaCorte, Chris; Zeszotek, Michelle

2006-01-01

Tests were performed to evaluate three different methods of utilizing air to provide thermal management control for compliant journal foil air bearings. The effectiveness of the methods was based on bearing bulk temperature and axial thermal gradient reductions during air delivery. The first method utilized direct impingement of air on the inner surface of a hollow test journal during operation. The second, less indirect method achieved heat removal by blowing air inside the test journal to simulate air flowing axially through a hollow, rotating shaft. The third method emulated the most common approach to removing heat by forcing air axially through the bearing s support structure. Internal bearing temperatures were measured with three, type K thermocouples embedded in the bearing that measured general internal temperatures and axial thermal gradients. Testing was performed in a 1 atm, 260 C ambient environment with the bearing operating at 60 krpm and supporting a load of 222 N. Air volumetric flows of 0.06, 0.11, and 0.17 cubic meters per minute at approximately 150 to 200 C were used. The tests indicate that all three methods provide thermal management but at different levels of effectiveness. Axial cooling of the bearing support structure had a greater effect on bulk temperature for each air flow and demonstrated that the thermal gradients could be influenced by the directionality of the air flow. Direct air impingement on the journal's inside surface provided uniform reductions in both bulk temperature and thermal gradients. Similar to the direct method, indirect journal cooling had a uniform cooling effect on both bulk temperatures and thermal gradients but was the least effective of the three methods.

Model-based morphological segmentation and labeling of coronary angiograms.

PubMed

Haris, K; Efstratiadis, S N; Maglaveras, N; Pappas, C; Gourassas, J; Louridas, G

1999-10-01

A method for extraction and labeling of the coronary arterial tree (CAT) using minimal user supervision in single-view angiograms is proposed. The CAT structural description (skeleton and borders) is produced, along with quantitative information for the artery dimensions and assignment of coded labels, based on a given coronary artery model represented by a graph. The stages of the method are: 1) CAT tracking and detection; 2) artery skeleton and border estimation; 3) feature graph creation; and iv) artery labeling by graph matching. The approximate CAT centerline and borders are extracted by recursive tracking based on circular template analysis. The accurate skeleton and borders of each CAT segment are computed, based on morphological homotopy modification and watershed transform. The approximate centerline and borders are used for constructing the artery segment enclosing area (ASEA), where the defined skeleton and border curves are considered as markers. Using the marked ASEA, an artery gradient image is constructed where all the ASEA pixels (except the skeleton ones) are assigned the gradient magnitude of the original image. The artery gradient image markers are imposed as its unique regional minima by the homotopy modification method, the watershed transform is used for extracting the artery segment borders, and the feature graph is updated. Finally, given the created feature graph and the known model graph, a graph matching algorithm assigns the appropriate labels to the extracted CAT using weighted maximal cliques on the association graph corresponding to the two given graphs. Experimental results using clinical digitized coronary angiograms are presented.

Parameter estimation for terrain modeling from gradient data. [navigation system for Martian rover

NASA Technical Reports Server (NTRS)

Dangelo, K. R.

1974-01-01

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

Nanophotonic particle simulation and inverse design using artificial neural networks.

PubMed

Peurifoy, John; Shen, Yichen; Jing, Li; Yang, Yi; Cano-Renteria, Fidel; DeLacy, Brendan G; Joannopoulos, John D; Tegmark, Max; Soljačić, Marin

2018-06-01

We propose a method to use artificial neural networks to approximate light scattering by multilayer nanoparticles. We find that the network needs to be trained on only a small sampling of the data to approximate the simulation to high precision. Once the neural network is trained, it can simulate such optical processes orders of magnitude faster than conventional simulations. Furthermore, the trained neural network can be used to solve nanophotonic inverse design problems by using back propagation, where the gradient is analytical, not numerical.

Galactic cosmic ray gradients, field-aligned and latitudinal, among Voyagers 1/2 and IMP-8

NASA Technical Reports Server (NTRS)

Roelof, E. C.; Decker, R. B.; Krimigis, S. M.; Venkatesan, D.; Lazarus, A. J.

1982-01-01

The present investigation represents a summary of a comprehensive analysis of the same subject conducted by Roelof et al. (1981). It is pointed out that the tandem earth-Jupiter trajectories of the Voyager 1/2 spacecraft, combined with baseline measurements from the earth-orbiting IMP 7/8 spacecraft, provide the first opportunity for unambiguously separating latitude from radial or field-aligned effects in galactic cosmic ray gradients. Attention is given to the method of data analysis, and the separation of field-aligned and latitudinal gradients. It is found that latitudinal gradients approximately equal to or greater than 1 percent per deg in the cosmic ray intensity were a common feature of the interplanetary medium between 1 and 5 AU in 1977-78. Except in the most disturbed periods, cosmic ray intensities are well-ordered in field-aligned structures.

A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics

NASA Astrophysics Data System (ADS)

Yao, Jianyao; Liu, G. R.

2014-10-01

A GSM-CFD solver for incompressible flows is developed based on the gradient smoothing method (GSM). A matrix-form algorithm and corresponding data structure for GSM are devised to efficiently approximate the spatial gradients of field variables using the gradient smoothing operation. The calculated gradient values on various test fields show that the proposed GSM is capable of exactly reproducing linear field and of second order accuracy on all kinds of meshes. It is found that the GSM is much more robust to mesh deformation and therefore more suitable for problems with complicated geometries. Integrated with the artificial compressibility approach, the GSM is extended to solve the incompressible flows. As an example, the flow simulation of carotid bifurcation is carried out to show the effectiveness of the proposed GSM-CFD solver. The blood is modeled as incompressible Newtonian fluid and the vessel is treated as rigid wall in this paper.

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

NASA Technical Reports Server (NTRS)

Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

1998-01-01

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover

NASA Astrophysics Data System (ADS)

Allen, Philip B.

2018-04-01

Simulations [e.g., X. W. Zhou et al., Phys. Rev. B 79, 115201 (2009), 10.1103/PhysRevB.79.115201] show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law j ⃗(r ⃗) =-κ ∇ ⃗T (r ⃗) . The heat current j ⃗(r ⃗) depends not just on the local temperature gradient ∇ ⃗T (r ⃗) but also on temperatures at points r⃗' within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in nonlocal form to analyze the spatial variation Δ T (r ⃗) . The relaxation-time approximation (RTA) is used because the full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity κ are proposed. Callaway invented an approximate method of correcting RTA for the q ⃗ (phonon wave vector or crystal momentum) conservation of N (Normal as opposed to Umklapp) anharmonic collisions. This method is generalized to the nonlocal case where κ (k ⃗) depends on the wave vector of the current j ⃗(k ⃗) and temperature gradient i k ⃗Δ T (k ⃗) .

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

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

2002-01-01

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Gradient pre-emphasis to counteract first-order concomitant fields on asymmetric MRI gradient systems.

PubMed

Tao, Shengzhen; Weavers, Paul T; Trzasko, Joshua D; Shu, Yunhong; Huston, John; Lee, Seung-Kyun; Frigo, Louis M; Bernstein, Matt A

2017-06-01

To develop a gradient pre-emphasis scheme that prospectively counteracts the effects of the first-order concomitant fields for any arbitrary gradient waveform played on asymmetric gradient systems, and to demonstrate the effectiveness of this approach using a real-time implementation on a compact gradient system. After reviewing the first-order concomitant fields that are present on asymmetric gradients, we developed a generalized gradient pre-emphasis model assuming arbitrary gradient waveforms to counteract their effects. A numerically straightforward, easily implemented approximate solution to this pre-emphasis problem was derived that was compatible with the current hardware infrastructure of conventional MRI scanners for eddy current compensation. The proposed method was implemented on the gradient driver subsystem, and its real-time use was tested using a series of phantom and in vivo data acquired from two-dimensional Cartesian phase-difference, echo-planar imaging, and spiral acquisitions. The phantom and in vivo results demonstrated that unless accounted for, first-order concomitant fields introduce considerable phase estimation error into the measured data and result in images with spatially dependent blurring/distortion. The resulting artifacts were effectively prevented using the proposed gradient pre-emphasis. We have developed an efficient and effective gradient pre-emphasis framework to counteract the effects of first-order concomitant fields of asymmetric gradient systems. Magn Reson Med 77:2250-2262, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Synthesis and First Principles Investigation of HMX/NMP Cocrystal Explosive

NASA Astrophysics Data System (ADS)

Lin, He; Zhu, Shun-Guan; Zhang, Lin; Peng, Xin-Hua; LI, Hong-Zhen

2013-10-01

1,3,5,7-Tetranitro-l,3,5,7-tetrazocine (HMX)/N-methyl-2-pyrrolidone (NMP) cocrystal explosive was prepared by a solution evaporation method. This cocrystal explosive crystallized in the trigonal system (space group ? ), with cell parameters a = 16.605(8) Å and c = 31.496(4) Å. Theoretical investigations of the formation mechanism of HMX/NMP cocrystal were carried out in Cambridge serial total energy package (CASTEP) based on dispersion-corrected density functional theory (DFT-D) with a plane wave scheme. The exchange-correlation potential was treated with the Perdew-Burke-Ernzerhof function of generalized gradient approximation, and dispersion force was correlated using Grimme's method. The band structure, density of states, projected density of states, and Mulliken populations were calculated at the generalized gradient approximation level. The results showed that the main host-guest interactions in HMX/NMP cocrystal were hydrogen bonds and stacking interactions, which were the same as those analyzed using X-ray diffraction. Theoretical investigations of HMX/NMP cocrystal explosive may provide the basis for the preparation of cocrystal explosive composed of HMX and energetic materials.

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

NASA Astrophysics Data System (ADS)

Péli, Zoltán; Nagy, Sándor; Sailer, Kornel

2018-02-01

The effect of the O(partial4) terms of the gradient expansion on the anomalous dimension η and the correlation length's critical exponent ν of the Wilson-Fisher fixed point has been determined for the Euclidean 3-dimensional O( N) models with N≥ 2 . Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory is well approximated by the effective average action preserving O( N) symmetry with an accuracy of O(η).

Electronic structure properties of UO2 as a Mott insulator

NASA Astrophysics Data System (ADS)

Sheykhi, Samira; Payami, Mahmoud

2018-06-01

In this work using the density functional theory (DFT), we have studied the structural, electronic and magnetic properties of uranium dioxide with antiferromagnetic 1k-, 2k-, and 3k-order structures. Ordinary approximations in DFT, such as the local density approximation (LDA) or generalized gradient approximation (GGA), usually predict incorrect metallic behaviors for this strongly correlated electron system. Using Hubbard term correction for f-electrons, LDA+U method, as well as using the screened Heyd-Scuseria-Ernzerhof (HSE) hybrid functional for the exchange-correlation (XC), we have obtained the correct ground-state behavior as an insulator, with band gaps in good agreement with experiment.

Interconfigurational energies in transition-metal atoms using gradient-corrected density-functional theory

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

Kutzler, F.W.; Painter, G.S.

1991-03-15

The rapid variation of charge and spin densities in atoms and molecules provides a severe test for local-density-functional theory and for the use of gradient corrections. In the study reported in this paper, we use the Langreth, Mehl, and Hu (LMH) functional and the generalized gradient approximation (GGA) of Perdew and Yue to calculate {ital s}-{ital d} transition energies, 4{ital s} ionization energies, and 3{ital d} ionization energies for the 3{ital d} transition-metal atoms. These calculations are compared with results from the local-density functional of Vosko, Wilk, and Nusair. By comparison with experimental energies, we find that the gradient functionalsmore » are only marginally more successful than the local-density approximation in calculating energy differences between states in transition-metal atoms. The GGA approximation is somewhat better than the LMH functional for most of the atoms studied, although there are several exceptions.« less

An adjoint method for gradient-based optimization of stellarator coil shapes

NASA Astrophysics Data System (ADS)

Paul, E. J.; Landreman, M.; Bader, A.; Dorland, W.

2018-07-01

We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for computation of the local sensitivity of figures of merit to normal displacements of the winding surface is presented, with potential applications for understanding engineering tolerances.

Effects of breast and colorectal cancer on labour market outcomes-average effects and educational gradients.

PubMed

Heinesen, Eskil; Kolodziejczyk, Christophe

2013-12-01

We estimate causal effects of breast and colorectal cancer on labour market outcomes 1-3 years after the diagnosis. Based on Danish administrative data we estimate average treatment effects on the treated by propensity score weighting methods using persons with no cancer diagnosis as control group. We conduct robustness checks using matching, difference-in-differences methods and an alternative control group of later cancer patients. The different methods give approximately the same results. Cancer increases the risks of leaving the labour force and receiving disability pension, and the effects are larger for the less educated. Effects on income are small and mostly insignificant. We investigate some of the mechanisms which may be important in explaining the educational gradient in effects of cancer on labour market attachment. Copyright © 2013 Elsevier B.V. All rights reserved.

Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory

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

Sato, Shunsuke A.; Taniguchi, Yasutaka; Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435

2015-12-14

We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functionalmore » which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.« less

The ab initio Calculation of Electric Field Gradient at the Site of P Impurity in α-Al3O2

NASA Astrophysics Data System (ADS)

Zhang, Qiao-Li; Yuan, Da-Qing; Zhang, Huan-Qiao; Fan, Ping; Zuo, Yi; Zheng, Yong-Nan; Masuta, K.; Fukuda, M.; Mihara, M.; Minamisono, T.; Kitagawa, A.; Zhu, Sheng-Yun

2012-09-01

An ab initio calculation of the electric-field gradient (EFG) at the site of a phosphorous impurity substituting an Al atom in α-Al2O3 is carried out using the WIEN2k code with the full-potential linearized augmented plane wave plus local orbital method (LAPW+lo) in the frame of density functional theory. The atomic lattice relaxations caused by the implanted impurities were calculated for two different charged states to well describe the electronic structure of the doped system. The EFG at the site of the phosphorous impurity in the charged supercell calculated with the exchange-correlation potential of the Wu-Cohen generalized gradient approximation (WC-GGA) is 0.573 × 1021 V/m2. Then, the nuclear quadrupole moment of the I = 3 state in 28P is deduced to be 137 mb from the quadrupole interaction frequency of 190 kHz measured recently by the β-NQR method.

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

NASA Technical Reports Server (NTRS)

Green, Lawrence; Carle, Alan; Fagan, Mike

1999-01-01

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.

PubMed

Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko

2010-06-28

We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.

Performance of local optimization in single-plane fluoroscopic analysis for total knee arthroplasty.

PubMed

Prins, A H; Kaptein, B L; Stoel, B C; Lahaye, D J P; Valstar, E R

2015-11-05

Fluoroscopy-derived joint kinematics plays an important role in the evaluation of knee prostheses. Fluoroscopic analysis requires estimation of the 3D prosthesis pose from its 2D silhouette in the fluoroscopic image, by optimizing a dissimilarity measure. Currently, extensive user-interaction is needed, which makes analysis labor-intensive and operator-dependent. The aim of this study was to review five optimization methods for 3D pose estimation and to assess their performance in finding the correct solution. Two derivative-free optimizers (DHSAnn and IIPM) and three gradient-based optimizers (LevMar, DoNLP2 and IpOpt) were evaluated. For the latter three optimizers two different implementations were evaluated: one with a numerically approximated gradient and one with an analytically derived gradient for computational efficiency. On phantom data, all methods were able to find the 3D pose within 1mm and 1° in more than 85% of cases. IpOpt had the highest success-rate: 97%. On clinical data, the success rates were higher than 85% for the in-plane positions, but not for the rotations. IpOpt was the most expensive method and the application of an analytically derived gradients accelerated the gradient-based methods by a factor 3-4 without any differences in success rate. In conclusion, 85% of the frames can be analyzed automatically in clinical data and only 15% of the frames require manual supervision. The optimal success-rate on phantom data (97% with IpOpt) on phantom data indicates that even less supervision may become feasible. Copyright © 2015 Elsevier Ltd. All rights reserved.

Nanophotonic particle simulation and inverse design using artificial neural networks

PubMed Central

Peurifoy, John; Shen, Yichen; Jing, Li; Cano-Renteria, Fidel; DeLacy, Brendan G.; Joannopoulos, John D.; Tegmark, Max

2018-01-01

We propose a method to use artificial neural networks to approximate light scattering by multilayer nanoparticles. We find that the network needs to be trained on only a small sampling of the data to approximate the simulation to high precision. Once the neural network is trained, it can simulate such optical processes orders of magnitude faster than conventional simulations. Furthermore, the trained neural network can be used to solve nanophotonic inverse design problems by using back propagation, where the gradient is analytical, not numerical. PMID:29868640

Cosmic Microwave Background Mapmaking with a Messenger Field

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.; Næss, Sigurd K.

2018-01-01

We apply a messenger field method to solve the linear minimum-variance mapmaking equation in the context of Cosmic Microwave Background (CMB) observations. In simulations, the method produces sky maps that converge significantly faster than those from a conjugate gradient descent algorithm with a diagonal preconditioner, even though the computational cost per iteration is similar. The messenger method recovers large scales in the map better than conjugate gradient descent, and yields a lower overall χ2. In the single, pencil beam approximation, each iteration of the messenger mapmaking procedure produces an unbiased map, and the iterations become more optimal as they proceed. A variant of the method can handle differential data or perform deconvolution mapmaking. The messenger method requires no preconditioner, but a high-quality solution needs a cooling parameter to control the convergence. We study the convergence properties of this new method and discuss how the algorithm is feasible for the large data sets of current and future CMB experiments.

Higher Nucleoporin-Importinβ Affinity at the Nuclear Basket Increases Nucleocytoplasmic Import

PubMed Central

Azimi, Mohammad; Mofrad, Mohammad R. K.

2013-01-01

Several in vitro studies have shown the presence of an affinity gradient in nuclear pore complex proteins for the import receptor Importinβ, at least partially contributing to nucleocytoplasmic transport, while others have historically argued against the presence of such a gradient. Nonetheless, the existence of an affinity gradient has remained an uncharacterized contributing factor. To shed light on the affinity gradient theory and better characterize how the existence of such an affinity gradient between the nuclear pore and the import receptor may influence the nucleocytoplasmic traffic, we have developed a general-purpose agent based modeling (ABM) framework that features a new method for relating rate constants to molecular binding and unbinding probabilities, and used our ABM approach to quantify the effects of a wide range of forward and reverse nucleoporin-Importinβ affinity gradients. Our results indicate that transport through the nuclear pore complex is maximized with an effective macroscopic affinity gradient of 2000 µM, 200 µM and 10 µM in the cytoplasmic, central channel and nuclear basket respectively. The transport rate at this gradient is approximately 10% higher than the transport rate for a comparable pore lacking any affinity gradient, which has a peak transport rate when all nucleoporins have an affinity of 200 µM for Importinβ. Furthermore, this optimal ratio of affinity gradients is representative of the ratio of affinities reported for the yeast nuclear pore complex – suggesting that the affinity gradient seen in vitro is highly optimized. PMID:24282617

Surface-from-gradients without discrete integrability enforcement: A Gaussian kernel approach.

PubMed

Ng, Heung-Sun; Wu, Tai-Pang; Tang, Chi-Keung

2010-11-01

Representative surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint in a discrete manner. While enforcing integrability allows the subsequent integration to produce surface heights, existing algorithms have one or more of the following disadvantages: They can only handle dense per-pixel gradient fields, smooth out sharp features in a partially integrable field, or produce severe surface distortion in the results. In this paper, we present a method which does not enforce discrete integrability and reconstructs a 3D continuous surface from a gradient or a height field, or a combination of both, which can be dense or sparse. The key to our approach is the use of kernel basis functions, which transfer the continuous surface reconstruction problem into high-dimensional space, where a closed-form solution exists. By using the Gaussian kernel, we can derive a straightforward implementation which is able to produce results better than traditional techniques. In general, an important advantage of our kernel-based method is that the method does not suffer discretization and finite approximation, both of which lead to surface distortion, which is typical of Fourier or wavelet bases widely adopted by previous representative approaches. We perform comparisons with classical and recent methods on benchmark as well as challenging data sets to demonstrate that our method produces accurate surface reconstruction that preserves salient and sharp features. The source code and executable of the system are available for downloading.

Approximate analysis of thermal convection in a crystal-growth cell for Spacelab 3

NASA Technical Reports Server (NTRS)

Dressler, R. F.

1982-01-01

The transient and steady thermal convection in microgravity is described. The approach is applicable to many three dimensional flows in containers of various shapes with various thermal gradients imposed. The method employs known analytical solutions to two dimensional thermal flows in simpler geometries, and does not require recourse to numerical calculations by computer.

Adsorbate Diffusion on Transition Metal Nanoparticles

DTIC Science & Technology

2015-01-01

different sizes and shapes using density functional theory calculations. We show that nanoparticles bind adsorbates more strongly than the...structure theoretical methods, a quantitative study with accurate density functional theory (DFT) calculations is still missing. Here, we perform a...functional theory . The projector augmented wave (PAW) potentials29,30 were used for electron- ion interactions and the generalized gradient approximation

Accuracy and efficiency considerations for wide-angle wavefield extrapolators and scattering operators

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2005-10-01

Several observations are made concerning the numerical implementation of wide-angle one-way wave equations, using for illustration scalar waves obeying the Helmholtz equation in two space dimensions. This simple case permits clear identification of a sequence of physically motivated approximations of use when the mathematically exact pseudo-differential operator (PSDO) one-way method is applied. As intuition suggests, these approximations largely depend on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow-angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so-called `standard-ordering' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane-wave synthesis lying at the heart of the calculations. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one-way propagator for the laterally varying case, representing the intuitive extension of classical integral-transform solutions for a laterally homogeneous medium. This exponential propagator permits larger forward stepsizes. Numerical comparisons with Helmholtz (i.e. full) wave-equation finite-difference solutions are presented for various canonical problems. These include propagation along an interfacial gradient, the effects of a compact inclusion and the formation of extended transmitted and backscattered wave trains by model roughness. The ideas extend to the 3-D, generally anisotropic case and to multiple scattering by invariant embedding. It is concluded that the method is very competitive, striking a new balance between simplifying approximations and computational labour. Complicated wave-scattering effects are retained without the need for expensive global solutions, providing a robust and flexible modelling tool.

Optimum gradient of mountain paths.

PubMed

Minetti, A E

1995-11-01

By combining the experiment results of R. Margaria (Atti Accad. Naz. Lincei Memorie 7: 299-368, 1938), regarding the metabolic cost of gradient locomotion, together with recent insights on gait biomechanics, a prediction about the most economical gradient of mountain paths (approximately 25%) is obtained and interpreted. The pendulum-like mechanism of walking produces a waste of mechanical work against gravity within the gradient range of up to 15% (the overall efficiency is dominated by the low transmission efficiency), whereas for steeper values only the muscular efficiency is responsible for the (slight) metabolic change (per meter of vertical displacement) with respect to gradient. The speeds at the optimum gradient turned out to be approximately 0.65 m/s (+0.16 m/s vertical) and 1.50 m/s (-0.36 m/s vertical), for uphill and downhill walking, respectively, and the ascensional energy expenditure was 0.4 and 2.0 ml O2.kg body mass-1.vertical m-1 climbed or descended. When the metabolic power becomes a burden, as in high-altitude mountaineering, the optimum gradient should be reduced. A sample of real mountain path gradients, experimentally measured, mimics the obtained predictions.

Archaeological Geology of the Fort Hood Military Reservation, Fort Hood, Texas

DTIC Science & Technology

1992-06-01

stream with a sinuosity of 1.3 and channel gradient of 1.4 m/km. Discharge records near Killeen over a six year period during the 1920’s and 1940’s...drains approximately 175 km2 of lower Cretaceous limestones, shales and marls (Fig. 2). Sinuosity is 1.3, channel gradient 3.2 m/km, and drainage...CREEK Within the study area Owl Creek drains approximately 72 km 2 of shales and limestones, has a sinuosity of 1.1, channel gradient of 3.4 m/kin, and

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

Limited-memory fast gradient descent method for graph regularized nonnegative matrix factorization.

PubMed

Guan, Naiyang; Wei, Lei; Luo, Zhigang; Tao, Dacheng

2013-01-01

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix X[Symbol:see text]R(m x n) to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r) and H[Symbol:see text]R(r x n) (r < min {m,n}) and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.

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.

A gradient-free method for the purification of infective dengue virus for protein-level investigations.

PubMed

Jensen, Stephanie M; Nguyen, Celina T; Jewett, John C

2016-09-01

Dengue virus (DENV) is a mosquito-transmitted flavivirus that infects approximately 100 million people annually. Multi-day protocols for purification of DENV reduce the infective titer due to viral sensitivity to both temperature and pH. Herein we describe a 5-h protocol for the purification of all DENV serotypes, utilizing traditional gradient-free ultracentrifugation followed by selective virion precipitation. This protocol allows for the separation of DENV from contaminating proteins - including intact C6/36 densovirus, for the production of infective virus at high concentration for protein-level analysis. Copyright © 2016 Elsevier B.V. All rights reserved.

Radiative transfer in dusty nebulae. III - The effects of dust albedo

NASA Technical Reports Server (NTRS)

Petrosian, V.; Dana, R. A.

1980-01-01

The effects of an albedo of internal dust, such as ionization structure and temperature of dust grain, were studied by the quasi-diffusion method with an iterative technique for solving the radiative heat transfer equations. It was found that the generalized on-the-spot approximation solution is adequate for most astrophysical applications for a zero albedo; for a nonzero albedo, the Eddington approximation is more accurate. The albedo increases the average energy of the diffuse photons, increasing the ionization level of hydrogen and heavy elements if the Eddington approximation is applied; the dust thermal gradient is reduced so that the infrared spectrum approaches blackbody spectrum with an increasing albedo.

Topological susceptibility in finite temperature (2 +1 )-flavor QCD using gradient flow

NASA Astrophysics Data System (ADS)

Taniguchi, Yusuke; Kanaya, Kazuyuki; Suzuki, Hiroshi; Umeda, Takashi; WHOT-QCD Collaboration

2017-03-01

We compute the topological charge and its susceptibility in finite temperature (2 +1 )-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively O (a ) -improved Wilson quarks, we perform simulations on a fine lattice with a ≃0.07 fm at a heavy u , d quark mass with mπ/mρ≃0.63 , but approximately physical s quark mass with mηss/mϕ≃0.74 . In a temperature range from T ≃174 MeV (Nt=16 ) to 697 MeV (Nt=4 ), we study two topics on the topological susceptibility. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Because the two definitions are related by chiral Ward-Takahashi identities, their equivalence is not trivial for lattice quarks which violate the chiral symmetry explicitly at finite lattice spacings. The gradient flow method enables us to compute them without being bothered by the chiral violation. We find a good agreement between the two definitions with Wilson quarks. The other is a comparison with a prediction of the dilute instanton gas approximation, which is relevant in a study of axions as a candidate of the dark matter in the evolution of the Universe. We find that the topological susceptibility shows a decrease in T which is consistent with the predicted χt(T )∝(T /Tpc)-8 for three-flavor QCD even at low temperature Tpc

Sensitivity Analysis for Coupled Aero-structural Systems

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.

1999-01-01

A novel method has been developed for calculating gradients of aerodynamic force and moment coefficients for an aeroelastic aircraft model. This method uses the Global Sensitivity Equations (GSE) to account for the aero-structural coupling, and a reduced-order modal analysis approach to condense the coupling bandwidth between the aerodynamic and structural models. Parallel computing is applied to reduce the computational expense of the numerous high fidelity aerodynamic analyses needed for the coupled aero-structural system. Good agreement is obtained between aerodynamic force and moment gradients computed with the GSE/modal analysis approach and the same quantities computed using brute-force, computationally expensive, finite difference approximations. A comparison between the computational expense of the GSE/modal analysis method and a pure finite difference approach is presented. These results show that the GSE/modal analysis approach is the more computationally efficient technique if sensitivity analysis is to be performed for two or more aircraft design parameters.

The Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient

NASA Technical Reports Server (NTRS)

Cohen, Clarence B; Reshotko, Eli

1956-01-01

An approximate method for the calculation of the compressible laminar boundary layer with heat transfer and arbitrary pressure gradient, based on Thwaites' correlation concept, is presented. With the definition of dimensionless shear and heat-transfer parameters and an assumed correlation of these parameters in terms of a momentum parameter, a complete system of relations for calculating skin friction and heat transfer results. Knowledge of velocity or temperature profiles is not necessary in using this calculation method. When the method is applied to a convergent-divergent, axially symmetric rocket nozzle, it shows that high rates of heat transfer are obtained at the initial stagnation point and at the throat of the nozzle. Also indicated are negative displacement thicknesses in the convergent portion of the nozzle; these occur because of the high density within the lower portions of the cooled boundary layer. (author)

A rapid and robust gradient measurement technique using dynamic single-point imaging.

PubMed

Jang, Hyungseok; McMillan, Alan B

2017-09-01

We propose a new gradient measurement technique based on dynamic single-point imaging (SPI), which allows simple, rapid, and robust measurement of k-space trajectory. To enable gradient measurement, we utilize the variable field-of-view (FOV) property of dynamic SPI, which is dependent on gradient shape. First, one-dimensional (1D) dynamic SPI data are acquired from a targeted gradient axis, and then relative FOV scaling factors between 1D images or k-spaces at varying encoding times are found. These relative scaling factors are the relative k-space position that can be used for image reconstruction. The gradient measurement technique also can be used to estimate the gradient impulse response function for reproducible gradient estimation as a linear time invariant system. The proposed measurement technique was used to improve reconstructed image quality in 3D ultrashort echo, 2D spiral, and multi-echo bipolar gradient-echo imaging. In multi-echo bipolar gradient-echo imaging, measurement of the k-space trajectory allowed the use of a ramp-sampled trajectory for improved acquisition speed (approximately 30%) and more accurate quantitative fat and water separation in a phantom. The proposed dynamic SPI-based method allows fast k-space trajectory measurement with a simple implementation and no additional hardware for improved image quality. Magn Reson Med 78:950-962, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Gradient Optimization for Analytic conTrols - GOAT

NASA Astrophysics Data System (ADS)

Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank

Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.

Design and fabrication of integrated micro/macrostructure for 3D functional gradient systems based on additive manufacturing

NASA Astrophysics Data System (ADS)

Yin, Ming; Xie, Luofeng; Jiang, Weifeng; Yin, Guofu

2018-05-01

Functional gradient systems have important applications in many areas. Although a 2D dielectric structure that serves as the gradient index medium for controlling electromagnetic waves is well established, it may not be suitable for application in 3D case. In this paper, we present a method to realize functional gradient systems with 3D integrated micro/macrostructure. The homogenization of the structure is studied in detail by conducting band diagram analysis. The analysis shows that the effective medium approximation is valid even when periodicity is comparable to wavelength. The condition to ensure the polarization-invariant, isotropic, and frequency-independent property is investigated. The scheme for the design and fabrication of 3D systems requiring spatial material property distribution is presented. By using the vat photopolymerization process, a large overall size of macrostructure at the system level and precise fine features of microstructure at the unit cell level are realized, thus demonstrating considerable scalability of the system for wave manipulation.

Ray Tracing Methods in Seismic Emission Tomography

NASA Astrophysics Data System (ADS)

Chebotareva, I. Ya.

2018-03-01

Highly efficient approximate ray tracing techniques which can be used in seismic emission tomography and in other methods requiring a large number of raypaths are described. The techniques are applicable for the gradient and plane-layered velocity sections of the medium and for the models with a complicated geometry of contrasting boundaries. The empirical results obtained with the use of the discussed ray tracing technologies and seismic emission tomography results, as well as the results of numerical modeling, are presented.

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

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

2001-01-01

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

A self-reference PRF-shift MR thermometry method utilizing the phase gradient

NASA Astrophysics Data System (ADS)

Langley, Jason; Potter, William; Phipps, Corey; Huang, Feng; Zhao, Qun

2011-12-01

In magnetic resonance (MR) imaging, the most widely used and accurate method for measuring temperature is based on the shift in proton resonance frequency (PRF). However, inter-scan motion and bulk magnetic field shifts can lead to inaccurate temperature measurements in the PRF-shift MR thermometry method. The self-reference PRF-shift MR thermometry method was introduced to overcome such problems by deriving a reference image from the heated or treated image, and approximates the reference phase map with low-order polynomial functions. In this note, a new approach is presented to calculate the baseline phase map in self-reference PRF-shift MR thermometry. The proposed method utilizes the phase gradient to remove the phase unwrapping step inherent to other self-reference PRF-shift MR thermometry methods. The performance of the proposed method was evaluated using numerical simulations with temperature distributions following a two-dimensional Gaussian function as well as phantom and in vivo experimental data sets. The results from both the numerical simulations and experimental data show that the proposed method is a promising technique for measuring temperature.

Small-Tip-Angle Spokes Pulse Design Using Interleaved Greedy and Local Optimization Methods

PubMed Central

Grissom, William A.; Khalighi, Mohammad-Mehdi; Sacolick, Laura I.; Rutt, Brian K.; Vogel, Mika W.

2013-01-01

Current spokes pulse design methods can be grouped into methods based either on sparse approximation or on iterative local (gradient descent-based) optimization of the transverse-plane spatial frequency locations visited by the spokes. These two classes of methods have complementary strengths and weaknesses: sparse approximation-based methods perform an efficient search over a large swath of candidate spatial frequency locations but most are incompatible with off-resonance compensation, multifrequency designs, and target phase relaxation, while local methods can accommodate off-resonance and target phase relaxation but are sensitive to initialization and suboptimal local cost function minima. This article introduces a method that interleaves local iterations, which optimize the radiofrequency pulses, target phase patterns, and spatial frequency locations, with a greedy method to choose new locations. Simulations and experiments at 3 and 7 T show that the method consistently produces single- and multifrequency spokes pulses with lower flip angle inhomogeneity compared to current methods. PMID:22392822

Solving large mixed linear models using preconditioned conjugate gradient iteration.

PubMed

Strandén, I; Lidauer, M

1999-12-01

Continuous evaluation of dairy cattle with a random regression test-day model requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using iteration on data is presented. In the new computing technique, the calculations in multiplication of a vector by a matrix were recorded to three steps instead of the commonly used two steps. The three-step method was implemented in a general mixed linear model program that used preconditioned conjugate gradient iteration. Performance of this program in comparison to other general solving programs was assessed via estimation of breeding values using univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, at best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at least 20 and 435% more time to solve the univariate and multivariate animal models, respectively. Computations of the second best iteration on data took approximately three and five times longer for the animal and test-day models, respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large breeding value problems is supported by our findings.

Approximate solution of the p-median minimization problem

NASA Astrophysics Data System (ADS)

Il'ev, V. P.; Il'eva, S. D.; Navrotskaya, A. A.

2016-09-01

A version of the facility location problem (the well-known p-median minimization problem) and its generalization—the problem of minimizing a supermodular set function—is studied. These problems are NP-hard, and they are approximately solved by a gradient algorithm that is a discrete analog of the steepest descent algorithm. A priori bounds on the worst-case behavior of the gradient algorithm for the problems under consideration are obtained. As a consequence, a bound on the performance guarantee of the gradient algorithm for the p-median minimization problem in terms of the production and transportation cost matrix is obtained.

Monitoring of the spatio-temporal change in the interplate coupling at northeastern Japan subduction zone based on the spatial gradients of surface velocity field

NASA Astrophysics Data System (ADS)

Iinuma, Takeshi

2018-04-01

A monitoring method to grasp the spatio-temporal change in the interplate coupling in a subduction zone based on the spatial gradients of surface displacement rate fields is proposed. I estimated the spatio-temporal change in the interplate coupling along the plate boundary in northeastern (NE) Japan by applying the proposed method to the surface displacement rates based on global positioning system observations. The gradient of the surface velocities is calculated in each swath configured along the direction normal to the Japan Trench for time windows such as 0.5, 1, 2, 3 and 5 yr being shifted by one week during the period of 1997-2016. The gradient of the horizontal velocities is negative and has a large magnitude when the interplate coupling at the shallow part (less than approximately 50 km in depth) beneath the profile is strong, and the sign of the gradient of the vertical velocity is sensitive to the existence of the coupling at the deep part (greater than approximately 50 km in depth). The trench-parallel variation of the spatial gradients of a displacement rate field clearly corresponds to the trench-parallel variation of the amplitude of the interplate coupling on the plate interface, as well as the rupture areas of previous interplate earthquakes. Temporal changes in the trench-parallel variation of the spatial gradient of the displacement rate correspond to the strengthening or weakening of the interplate coupling. We can monitor the temporal change in the interplate coupling state by calculating the spatial gradients of the surface displacement rate field to some extent without performing inversion analyses with applying certain constraint conditions that sometimes cause over- and/or underestimation at areas of limited spatial resolution far from the observation network. The results of the calculation confirm known interplate events in the NE Japan subduction zone, such as the post-seismic slip of the 2003 M8.0 Tokachi-oki and 2005 M7.2 Miyagi-oki earthquakes and the recovery of the interplate coupling around the rupture area of the 1994 M7.6 Sanriku-Haruka-oki earthquake. The results also indicate the semi-periodic occurrence of slow slip events and the expansion of the area of slow slip events before the 2011 Tohoku-oki earthquake (M9.0) approaching the hypocentre of the Tohoku-oki earthquake.

Compressibility Corrections to Closure Approximations for Turbulent Flow Simulations

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

Cloutman, L D

2003-02-01

We summarize some modifications to the usual closure approximations for statistical models of turbulence that are necessary for use with compressible fluids at all Mach numbers. We concentrate here on the gradient-flu approximation for the turbulent heat flux, on the buoyancy production of turbulence kinetic energy, and on a modification of the Smagorinsky model to include buoyancy. In all cases, there are pressure gradient terms that do not appear in the incompressible models and are usually omitted in compressible-flow models. Omission of these terms allows unphysical rates of entropy change.

Recent developments in LIBXC - A comprehensive library of functionals for density functional theory

NASA Astrophysics Data System (ADS)

Lehtola, Susi; Steigemann, Conrad; Oliveira, Micael J. T.; Marques, Miguel A. L.

2018-01-01

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

Gradient Augmented Level Set Method for Two Phase Flow Simulations with Phase Change

NASA Astrophysics Data System (ADS)

Anumolu, C. R. Lakshman; Trujillo, Mario F.

2016-11-01

A sharp interface capturing approach is presented for two-phase flow simulations with phase change. The Gradient Augmented Levelset method is coupled with the two-phase momentum and energy equations to advect the liquid-gas interface and predict heat transfer with phase change. The Ghost Fluid Method (GFM) is adopted for velocity to discretize the advection and diffusion terms in the interfacial region. Furthermore, the GFM is employed to treat the discontinuity in the stress tensor, velocity, and temperature gradient yielding an accurate treatment in handling jump conditions. Thermal convection and diffusion terms are approximated by explicitly identifying the interface location, resulting in a sharp treatment for the energy solution. This sharp treatment is extended to estimate the interfacial mass transfer rate. At the computational cell, a d-cubic Hermite interpolating polynomial is employed to describe the interface location, which is locally fourth-order accurate. This extent of subgrid level description provides an accurate methodology for treating various interfacial processes with a high degree of sharpness. The ability to predict the interface and temperature evolutions accurately is illustrated by comparing numerical results with existing 1D to 3D analytical solutions.

Anomalous cosmic ray oxygen gradients throughout the heliosphere

NASA Technical Reports Server (NTRS)

Cummings, A. C.; Mewaldt, R. A.; Blake, J. B.; Cummings, J. R.; Franz, M.; Hovestadt, D.; Klecker, B.; Mason, G. M.; Mazur, J. E.; Stone, E. C.

1995-01-01

We have used data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX), Ulysses, Voyager 1, Voyager 2, and Pioneer 10 spacecraft to determine the radial and latitudinal gradients of anomalous cosmic ray oxygen at 10 MeV/nuc during the last half of 1993. These five spacecraft cover radial distances from 1 AU (SAMPEX) to 58 AU (P10) and latitudes to 41 deg S (Ulysses) and 32 deg N (V1). We find that the radial gradient is a decreasing function of radial distance, approximately r(exp -n), with n = 1.7 +/- 0.7. The large-scale radial gradient between the inner and outer heliosphere is much smaller than it was during the last solar minimum period in approximately 1987. The latitudinal gradient is small and positive, 1.3 +/- 0.4 %/deg, as opposed to the large and negative latitudinal gradients found during 1987, but similar to the small positive latitudinal gradient measured during 1976 for anomalous cosmic ray helium. These observations confirm that effects of curvature and gradient drift in the large scale magnetic field of the Sun are important for establishing the three-dimensional intensity distributions of these particles in the heliosphere during periods of solar minimum conditions.

Efficient boundary hunting via vector quantization

NASA Astrophysics Data System (ADS)

Diamantini, Claudia; Panti, Maurizio

2001-03-01

A great amount of information about a classification problem is contained in those instances falling near the decision boundary. This intuition dates back to the earliest studies in pattern recognition, and in the more recent adaptive approaches to the so called boundary hunting, such as the work of Aha et alii on Instance Based Learning and the work of Vapnik et alii on Support Vector Machines. The last work is of particular interest, since theoretical and experimental results ensure the accuracy of boundary reconstruction. However, its optimization approach has heavy computational and memory requirements, which limits its application on huge amounts of data. In the paper we describe an alternative approach to boundary hunting based on adaptive labeled quantization architectures. The adaptation is performed by a stochastic gradient algorithm for the minimization of the error probability. Error probability minimization guarantees the accurate approximation of the optimal decision boundary, while the use of a stochastic gradient algorithm defines an efficient method to reach such approximation. In the paper comparisons to Support Vector Machines are considered.

First-principles study of structural, electronic, linear and nonlinear optical properties of Ga{2}PSb ternary chalcopyrite

NASA Astrophysics Data System (ADS)

Ouahrani, T.; Reshak, A. H.; de La Roza, A. Otero; Mebrouki, M.; Luaña, V.; Khenata, R.; Amrani, B.

2009-12-01

We report results from first-principles density functional calculations using the full-potential linear augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) and the Engel-Vosko-generalized gradient approximation (EV-GGA) were used for the exchange-correlation energy of the structural, electronic, linear and nonlinear optical properties of the chalcopyrite Ga2PSb compound. The valence band maximum (VBM) is located at the Γv point, and the conduction band minimum (CBM) is located at the Γc point, resulting in a direct band gap of about 0.365 eV for GGA and 0.83 eV for EV-GGA. In comparison with the experimental one (1.2 eV) we found that EV-GGA calculation gives energy gap in reasonable agreement with the experiment. The spin orbit coupling has marginal influence on the optical properties. The ground state quantities such as lattice parameters (a, c and u), bulk modules B and its pressure derivative B^primeare evaluated.

Gradient free energy in the axially anisotropic superfluid phases of /sup 3/He in the BCS approximation

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

Brand, H.; Doerfle, M.

1981-02-01

We present the gradient free energy in the BCS approximation for the A phase in high magnetic fields and the A/sub 1/ phase. The A phase without external magnetic field, which has been considered previously by Blount and Cross, emerges as a special case of the result for the A phase in high magnetic fields.

Kurtosis Approach for Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Improving the time efficiency of the Fourier synthesis method for slice selection in magnetic resonance imaging.

PubMed

Tahayori, B; Khaneja, N; Johnston, L A; Farrell, P M; Mareels, I M Y

2016-01-01

The design of slice selective pulses for magnetic resonance imaging can be cast as an optimal control problem. The Fourier synthesis method is an existing approach to solve these optimal control problems. In this method the gradient field as well as the excitation field are switched rapidly and their amplitudes are calculated based on a Fourier series expansion. Here, we provide a novel insight into the Fourier synthesis method via representing the Bloch equation in spherical coordinates. Based on the spherical Bloch equation, we propose an alternative sequence of pulses that can be used for slice selection which is more time efficient compared to the original method. Simulation results demonstrate that while the performance of both methods is approximately the same, the required time for the proposed sequence of pulses is half of the original sequence of pulses. Furthermore, the slice selectivity of both sequences of pulses changes with radio frequency field inhomogeneities in a similar way. We also introduce a measure, referred to as gradient complexity, to compare the performance of both sequences of pulses. This measure indicates that for a desired level of uniformity in the excited slice, the gradient complexity for the proposed sequence of pulses is less than the original sequence. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

A simple orbit-attitude coupled modelling method for large solar power satellites

NASA Astrophysics Data System (ADS)

Li, Qingjun; Wang, Bo; Deng, Zichen; Ouyang, Huajiang; Wei, Yi

2018-04-01

A simple modelling method is proposed to study the orbit-attitude coupled dynamics of large solar power satellites based on natural coordinate formulation. The generalized coordinates are composed of Cartesian coordinates of two points and Cartesian components of two unitary vectors instead of Euler angles and angular velocities, which is the reason for its simplicity. Firstly, in order to develop natural coordinate formulation to take gravitational force and gravity gradient torque of a rigid body into account, Taylor series expansion is adopted to approximate the gravitational potential energy. The equations of motion are constructed through constrained Hamilton's equations. Then, an energy- and constraint-conserving algorithm is presented to solve the differential-algebraic equations. Finally, the proposed method is applied to simulate the orbit-attitude coupled dynamics and control of a large solar power satellite considering gravity gradient torque and solar radiation pressure. This method is also applicable to dynamic modelling of other rigid multibody aerospace systems.

Numerical simulations of incompressible laminar flows using viscous-inviscid interaction procedures

NASA Astrophysics Data System (ADS)

Shatalov, Alexander V.

The present method is based on Helmholtz velocity decomposition where velocity is written as a sum of irrotational (gradient of a potential) and rotational (correction due to vorticity) components. Substitution of the velocity decomposition into the continuity equation yields an equation for the potential, while substitution into the momentum equations yields equations for the velocity corrections. A continuation approach is used to relate the pressure to the gradient of the potential through a modified Bernoulli's law, which allows the elimination of the pressure variable from the momentum equations. The present work considers steady and unsteady two-dimensional incompressible flows over an infinite cylinder and NACA 0012 airfoil shape. The numerical results are compared against standard methods (stream function-vorticity and SMAC methods) and data available in literature. The results demonstrate that the proposed formulation leads to a good approximation with some possible benefits compared to the available formulations. The method is not restricted to two-dimensional flows and can be used for viscous-inviscid domain decomposition calculations.

Optimization of OT-MACH Filter Generation for Target Recognition

NASA Technical Reports Server (NTRS)

Johnson, Oliver C.; Edens, Weston; Lu, Thomas T.; Chao, Tien-Hsin

2009-01-01

An automatic Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter generator for use in a gray-scale optical correlator (GOC) has been developed for improved target detection at JPL. While the OT-MACH filter has been shown to be an optimal filter for target detection, actually solving for the optimum is too computationally intensive for multiple targets. Instead, an adaptive step gradient descent method was tested to iteratively optimize the three OT-MACH parameters, alpha, beta, and gamma. The feedback for the gradient descent method was a composite of the performance measures, correlation peak height and peak to side lobe ratio. The automated method generated and tested multiple filters in order to approach the optimal filter quicker and more reliably than the current manual method. Initial usage and testing has shown preliminary success at finding an approximation of the optimal filter, in terms of alpha, beta, gamma values. This corresponded to a substantial improvement in detection performance where the true positive rate increased for the same average false positives per image.

Retrieval of phase-derivative discontinuities in digital speckle pattern interferometry fringes using the Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Federico, Alejandro; Kaufmann, Guillermo H.

2004-08-01

We evaluate the application of the Wigner-Ville distribution (WVD) to measure phase gradient maps in digital speckle pattern interferometry (DSPI), when the generated correlation fringes present phase discontinuities. The performance of the WVD method is evaluated using computer-simulated fringes. The influence of the filtering process to smooth DSPI fringes and additional drawbacks that emerge when this method is applied are discussed. A comparison with the conventional method based on the continuous wavelet transform in the stationary phase approximation is also presented.

Inverse kinematic problem for a random gradient medium in geometric optics approximation

NASA Astrophysics Data System (ADS)

Petersen, N. V.

1990-03-01

Scattering at random inhomogeneities in a gradient medium results in systematic deviations of the rays and travel times of refracted body waves from those corresponding to the deterministic velocity component. The character of the difference depends on the parameters of the deterministic and random velocity component. However, at great distances to the source, independently of the velocity parameters (weakly or strongly inhomogeneous medium), the most probable depth of the ray turning point is smaller than that corresponding to the deterministic velocity component, the most probable travel times also being lower. The relative uncertainty in the deterministic velocity component, derived from the mean travel times using methods developed for laterally homogeneous media (for instance, the Herglotz-Wiechert method), is systematic in character, but does not exceed the contrast of velocity inhomogeneities by magnitude. The gradient of the deterministic velocity component has a significant effect on the travel-time fluctuations. The variance at great distances to the source is mainly controlled by shallow inhomogeneities. The travel-time flucutations are studied only for weakly inhomogeneous media.

Statistical Mechanics of the Delayed Reward-Based Learning with Node Perturbation

NASA Astrophysics Data System (ADS)

Hiroshi Saito,; Kentaro Katahira,; Kazuo Okanoya,; Masato Okada,

2010-06-01

In reward-based learning, reward is typically given with some delay after a behavior that causes the reward. In machine learning literature, the framework of the eligibility trace has been used as one of the solutions to handle the delayed reward in reinforcement learning. In recent studies, the eligibility trace is implied to be important for difficult neuroscience problem known as the “distal reward problem”. Node perturbation is one of the stochastic gradient methods from among many kinds of reinforcement learning implementations, and it searches the approximate gradient by introducing perturbation to a network. Since the stochastic gradient method does not require a objective function differential, it is expected to be able to account for the learning mechanism of a complex system, like a brain. We study the node perturbation with the eligibility trace as a specific example of delayed reward-based learning, and analyzed it using a statistical mechanics approach. As a result, we show the optimal time constant of the eligibility trace respect to the reward delay and the existence of unlearnable parameter configurations.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

PubMed

Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PubMed Central

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

First-principles elastic constants of α- and θ-Al2O3

NASA Astrophysics Data System (ADS)

Shang, Shunli; Wang, Yi; Liu, Zi-Kui

2007-03-01

Using an efficient strain-stress method, the first-principles elastic constants cij's of α-Al2O3 and θ-Al2O3 have been predicted within the local density approximation and the generalized gradient approximation. It is indicated that more accurate calculations of cij's can be accomplished by the local density approximation. The predicted cij's of θ-Al2O3 provide helpful guidance for future measurements, especially the predicted negative c15. The present results make the stress estimation in thermally grown oxides containing of α- and θ-Al2O3 possible, which in turn provide helpful insights for preventing the failure of thermal barrier coatings on components in gas-turbine engines.

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics

PubMed Central

Jakse, Noel; Pasturel, Alain

2013-01-01

We present a study of dynamic properties of liquid aluminum using density-functional theory within the local-density (LDA) and generalized gradient (GGA) approximations. We determine the temperature dependence of the self-diffusion coefficient as well the viscosity using direct methods. Comparisons with experimental data favor the LDA approximation to compute dynamic properties of liquid aluminum. We show that the GGA approximation induce more important backscattering effects due to an enhancement of the icosahedral short range order (ISRO) that impact directly dynamic properties like the self-diffusion coefficient. All these results are then used to test the Stokes-Einstein relation and the universal scaling law relating the diffusion coefficient and the excess entropy of a liquid. PMID:24190311

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

A microchip fabricated with a vapor-diffusion self-assembled-monolayer method to transport droplets across superhydrophobic to hydrophilic surfaces.

PubMed

Lai, Yu-Hsuan; Yang, Jing-Tang; Shieh, Dar-Bin

2010-02-21

A wettability gradient to transport a droplet across superhydrophobic to hydrophilic surfaces is fabricated on combining a structure gradient and a self-assembled-monolayer (SAM) gradient. The combination of these two gradients is realized with a simple but versatile SAM technique, in which the textured silicon wafer strip is placed vertically in a bottle that contains a decyltrichlorosilane solution to form concurrently a saturated SAM below the liquid surface and a wettability gradient above. The platform fabricated in this way has a water-contact angle from 151.2 degrees to 39.7 degrees; the self-transport distance is hence increased significantly to about 9 mm. A theoretical model that approximates the shape of a moving drop to a spheroidal cap is developed to predict the self-transport behavior. Satisfactory agreement is shown for most regions except where the hysteresis effect is unmeasurable and an unsymmetrical deformation occurs. A double-directional gradient surface to alter the direction of movement of a droplet is also realized. The platforms we developed serve not only to transport a fluid over a long distance but also for a broad spectrum of biomedical applications such as protein adsorption, cell adhesion and DNA-based biosensors.

Problems with heterogeneous and non-isotropic media or distorted grids

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

Hyman, J.; Shashkov, M.; Steinberg, S.

1996-08-01

This paper defines discretizations of the divergence and flux operators that produce symmetric, positive-definite, and accurate approximations to steady-state diffusion problems. Because discontinuous material properties and highly distorted grids are allowed, the flux operator, rather than the gradient, is used as a fundamental operator to be discretized. Resulting finite-difference scheme is similar to those obtained from the mixed finite-element method.

Influences of a temperature gradient and fluid inertia on acoustic streaming in a standing wave.

PubMed

Thompson, Michael W; Atchley, Anthony A; Maccarone, Michael J

2005-04-01

Following the experimental method of Thompson and Atchley [J. Acoust. Soc. Am. 117, 1828-1838 (2005)] laser Doppler anemometry (LDA) is used to investigate the influences of a thermoacoustically induced axial temperature gradient and of fluid inertia on the acoustic streaming generated in a cylindrical standing-wave resonator filled with air driven sinusoidally at a frequency of 308 Hz. The axial component of Lagrangian streaming velocity is measured along the resonator axis and across the diameter at acoustic-velocity amplitudes of 2.7, 4.3, 6.1, and 8.6 m/s at the velocity antinodes. The magnitude of the axial temperature gradient along the resonator wall is varied between approximately 0 and 8 K/m by repeating measurements with the resonator either surrounded by a water jacket, suspended within an air-filled tank, or wrapped in foam insulation. A significant correlation is observed between the temperature gradient and the behavior of the streaming: as the magnitude of the temperature gradient increases, the magnitude of the streaming decreases and the shape of the streaming cell becomes increasingly distorted. The observed steady-state streaming velocities are not in agreement with any available theory.

Speed and convergence properties of gradient algorithms for optimization of IMRT.

PubMed

Zhang, Xiaodong; Liu, Helen; Wang, Xiaochun; Dong, Lei; Wu, Qiuwen; Mohan, Radhe

2004-05-01

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

Structural, electronic and magnetic properties of LaCr2Si2C: Ab initio calculation, mean field approximation and Monte-Carlo simulation

NASA Astrophysics Data System (ADS)

Endichi, A.; Zaari, H.; Benyoussef, A.; El Kenz, A.

2018-06-01

The magnetic behavior of LaCr2Si2C compound is investigated in this work, using first principle methods, Monte Carlo simulation (MCS) and mean field approximation (MFA). The structural, electronic and magnetic properties are described using ab initio method in the framework of the Generalized Gradient Approximation (GGA), and the Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method implemented in the WIEN2K packages. We have also computed the coupling terms between magnetic atoms which are used in Hamiltonian model. A theoretical study realized by mean field approximation and Monte Carlo Simulation within the Ising model is used to more understand the magnetic properties of this compound. Thereby, our results showed a ferromagnetic ordering of the Cr magnetic moments below the Curie temperature of 30 K (Tc < 30 K) in LaCr2Si2C. Other parameters are also computed as: the magnetization, the energy, the specific heat and the susceptibility. This material shows the small sign of supra-conductivity; and future researches could be focused to enhance the transport and magnetic properties of this system.

Sparse Representation with Spatio-Temporal Online Dictionary Learning for Efficient Video Coding.

PubMed

Dai, Wenrui; Shen, Yangmei; Tang, Xin; Zou, Junni; Xiong, Hongkai; Chen, Chang Wen

2016-07-27

Classical dictionary learning methods for video coding suer from high computational complexity and interfered coding eciency by disregarding its underlying distribution. This paper proposes a spatio-temporal online dictionary learning (STOL) algorithm to speed up the convergence rate of dictionary learning with a guarantee of approximation error. The proposed algorithm incorporates stochastic gradient descents to form a dictionary of pairs of 3-D low-frequency and highfrequency spatio-temporal volumes. In each iteration of the learning process, it randomly selects one sample volume and updates the atoms of dictionary by minimizing the expected cost, rather than optimizes empirical cost over the complete training data like batch learning methods, e.g. K-SVD. Since the selected volumes are supposed to be i.i.d. samples from the underlying distribution, decomposition coecients attained from the trained dictionary are desirable for sparse representation. Theoretically, it is proved that the proposed STOL could achieve better approximation for sparse representation than K-SVD and maintain both structured sparsity and hierarchical sparsity. It is shown to outperform batch gradient descent methods (K-SVD) in the sense of convergence speed and computational complexity, and its upper bound for prediction error is asymptotically equal to the training error. With lower computational complexity, extensive experiments validate that the STOL based coding scheme achieves performance improvements than H.264/AVC or HEVC as well as existing super-resolution based methods in ratedistortion performance and visual quality.

Validating Experimental and Theoretical Langmuir Probe Analyses

NASA Astrophysics Data System (ADS)

Pilling, Lawrence Stuart; Carnegie, Dale

2004-11-01

Analysis of Langmuir probe characteristics contains a paradox in that it is unknown a priori which theory is applicable before it is applied. Often theories are assumed to be correct when certain criteria are met although they may not validate the approach used. We have analysed the Langmuir probe data from cylindrical double and single probes acquired from a DC discharge plasma over a wide variety of conditions. This discharge contains a dual temperature distribution and hence fitting a theoretically generated curve is impractical. To determine the densities an examination of the current theories was necessary. For the conditions where the probe radius is the same order of magnitude as the Debye length, the gradient expected for orbital motion limited (OML) is approximately the same as the radial motion gradients. An analysis of the gradients from the radial motion theory was able to resolve the differences from the OML gradient value of two. The method was also able to determine whether radial or OML theories applied without knowledge of the electron temperature. Only the position of the space charge potential is necessary to determine the applicable theory.

Gradient optimization of finite projected entangled pair states

NASA Astrophysics Data System (ADS)

Liu, Wen-Yuan; Dong, Shao-Jun; Han, Yong-Jian; Guo, Guang-Can; He, Lixin

2017-05-01

Projected entangled pair states (PEPS) methods have been proven to be powerful tools to solve strongly correlated quantum many-body problems in two dimensions. However, due to the high computational scaling with the virtual bond dimension D , in a practical application, PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, frustrated systems. Optimization of the ground state using the imaginary time evolution method with a simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that by combining the imaginary time evolution method with a simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking advantage of massive parallel computing, we can study quantum systems with larger bond dimensions up to D =10 without resorting to any symmetry. Benchmark tests of the method on the J1-J2 model give impressive accuracy compared with exact results.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

NASA Astrophysics Data System (ADS)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

A high speed model-based approach for wavefront sensorless adaptive optics systems

NASA Astrophysics Data System (ADS)

Lianghua, Wen; Yang, Ping; Shuai, Wang; Wenjing, Liu; Shanqiu, Chen; Xu, Bing

2018-02-01

To improve temporal-frequency property of wavefront sensorless adaptive optics (AO) systems, a fast general model-based aberration correction algorithm is presented. The fast general model-based approach is based on the approximately linear relation between the mean square of the aberration gradients and the second moment of far-field intensity distribution. The presented model-based method is capable of completing a mode aberration effective correction just applying one disturbing onto the deformable mirror(one correction by one disturbing), which is reconstructed by the singular value decomposing the correlation matrix of the Zernike functions' gradients. Numerical simulations of AO corrections under the various random and dynamic aberrations are implemented. The simulation results indicate that the equivalent control bandwidth is 2-3 times than that of the previous method with one aberration correction after applying N times disturbing onto the deformable mirror (one correction by N disturbing).

Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates

NASA Astrophysics Data System (ADS)

Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma

2016-10-01

This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.

Low-memory iterative density fitting.

PubMed

Grajciar, Lukáš

2015-07-30

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

Frequency-domain elastic full waveform inversion using encoded simultaneous sources

NASA Astrophysics Data System (ADS)

Jeong, W.; Son, W.; Pyun, S.; Min, D.

2011-12-01

Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results provided by the approximate Hessian matrix, it is noted that the latter are better than the former for deeper parts of the model. This work was financially supported by the Brain Korea 21 project of Energy System Engineering, by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0006155), by the Energy Efficiency & Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 2010T100200133).

A study of the radiative transfer equation using a spherical harmonics-nodal collocation method

NASA Astrophysics Data System (ADS)

Capilla, M. T.; Talavera, C. F.; Ginestar, D.; Verdú, G.

2017-03-01

Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.

History matching by spline approximation and regularization in single-phase areal reservoirs

NASA Technical Reports Server (NTRS)

Lee, T. Y.; Kravaris, C.; Seinfeld, J.

1986-01-01

An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity distributions and on the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional real reservoir from well pressure data. The regularization feature of the algorithm is used to convert the ill-posed history matching problem into a well-posed problem. The algorithm employs the conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (non-regularized) automatic history matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.

Control of Complex Dynamic Systems by Neural Networks

NASA Technical Reports Server (NTRS)

Spall, James C.; Cristion, John A.

1993-01-01

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

First-principles calculations for elastic properties of OsB 2 under pressure

NASA Astrophysics Data System (ADS)

Yang, Jun-Wei; Chen, Xiang-Rong; Luo, Fen; Ji, Guang-Fu

2009-11-01

The structure, elastic properties and elastic anisotropy of orthorhombic OsB 2 are investigated by density functional theory method with the ultrasoft pseudopotential scheme in the frame of the generalized gradient approximation (GGA) as well as local density approximation (LDA). The obtained structural parameters, elastic constants, elastic anisotropy and Debye temperature for OsB 2 under pressure are consistent with the available experimental data and other theoretical results. It is found that the elastic constants, bulk modulus and Debye temperature of OsB 2 tend to increase with increasing pressure. It is predicted that OsB 2 is not a superhard material from our calculations.

Kurtosis Approach Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Thermally induced stresses in cross-ply composite tubes

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Cooper, D. E.; Tompkins, S. S.

1986-01-01

An approximate solution for determining stresses in cross-ply composite tubes subjected to a circumferential temperature gradient is presented. The solution is based on the principle of complementary virtual work (PCVW) in conjunction with a Ritz approximation on the stress field and accounts for the temperature dependence of material properties. The PCVW method is compared with a planar elasticity solution using temperature-independent material properties and a Navier approach. The net effect of including temperature-dependent material properties is that the peak absolute values of the stresses are reduced. The dependence of the stresses on the circumferential location is also reduced in comparison with the case of temperature-independent properties.

Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

PubMed

Johnson, Marcus; Kamalapurkar, Rushikesh; Bhasin, Shubhendu; Dixon, Warren E

2015-08-01

An approximate online equilibrium solution is developed for an N -player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics. A Lyapunov-based stability analysis shows that uniformly ultimately bounded tracking is achieved, and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions. The actor, critic, and identifier structures are implemented in real time continuously and simultaneously. Simulations on two and three player games illustrate the performance of the developed method.

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

Castaño-González, E.-E.; Seña, N.; Mendoza-Estrada, V.

In this paper, we carried out first-principles calculations in order to investigate the structural and electronic properties of the binary compound gallium antimonide (GaSb). This theoretical study was carried out using the Density Functional Theory within the plane-wave pseudopotential method. The effects of exchange and correlation (XC) were treated using the functional Local Density Approximation (LDA), generalized gradient approximation (GGA): Perdew–Burke–Ernzerhof (PBE), Perdew-Burke-Ernzerhof revised for solids (PBEsol), Perdew-Wang91 (PW91), revised Perdew–Burke–Ernzerhof (rPBE), Armiento–Mattson 2005 (AM05) and meta-generalized gradient approximation (meta-GGA): Tao–Perdew–Staroverov–Scuseria (TPSS) and revised Tao–Perdew–Staroverov–Scuseria (RTPSS) and modified Becke-Johnson (MBJ). We calculated the densities of state (DOS) and band structuremore » with different XC potentials identified and compared them with the theoretical and experimental results reported in the literature. It was discovered that functional: LDA, PBEsol, AM05 and RTPSS provide the best results to calculate the lattice parameters (a) and bulk modulus (B{sub 0}); while for the cohesive energy (E{sub coh}), functional: AM05, RTPSS and PW91 are closer to the values obtained experimentally. The MBJ, Rtpss and AM05 values found for the band gap energy is slightly underestimated with those values reported experimentally.« less

First principle study of structural, electronic and fermi surface properties of aluminum praseodymium

NASA Astrophysics Data System (ADS)

Shugani, Mani; Aynyas, Mahendra; Sanyal, S. P.

2018-05-01

We present a structural, Electronic and Fermi surface properties of Aluminum Praseodymium (AlPr) using First-principles density functional calculation by using full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation (GGA). The ground state properties along with electronic and Fermi surface properties are studied. It is found that AlPr is metallic and the bonding between Al and Pr is covalent.

Dexamethasone concentration gradients along scala tympani after application to the round window membrane

PubMed Central

Salt, Alec N

2008-01-01

Hypothesis Local application of dexamethasone-21-dihydrogene-phosphate (Dex-P) to the round window membrane (RWM) of guinea pigs produces a substantial basal-apical concentration gradient in scala tympani (ST) perilymph. Background In recent years, intratympanically-applied glucocorticoids are increasingly being used for the treatment of inner ear disease. Although measurements of intracochlear concentrations after round window (RW) application exist, there is limited information on the distribution of these drugs in the inner ear fluids. It has been predicted from computer simulations that substantial concentration gradients will occur with lower concentrations expected in apical turns after RW application. Concentration gradients of other substances along the cochlea have recently been confirmed using a sequential apical sampling method to obtain perilymph. Methods Dex-P (10mg/ml) was administered to the RWM of guinea pigs (n=9) in vivo for 2 to 3 hours. Perilymph was then collected using a protocol in which ten samples, each of approximately 1μl, were taken sequentially from the cochlear apex into capillary tubes. Dex-P concentration of the samples was determined by HPLC. Interpretation of sample data using a finite element model allowed the longitudinal gradients of Dex-P in scala tympani to be quantified. Results The Dex-P content of the first sample in each experiment (dominated by perilymph from apical regions) was substantially lower than that of the third and fourth sample (dominated by basal turn perilymph). These findings qualitatively demonstrated the existence of a concentration gradient along scala tympani (ST). After detailed analysis of the measured sample concentrations using an established finite element computer model, the mean basal-apical concentration gradient was estimated to be 17•103. Both absolute concentrations of Dex-P in ST and the basal-apical gradients were found to vary substantially. Conclusion The existence of substantial basal-apical concentration gradients of Dex-P in ST perilymph was demonstrated experimentally. If the variability in peak concentration and gradient is also present under clinical conditions this may contribute to the heterogeneity of outcome that is observed after intratympanic application of glucocorticoids for various inner ear diseases. PMID:18277312

Push it to the limit: Characterizing the convergence of common sequences of basis sets for intermolecular interactions as described by density functional theory

NASA Astrophysics Data System (ADS)

Witte, Jonathon; Neaton, Jeffrey B.; Head-Gordon, Martin

2016-05-01

With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions—noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms—with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.

Semiempirical methods for computing turbulent flows

NASA Technical Reports Server (NTRS)

Belov, I. A.; Ginzburg, I. P.

1986-01-01

Two semiempirical theories which provide a basis for determining the turbulent friction and heat exchange near a wall are presented: (1) the Prandtl-Karman theory, and (2) the theory utilizing an equation for the energy of turbulent pulsations. A comparison is made between exact numerical methods and approximate integral methods for computing the turbulent boundary layers in the presence of pressure, blowing, or suction gradients. Using the turbulent flow around a plate as an example, it is shown that, when computing turbulent flows with external turbulence, it is preferable to construct a turbulence model based on the equation for energy of turbulent pulsations.

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging.

PubMed

van Dongen, Koen W A; Wright, William M D

2006-10-01

Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

NASA Astrophysics Data System (ADS)

Wang, Tai-Han; Huang, Da-Nian; Ma, Guo-Qing; Meng, Zhao-Hai; Li, Ye

2017-06-01

With the continuous development of full tensor gradiometer (FTG) measurement techniques, three-dimensional (3D) inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit (GPU) and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation (SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm (ICCG). Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit (CPU). Real airborne gravity-gradiometry data from Vinton salt dome (southwest Louisiana, USA) are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Remote loading of doxorubicin into liposomes driven by a transmembrane phosphate gradient.

PubMed

Fritze, Andreas; Hens, Felicitas; Kimpfler, Andrea; Schubert, Rolf; Peschka-Süss, Regine

2006-10-01

This study examines a new method for the remote loading of doxorubicin into liposomes. It was shown that doxorubicin can be loaded to a level of up to 98% into large unilamellar vesicles composed of egg phosphatidylcholine/cholesterol (7/3 mol/mol) with a transmembrane phosphate gradient. The different encapsulation efficiencies which were achieved with ammonium salts (citrate 100%, phosphate 98%, sulfate 95%, acetate 77%) were significantly higher as compared to the loading via sodium salts (citrate 54%, phosphate 52%, sulfate 44%, acetate 16%). Various factors, including pH-value, buffer capacity, solubility of doxorubicin in different salt solutions and base counter-flow, which likely has an influence on drug accumulation in the intraliposomal interior are taken into account. In contrast to other methods, the newly developed remote loading method exhibits a pH-dependent drug release property which may be effective in tumor tissues. At physiological pH-value doxorubicin is retained in the liposomes, whereas drug release is achieved by lowering the pH to 5.5 (approximately 25% release at 25 degrees C or 30% at 37 degrees C within two h). The DXR release of liposomes which were loaded via a sulfate gradient showed a maximum of 3% at pH 5.5.

Heating of metallic implants and instruments induced by gradient switching in a 1.5-Tesla whole-body unit.

PubMed

Graf, Hansjörg; Steidle, Günter; Schick, Fritz

2007-11-01

To examine gradient switching-induced heating of metallic parts. Copper and titanium frames and sheets ( approximately 50 x 50 mm(2), 1.5 mm thick, frame width = 3 mm) surrounded by air were positioned in the scanner perpendicular to the static field horizontally 20 cm off-center. During the execution of a sequence (three-dimensional [3D] true fast imaging with steady precession [True-FISP], TR = 6.4 msec) exploiting the gradient capabilities (maximum gradient = 40 mT/m, maximum slew rate = 200 T/m/second), heating was measured with an infrared camera. Radio frequency (RF) amplitude was set to zero volts. Heating of a copper frame with a narrowing to 1 mm over 20 mm at one side was examined in air and in addition surrounded by several liters of gelled saline using fiber-optic thermography. Further heating studies were performed using an artificial hip made of titanium, and an aluminum replica of the hip prosthesis with the same geometry. For the copper specimens, considerable heating (>10 degrees C) in air and in gelled saline (>1.2 degrees C) could be observed. Heating of the titanium specimens was markedly less ( approximately 1 degrees C in air). For the titanium artificial hip no heating could be detected, while the rise in temperature for the aluminum replica was approximately 2.2 degrees C. Heating of more than 10 degrees C solely due to gradient switching without any RF irradiation was demonstrated in isolated copper wire frames. Under specific conditions (high gradient duty cycle, metallic loop of sufficient inductance and low resistance, power matching) gradient switching-induced heating of conductive specimens must be considered.

Radiative cooling in shock-heated hydrogen-helium plasmas. [for planetary entry probe heat shields

NASA Technical Reports Server (NTRS)

Poon, P. T. Y.; Stickford, G. H., Jr.

1978-01-01

Axial and off-axis radiative cooling of cylindrical shock-heated hydrogen-helium plasmas is investigated theoretically and experimentally. The coupled fluid dynamic-radiative transfer equations are solved by a combination of approximation techniques aimed at simplifying the computation of the flux divergence term, namely, the quasi-isothermal approximation and the exponential approximation developed for the solid angle integration. The accuracy of the approximation schemes has been assessed and found acceptable for applying the methods to the rapid computation of the radiatively coupled flow problem. Radiative cooling experiments were conducted in a 6-inch annular arc accelerator shock tube (ANAA) for an initial pressure of 1 torr and shock speeds from 35 to 45 Km/sec. The results indicate that the lateral cooling is small compared with the axial cooling, and that better agreement is achieved between the data and the theoretical results by inclusion of the lateral temperature gradient.

Ab-initio calculation of EuO doped with 5% of (Ti, V, Cr and Fe): GGA and SIC approximation

NASA Astrophysics Data System (ADS)

Rouchdi, M.; Salmani, E.; Bekkioui, N.; Ez-Zahraouy, H.; Hassanain, N.; Benyoussef, A.; Mzerd, A.

2017-12-01

In this research, a simple theoretical method is proposed to investigate the electronic, magnetic and optical properties of Europium oxide (EuO) doped with 5% of (Ti, V, Cr and Fe). For a basic understanding of these properties, we employed Density-Functional Theory (DFT) based calculations with the Korringa-Kohn-Rostoker code (KKR) combined with the Coherent Potential Approximation (CPA). Also we investigated the half-metallic ferromagnetic behavior of EuO doped with 5% of (Ti, V, Cr and Fe) within the self-interaction-corrected Generalized Gradient Approximation (GGA-SIC). Our calculated results revealed that the Eu0.95TM0.05O is ferromagnetic with a high transition temperature. Moreover, the optical absorption spectra revealed that the half metallicity has been also predicted.

Double-hybrid density-functional theory with meta-generalized-gradient approximations

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

Souvi, Sidi M. O., E-mail: sidi.souvi@irsn.fr; Sharkas, Kamal; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr

2014-02-28

We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.

Rapid dark-blood carotid vessel-wall imaging with random bipolar gradients in a radial SSFP acquisition.

PubMed

Lin, Hung-Yu; Flask, Chris A; Dale, Brian M; Duerk, Jeffrey L

2007-06-01

To investigate and evaluate a new rapid dark-blood vessel-wall imaging method using random bipolar gradients with a radial steady-state free precession (SSFP) acquisition in carotid applications. The carotid artery bifurcations of four asymptomatic volunteers (28-37 years old, mean age = 31 years) were included in this study. Dark-blood contrast was achieved through the use of random bipolar gradients applied prior to the signal acquisition of each radial projection in a balanced SSFP acquisition. The resulting phase variation for moving spins established significant destructive interference in the low-frequency region of k-space. This phase variation resulted in a net nulling of the signal from flowing spins, while the bipolar gradients had a minimal effect on the static spins. The net effect was that the regular SSFP signal amplitude (SA) in stationary tissues was preserved while dark-blood contrast was achieved for moving spins. In this implementation, application of the random bipolar gradient pulses along all three spatial directions nulled the signal from both in-plane and through-plane flow in phantom and in vivo studies. In vivo imaging trials confirmed that dark-blood contrast can be achieved with the radial random bipolar SSFP method, thereby substantially reversing the vessel-to-lumen contrast-to-noise ratio (CNR) of a conventional rectilinear SSFP "bright-blood" acquisition from bright blood to dark blood with only a modest increase in TR (approximately 4 msec) to accommodate the additional bipolar gradients. Overall, this sequence offers a simple and effective dark-blood contrast mechanism for high-SNR SSFP acquisitions in vessel wall imaging within a short acquisition time.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

PubMed

Thygesen, Uffe Høgsbro

2016-03-01

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

Electronic and magnetic properties of NiS2, NiSSe and NiSe2 by a combination of theoretical methods

NASA Astrophysics Data System (ADS)

Schuster, Cosima; Gatti, Matteo; Rubio, Angel

2012-09-01

We investigate the electronic and magnetic properties of NiS2, which, by varying the chemical composition substituting S by Se atoms or applying pressure, can be driven across various electronic and magnetic phase transitions. By combining several theoretical methods, we highlight the different role played by the chalcogen dimers and the volume compression in determining the phase transitions, through variations of the chalcogen p bonding-antibonding gap, the crystal-field splitting and the broadening of the bandwidths. While the generalized gradient approximation (GGA) of density-functional theory fails to reproduce the insulating nature of NiS2, it describes well the magnetic boundaries of the phase diagram. The large GGA delocalization error is corrected to a large extent by the use of GGA + U, hybrid functionals or the self-consistent COHSEX + GW approximation. We also discuss the advantages and the shortcomings of the different approximations in the various regions of the phase diagram of this prototypical correlated compound.

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

PubMed

Lin, Guoxing

2016-11-21

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Stan : A Probabilistic Programming Language

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

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Stan : A Probabilistic Programming Language

DOE PAGES

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; ...

2017-01-01

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Electrokinetic Stabilisation Method of Soft Clay in Pure System using Electrokinetic Geosynthetic Electrode

NASA Astrophysics Data System (ADS)

Azhar, A. T. S.; Jefferson, I.; Madun, A.; Abidin, M. H. Z.; Rogers, C. D. F.

2018-04-01

Electrokinetic stabilisation (EKS) method has the ability to solve the problems of soft highly compressibility soil. This study will present the results from an experimental study of EKS on soft soils using inactive kaolinite clay, inert electrode and distilled water (DW) as a pure system mechanism before any chemical stabilisers being used in this research. Therefore, this will provide a baseline study to improve the efficiency of EKS approach. The test model was using inert electrode of Electrokinetic Geosythentic (EKG) developed at the Newcastle University to apply a constant voltage gradient of 50 V/m across a soil sample approximately 400 mm. Distilled water was used at the pore electrolyte fluid compartments supplied under zero hydraulic gradient conditions for the periods of 3, 7 and 14 days. Throughout the monitoring, physical and chemical characteristics were measured. Results from the monitoring data, physical and chemical properties of the pure system showed the development of pH gradient, the changes of electrical conductivity and chemical concentrations with regards to the distance from anode and treatment periods due to the electrochemical effects even though there was no chemical stabilisers were introduced or released from the degradation of electrodes.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations.

PubMed

Aviat, Félix; Levitt, Antoine; Stamm, Benjamin; Maday, Yvon; Ren, Pengyu; Ponder, Jay W; Lagardère, Louis; Piquemal, Jean-Philip

2017-01-10

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations

PubMed Central

2016-01-01

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration (“peek”), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. PMID:28068773

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Computing the Free Energy along a Reaction Coordinate Using Rigid Body Dynamics.

PubMed

Tao, Peng; Sodt, Alexander J; Shao, Yihan; König, Gerhard; Brooks, Bernard R

2014-10-14

The calculations of potential of mean force along complex chemical reactions or rare events pathways are of great interest because of their importance for many areas in chemistry, molecular biology, and material science. The major difficulty for free energy calculations comes from the great computational cost for adequate sampling of the system in high-energy regions, especially close to the reaction transition state. Here, we present a method, called FEG-RBD, in which the free energy gradients were obtained from rigid body dynamics simulations. Then the free energy gradients were integrated along a reference reaction pathway to calculate free energy profiles. In a given system, the reaction coordinates defining a subset of atoms (e.g., a solute, or the quantum mechanics (QM) region of a quantum mechanics/molecular mechanics simulation) are selected to form a rigid body during the simulation. The first-order derivatives (gradients) of the free energy with respect to the reaction coordinates are obtained through the integration of constraint forces within the rigid body. Each structure along the reference reaction path is separately subjected to such a rigid body simulation. The individual free energy gradients are integrated along the reference pathway to obtain the free energy profile. Test cases provided demonstrate both the strengths and weaknesses of the FEG-RBD method. The most significant benefit of this method comes from the fast convergence rate of the free energy gradient using rigid-body constraints instead of restraints. A correction to the free energy due to approximate relaxation of the rigid-body constraint is estimated and discussed. A comparison with umbrella sampling using a simple test case revealed the improved sampling efficiency of FEG-RBD by a factor of 4 on average. The enhanced efficiency makes this method effective for calculating the free energy of complex chemical reactions when the reaction coordinate can be unambiguously defined by a small subset of atoms within the system.

Computing the Free Energy along a Reaction Coordinate Using Rigid Body Dynamics

PubMed Central

2015-01-01

The calculations of potential of mean force along complex chemical reactions or rare events pathways are of great interest because of their importance for many areas in chemistry, molecular biology, and material science. The major difficulty for free energy calculations comes from the great computational cost for adequate sampling of the system in high-energy regions, especially close to the reaction transition state. Here, we present a method, called FEG-RBD, in which the free energy gradients were obtained from rigid body dynamics simulations. Then the free energy gradients were integrated along a reference reaction pathway to calculate free energy profiles. In a given system, the reaction coordinates defining a subset of atoms (e.g., a solute, or the quantum mechanics (QM) region of a quantum mechanics/molecular mechanics simulation) are selected to form a rigid body during the simulation. The first-order derivatives (gradients) of the free energy with respect to the reaction coordinates are obtained through the integration of constraint forces within the rigid body. Each structure along the reference reaction path is separately subjected to such a rigid body simulation. The individual free energy gradients are integrated along the reference pathway to obtain the free energy profile. Test cases provided demonstrate both the strengths and weaknesses of the FEG-RBD method. The most significant benefit of this method comes from the fast convergence rate of the free energy gradient using rigid-body constraints instead of restraints. A correction to the free energy due to approximate relaxation of the rigid-body constraint is estimated and discussed. A comparison with umbrella sampling using a simple test case revealed the improved sampling efficiency of FEG-RBD by a factor of 4 on average. The enhanced efficiency makes this method effective for calculating the free energy of complex chemical reactions when the reaction coordinate can be unambiguously defined by a small subset of atoms within the system. PMID:25328492

A practical approach for predicting retention time shifts due to pressure and temperature gradients in ultra-high-pressure liquid chromatography.

PubMed

Åsberg, Dennis; Chutkowski, Marcin; Leśko, Marek; Samuelsson, Jörgen; Kaczmarski, Krzysztof; Fornstedt, Torgny

2017-01-06

Large pressure gradients are generated in ultra-high-pressure liquid chromatography (UHPLC) using sub-2μm particles causing significant temperature gradients over the column due to viscous heating. These pressure and temperature gradients affect retention and ultimately result in important selectivity shifts. In this study, we developed an approach for predicting the retention time shifts due to these gradients. The approach is presented as a step-by-step procedure and it is based on empirical linear relationships describing how retention varies as a function of temperature and pressure and how the average column temperature increases with the flow rate. It requires only four experiments on standard equipment, is based on straightforward calculations, and is therefore easy to use in method development. The approach was rigorously validated against experimental data obtained with a quality control method for the active pharmaceutical ingredient omeprazole. The accuracy of retention time predictions was very good with relative errors always less than 1% and in many cases around 0.5% (n=32). Selectivity shifts observed between omeprazole and the related impurities when changing the flow rate could also be accurately predicted resulting in good estimates of the resolution between critical peak pairs. The approximations which the presented approach are based on were all justified. The retention factor as a function of pressure and temperature was studied in an experimental design while the temperature distribution in the column was obtained by solving the fundamental heat and mass balance equations for the different experimental conditions. We strongly believe that this approach is sufficiently accurate and experimentally feasible for this separation to be a valuable tool when developing a UHPLC method. After further validation with other separation systems, it could become a useful approach in UHPLC method development, especially in the pharmaceutical industry where demands are high for robustness and regulatory oversight. Copyright © 2016 Elsevier B.V. All rights reserved.

Turbulent heat transfer prediction method for application to scramjet engines

NASA Technical Reports Server (NTRS)

Pinckney, S. Z.

1974-01-01

An integral method for predicting boundary layer development in turbulent flow regions on two-dimensional or axisymmetric bodies was developed. The method has the capability of approximating nonequilibrium velocity profiles as well as the local surface friction in the presence of a pressure gradient. An approach was developed for the problem of predicting the heat transfer in a turbulent boundary layer in the presence of a high pressure gradient. The solution was derived with particular emphasis on its applicability to supersonic combustion; thus, the effects of real gas flows were included. The resulting integrodifferential boundary layer method permits the estimation of cooling reguirements for scramjet engines. Theoretical heat transfer results are compared with experimental combustor and noncombustor heat transfer data. The heat transfer method was used in the development of engine design concepts which will produce an engine with reduced cooling requirements. The Langley scramjet engine module was designed by utilizing these design concepts and this engine design is discussed along with its corresponding cooling requirements. The heat transfer method was also used to develop a combustor cooling correlation for a combustor whose local properties are computed one dimensionally by assuming a linear area variation and a given heat release schedule.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

A high-order staggered meshless method for elliptic problems

DOE PAGES

Trask, Nathaniel; Perego, Mauro; Bochev, Pavel Blagoveston

2017-03-21

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attainsmore » $$O(h^{m})$$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.« less

Front dynamics and entanglement in the XXZ chain with a gradient

NASA Astrophysics Data System (ADS)

Eisler, Viktor; Bauernfeind, Daniel

2017-11-01

We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field, it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Recent work on material interface reconstruction

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

Mosso, S.J.; Swartz, B.K.

1997-12-31

For the last 15 years, many Eulerian codes have relied on a series of piecewise linear interface reconstruction algorithms developed by David Youngs. In a typical Youngs` method, the material interfaces were reconstructed based upon nearly cell values of volume fractions of each material. The interfaces were locally represented by linear segments in two dimensions and by pieces of planes in three dimensions. The first step in such reconstruction was to locally approximate an interface normal. In Youngs` 3D method, a local gradient of a cell-volume-fraction function was estimated and taken to be the local interface normal. A linear interfacemore » was moved perpendicular to the now known normal until the mass behind it matched the material volume fraction for the cell in question. But for distorted or nonorthogonal meshes, the gradient normal estimate didn`t accurately match that of linear material interfaces. Moreover, curved material interfaces were also poorly represented. The authors will present some recent work in the computation of more accurate interface normals, without necessarily increasing stencil size. Their estimate of the normal is made using an iterative process that, given mass fractions for nearby cells of known but arbitrary variable density, converges in 3 or 4 passes in practice (and quadratically--like Newton`s method--in principle). The method reproduces a linear interface in both orthogonal and nonorthogonal meshes. The local linear approximation is generally 2nd-order accurate, with a 1st-order accurate normal for curved interfaces in both two and three dimensional polyhedral meshes. Recent work demonstrating the interface reconstruction for curved surfaces will /be discussed.« less

Variational and perturbative formulations of quantum mechanical/molecular mechanical free energy with mean-field embedding and its analytical gradients.

PubMed

Yamamoto, Takeshi

2008-12-28

Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an S(N)2 Menshutkin reaction in water, NH(3)+CH(3)Cl-->NH(3)CH(3) (+)+Cl(-), for which free energy profiles are obtained at the Hartree-Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be <0.5 kcal/mol using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water.

Wetting of flat gradient surfaces.

PubMed

Bormashenko, Edward

2018-04-01

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed. Copyright © 2018 Elsevier Inc. All rights reserved.

Density functional theory calculations of III-N based semiconductors with mBJLDA

NASA Astrophysics Data System (ADS)

Gürel, Hikmet Hakan; Akıncı, Özden; Ünlü, Hilmi

2017-02-01

In this work, we present first principles calculations based on a full potential linear augmented plane-wave method (FP-LAPW) to calculate structural and electronic properties of III-V based nitrides such as GaN, AlN, InN in a zinc-blende cubic structure. First principles calculation using the local density approximation (LDA) and generalized gradient approximation (GGA) underestimate the band gap. We proposed a new potential called modified Becke-Johnson local density approximation (MBJLDA) that combines modified Becke-Johnson exchange potential and the LDA correlation potential to get better band gap results compared to experiment. We compared various exchange-correlation potentials (LSDA, GGA, HSE, and MBJLDA) to determine band gaps and structural properties of semiconductors. We show that using MBJLDA density potential gives a better agreement with experimental data for band gaps III-V nitrides based semiconductors.

ShinyKGode: an interactive application for ODE parameter inference using gradient matching.

PubMed

Wandy, Joe; Niu, Mu; Giurghita, Diana; Daly, Rónán; Rogers, Simon; Husmeier, Dirk

2018-07-01

Mathematical modelling based on ordinary differential equations (ODEs) is widely used to describe the dynamics of biological systems, particularly in systems and pathway biology. Often the kinetic parameters of these ODE systems are unknown and have to be inferred from the data. Approximate parameter inference methods based on gradient matching (which do not require performing computationally expensive numerical integration of the ODEs) have been getting popular in recent years, but many implementations are difficult to run without expert knowledge. Here, we introduce ShinyKGode, an interactive web application to perform fast parameter inference on ODEs using gradient matching. ShinyKGode can be used to infer ODE parameters on simulated and observed data using gradient matching. Users can easily load their own models in Systems Biology Markup Language format, and a set of pre-defined ODE benchmark models are provided in the application. Inferred parameters are visualized alongside diagnostic plots to assess convergence. The R package for ShinyKGode can be installed through the Comprehensive R Archive Network (CRAN). Installation instructions, as well as tutorial videos and source code are available at https://joewandy.github.io/shinyKGode. Supplementary data are available at Bioinformatics online.

Validating experimental and theoretical Langmuir probe analyses

NASA Astrophysics Data System (ADS)

Pilling, L. S.; Carnegie, D. A.

2007-08-01

Analysis of Langmuir probe characteristics contains a paradox in that it is unknown a priori which theory is applicable before it is applied. Often theories are assumed to be correct when certain criteria are met although they may not validate the approach used. We have analysed the Langmuir probe data from cylindrical double and single probes acquired from a dc discharge plasma over a wide variety of conditions. This discharge contains a dual-temperature distribution and hence fitting a theoretically generated curve is impractical. To determine the densities, an examination of the current theories was necessary. For the conditions where the probe radius is the same order of magnitude as the Debye length, the gradient expected for orbital-motion limited (OML) is approximately the same as the radial-motion gradients. An analysis of the 'gradients' from the radial-motion theory was able to resolve the differences from the OML gradient value of two. The method was also able to determine whether radial or OML theories applied without knowledge of the electron temperature, or separation of the ion and electron contributions. Only the value of the space potential is necessary to determine the applicable theory.

Gradient descent for robust kernel-based regression

NASA Astrophysics Data System (ADS)

Guo, Zheng-Chu; Hu, Ting; Shi, Lei

2018-06-01

In this paper, we study the gradient descent algorithm generated by a robust loss function over a reproducing kernel Hilbert space (RKHS). The loss function is defined by a windowing function G and a scale parameter σ, which can include a wide range of commonly used robust losses for regression. There is still a gap between theoretical analysis and optimization process of empirical risk minimization based on loss: the estimator needs to be global optimal in the theoretical analysis while the optimization method can not ensure the global optimality of its solutions. In this paper, we aim to fill this gap by developing a novel theoretical analysis on the performance of estimators generated by the gradient descent algorithm. We demonstrate that with an appropriately chosen scale parameter σ, the gradient update with early stopping rules can approximate the regression function. Our elegant error analysis can lead to convergence in the standard L 2 norm and the strong RKHS norm, both of which are optimal in the mini-max sense. We show that the scale parameter σ plays an important role in providing robustness as well as fast convergence. The numerical experiments implemented on synthetic examples and real data set also support our theoretical results.

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Flow structure in continuous flow electrophoresis chambers

NASA Technical Reports Server (NTRS)

Deiber, J. A.; Saville, D. A.

1982-01-01

There are at least two ways that hydrodynamic processes can limit continiuous flow electrophoresis. One arises from the sensitivity of the flow to small temerature gradients, especially at low flow rates and power levels. This sensitivity can be suppressed, at least in principle, by providing a carefully tailored, stabilizing temperature gradient in the cooling system that surrounds the flow channel. At higher power levels another limitation arises due to a restructuring of the main flow. This restructuring is caused by buoyancy, which is in turn affected by the electro-osmotic crossflow. Approximate solutions to appropriate partial differential equations have been computed by finite difference methods. One set of results is described here to illustrate the strong coupling between the structure of the main (axial) flow and the electro-osmotic flow.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table.

PubMed

Aquilante, Francesco; Autschbach, Jochen; Carlson, Rebecca K; Chibotaru, Liviu F; Delcey, Mickaël G; De Vico, Luca; Fdez Galván, Ignacio; Ferré, Nicolas; Frutos, Luis Manuel; Gagliardi, Laura; Garavelli, Marco; Giussani, Angelo; Hoyer, Chad E; Li Manni, Giovanni; Lischka, Hans; Ma, Dongxia; Malmqvist, Per Åke; Müller, Thomas; Nenov, Artur; Olivucci, Massimo; Pedersen, Thomas Bondo; Peng, Daoling; Plasser, Felix; Pritchard, Ben; Reiher, Markus; Rivalta, Ivan; Schapiro, Igor; Segarra-Martí, Javier; Stenrup, Michael; Truhlar, Donald G; Ungur, Liviu; Valentini, Alessio; Vancoillie, Steven; Veryazov, Valera; Vysotskiy, Victor P; Weingart, Oliver; Zapata, Felipe; Lindh, Roland

2016-02-15

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization. © 2015 Wiley Periodicals, Inc.

Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

Győrffy, Werner; Knizia, Gerald; Werner, Hans-Joachim

2017-12-01

We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.

The quiet evening auroral arc and the structure of the growth phase near-Earth plasma sheet

NASA Astrophysics Data System (ADS)

Coroniti, F. V.; Pritchett, P. L.

2014-03-01

The plasma pressure and current configuration of the near-Earth plasma sheet that creates and sustains the quiet evening auroral arc during the growth phase of magnetospheric substorms is investigated. We propose that the quiet evening arc (QEA) connects to the thin near-Earth current sheet, which forms during the development of the growth phase enhancement of convection. The current sheet's large polarization electric fields are shielded from the ionosphere by an Inverted-V parallel potential drop, thereby producing the electron precipitation responsible for the arc's luminosity. The QEA is located in the plasma sheet region of maximal radial pressure gradient and, in the east-west direction, follows the vanishing of the approximately dawn-dusk-directed gradient or fold in the plasma pressure. In the evening sector, the boundary between the Region1 and Region 2 current systems occurs where the pressure maximizes (approximately radial gradient of the pressure vanishes) and where the approximately radial gradient of the magnetic flux tube volume also vanishes in an inflection region. The proposed intricate balance of plasma sheet pressure and currents may well be very sensitive to disruption by the arrival of equatorward traveling auroral streamers and their associated earthward traveling dipolarization fronts.

Hubble Space Telescope Medium Deep Survey. 2: Deconvolution of Wide Field Camera field galaxy images in the 13 hour + 43 deg field

NASA Technical Reports Server (NTRS)

Windhorst, R. A.; Schmidtke, P. C.; Pascarelle, S. M.; Gordon, J. M.; Griffiths, R. E.; Ratnatunga, K. U.; Neuschaefer, L. W.; Ellis, R. S.; Gilmore, G.; Glazebrook, K.

1994-01-01

We present isophotal profiles of six faint field galaxies from some of the first deep images taken for the Hubble Space Telescope (HST) Medium Deep Survey (MDS). These have redshifts in the range z = 0.126 to 0.402. The images were taken with the Wide Field Camera (WFC) in `parallel mode' and deconvolved with the Lucy method using as the point-spread function nearby stars in the image stack. The WFC deconvolutions have a dynamic range of 16 to 20 dB (4 to 5 mag) and an effective resolution approximately less than 0.2 sec (FWHM). The multiorbit HST images allow us to trace the morphology, light profiles, and color gradients of faint field galaxies down to V approximately equal to 22 to 23 mag at sub-kpc resolution, since the redshift range covered is z = 0.1 to 0.4. The goals of the MDS are to study the sub-kpc scale morphology, light profiles, and color gradients for a large samole of faint field galaxies down to V approximately equal to 23 mag, and to trace the fraction of early to late-type galaxies as function of cosmic time. In this paper we study the brighter MDS galaxies in the 13 hour + 43 deg MDS field in detail, and investigate to what extent model fits with pure exponential disks or a(exp 1/4) bulges are justified at V approximately less than 22 mag. Four of the six field galaxies have light profiles that indicate (small) inner bulges following r(exp 1/4) laws down to 0.2 sec resolution, plus a dominant surrounding exponential disk with little or no color gradients. Two occur in a group at z = 0.401, two are barred spiral galaxies at z = 0.179 and z = 0.302, and two are rather subluminous (and edge-on) disk galaxies at z = 0.126 and z = 0.179. Our deep MDS images can detect galaxies down to V, I approximately less than 25 to 26 mag, and demonstrate the impressive potential of HST--even with its pre-refurbished optics--to resolve morphological details in galaxies at cosmologically significant distances (v approximately less than 23 mag). Since the median redshift of these galaxies is approximately less than 0.4, the HST resolution allows us to study sub kpc size scales at the galaxy, which cannot be done with stable images over wide fields from the best ground-based sites.

The magnetic lead field theorem in the quasi-static approximation and its use for magnetoencephalography forward calculation in realistic volume conductors.

PubMed

Nolte, Guido

2003-11-21

The equation for the magnetic lead field for a given magnetoencephalography (MEG) channel is well known for arbitrary frequencies omega but is not directly applicable to MEG in the quasi-static approximation. In this paper we derive an equation for omega = 0 starting from the very definition of the lead field instead of using Helmholtz's reciprocity theorems. The results are (a) the transpose of the conductivity times the lead field is divergence-free, and (b) the lead field differs from the one in any other volume conductor by a gradient of a scalar function. Consequently, for a piecewise homogeneous and isotropic volume conductor, the lead field is always tangential at the outermost surface. Based on this theoretical result, we formulated a simple and fast method for the MEG forward calculation for one shell of arbitrary shape: we correct the corresponding lead field for a spherical volume conductor by a superposition of basis functions, gradients of harmonic functions constructed here from spherical harmonics, with coefficients fitted to the boundary conditions. The algorithm was tested for a prolate spheroid of realistic shape for which the analytical solution is known. For high order in the expansion, we found the solutions to be essentially exact and for reasonable accuracies much fewer multiplications are needed than in typical implementations of the boundary element methods. The generalization to more shells is straightforward.

Large CO 2 effluxes at night and during synoptic weather events significantly contribute to CO 2 emissions from a reservoir

DOE PAGES

Liu, Heping; Zhang, Qianyu; Katul, Gabriel G.; ...

2016-05-24

CO 2 emissions from inland waters are commonly determined by indirect methods that are based on the product of a gas transfer coefficient and the concentration gradient at the air water interface (e.g., wind-based gas transfer models). The measurements of concentration gradient are typically collected during the day in fair weather throughout the course of a year. Direct measurements of eddy covariance CO 2 fluxes from a large inland water body (Ross Barnett reservoir, Mississippi, USA) show that CO 2 effluxes at night are approximately 70% greater than those during the day. At longer time scales, frequent synoptic weather eventsmore » associated with extratropical cyclones induce CO 2 flux pulses, resulting in further increase in annual CO 2 effluxes by 16%. Therefore, CO 2 emission rates from this reservoir, if these diel and synoptic processes are under-sampled, are likely to be underestimated by approximately 40%. Our results also indicate that the CO 2 emission rates from global inland waters reported in the literature, when based on indirect methods, are likely underestimated. Field samplings and indirect modeling frameworks that estimate CO 2 emissions should account for both daytime-nighttime efflux difference and enhanced emissions during synoptic weather events. Furthermore, the analysis here can guide carbon emission sampling to improve regional carbon estimates.« less

Large CO 2 effluxes at night and during synoptic weather events significantly contribute to CO 2 emissions from a reservoir

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

Liu, Heping; Zhang, Qianyu; Katul, Gabriel G.

CO 2 emissions from inland waters are commonly determined by indirect methods that are based on the product of a gas transfer coefficient and the concentration gradient at the air water interface (e.g., wind-based gas transfer models). The measurements of concentration gradient are typically collected during the day in fair weather throughout the course of a year. Direct measurements of eddy covariance CO 2 fluxes from a large inland water body (Ross Barnett reservoir, Mississippi, USA) show that CO 2 effluxes at night are approximately 70% greater than those during the day. At longer time scales, frequent synoptic weather eventsmore » associated with extratropical cyclones induce CO 2 flux pulses, resulting in further increase in annual CO 2 effluxes by 16%. Therefore, CO 2 emission rates from this reservoir, if these diel and synoptic processes are under-sampled, are likely to be underestimated by approximately 40%. Our results also indicate that the CO 2 emission rates from global inland waters reported in the literature, when based on indirect methods, are likely underestimated. Field samplings and indirect modeling frameworks that estimate CO 2 emissions should account for both daytime-nighttime efflux difference and enhanced emissions during synoptic weather events. Furthermore, the analysis here can guide carbon emission sampling to improve regional carbon estimates.« less

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

On the usefulness of gradient information in multi-objective deformable image registration using a B-spline-based dual-dynamic transformation model: comparison of three optimization algorithms

NASA Astrophysics Data System (ADS)

Pirpinia, Kleopatra; Bosman, Peter A. N.; Sonke, Jan-Jakob; van Herk, Marcel; Alderliesten, Tanja

2015-03-01

The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial

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

NASA Astrophysics Data System (ADS)

Zhu, Minjie; Scott, Michael H.

2017-07-01

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

An interior-point method for total variation regularized positron emission tomography image reconstruction

NASA Astrophysics Data System (ADS)

Bai, Bing

2012-03-01

There has been a lot of work on total variation (TV) regularized tomographic image reconstruction recently. Many of them use gradient-based optimization algorithms with a differentiable approximation of the TV functional. In this paper we apply TV regularization in Positron Emission Tomography (PET) image reconstruction. We reconstruct the PET image in a Bayesian framework, using Poisson noise model and TV prior functional. The original optimization problem is transformed to an equivalent problem with inequality constraints by adding auxiliary variables. Then we use an interior point method with logarithmic barrier functions to solve the constrained optimization problem. In this method, a series of points approaching the solution from inside the feasible region are found by solving a sequence of subproblems characterized by an increasing positive parameter. We use preconditioned conjugate gradient (PCG) algorithm to solve the subproblems directly. The nonnegativity constraint is enforced by bend line search. The exact expression of the TV functional is used in our calculations. Simulation results show that the algorithm converges fast and the convergence is insensitive to the values of the regularization and reconstruction parameters.

On the Concentration Gradient across a Spherical Source Washed by Slow Flow

PubMed Central

Jaffe, Lionel

1965-01-01

A model has been numerically analyzed to help interpret the orienting effects of flow upon cells. The model is a sphere steadily and uniformly emitting a diffusible stuff into a medium otherwise free of it and moving past with Stokes flow. Its properties depend primarily upon the Peclet number, Pe, equal to a · v∞/D, i.e., the sphere's radius, a, times the free stream speed, v∞, over the stuff's diffusion constant, D. As Pe rises, and washing becomes more effective, the average surface concentration, C̄s a falls (Figs. 2 and 5) and the residual material becomes relatively concentrated on the sphere's lee pole (Figs. 2 and 4). Specifically, as Pe rises from 0.1 to 1, the relative concentration gradient, G, rises from 0.7 to 5.0 per cent and to the point where it is rising at about 8 per cent per decade; by Pe 1000, G = 22.1 per cent. From Pe 1 through 1000, G/(1 - C̄s a), or the gradient per concentration deficiency remains at about 26 per cent suggesting that G approaches a ceiling of about 26 per cent. Also from Pe 1 through 1000, the average mass transfer co-efficient nearly equals that previously calculated for spheres maintaining constant surface concentration instead of flux. The complete differential equation without approximations, the Gauss-Seidel method, and an approximation for the outer boundary condition were used. PMID:14268954

Major Depression Prevalence Increases with Latitude in Canada

PubMed Central

Williams, Jeanne V. A.; Lavorato, Dina H.; Wang, Jian Li; Bulloch, Andrew G. M.

2016-01-01

Objective: To determine whether there is an association between latitude and annual major depressive episode (MDE) prevalence in Canada. Methods: Data from 2 national survey programs (the National Population Health Survey and the Canadian Community Health Survey) were used, providing 10 data sets collected between 1996 and 2013, together including 922,260 respondents, of whom 495,739 were assessed for MDE using 1 of 2 versions of the Composite International Diagnostic Interview, a short-form version (8 studies), and a Canadian adaptation of the World Mental Health version (2 studies). Approximate latitude was determined by linkage to postal code data. Data were analyzed using logistic regression and pooled across surveys using individual-level meta-analytic methods. Results: In models including latitude as a continuous variable, a statistically significant association was observed, with prevalence increasing with increasing latitude. This association persisted after adjustment for a set of known risk factors. The latitude gradient was modest in magnitude, a 1% to 2% increase in the prevalence odds of MDE per degree of latitude was observed. Due to sparse data, this gradient cannot be confidently generalized beyond major population centres, which tend to occur at less than 55° latitude in Canada. Conclusion: A latitude gradient has not previously been reported. If replicated, the gradient may have implications for the planning of services and generation of aetiological hypotheses. However, this cross-sectional analysis cannot confirm aetiology and could not evaluate the potential contributions of variables such as light exposure, weather patterns, or social determinants. PMID:27729573

Motion of a Drop on a Solid Surface Due to a Wettability Gradient

NASA Technical Reports Server (NTRS)

Subramanian, R.; Moumen, Nadjoua; McLaughlin, John B.

2005-01-01

The hydrodynamic force experienced by a spherical-cap drop moving on a solid surface is obtained from two approximate analytical solutions and used to predict the quasi-steady speed of the drop in a wettability gradient. One solution is based on approximation of the shape of the drop as a collection of wedges, and the other is based on lubrication theory. Also, asymptotic results from both approximations for small contact angles, as well as an asymptotic result from lubrication theory that is good when the length scale of the drop is large compared with the slip length, are given. The results for the hydrodynamic force also can be used to predict the quasi-steady speed of a drop sliding down an incline.

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

NASA Astrophysics Data System (ADS)

Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

2013-08-01

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

A general strategy for performing temperature-programming in high performance liquid chromatography--prediction of segmented temperature gradients.

PubMed

Wiese, Steffen; Teutenberg, Thorsten; Schmidt, Torsten C

2011-09-28

In the present work it is shown that the linear elution strength (LES) model which was adapted from temperature-programming gas chromatography (GC) can also be employed to predict retention times for segmented-temperature gradients based on temperature-gradient input data in liquid chromatography (LC) with high accuracy. The LES model assumes that retention times for isothermal separations can be predicted based on two temperature gradients and is employed to calculate the retention factor of an analyte when changing the start temperature of the temperature gradient. In this study it was investigated whether this approach can also be employed in LC. It was shown that this approximation cannot be transferred to temperature-programmed LC where a temperature range from 60°C up to 180°C is investigated. Major relative errors up to 169.6% were observed for isothermal retention factor predictions. In order to predict retention times for temperature gradients with different start temperatures in LC, another relationship is required to describe the influence of temperature on retention. Therefore, retention times for isothermal separations based on isothermal input runs were predicted using a plot of the natural logarithm of the retention factor vs. the inverse temperature and a plot of the natural logarithm of the retention factor vs. temperature. It could be shown that a plot of lnk vs. T yields more reliable isothermal/isocratic retention time predictions than a plot of lnk vs. 1/T which is usually employed. Hence, in order to predict retention times for temperature-gradients with different start temperatures in LC, two temperature gradient and two isothermal measurements have been employed. In this case, retention times can be predicted with a maximal relative error of 5.5% (average relative error: 2.9%). In comparison, if the start temperature of the simulated temperature gradient is equal to the start temperature of the input data, only two temperature-gradient measurements are required. Under these conditions, retention times can be predicted with a maximal relative error of 4.3% (average relative error: 2.2%). As an example, the systematic method development for an isothermal as well as a temperature gradient separation of selected sulfonamides by means of the adapted LES model is demonstrated using a pure water mobile phase. Both methods are compared and it is shown that the temperature-gradient separation provides some advantages over the isothermal separation in terms of limits of detection and analysis time. Copyright © 2011 Elsevier B.V. All rights reserved.

Dynamic Sensor Tasking for Space Situational Awareness via Reinforcement Learning

NASA Astrophysics Data System (ADS)

Linares, R.; Furfaro, R.

2016-09-01

This paper studies the Sensor Management (SM) problem for optical Space Object (SO) tracking. The tasking problem is formulated as a Markov Decision Process (MDP) and solved using Reinforcement Learning (RL). The RL problem is solved using the actor-critic policy gradient approach. The actor provides a policy which is random over actions and given by a parametric probability density function (pdf). The critic evaluates the policy by calculating the estimated total reward or the value function for the problem. The parameters of the policy action pdf are optimized using gradients with respect to the reward function. Both the critic and the actor are modeled using deep neural networks (multi-layer neural networks). The policy neural network takes the current state as input and outputs probabilities for each possible action. This policy is random, and can be evaluated by sampling random actions using the probabilities determined by the policy neural network's outputs. The critic approximates the total reward using a neural network. The estimated total reward is used to approximate the gradient of the policy network with respect to the network parameters. This approach is used to find the non-myopic optimal policy for tasking optical sensors to estimate SO orbits. The reward function is based on reducing the uncertainty for the overall catalog to below a user specified uncertainty threshold. This work uses a 30 km total position error for the uncertainty threshold. This work provides the RL method with a negative reward as long as any SO has a total position error above the uncertainty threshold. This penalizes policies that take longer to achieve the desired accuracy. A positive reward is provided when all SOs are below the catalog uncertainty threshold. An optimal policy is sought that takes actions to achieve the desired catalog uncertainty in minimum time. This work trains the policy in simulation by letting it task a single sensor to "learn" from its performance. The proposed approach for the SM problem is tested in simulation and good performance is found using the actor-critic policy gradient method.

First-principles calculations of electronic, magnetic and optical properties of HoN doped with TM (Ti, V, Cr, Mn, Co and Ni)

NASA Astrophysics Data System (ADS)

Rouchdi, M.; Salmani, E.; Dehmani, M.; Ez-Zahraouy, H.; Hassanain, N.; Benyoussef, A.; Mzerd, A.

2018-02-01

Using the first-principles calculations within the Korringa-Kohn-Rostoker (KKR) method combined with the coherent potential approximation (CPA), the structural, optical and magnetic properties of rare-earth nitride Ho0.95TM0.05N doped with transition metal (TM) atoms (Ti, V, Cr, Mn, Co and Ni) are investigated as a function the generalized gradient approximation and self-interaction correction (GGA-SIC) approximation. The optical properties are studied in detail by using ab-initio calculations. Using GGA-SIC we have showed that the bandgap value is in good agreement with the experimental value. Using GGA-SIC approximation for HoN, we have obtained a bandgap of 0.9 eV. Some of the dilute magnetic semiconductors (DMS) like Ho0.95TM0.05N under study exhibit a half-metallic behavior, which makes them suitable for spintronic applications. Moreover, the optical absorption spectra confirm the ferromagnetic stability based on the charge state of magnetic impurities.

About one discrete model of splitting by the physical processes of a piezoconductive medium with gas hydrate inclusions

NASA Astrophysics Data System (ADS)

Poveshchenko, Yu A.; Podryga, V. O.; Rahimly, P. I.; Sharova, Yu S.

2018-01-01

The thermodynamically equilibrium model for splitting by the physical processes of a two-component three-phase filtration fluid dynamics with gas hydrate inclusions is considered in the paper, for which a family of two-layer completely conservative difference schemes of the support operators method with time weights profiled in space is constructed. On the irregular grids of the theory of the support-operators method applied to the specifics of the processes of transfer of saturations and internal energies of water and gas in a medium with gas hydrate inclusions, methods of directwind approximation of these processes are considered. These approximations preserve the continual properties of divergence-gradient operations in their difference form and are related to the velocity field providing saturations transfer and internal energies of fluids. Fluid dynamics with gas hydrate inclusions are also calculated on the basis of the proposed approach, in particular, in areas of severe pressure depression in the collector space.

Trajectory optimization for an asymmetric launch vehicle. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Sullivan, Jeanne Marie

1990-01-01

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1987-01-01

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Quantification of Water Flux in Vesicular Systems.

PubMed

Hannesschläger, Christof; Barta, Thomas; Siligan, Christine; Horner, Andreas

2018-06-04

Water transport across lipid membranes is fundamental to all forms of life and plays a major role in health and disease. However, not only typical water facilitators like aquaporins facilitate water flux, but also transporters, ion channels or receptors represent potent water pathways. The efforts directed towards a mechanistic understanding of water conductivity determinants in transmembrane proteins, the development of water flow inhibitors, and the creation of biomimetic membranes with incorporated membrane proteins or artificial water channels depend on reliable and accurate ways of quantifying water permeabilities P f . A conventional method is to subject vesicles to an osmotic gradient in a stopped-flow device: Fast recordings of scattered light intensity are converted into the time course of vesicle volume change. Even though an analytical solution accurately acquiring P f from scattered light intensities exists, approximations potentially misjudging P f by orders of magnitude are used. By means of computational and experimental data we point out that erroneous results such as that the single channel water permeability p f depends on the osmotic gradient are direct results of such approximations. Finally, we propose an empirical solution of which calculated permeability values closely match those calculated with the analytical solution in the relevant range of parameters.

Absence of B1-B2 structural transition in lithium halides under hydrostatic pressure

NASA Astrophysics Data System (ADS)

de Coss, Romeo; Murrieta, Gabriel

2005-03-01

We have investigated the B1-B2 structural transition in LiF, LiCl, LiBr, and LiI under hydrostatic pressure by means of first-principles total-energy calculations using the Full- Potential LAPW method. In order to analyze the gradient effects, we have performed calculations using the local density approximation (LDA) and the generalized gradient approximation (GGA), for the exchange and correlation potential. In agreement with the experimental observations, we find that even for pressures higher than 100 GPa, the Li halides do not present the B1-B2 structural transition. In order to understand this behavior, we have calculated the distribution of the electron densities. From the analysis of the distribution of electron densities for the Li halides in the B1 and B2 phases, we find that for this group of ionic compounds the B1 phase have a distribution of electron densities more homogeneous than in the B2 phase, preventing the B1-B2 structural transition. This work was partially supported by Consejo Nacional de Ciencia y Tecnolog'ia (CONACYT, M'exico) under Grant No. 43830-F.

Near-edge band structures and band gaps of Cu-based semiconductors predicted by the modified Becke-Johnson potential plus an on-site Coulomb U

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

Zhang, Yubo; Zhang, Jiawei; Wang, Youwei

Diamond-like Cu-based multinary semiconductors are a rich family of materials that hold promise in a wide range of applications. Unfortunately, accurate theoretical understanding of the electronic properties of these materials is hindered by the involvement of Cu d electrons. Density functional theory (DFT) based calculations using the local density approximation or generalized gradient approximation often give qualitative wrong electronic properties of these materials, especially for narrow-gap systems. The modified Becke-Johnson (mBJ) method has been shown to be a promising alternative to more elaborate theory such as the GW approximation for fast materials screening and predictions. However, straightforward applications of themore » mBJ method to these materials still encounter significant difficulties because of the insufficient treatment of the localized d electrons. We show that combining the promise of mBJ potential and the spirit of the well-established DFT + U method leads to a much improved description of the electronic structures, including the most challenging narrow-gap systems. A survey of the band gaps of about 20 Cu-based semiconductors calculated using the mBJ + U method shows that the results agree with reliable values to within ±0.2 eV.« less

Importance of van der Waals interaction on structural, vibrational, and thermodynamic properties of NaCl

NASA Astrophysics Data System (ADS)

Marcondes, Michel L.; Wentzcovitch, Renata M.; Assali, Lucy V. C.

2018-05-01

Thermal equations of state (EOS) are essential in several scientific domains. However, experimental determination of EOS parameters may be limited at extreme conditions, therefore, ab initio calculations have become an important method to obtain them. Density functional theory (DFT) and its extensions with various degrees of approximations for the exchange and correlation (XC) energy is the method of choice, but large errors in the EOS parameters are still common. The alkali halides have been problematic from the onset of this field and the quest for appropriate DFT functionals for such ionic and relatively weakly bonded systems has remained an active topic of research. Here we use DFT + van der Waals functionals to calculate vibrational properties, thermal EOS, thermodynamic properties, and the B1 to B2 phase boundary of NaCl with high precision. Our results reveal a remarkable improvement over the performance of standard local density approximation and generalized gradient approximation functionals for all these properties and phase transition boundary, as well as great sensitivity of anharmonic effects on the choice of XC functional.

The variability of atmospheric equivalent temperature for radar altimeter range correction

NASA Technical Reports Server (NTRS)

Liu, W. Timothy; Mock, Donald

1990-01-01

Two sets of data were used to test the validity of the presently used approximation for radar altimeter range correction due to atmospheric water vapor. The approximation includes an assumption of constant atmospheric equivalent temperature. The first data set includes monthly, three-dimensional, gridded temperature and humidity fields over global oceans for a 10-year period, and the second is comprised of daily or semidaily rawinsonde data at 17 island stations for a 7-year period. It is found that the standard method underestimates the variability of the equivalent temperature, and the approximation could introduce errors of 2 cm for monthly means. The equivalent temperature is found to have a strong meridional gradient, and the highest temporal variabilities are found over western boundary currents. The study affirms that the atmospheric water vapor is a good predictor for both the equivalent temperature and the range correction. A relation is proposed to reduce the error.

A novel single neuron perceptron with universal approximation and XOR computation properties.

PubMed

Lotfi, Ehsan; Akbarzadeh-T, M-R

2014-01-01

We propose a biologically motivated brain-inspired single neuron perceptron (SNP) with universal approximation and XOR computation properties. This computational model extends the input pattern and is based on the excitatory and inhibitory learning rules inspired from neural connections in the human brain's nervous system. The resulting architecture of SNP can be trained by supervised excitatory and inhibitory online learning rules. The main features of proposed single layer perceptron are universal approximation property and low computational complexity. The method is tested on 6 UCI (University of California, Irvine) pattern recognition and classification datasets. Various comparisons with multilayer perceptron (MLP) with gradient decent backpropagation (GDBP) learning algorithm indicate the superiority of the approach in terms of higher accuracy, lower time, and spatial complexity, as well as faster training. Hence, we believe the proposed approach can be generally applicable to various problems such as in pattern recognition and classification.

Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory

NASA Astrophysics Data System (ADS)

Langenbach, K.; Heilig, M.; Horsch, M.; Hasse, H.

2018-03-01

A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO2). The molecular model of CO2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory.

PubMed

Langenbach, K; Heilig, M; Horsch, M; Hasse, H

2018-03-28

A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO 2 ). The molecular model of CO 2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

Nonseparable exchange–correlation functional for molecules, including homogeneous catalysis involving transition metals

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

Yu, Haoyu S.; Zhang, Wenjing; Verma, Pragya

2015-01-01

The goal of this work is to develop a gradient approximation to the exchange–correlation functional of Kohn–Sham density functional theory for treating molecular problems with a special emphasis on the prediction of quantities important for homogeneous catalysis and other molecular energetics. Our training and validation of exchange–correlation functionals is organized in terms of databases and subdatabases. The key properties required for homogeneous catalysis are main group bond energies (database MGBE137), transition metal bond energies (database TMBE32), reaction barrier heights (database BH76), and molecular structures (database MS10). We also consider 26 other databases, most of which are subdatabases of a newlymore » extended broad database called Database 2015, which is presented in the present article and in its ESI. Based on the mathematical form of a nonseparable gradient approximation (NGA), as first employed in the N12 functional, we design a new functional by using Database 2015 and by adding smoothness constraints to the optimization of the functional. The resulting functional is called the gradient approximation for molecules, or GAM. The GAM functional gives better results for MGBE137, TMBE32, and BH76 than any available generalized gradient approximation (GGA) or than N12. The GAM functional also gives reasonable results for MS10 with an MUE of 0.018 Å. The GAM functional provides good results both within the training sets and outside the training sets. The convergence tests and the smooth curves of exchange–correlation enhancement factor as a function of the reduced density gradient show that the GAM functional is a smooth functional that should not lead to extra expense or instability in optimizations. NGAs, like GGAs, have the advantage over meta-GGAs and hybrid GGAs of respectively smaller grid-size requirements for integrations and lower costs for extended systems. These computational advantages combined with the relatively high accuracy for all the key properties needed for molecular catalysis make the GAM functional very promising for future applications.« less

A General Method for Solving Systems of Non-Linear Equations

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)

1995-01-01

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Comparison of infrared thermometer with thermocouple for monitoring skin temperature.

PubMed

Matsukawa, T; Ozaki, M; Nishiyama, T; Imamura, M; Kumazawa, T

2000-02-01

To test the hypothesis that the infrared thermometer (Genius) is comparably useful with thermocouples that are routinely used for skin temperature monitoring. Prospective, controlled, not blinded study. Operating room of a university hospital. Ten healthy male volunteers. Volunteers were minimally clothed and were initially warmed by a forced air warmer until they became vasodilated at the finger and the foot for approximately 30 mins. Subsequently, they were kept in the room with no blanket. Skin temperatures were measured continuously with the Mon-a-Therm thermocouple and were also measured with the Genius thermometer just before and after the warming and subsequently every 10 mins for 70 mins. Forearm and finger-tip skin temperatures and skin-surface temperature gradients (from arm to finger and from calf to toe) measured by the Genius thermometer were compared with those measured by the Mon-a-Therm thermocouple using linear regression and Bland and Altman statistics. Forearm temperature and finger-tip temperature ranged from approximately 31 degrees to approximately 36.5 degrees C (87.8-97.7 degrees F) and approximately 22.5 degrees to approximately 36 degrees C (72.5-96.8 degrees F), respectively. Gradients (from arm to finger and from calf to toe) ranged from approximately -3 degrees to approximately 10 degrees C (26.6-50.0 degrees F) and approximately -3 degrees to approximately 11 degrees C (26.6-51.8 degrees F), respectively. Correlations between the temperatures measured by the Genius thermometer and those by the Mon-a-Therm thermocouple were similar and reliable. The correlation coefficients were as follows: 0.78 at forearm, 0.97 at finger-tip, and 0.97 at skin-surface temperature gradients. The infrared thermometer with a special probe is useful to measure the change of skin-surface temperatures and to evaluate the severity of shock in patients.

Time-Parallel Solutions to Ordinary Differential Equations on GPUs with a New Functional Optimization Approach Related to the Sobolev Gradient Method

DTIC Science & Technology

2012-10-01

black and approximations in cyan and magenta. The second ODE is the pendulum equation, given by: This ODE was also implemented using Crank...The drawback of approaches like the one proposed can be observed with a very simple example. Suppose vector is found by applying 4 linear...public release; distribution unlimited Figure 2. A phase space plot of the Pendulum example. Fine solution (black) contains 32768 time steps

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

Verma, U. P.; Nayak, V.

Quantum mechanical first principle calculations have been performed to study the electronic and structural properties of TiN and TiAs in zinc blende (ZB) and rock salt (RS) structures. The full-potential linearized augmented plane wave (FP-LAPW) method has been used within the framework of density functional theory (DFT). The exchange correlation functional has been solved employing generalized gradient approximation (GGA). Our predicted results for lattice constants are in good agreement with the earlier findings. The electronic band structures of TiX are metallic in both the phases.

Ab-initio study of electronic structure and elastic properties of ZrC

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

Mund, H. S., E-mail: hmoond@gmail.com; Ahuja, B. L.

2016-05-23

The electronic and elastic properties of ZrC have been investigated using the linear combination of atomic orbitals method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within generalized gradient approximation. We have computed energy bands, density of states, elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the rock salt structure type ZrC.

Modeling of glow discharge in a gas flow

NASA Astrophysics Data System (ADS)

Galeev, I. G.; Asadullin, T. Ya

2017-11-01

The discharge plasma of positive column in electronegative gas flow has been described by two-dimensional integro-differential system of equations written in the approximation of “narrow channel”. An efficient algorithm of solving this system of equations is suggested. In this work an implicit method is used of solution with selection gradient of the electric field along the channel. The simulation of discharge characteristics was conducted under various boundary conditions at the inlet of the discharge area and with various full discharge currents.

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

DFT calculations of electronic and optical properties of SrS with LDA, GGA and mGGA functionals

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

Sharma, Shatendra, E-mail: shatendra@gmai.com; Sharma, Jyotsna; Sharma, Yogita

2016-05-06

The theoretical investigations of electronic and optical properties of SrS are made using the first principle DFT calculations. The calculations are performed for the local-density approximation (LDA), generalized gradient approximation (GGA) and for an alternative form of GGA i.e. metaGGA for both rock salt type (B1, Fm3m) and cesium chloride (B2, Pm3m) structures. The band structure, density of states and optical spectra are calculated under various available functional. The calculations with LDA and GGA functional underestimate the values of band gaps with all functional, however the values with mGGA show reasonably good agreement with experimental and those calculated by usingmore » other methods.« less

A density functional theory study of the influence of exchange-correlation functionals on the properties of FeAs.

PubMed

Griffin, Sinéad M; Spaldin, Nicola A

2017-06-01

We use density functional theory within the local density approximation (LDA), LDA  +  U, generalised gradient approximation (GGA), GGA  +  U, and hybrid-functional methods to calculate the properties of iron monoarsenide. FeAs, which forms in the MnP structure, is of current interest for potential spintronic applications as well as being the parent compound for the pnictide superconductors. We compare the calculated structural, magnetic and electronic properties obtained using the different functionals to each other and to experiment, and investigate the origin of a recently reported magnetic spiral. Our results indicate the appropriateness or otherwise of the various functionals for describing FeAs and the related Fe-pnictide superconductors.

Electron momentum density and band structure calculations of α- and β-GeTe

NASA Astrophysics Data System (ADS)

Vadkhiya, Laxman; Arora, Gunjan; Rathor, Ashish; Ahuja, B. L.

2011-12-01

We have measured isotropic experimental Compton profile of α-GeTe by employing high energy (662 keV) γ-radiation from a 137Cs isotope. To compare our experiment, we have also computed energy bands, density of states, electron momentum densities and Compton profiles of α- and β-phases of GeTe using the linear combination of atomic orbitals method. The electron momentum density is found to play a major role in understanding the topology of bands in the vicinity of the Fermi level. It is seen that the density functional theory (DFT) with generalised gradient approximation is relatively in better agreement with the experiment than the local density approximation and hybrid Hartree-Fock/DFT.

Dai-Kou type conjugate gradient methods with a line search only using gradient.

PubMed

Huang, Yuanyuan; Liu, Changhe

2017-01-01

In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.

Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Padé approximant

NASA Astrophysics Data System (ADS)

Sergeev, A.; Alharbi, F. H.; Jovanovic, R.; Kais, S.

2016-04-01

The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke’s law model for two-electron atoms.

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Eleshaky, Mohamed E.

1991-01-01

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Generation and precise control of dynamic biochemical gradients for cellular assays

NASA Astrophysics Data System (ADS)

Saka, Yasushi; MacPherson, Murray; Giuraniuc, Claudiu V.

2017-03-01

Spatial gradients of diffusible signalling molecules play crucial roles in controlling diverse cellular behaviour such as cell differentiation, tissue patterning and chemotaxis. In this paper, we report the design and testing of a microfluidic device for diffusion-based gradient generation for cellular assays. A unique channel design of the device eliminates cross-flow between the source and sink channels, thereby stabilizing gradients by passive diffusion. The platform also enables quick and flexible control of chemical concentration that makes highly dynamic gradients in diffusion chambers. A model with the first approximation of diffusion and surface adsorption of molecules recapitulates the experimentally observed gradients. Budding yeast cells cultured in a gradient of a chemical inducer expressed a reporter fluorescence protein in a concentration-dependent manner. This microfluidic platform serves as a versatile prototype applicable to a broad range of biomedical investigations.

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses.

NASA Technical Reports Server (NTRS)

Wing, L. D.

1973-01-01

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN IV for an IBM 360/91 computer.

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses

NASA Technical Reports Server (NTRS)

Wing, L. D.

1972-01-01

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN 4 for an IBM 360/91 computer.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

PubMed

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Characterization of Thin Film Materials using SCAN meta-GGA, an Accurate Nonempirical Density Functional

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

Buda, I. G.; Lane, C.; Barbiellini, B.

We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functionalmore » for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.« less

Characterization of Thin Film Materials using SCAN meta-GGA, an Accurate Nonempirical Density Functional

DOE PAGES

Buda, I. G.; Lane, C.; Barbiellini, B.; ...

2017-03-23

We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functionalmore » for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.« less

Upper Water Structure and Mixed Layer Depth in Sub-Tropical Waters: The Seats Station in the Northern South China Sea

NASA Astrophysics Data System (ADS)

Wong, G. T. F.; Tai, J. H.

2014-12-01

702 CTD profiles were collected in the subtropical northern South China Sea at and in the vicinity of the SouthEast Asian Time-series Study (SEATS) station (18.2oN, 115.8oE) between 17.5 and 18.5oN and 115.3 and 116.3oE in 64 cruises in 1997 to 2013. The hydrographic structure of the upper water above the permanent thermocline may be classified into 4 principal types: (a) classic type (an almost isopycnic upper water); (b) stepwise type (with one or more small but significant step-increases in σθ in the upper water); (c) graded type (an approximately constant depth gradient in a monotonic increase in σθ in the upper water); and (d) mixed type (a combination of the stepwise and graded types). The 4 types of upper water were found in 75, 14, 5, and 6% of the cruises, respectively. Ten schemes were applied to these data to determine the mixed layer depth (MLD): 4 fixed temperature difference (FTD) methods (0.2, 0.5, 0.8 and 1.0oC decrease from 10 m); 1 fixed density difference (FDD) method (0.125 σθ increase from 10 m); 1 fixed temperature gradient (FTG) method (at 0.05oC/m); 3 fixed density gradient (FDG) methods (at 0.01, 0.05 and 0.1 σθ/m); and the maximum density gradient (MDG) method. MLD could not be clearly depicted in the 3 minor types of upper water. In the classical type, while similar MLD-s were found in a large majority of the cruises among all 10 methods, substantial discrepancies among methods could be found. The most consistent results, generally within ±5 m, were found among the FDG method at 0.05, 0.1 σθ/m and FTD method at 0.8 and 1.0oC. The MDG method gave consistently deeper MLD by ~8 m. If that difference was taken into account, the results were generally consistent with those from the other 4 methods. The remaining 5 methods could all yield MLD-s shallower than the first 4 methods by >10 m as they failed to capture the bottom of the mixed layer as indicated by visual inspection.

A simulation of the intracluster medium with feedback from cluster galaxies

NASA Technical Reports Server (NTRS)

Metzler, Christopher A.; Evrard, August E.

1994-01-01

We detail method and report first results from a three-dimensional hydrodynamical and N-body simulation of the formation and evolution of a Coma-sized cluster of galaxies, with the intent of studying the history of the hot, X-ray emitting intracluster medium. Cluster gas, galaxies, and dark matter are included in the model. The galaxies and dark matter fell gravitational forces; the cluster gas also undergoes hydrodynamical effects such as shock heating and PdV work. For the first time in three dimensions, we include modeling of ejection of processed gas from the simulated galaxies by winds, including heating and heavy element enrichment. For comparison, we employ a `pure infall' simulation using the same initial conditions but with no galaxies or winds. We employ an extreme ejection history for galactic feedback in order to define the boundary of likely models. As expected, feedback raises the entropy of the intracluster gas, preventing it from collapsing to densities as high as those attained in the infall model. The effect is more pronounced in subclusters formed at high redshift. The cluster with feedback is always less X-ray luminous, but experiences more rapid luminosity evolution, than the pure infall cluster. Even employing an extreme ejection model, the final gas temperature is only approximately 15% larger than in the infall model. The radial temperature profile is very nearly isothermal within 1.5 Mpc. The cluster galaxies in the feedback model have a velocity dispersion approximately 15% lower than the dark matter. This results in the true ratio of specific energies in galaxies to gas being less than one, beta(sub spec) approximately 0.7. The infall model predicts beta(sub spec) approximately 1.2. Large excursions in these values occur over time, following the complex dynamical history of the cluster. The morphology of the X-ray emission is little affected by feedback. The emission profiles of both clusters are well described by the standard beta-model with beta(sub fit) approximately equal to 0.7 - 0.9. X-ray mass estimates based on the assumptions of hydrostatic equilibrium and the applicability of the beta-model are quite accurate in both cases. A strong, radial iron abundance gradient is present, which develops as a consequence of the steepening of the galaxy density profile over time. Spectroscopic observations using nonimaging detectors with wide (approximately 45 min) fields of view dramatically smear the gradient. Observations with arcminute resolution, made available with the ASCA satellite, would readily resolve the gradient.

Heat-Electric Power Conversion Without Temperature Difference Using Only n-Type Ba8Au x Si46-x Clathrate with Au Compositional Gradient

NASA Astrophysics Data System (ADS)

Osakabe, Yuki; Tatsumi, Shota; Kotsubo, Yuichi; Iwanaga, Junpei; Yamasoto, Keita; Munetoh, Shinji; Furukimi, Osamu; Nakashima, Kunihiko

2018-02-01

Thermoelectric power generation is typically based on the Seebeck effect under a temperature gradient. However, the heat flux generated by the temperature difference results in low conversion efficiency. Recently, we developed a heat-electric power conversion mechanism using a material consisting of a wide-bandgap n-type semiconductor, a narrow-bandgap intrinsic semiconductor, and a wide-bandgap p-type semiconductor. In this paper, we propose a heat-electric power conversion mechanism in the absence of a temperature difference using only n-type Ba8Au x Si46-x clathrate. Single-crystal Ba8Au x Si46-x clathrate with a Au compositional gradient was synthesized by Czochralski method. Based on the results of wavelength-dispersive x-ray spectroscopy and Seebeck coefficient measurements, the presence of a Au compositional gradient in the sample was confirmed. It also observed that the electrical properties changed gradually from wide-bandgap n-type to narrow-bandgap n-type. When the sample was heated in the absence of a temperature difference, the voltage generated was approximately 0.28 mV at 500°C. These results suggest that only an n-type semiconductor with a controlled bandgap can generate electric power in the absence of a temperature difference.

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

NASA Technical Reports Server (NTRS)

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

2004-01-01

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Diffusion pore imaging with generalized temporal gradient profiles.

PubMed

Laun, Frederik B; Kuder, Tristan A

2013-09-01

In porous material research, one main interest of nuclear magnetic resonance diffusion (NMR) experiments is the determination of the shape of pores. While it has been a longstanding question if this is in principle achievable, it has been shown recently that it is indeed possible to perform NMR-based diffusion pore imaging. In this work we present a generalization of these previous results. We show that the specific temporal gradient profiles that were used so far are not unique as more general temporal diffusion gradient profiles may be used. These temporal gradient profiles may consist of any number of "short" gradient pulses, which fulfil the short-gradient approximation. Additionally, "long" gradient pulses of small amplitude may be present, which can be used to fulfil the rephasing condition for the complete profile. Some exceptions exist. For example, classical q-space gradients consisting of two short gradient pulses of opposite sign cannot be used as the phase information is lost due to the temporal antisymmetry of this profile. Copyright © 2013 Elsevier Inc. All rights reserved.

Gravity and gravity gradient changes caused by a point dislocation

NASA Astrophysics Data System (ADS)

Huang, Jian-Liang; Li, Hui; Li, Rui-Hao

1995-02-01

In this paper we studied gravitational potential, gravity and its gradient changes, which are caused by a point dislocation, and gave the concise mathematical deduction with definite physical implication in dealing with the singular integral at a seismic source. We also analysed the features of the fields of gravity and gravity gradient, gravity-vertical-displacement gradient. The conclusions are: (1) Gravity and gravity gradient changes are very small with the change of vertical position; (2) Gravity change is much greater than the gravity gradient change which is not so distinct; (3) The gravity change due to redistribution of mass accounts for 10 50 percent of the total gravity change caused by dislocation. The signs (positive or negative) of total gravity change and vertical displacement are opposite each other at the same point for strike slip and dip slip; (4) Gravity-vertical-displacement-gradient is not constant; it manifests a variety of patterns for different dislocation models; (5) Gravity-vertical-displacement-gradient is approximately equal to apparent gravity-vertical-displacement-gradient.

On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov's fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization.

On the Convergence Analysis of the Optimized Gradient Method

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2016-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov’s fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization. PMID:28461707

Multipolar Ewald methods, 1: theory, accuracy, and performance.

PubMed

Giese, Timothy J; Panteva, Maria T; Chen, Haoyuan; York, Darrin M

2015-02-10

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Model-Free Optimal Tracking Control via Critic-Only Q-Learning.

PubMed

Luo, Biao; Liu, Derong; Huang, Tingwen; Wang, Ding

2016-10-01

Model-free control is an important and promising topic in control fields, which has attracted extensive attention in the past few years. In this paper, we aim to solve the model-free optimal tracking control problem of nonaffine nonlinear discrete-time systems. A critic-only Q-learning (CoQL) method is developed, which learns the optimal tracking control from real system data, and thus avoids solving the tracking Hamilton-Jacobi-Bellman equation. First, the Q-learning algorithm is proposed based on the augmented system, and its convergence is established. Using only one neural network for approximating the Q-function, the CoQL method is developed to implement the Q-learning algorithm. Furthermore, the convergence of the CoQL method is proved with the consideration of neural network approximation error. With the convergent Q-function obtained from the CoQL method, the adaptive optimal tracking control is designed based on the gradient descent scheme. Finally, the effectiveness of the developed CoQL method is demonstrated through simulation studies. The developed CoQL method learns with off-policy data and implements with a critic-only structure, thus it is easy to realize and overcome the inadequate exploration problem.

Valence electronic properties of porphyrin derivatives.

PubMed

Stenuit, G; Castellarin-Cudia, C; Plekan, O; Feyer, V; Prince, K C; Goldoni, A; Umari, P

2010-09-28

We present a combined experimental and theoretical investigation of the valence electronic structure of porphyrin-derived molecules. The valence photoemission spectra of the free-base tetraphenylporphyrin and of the octaethylporphyrin molecule were measured using synchrotron radiation and compared with theoretical spectra calculated using the GW method and the density-functional method within the generalized gradient approximation. Only the GW results could reproduce the experimental data. We found that the contribution to the orbital energies due to electronic correlations has the same linear behavior in both molecules, with larger deviations in the vicinity of the HOMO level. This shows the importance of adequate treatment of electronic correlations in these organic systems.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

Pascazio, Vito; Schirinzi, Gilda

2002-01-01

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Theoretical investigations on structural, elastic and electronic properties of thallium halides

NASA Astrophysics Data System (ADS)

Singh, Rishi Pal; Singh, Rajendra Kumar; Rajagopalan, Mathrubutham

2011-04-01

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme.

PubMed

Li, Shaohong L; Truhlar, Donald G

2015-07-14

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations and atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme

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

Li, Shaohong L.; Truhlar, Donald G.

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations andmore » atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.« less

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme

DOE PAGES

Li, Shaohong L.; Truhlar, Donald G.

2015-05-22

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations andmore » atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.« less

Effects of urban land-use change on streamflow and water quality in Oakland County, Michigan, 1970-2003, as inferred from urban gradient and temporal analysis

USGS Publications Warehouse

Aichele, Stephen S.

2005-01-01

This apparent contradiction may be caused by the differences in the changes measured in each analysis. The change-through-time approach describes change from a fixed starting point of approximately 1970; the gradient approach describes the cumulative effect of all change up to approximately 2000. These findings indicate that although urbanization in Oakland County results in most of the effects observed in the literature, as evidenced in the gradient approach, relatively few of the anticipated effects have been observed during the past three decades. This relative stability despite rapid land-cover change may be related to efforts to mitigate the effects of development and a general decrease in the density of new residential development. It may also be related to external factors such as climate variability and reduced atmospheric deposition of specific chemicals. 

Injection and swirl driven flowfields in solid and liquid rocket motors

NASA Astrophysics Data System (ADS)

Vyas, Anand B.

In this work, we seek approximate analytical solutions to describe the bulk flow motion in certain types of solid and liquid rocket motors. In the case of an idealized solid rocket motor, a cylindrical double base propellant grain with steady regression rate is considered. The well known inviscid profile determined by Culick is extended here to include the effects of viscosity and steady grain regression. The approximate analytical solution for the cold flow is obtained from similarity principles, perturbation methods and the method of variation of parameters. The velocity, vorticity, pressure gradient and the shear stress distributions are determined and interpreted for different rates of wall regression and injection Reynolds number. The liquid propellant rocket engine considered here is based on a novel design that gives rise to a cyclonic flow. The resulting bidirectional motion is triggered by the tangential injection of an oxidizer just upstream of the chamber nozzle. Velocity, vorticity and pressure gradient distributions are determined for the bulk gas dynamics using a non-reactive inviscid model. Viscous corrections are then incorporated to explain the formation of a forced vortex near the core. Our results compare favorably with numerical simulations and experimental measurements obtained by other researchers. They also indicate that the bidirectional vortex in a cylindrical chamber is a physical solution of the Euler equations. In closing, we investigate the possibility of multi-directional flow behavior as predicted by Euler's equation and as reported recently in laboratory experiments.

A Truncated Nuclear Norm Regularization Method Based on Weighted Residual Error for Matrix Completion.

PubMed

Qing Liu; Zhihui Lai; Zongwei Zhou; Fangjun Kuang; Zhong Jin

2016-01-01

Low-rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision. Most existing methods formulate the task as a low-rank matrix approximation problem. A truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm. The corresponding optimization method, truncated nuclear norm regularization (TNNR), converges better than the nuclear norm minimization-based methods. However, it is not robust to the number of subtracted singular values and requires a large number of iterations to converge. In this paper, a TNNR method based on weighted residual error (TNNR-WRE) for matrix completion and its extension model (ETNNR-WRE) are proposed. TNNR-WRE assigns different weights to the rows of the residual error matrix in an augmented Lagrange function to accelerate the convergence of the TNNR method. The ETNNR-WRE is much more robust to the number of subtracted singular values than the TNNR-WRE, TNNR alternating direction method of multipliers, and TNNR accelerated proximal gradient with Line search methods. Experimental results using both synthetic and real visual data sets show that the proposed TNNR-WRE and ETNNR-WRE methods perform better than TNNR and Iteratively Reweighted Nuclear Norm (IRNN) methods.

Multiconfiguration Pair-Density Functional Theory.

PubMed

Li Manni, Giovanni; Carlson, Rebecca K; Luo, Sijie; Ma, Dongxia; Olsen, Jeppe; Truhlar, Donald G; Gagliardi, Laura

2014-09-09

We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.

ASCA observation of NGC 4636: Dark matter and metallicity gradient

NASA Technical Reports Server (NTRS)

Mushotzky, R. F.; Loewenstein, M.; Awaki, H.; Makishima, K.; Matsushita, K.; Matsumoto, H.

1994-01-01

We present our analysis of ASCA PV phase observation of the elliptical galaxy NGC 4636. Solid state imaging spectrometer (SIS) spectra in six concentric annuli centered on NGC 4636 are used to derive temperature, metallicity, and column density profiles for the hot interstellar medium. Outside of the central 3 min the temperature is roughly constant at approximately 0.85 keV, while the metallicity decreases from greater than 0.36 solar at the center to less than 0.12 solar at R approximately 9 min. The implications of this gradient for elliptical galaxy formation and the enrichment of intracluster gas are discussed. We derive a detailed mass profile consistent with the stellar velocity dispersion and with ROSAT position sensitive proportional counter (PSPC) and ASCA SIS X-ray temperature profiles. We find that NGC 4636 becomes dark matter dominated at roughly the de Vaucouleurs radius, and, at r approximately 100 kpc, the ratio of dark to luminous matter density is approximately 80 and solar mass/solar luminosity approximately equal to 150. Evidence for the presence of a cooling flow is also discussed.

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations.

PubMed

Hardy, David J; Wolff, Matthew A; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D

2016-03-21

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Hardy, David J.; Wolff, Matthew A.; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D.

2016-03-01

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.

[Theory, method and application of method R on estimation of (co)variance components].

PubMed

Liu, Wen-Zhong

2004-07-01

Theory, method and application of Method R on estimation of (co)variance components were reviewed in order to make the method be reasonably used. Estimation requires R values,which are regressions of predicted random effects that are calculated using complete dataset on predicted random effects that are calculated using random subsets of the same data. By using multivariate iteration algorithm based on a transformation matrix,and combining with the preconditioned conjugate gradient to solve the mixed model equations, the computation efficiency of Method R is much improved. Method R is computationally inexpensive,and the sampling errors and approximate credible intervals of estimates can be obtained. Disadvantages of Method R include a larger sampling variance than other methods for the same data,and biased estimates in small datasets. As an alternative method, Method R can be used in larger datasets. It is necessary to study its theoretical properties and broaden its application range further.

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

Steep, Transient Density Gradients in the Martian Ionosphere Similar to the Ionopause at Venus

NASA Astrophysics Data System (ADS)

Duru, Firdevs; Gurnett, Donald; Frahm, Rudy; Winningham, D. L.; Morgan, David; Howes, Gregory

Using Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) on the Mars Express (MEX) spacecraft, the electron density can be measured by two methods: from the excitation of local plasma oscillations and from remote sounding. A study of the local electron density versus time for 1664 orbits revealed that in 132 orbits very sharp gradients in the electron density occurred that are similar to the ionopause boundary commonly observed at Venus. In 40 of these cases, remote sounding data have also confirmed identical locations of steep ionopause-like density gradients. Measurements from the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) Electron Spectrometer (ELS) and Ion Mass Analyzer (IMA) instruments (also on Mars Express) verify that these sharp decreases in the electron density occur somewhere between the end of the region where ionospheric photoelectrons are dominant and the magnetosheath. Combined studies of the two experiments reveal that the steep density gradients define a boundary where the magnetic fields change from open to closed. This study shows that, although the individual cases are from a wide range of altitudes, the average altitude of the boundary as a function of solar zenith angle is almost constant. The average altitude is approximately 500 km up to solar zenith angles of 60o, after which it shows a slight increase. The average thickness of the boundary is about 22 km according to remote sounding measurements. The altitude of the steep gradients shows an increase at locations with strong crustal magnetic fields.

Improved L-BFGS diagonal preconditioners for a large-scale 4D-Var inversion system: application to CO2 flux constraints and analysis error calculation

NASA Astrophysics Data System (ADS)

Bousserez, Nicolas; Henze, Daven; Bowman, Kevin; Liu, Junjie; Jones, Dylan; Keller, Martin; Deng, Feng

2013-04-01

This work presents improved analysis error estimates for 4D-Var systems. From operational NWP models to top-down constraints on trace gas emissions, many of today's data assimilation and inversion systems in atmospheric science rely on variational approaches. This success is due to both the mathematical clarity of these formulations and the availability of computationally efficient minimization algorithms. However, unlike Kalman Filter-based algorithms, these methods do not provide an estimate of the analysis or forecast error covariance matrices, these error statistics being propagated only implicitly by the system. From both a practical (cycling assimilation) and scientific perspective, assessing uncertainties in the solution of the variational problem is critical. For large-scale linear systems, deterministic or randomization approaches can be considered based on the equivalence between the inverse Hessian of the cost function and the covariance matrix of analysis error. For perfectly quadratic systems, like incremental 4D-Var, Lanczos/Conjugate-Gradient algorithms have proven to be most efficient in generating low-rank approximations of the Hessian matrix during the minimization. For weakly non-linear systems though, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), a quasi-Newton descent algorithm, is usually considered the best method for the minimization. Suitable for large-scale optimization, this method allows one to generate an approximation to the inverse Hessian using the latest m vector/gradient pairs generated during the minimization, m depending upon the available core memory. At each iteration, an initial low-rank approximation to the inverse Hessian has to be provided, which is called preconditioning. The ability of the preconditioner to retain useful information from previous iterations largely determines the efficiency of the algorithm. Here we assess the performance of different preconditioners to estimate the inverse Hessian of a large-scale 4D-Var system. The impact of using the diagonal preconditioners proposed by Gilbert and Le Maréchal (1989) instead of the usual Oren-Spedicato scalar will be first presented. We will also introduce new hybrid methods that combine randomization estimates of the analysis error variance with L-BFGS diagonal updates to improve the inverse Hessian approximation. Results from these new algorithms will be evaluated against standard large ensemble Monte-Carlo simulations. The methods explored here are applied to the problem of inferring global atmospheric CO2 fluxes using remote sensing observations, and are intended to be integrated with the future NASA Carbon Monitoring System.

Atmospheric refraction errors in laser ranging systems

NASA Technical Reports Server (NTRS)

Gardner, C. S.; Rowlett, J. R.

1976-01-01

The effects of horizontal refractivity gradients on the accuracy of laser ranging systems were investigated by ray tracing through three dimensional refractivity profiles. The profiles were generated by performing a multiple regression on measurements from seven or eight radiosondes, using a refractivity model which provided for both linear and quadratic variations in the horizontal direction. The range correction due to horizontal gradients was found to be an approximately sinusoidal function of azimuth having a minimum near 0 deg azimuth and a maximum near 180 deg azimuth. The peak to peak variation was approximately 5 centimeters at 10 deg elevation and decreased to less than 1 millimeter at 80 deg elevation.

Photopions from nuclei in the distorted-wave impulse approximation

NASA Astrophysics Data System (ADS)

Girija, V.; Devanathan, V.

1982-11-01

The formalism for photoproduction of pions from nuclei has been developed in the distorted-wave impulse approximation, taking into account the effect of the change in pion momentum in nuclear medium. Detailed calculations have been done for the reaction 16O(γ, π+)16N for photon energies from 170 to 380 MeV, with a view to investigate the effect due to the gradient operator ∇-->π for momentum of the pion and test the sensitivity of the photopion cross sections to the details of the pion-nucleus optical potential. The results clearly establish that the gradient operator increases the cross sections throughout the energy region considered, the increase being small at lower energies. Also with ∇-->π, the cross sections are rendered less sensitive to the optical potential. The calculated differential cross sections agree very well with the recent experimental data of Shoda et al. for γ-ray energy of 200 MeV. However, the cross sections obtained at medium energies are higher when compared to the available experimental data. NUCLEAR REACTIONS π+ photoproduction from 16O; distorted wave impulse approximation; pion-nucleus optical potentials; gradient operator for the pion momentum.

Nonlinear identification using a B-spline neural network and chaotic immune approaches

NASA Astrophysics Data System (ADS)

dos Santos Coelho, Leandro; Pessôa, Marcelo Wicthoff

2009-11-01

One of the important applications of B-spline neural network (BSNN) is to approximate nonlinear functions defined on a compact subset of a Euclidean space in a highly parallel manner. Recently, BSNN, a type of basis function neural network, has received increasing attention and has been applied in the field of nonlinear identification. BSNNs have the potential to "learn" the process model from input-output data or "learn" fault knowledge from past experience. BSNN can be used as function approximators to construct the analytical model for residual generation too. However, BSNN is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of a modified artificial immune network inspired optimization method - the opt-aiNet - combined with sequences generate by Hénon map to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods are useful for building good BSNN model for the nonlinear identification of two case studies: (i) the benchmark of Box and Jenkins gas furnace, and (ii) an experimental ball-and-tube system.

A rotor optimization using regression analysis

NASA Technical Reports Server (NTRS)

Giansante, N.

1984-01-01

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Stability and nuclear dynamics of the Bicoid morphogen gradient

PubMed Central

Gregor, Thomas; Wieschaus, Eric F.; McGregor, Alistair P.; Bialek, William; Tank, David W.

2008-01-01

Patterning in multicellular organisms results from spatial gradients in morphogen concentration, but the dynamics of these gradients remains largely unexplored. We characterize, through in vivo optical imaging, the development and stability of the Bicoid morphogen gradient in Drosophila embryos that express a Bicoid-eGFP fusion protein. The gradient is established rapidly (~1 hour after fertilization) with nuclear Bicoid concentration rising and falling during mitosis. Interphase levels result from a rapid equilibrium between Bicoid uptake and removal. Initial interphase concentration in nuclei in successive cycles is constant (±10%), demonstrating a form of gradient stability, but subsequently decays by approximately 30%. Both direct photobleaching measurements and indirect estimates of Bicoid-eGFP diffusion constants (D ≤ 1 μm2/s), provide a consistent picture of Bicoid transport on short (~min) time scales, but challenge traditional models of long range gradient formation. A new model is presented emphasizing the possible role of nuclear dynamics in shaping and scaling the gradient. PMID:17632061

Assimilation and subcellular partitioning of elements by grass shrimp collected along an impact gradient.

PubMed

Seebaugh, David R; Wallace, William G

2009-06-28

Chronic exposure to polluted field conditions can impact metal bioavailability in prey and may influence metal transfer to predators. The present study investigated the assimilation of Cd, Hg and organic carbon by grass shrimp Palaemonetes pugio, collected along an impact gradient within the New York/New Jersey Harbor Estuary. Adult shrimp were collected from five Staten Island, New York study sites, fed (109)Cd- or (203)Hg-labeled amphipods or (14)C-labeled meals and analyzed for assimilation efficiencies (AE). Subsamples of amphipods and shrimp were subjected to subcellular fractionation to isolate metal associated with a compartment presumed to contain trophically available metal (TAM) (metal associated with heat-stable proteins [HSP - e.g., metallothionein-like proteins], heat-denatured proteins [HDP - e.g., enzymes] and organelles [ORG]). TAM-(109)Cd% and TAM-(203)Hg% in radiolabeled amphipods were approximately 64% and approximately 73%, respectively. Gradients in AE-(109)Cd% ( approximately 54% to approximately 75%) and AE-(203)Hg% ( approximately 61% to approximately 78%) were observed for grass shrimp, with the highest values exhibited by shrimp collected from sites within the heavily polluted Arthur Kill complex. Population differences in AE-(14)C% were not observed. Assimilated (109)Cd% partitioned to the TAM compartment in grass shrimp varied between approximately 67% and approximately 75%. (109)Cd bound to HSP in shrimp varied between approximately 15% and approximately 47%, while (109)Cd associated with metal-sensitive HDP was approximately 17% to approximately 44%. Percentages of assimilated (109)Cd bound to ORG were constant at approximately 10%. Assimilated (203)Hg% associated with TAM in grass shrimp did not exhibit significant variation. Percentages of assimilated (203)Hg bound to HDP ( approximately 47%) and ORG ( approximately 11%) did not vary among populations and partitioning of (203)Hg to HSP was not observed. Using a simplified biokinetic model of metal accumulation from the diet, it is estimated that site-specific variability in Cd AE by shrimp and tissue Cd burdens in field-collected prey (polychaetes Nereis spp.) could potentially result in up to approximately 3.2-fold differences in the dose of Cd assimilated by shrimp from a meal in the field. The results of this study also suggest that chronic field exposure can impact mechanisms of metal transport across the gut epithelium that do not influence carbon assimilation. Differences in the assimilation and subcellular partitioning of metal may have important implications for metal toxicity in impacted shrimp populations.

Elliptic flow computation by low Reynolds number two-equation turbulence models

NASA Technical Reports Server (NTRS)

Michelassi, V.; Shih, T.-H.

1991-01-01

A detailed comparison of ten low-Reynolds-number k-epsilon models is carried out. The flow solver, based on an implicit approximate factorization method, is designed for incompressible, steady two-dimensional flows. The conservation of mass is enforced by the artificial compressibility approach and the computational domain is discretized using centered finite differences. The turbulence model predictions of the flow past a hill are compared with experiments at Re = 10 exp 6. The effects of the grid spacing together with the numerical efficiency of the various formulations are investigated. The results show that the models provide a satisfactory prediction of the flow field in the presence of a favorable pressure gradient, while the accuracy rapidly deteriorates when a strong adverse pressure gradient is encountered. A newly proposed model form that does not explicitly depend on the wall distance seems promising for application to complex geometries.

Accelerating IMRT optimization by voxel sampling

NASA Astrophysics Data System (ADS)

Martin, Benjamin C.; Bortfeld, Thomas R.; Castañon, David A.

2007-12-01

This paper presents a new method for accelerating intensity-modulated radiation therapy (IMRT) optimization using voxel sampling. Rather than calculating the dose to the entire patient at each step in the optimization, the dose is only calculated for some randomly selected voxels. Those voxels are then used to calculate estimates of the objective and gradient which are used in a randomized version of a steepest descent algorithm. By selecting different voxels on each step, we are able to find an optimal solution to the full problem. We also present an algorithm to automatically choose the best sampling rate for each structure within the patient during the optimization. Seeking further improvements, we experimented with several other gradient-based optimization algorithms and found that the delta-bar-delta algorithm performs well despite the randomness. Overall, we were able to achieve approximately an order of magnitude speedup on our test case as compared to steepest descent.

The effect of viscous flow and thermal flux on the rate of chemical reaction in dilute gases

NASA Astrophysics Data System (ADS)

Cukrowski, A. S.; Popielawski, J.

1986-11-01

Expression for the corrections describing the effect of viscous flow and thermal flux on the rate of chemical reaction have been derived for the reaction A + A = B + C described by Prigogine-Xhrouet and Present. These corrections are calculated for the velocity distribution function up to the second-order approximation for the Chapman-Enskog solution of the Boltzmann equation. These corrections are shown to be the same as those which would follow after application of the method of linearized-moments equations described by Eu and Li. The effects of viscous flow and thermal flux are presented as functions of activation energy of chemical reaction, temperature, density, coefficients of shear viscosity of thermal conductivity, and relevant gradients of mean molecular velocity or temperature. It is pointed out that for very slow reactions and for very large gradients (e.g. in shock waves) these effects can be quite significant.

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

Two-dimensional strain gradient damage modeling: a variational approach

NASA Astrophysics Data System (ADS)

Placidi, Luca; Misra, Anil; Barchiesi, Emilio

2018-06-01

In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

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

Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

2015-09-01

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method

NASA Astrophysics Data System (ADS)

Aykol, Muratahan; Doak, Jeff W.; Wolverton, C.

2017-06-01

We evaluate the energetic stabilities of white, red, and black allotropes of phosphorus using density functional theory (DFT) and hybrid functional methods, van der Waals (vdW) corrections (DFT+vdW and hybrid+vdW), vdW density functionals, and random phase approximation (RPA). We find that stability of black phosphorus over red-V (i.e., the violet form) is not ubiquitous among these methods, and the calculated enthalpies for the reaction phosphorus (red-V)→phosphorus (black) are scattered between -20 and 40 meV/atom. With local density and generalized gradient approximations, and hybrid functionals, mean absolute errors (MAEs) in densities of P allotropes relative to experiments are found to be around 10%-25%, whereas with vdW-inclusive methods, MAEs in densities drop below ˜5 %. While the inconsistency among the density functional methods could not shed light on the stability puzzle of black versus red phosphorus, comparison of their accuracy in predicting densities and the supplementary RPA results on relative stabilities indicate that opposite to the common belief, black and red phosphorus are almost degenerate, or the red-V (violet) form of phosphorus might even be the ground state.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Computational studies of transthoracic and transvenous defibrillation in a detailed 3-D human thorax model.

PubMed

Jorgenson, D B; Haynor, D R; Bardy, G H; Kim, Y

1995-02-01

A method for constructing and solving detailed patient-specific 3-D finite element models of the human thorax is presented for use in defibrillation studies. The method utilizes the patient's own X-ray CT scan and a simplified meshing scheme to quickly and efficiently generate a model typically composed of approximately 400,000 elements. A parameter sensitivity study on one human thorax model to examine the effects of variation in assigned tissue resistivity values, level of anatomical detail included in the model, and number of CT slices used to produce the model is presented. Of the seven tissue types examined, the average left ventricular (LV) myocardial voltage gradient was most sensitive to the values of myocardial and blood resistivity. Incorrectly simplifying the model, for example modeling the heart as a homogeneous structure by ignoring the blood in the chambers, caused the average LV myocardial voltage gradient to increase by 12%. The sensitivity of the model to variations in electrode size and position was also examined. Small changes (< 2.0 cm) in electrode position caused average LV myocardial voltage gradient values to increase by up to 12%. We conclude that patient-specific 3-D finite element modeling of human thoracic electric fields is feasible and may reduce the empiric approach to insertion of implantable defibrillators and improve transthoracic defibrillation techniques.

Segmentation of knee MRI using structure enhanced local phase filtering

NASA Astrophysics Data System (ADS)

Lim, Mikhiel; Hacihaliloglu, Ilker

2016-03-01

The segmentation of bone surfaces from magnetic resonance imaging (MRI) data has applications in the quanti- tative measurement of knee osteoarthritis, surgery planning for patient specific total knee arthroplasty and its subsequent fabrication of artificial implants. However, due to the problems associated with MRI imaging such as low contrast between bone and surrounding tissues, noise, bias fields, and the partial volume effect, segmentation of bone surfaces continues to be a challenging operation. In this paper, a new framework is presented for the enhancement of knee MRI scans prior to segmentation in order to obtain high contrast bone images. During the first stage, a new contrast enhanced relative total variation (RTV) regularization method is used in order to remove textural noise from the bone structures and surrounding soft tissue interface. This salient bone edge information is further enhanced using a sparse gradient counting method based on L0 gradient minimization, which globally controls how many non-zero gradients are resulted in order to approximate prominent bone structures in a structure-sparsity-management manner. The last stage of the framework involves incorporation of local phase bone boundary information in order to provide an intensity invariant enhancement of contrast between the bone and surrounding soft tissue. The enhanced images are segmented using a fast random walker algorithm. Validation against expert segmentation was performed on 10 clinical knee MRI images, and achieved a mean dice similarity coefficient (DSC) of 0.975.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

Dexamethasone concentration gradients along scala tympani after application to the round window membrane.

PubMed

Plontke, Stefan K; Biegner, Thorsten; Kammerer, Bernd; Delabar, Ursular; Salt, Alec N

2008-04-01

Local application of dexamethasone-21-dihydrogen-phosphate (Dex-P) to the round window (RW) membrane of guinea pigs produces a substantial basal-apical concentration gradient in scala tympani (ST) perilymph. In recent years, intratympanically applied glucocorticoids are increasingly being used for the treatment of inner ear disease. Although measurements of intracochlear concentrations after RW application exist, there is limited information on the distribution of these drugs in the inner ear fluids. It has been predicted from computer simulations that substantial concentration gradients will occur after RW application, with lower concentrations expected in apical turns. Concentration gradients of other substances along the cochlea have recently been confirmed using a sequential apical sampling method to obtain perilymph. Dexamethasone-21-dihydrogen-phosphate (10 mg/ml) was administered to the RW membrane of guinea pigs (n = 9) in vivo for 2 to 3 hours. Perilymph was then collected using a protocol in which 10 samples, each of approximately 1 mul, were taken sequentially from the cochlear apex into capillary tubes. Dexamethasone-21-dihydrogen-phosphate concentration of the samples was analyzed by high-performance liquid chromatography. Interpretation of sample data using a finite element model allowed the longitudinal gradients of Dex-P in ST to be quantified. The Dex-P content of the first sample in each experiment (dominated by perilymph from apical regions) was substantially lower than that of the third and fourth sample (dominated by basal turn perilymph). These findings qualitatively demonstrated the existence of a concentration gradient along ST. After detailed analysis of the measured sample concentrations using an established finite element computer model, the mean basal-apical concentration gradient was estimated to be 17,000. Both absolute concentrations of Dex-P in ST and the basal-apical gradients were found to vary substantially. The existence of substantial basal-apical concentration gradients of Dex-P in ST perilymph were demonstrated experimentally. If the variability in peak concentration and gradient is also present under clinical conditions, this may contribute to the heterogeneity of outcome that is observed after intratympanic application of glucocorticoids for various inner ear diseases.

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

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

Hardy, David J., E-mail: dhardy@illinois.edu; Schulten, Klaus; Wolff, Matthew A.

2016-03-21

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation methodmore » (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle–mesh Ewald method falls short.« less

Large-Scale Optimization for Bayesian Inference in Complex Systems

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

Willcox, Karen; Marzouk, Youssef

2013-11-12

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of themore » SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems

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

Ghattas, Omar

2013-10-15

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUAROmore » Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

STUDIES ON ISOLATED NUCLEI. I. ISOLATION AND CHEMICAL CHARACTERIZATION OF A NUCLEAR FRACTION FROM GUINEA PIG LIVER.

PubMed

MAGGIO, R; SIEKEVITZ, P; PALADE, G E

1963-08-01

This article describes a method for the isolation of nuclei from guinea pig liver. It involves the homogenization of the tissue in 0.88 M sucrose-1.5 mM CaCl(2) followed by centrifugation in a discontinuous density gradient in which the upper phase is the homogenate and the lower phase is 2.2 M sucrose-0.5 mM CaCl(2). Based on DNA recovery, the isolated fraction contains 25 to 30 per cent of the nuclei of the original homogenate. Electron microscopical observations showed that approximately 88 per cent of the isolated nuclei come from liver cells (the rest from von Kupffer cells and leucocytes) and that approximately 90 per cent of the nuclei appear intact, with well preserved nucleoli, nucleoplasm, nuclear envelope, and pores. Cytoplasmic contamination is minimal and consists primarily of the nuclear envelope and its attached ribosomes. The nuclear fraction consists of approximately 22.3 per cent DNA, approximately 4.7 per cent RNA, and approximately 73 per cent protein, the DNA/RNA ratio being 4.7. Data on RNA extractibility by phosphate and salt and on the base composition of total nuclear RNA are included.

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

Bacterial Population Changes in a Membrane Bioreactor for Graywater Treatment Monitored by Denaturing Gradient Gel Electrophoretic Analysis of 16S rRNA Gene Fragments

PubMed Central

Stamper, David M.; Walch, Marianne; Jacobs, Rachel N.

2003-01-01

The bacterial population of a graywater treatment system was monitored over the course of 100 days, along with several wastewater biochemical parameters. The graywater treatment system employed an 1,800-liter membrane bioreactor (MBR) to process the waste, with essentially 100% recycling of the biomass. Graywater feed consisting of 10% galley water and 90% laundry water, selected to approximate the graywater composition on board U.S. Navy ships, was collected offsite. Five-day biological oxygen demand (BOD5), oils and greases (O/G), nitrogen, and phosphorus were monitored in the feed and were found to vary greatly day to day. Changes in the bacterial population were monitored by PCR amplification of region 332 to 518 (Escherichia coli numbering) of the 16S rRNA gene and denaturing gradient gel electrophoresis (DGGE) analysis of the resultant PCR products. DGGE analysis indicated a diverse and unstable bacterial population throughout the 100-day period, with spikes in feed strength causing significant changes in community structure. Long-term similarity between the communities was 0 to 25%, depending on the method of analysis. In spite of the unstable bacterial population, the MBR system was able to meet effluent quality parameters approximately 90% of the time. PMID:12571004

First-principles calculations of the structural, electronic, optical and thermal properties of the BNxAs1-x alloys

NASA Astrophysics Data System (ADS)

Hamioud, L.; Boumaza, A.; Touam, S.; Meradji, H.; Ghemid, S.; El Haj Hassan, F.; Khenata, R.; Omran, S. Bin

2016-06-01

The present paper aims to study the structural, electronic, optical and thermal properties of the boron nitride (BN) and BAs bulk materials as well as the BNxAs1-x ternary alloys by employing the full-potential-linearised augmented plane wave method within the density functional theory. The structural properties are determined using the Wu-Cohen generalised gradient approximation that is based on the optimisation of the total energy. For band structure calculations, both the Wu-Cohen generalised gradient approximation and the modified Becke-Johnson of the exchange-correlation energy and potential, respectively, are used. We investigated the effect of composition on the lattice constants, bulk modulus and band gap. Deviations of the lattice constants and the bulk modulus from the Vegard's law and the linear concentration dependence, respectively, were observed for the alloys where this result allows us to explain some specific behaviours in the electronic properties of the alloys. For the optical properties, the calculated refractive indices and the optical dielectric constants were found to vary nonlinearly with the N composition. Finally, the thermal effect on some of the macroscopic properties was predicted using the quasi-harmonic Debye model in which the lattice vibrations are taken into account.

Bacterial population changes in a membrane bioreactor for graywater treatment monitored by denaturing gradient gel electrophoretic analysis of 16S rRNA gene fragments.

PubMed

Stamper, David M; Walch, Marianne; Jacobs, Rachel N

2003-02-01

The bacterial population of a graywater treatment system was monitored over the course of 100 days, along with several wastewater biochemical parameters. The graywater treatment system employed an 1,800-liter membrane bioreactor (MBR) to process the waste, with essentially 100% recycling of the biomass. Graywater feed consisting of 10% galley water and 90% laundry water, selected to approximate the graywater composition on board U.S. Navy ships, was collected offsite. Five-day biological oxygen demand (BOD(5)), oils and greases (O/G), nitrogen, and phosphorus were monitored in the feed and were found to vary greatly day to day. Changes in the bacterial population were monitored by PCR amplification of region 332 to 518 (Escherichia coli numbering) of the 16S rRNA gene and denaturing gradient gel electrophoresis (DGGE) analysis of the resultant PCR products. DGGE analysis indicated a diverse and unstable bacterial population throughout the 100-day period, with spikes in feed strength causing significant changes in community structure. Long-term similarity between the communities was 0 to 25%, depending on the method of analysis. In spite of the unstable bacterial population, the MBR system was able to meet effluent quality parameters approximately 90% of the time.

The susceptibility analysis of landslides induced by earthquake in Aso volcanic area, Japan, scoping the prediction

NASA Astrophysics Data System (ADS)

Kubota, Tetsuya; Takeda, Tsuyoshi

2017-04-01

Kumamoto earthquake on April 16th 2016 in Kumamoto prefecture, Kyushu Island, Japan with intense seismic scale of M7.3 (maximum acceleration = 1316 gal in Aso volcanic region) yielded countless instances of landslide and debris flow that induced serious damages and causalities in the area, especially in the Aso volcanic mountain range. Hence, field investigation and numerical slope stability analysis were conducted to delve into the characteristics or the prediction factors of the landslides induced by this earthquake. For the numerical analysis, Finite Element Method (FEM) and CSSDP (Critical Slip Surface analysis by Dynamic Programming theory based on limit equilibrium method) were applied to the landslide slopes with seismic acceleration observed. These numerical analysis methods can automatically detect the landslide slip surface which has minimum Fs (factor of safety). The various results and the information obtained through this investigation and analysis were integrated to predict the landslide susceptible slopes in volcanic area induced by earthquakes and rainfalls of their aftermath, considering geologic-geomorphologic features, geo-technical characteristics of the landslides and vegetation effects on the slope stability. Based on the FEM or CSSDP results, the landslides occurred in this earthquake at the mild gradient slope on the ridge have the safety factor of slope Fs=2.20 approximately (without rainfall nor earthquake, and Fs>=1.0 corresponds to stable slope without landslide) and 1.78 2.10 (with the most severe rainfall in the past) while they have approximately Fs=0.40 with the seismic forces in this earthquake (horizontal direction 818 gal, vertical direction -320 gal respectively, observed in the earthquake). It insists that only in case of earthquakes the landslide in volcanic sediment apt to occur at the mild gradient slopes as well as on the ridges with convex cross section. Consequently, the following results are obtained. 1) At volcanic hillside, mild slopes of 7-10 ° gradient with volcanic sediment such as pumice are prone to collapse to be landslide by strong earthquake. 2) The slopes at the mountain ridge with convex cross section where the seismic vibration tends to concentrate are prone to form landslides in case of earthquake. 3) Due to the most severe precipitation of the past or in the aftermath of earthquake, no landslides occurred in these mild gradient slopes or on the mountain ridges with convex cross section. This information will be a great help in the aspect of landslide prediction.

EEG Artifact Removal Using a Wavelet Neural Network

NASA Technical Reports Server (NTRS)

Nguyen, Hoang-Anh T.; Musson, John; Li, Jiang; McKenzie, Frederick; Zhang, Guangfan; Xu, Roger; Richey, Carl; Schnell, Tom

2011-01-01

!n this paper we developed a wavelet neural network. (WNN) algorithm for Electroencephalogram (EEG) artifact removal without electrooculographic (EOG) recordings. The algorithm combines the universal approximation characteristics of neural network and the time/frequency property of wavelet. We. compared the WNN algorithm with .the ICA technique ,and a wavelet thresholding method, which was realized by using the Stein's unbiased risk estimate (SURE) with an adaptive gradient-based optimal threshold. Experimental results on a driving test data set show that WNN can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy data.

Baseline mathematics and geodetics for tracking operations

NASA Technical Reports Server (NTRS)

James, R.

1981-01-01

Various geodetic and mapping algorithms are analyzed as they apply to radar tracking systems and tested in extended BASIC computer language for real time computer applications. Closed-form approaches to the solution of converting Earth centered coordinates to latitude, longitude, and altitude are compared with classical approximations. A simplified approach to atmospheric refractivity called gradient refraction is compared with conventional ray tracing processes. An extremely detailed set of documentation which provides the theory, derivations, and application of algorithms used in the programs is included. Validation methods are also presented for testing the accuracy of the algorithms.

Optimal control of a variable spin speed CMG system for space vehicles. [Control Moment Gyros

NASA Technical Reports Server (NTRS)

Liu, T. C.; Chubb, W. B.; Seltzer, S. M.; Thompson, Z.

1973-01-01

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Including screening in van der Waals corrected density functional theory calculations: the case of atoms and small molecules physisorbed on graphene.

PubMed

Silvestrelli, Pier Luigi; Ambrosetti, Alberto

2014-03-28

The Density Functional Theory (DFT)/van der Waals-Quantum Harmonic Oscillator-Wannier function (vdW-QHO-WF) method, recently developed to include the vdW interactions in approximated DFT by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique, is applied to the cases of atoms and small molecules (X=Ar, CO, H2, H2O) weakly interacting with benzene and with the ideal planar graphene surface. Comparison is also presented with the results obtained by other DFT vdW-corrected schemes, including PBE+D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal generalized gradient approximation approaches. While for the X-benzene systems all the considered vdW-corrected schemes perform reasonably well, it turns out that an accurate description of the X-graphene interaction requires a proper treatment of many-body contributions and of short-range screening effects, as demonstrated by adopting an improved version of the DFT/vdW-QHO-WF method. We also comment on the widespread attitude of relying on LDA to get a rough description of weakly interacting systems.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Three-dimensional imaging of buried objects in very lossy earth by inversion of VETEM data

USGS Publications Warehouse

Cui, T.J.; Aydiner, A.A.; Chew, W.C.; Wright, D.L.; Smith, D.V.

2003-01-01

The very early time electromagnetic system (VETEM) is an efficient tool for the detection of buried objects in very lossy earth, which allows a deeper penetration depth compared to the ground-penetrating radar. In this paper, the inversion of VETEM data is investigated using three-dimensional (3-D) inverse scattering techniques, where multiple frequencies are applied in the frequency range from 0-5 MHz. For small and moderately sized problems, the Born approximation and/or the Born iterative method have been used with the aid of the singular value decomposition and/or the conjugate gradient method in solving the linearized integral equations. For large-scale problems, a localized 3-D inversion method based on the Born approximation has been proposed for the inversion of VETEM data over a large measurement domain. Ways to process and to calibrate the experimental VETEM data are discussed to capture the real physics of buried objects. Reconstruction examples using synthesized VETEM data and real-world VETEM data are given to test the validity and efficiency of the proposed approach.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-07-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

A coupled electro-thermal Discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Homsi, L.; Geuzaine, C.; Noels, L.

2017-11-01

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree.

Automatic threshold optimization in nonlinear energy operator based spike detection.

PubMed

Malik, Muhammad H; Saeed, Maryam; Kamboh, Awais M

2016-08-01

In neural spike sorting systems, the performance of the spike detector has to be maximized because it affects the performance of all subsequent blocks. Non-linear energy operator (NEO), is a popular spike detector due to its detection accuracy and its hardware friendly architecture. However, it involves a thresholding stage, whose value is usually approximated and is thus not optimal. This approximation deteriorates the performance in real-time systems where signal to noise ratio (SNR) estimation is a challenge, especially at lower SNRs. In this paper, we propose an automatic and robust threshold calculation method using an empirical gradient technique. The method is tested on two different datasets. The results show that our optimized threshold improves the detection accuracy in both high SNR and low SNR signals. Boxplots are presented that provide a statistical analysis of improvements in accuracy, for instance, the 75th percentile was at 98.7% and 93.5% for the optimized NEO threshold and traditional NEO threshold, respectively.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Effects of horizontal refractivity gradients on the accuracy of laser ranging to satellites

NASA Technical Reports Server (NTRS)

Gardner, C. S.

1976-01-01

Numerous formulas have been developed to partially correct laser ranging data for the effects of atmospheric refraction. All the formulas assume the atmospheric refractivity profile is spherically symmetric. The effects of horizontal refractivity gradients are investigated by ray tracing through spherically symmetric and three-dimensional refractivity profiles. The profiles are constructed from radiosonde data. The results indicate that the horizontal gradients introduce an rms error of approximately 3 cm when the satellite is near 10 deg elevation. The error decreases to a few millimeters near zenith.

A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

PubMed

Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn

2007-01-01

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

Incidence of twolined chestnut borer and Hypoxylon atropunctatum on dead oaks along an acidic deposition gradient from Arkansas to Ohio

Treesearch

R.A. Haack; R.W. Blank

1991-01-01

The incidence of twolined chestnut borer (TLCB), Agrilus bilineatus (Weber), and the canker fungus Hypoxylon atropunctatum (Schw. ex Fr.) Cke. was recoreded on dead oak (Quercus) trees !Y7 cm diameter at breast height (DBH) along an acidic deposition gradient from Arkansas to Ohio in 1989 and 1990. Approximately...

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Free energy calculations: an efficient adaptive biasing potential method.

PubMed

Dickson, Bradley M; Legoll, Frédéric; Lelièvre, Tony; Stoltz, Gabriel; Fleurat-Lessard, Paul

2010-05-06

We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is computed directly from the population along the coordinates of the free energy. Because of the mollifier, the bias potential is "nonlocal", and its gradient admits a simple analytic expression. A single observation of the reaction coordinate can thus be used to update the approximate free energy at every point within a neighborhood of the observation. This greatly reduces the equilibration time of the adaptive bias potential. This approximation introduces two parameters: strength of mollification and the zero of energy of the bias potential. While we observe that the approximate free energy is a very good estimate of the actual free energy for a large range of mollification strength, we demonstrate that the errors associated with the mollification may be removed via deconvolution. The zero of energy of the bias potential, which is easy to choose, influences the speed of convergence but not the limiting accuracy. This method is simple to apply to free energy or mean force computation in multiple dimensions and does not involve second derivatives of the reaction coordinates, matrix manipulations nor on-the-fly adaptation of parameters. For the alanine dipeptide test case, the new method is found to gain as much as a factor of 10 in efficiency as compared to two basic implementations of the adaptive biasing force methods, and it is shown to be as efficient as well-tempered metadynamics with the postprocess deconvolution giving a clear advantage to the mollified density of states method.

Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Mejia-Rodriguez, Daniel; Trickey, S. B.

2017-11-01

We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic-energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization, but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, Tao-Perdew-Staroverov-Scuseria, and strongly constrained and appropriately normed functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.

Radial evolution of power spectra of interplanetary Alfvenic turbulence

NASA Technical Reports Server (NTRS)

Bavassano, B.; Dobrowolny, M.; Mariani, F.; Ness, N. F.

1981-01-01

The radial evolution of the power spectra of the MHD turbulence within the trailing edge of high speed streams in the solar wind was investigated with the magnetic field data of Helios 1 and 2 for heliocentric distance between 0.3 and 0.9 AU. In the analyzed frequency range (.00028 Hz to .0083 Hz) the computed spectra have, near the Earth, values of the spectral index close to that predicted for an incompressible hydromagnetic turbulence in a stationary state. Approaching the Sun the spectral slope remains unchanged for frequencies f or approximately .00 Hz, whereas at lower frequencies, a clear evolution toward a less steep fall off with frequency is found. The radial gradient of the power in Alfvenic fluctuations depends on frequency and it increases upon increasing frequency. For frequencies f or approximately .00 Hz, however, the radial gradient remains approximately the same. Possible theoretical implications of the observational features are discussed.

Applying the Zel'dovich approximation to general relativity

NASA Astrophysics Data System (ADS)

Croudace, K. M.; Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

Starting from general relativity, we give a systematic derivation of the Zel'dovich approximation describing the nonlinear evolution of collisionless dust. We begin by evolving dust along world lines, and we demonstrate that the Szekeres line element is an exact but apparently unstable solution of the evolution equations describing pancake collapse. Next, we solve the Einstein field equations by employing Hamilton-Jacobi techniques and a spatial gradient expansion. We give a prescription for evolving a primordial or 'seed' metric up to the formation of pancakes, and demonstrate its validity by rederiving the Szekeres solution approximately at third order and exactly at fifth order in spatial gradients. Finally we show that the range of validity of the expansion can be improved quite significantly if one notes that the 3-metric must have nonnegative eigenvalues. With this improvement the exact Szekeres solution is obtained after only one iteration.

Density functional theory calculations of the water interactions with ZrO2 nanoparticles Y2O3 doped

NASA Astrophysics Data System (ADS)

Subhoni, Mekhrdod; Kholmurodov, Kholmirzo; Doroshkevich, Aleksandr; Asgerov, Elmar; Yamamoto, Tomoyuki; Lyubchyk, Andrei; Almasan, Valer; Madadzada, Afag

2018-03-01

Development of a new electricity generation techniques is one of the most relevant tasks, especially nowadays under conditions of extreme growth in energy consumption. The exothermic heterogeneous electrochemical energy conversion to the electric energy through interaction of the ZrO2 based nanopowder system with atmospheric moisture is one of the ways of electric energy obtaining. The questions of conversion into the electric form of the energy of water molecules adsorption in 3 mol% Y2O3 doped ZrO2 nanopowder systems were investigated using the density functional theory calculations. The density functional theory calculations has been realized as in the Kohn-Sham formulation, where the exchange-correlation potential is approximated by a functional of the electronic density. The electronic density, total energy and band structure calculations are carried out using the all-electron, full potential, linear augmented plane wave method of the electronic density and related approximations, i.e. the local density, the generalized gradient and their hybrid approximations.

Algorithm for ion beam figuring of low-gradient mirrors.

PubMed

Jiao, Changjun; Li, Shengyi; Xie, Xuhui

2009-07-20

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100 lambda.

Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model.

PubMed

Paninski, Liam; Haith, Adrian; Szirtes, Gabor

2008-02-01

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

Solving the scalability issue in quantum-based refinement: Q|R#1.

PubMed

Zheng, Min; Moriarty, Nigel W; Xu, Yanting; Reimers, Jeffrey R; Afonine, Pavel V; Waller, Mark P

2017-12-01

Accurately refining biomacromolecules using a quantum-chemical method is challenging because the cost of a quantum-chemical calculation scales approximately as n m , where n is the number of atoms and m (≥3) is based on the quantum method of choice. This fundamental problem means that quantum-chemical calculations become intractable when the size of the system requires more computational resources than are available. In the development of the software package called Q|R, this issue is referred to as Q|R#1. A divide-and-conquer approach has been developed that fragments the atomic model into small manageable pieces in order to solve Q|R#1. Firstly, the atomic model of a crystal structure is analyzed to detect noncovalent interactions between residues, and the results of the analysis are represented as an interaction graph. Secondly, a graph-clustering algorithm is used to partition the interaction graph into a set of clusters in such a way as to minimize disruption to the noncovalent interaction network. Thirdly, the environment surrounding each individual cluster is analyzed and any residue that is interacting with a particular cluster is assigned to the buffer region of that particular cluster. A fragment is defined as a cluster plus its buffer region. The gradients for all atoms from each of the fragments are computed, and only the gradients from each cluster are combined to create the total gradients. A quantum-based refinement is carried out using the total gradients as chemical restraints. In order to validate this interaction graph-based fragmentation approach in Q|R, the entire atomic model of an amyloid cross-β spine crystal structure (PDB entry 2oNA) was refined.

Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization.

PubMed

Lu, Hanbing; Jesmanowicz, Andrzej; Li, Shi-Jiang; Hyde, James S

2004-01-01

MRI gradient coil design is a type of nonlinear constrained optimization. A practical problem in transverse gradient coil design using the conjugate gradient descent (CGD) method is that wire elements move at different rates along orthogonal directions (r, phi, z), and tend to cross, breaking the constraints. A momentum-weighted conjugate gradient descent (MW-CGD) method is presented to overcome this problem. This method takes advantage of the efficiency of the CGD method combined with momentum weighting, which is also an intrinsic property of the Levenberg-Marquardt algorithm, to adjust step sizes along the three orthogonal directions. A water-cooled, 12.8 cm inner diameter, three axis torque-balanced gradient coil for rat imaging was developed based on this method, with an efficiency of 2.13, 2.08, and 4.12 mT.m(-1).A(-1) along X, Y, and Z, respectively. Experimental data demonstrate that this method can improve efficiency by 40% and field uniformity by 27%. This method has also been applied to the design of a gradient coil for the human brain, employing remote current return paths. The benefits of this design include improved gradient field uniformity and efficiency, with a shorter length than gradient coil designs using coaxial return paths. Copyright 2003 Wiley-Liss, Inc.

Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement

NASA Astrophysics Data System (ADS)

Tran, Fabien; Ehsan, Sohaib; Blaha, Peter

2018-02-01

Based on the work of Gritsenko et al. (GLLB) [Phys. Rev. A 51, 1944 (1995), 10.1103/PhysRevA.51.1944], the method of Kuisma et al. [Phys. Rev. B 82, 115106 (2010), 10.1103/PhysRevB.82.115106] to calculate the band gap in solids was shown to be much more accurate than the common local density approximation (LDA) and generalized gradient approximation (GGA). The main feature of the GLLB-SC potential (SC stands for solid and correlation) is to lead to a nonzero derivative discontinuity that can be conveniently calculated and then added to the Kohn-Sham band gap for a comparison with the experimental band gap. In this work, a thorough comparison of GLLB-SC with other methods, e.g., the modified Becke-Johnson (mBJ) potential [Tran and Blaha, Phys. Rev. Lett. 102, 226401 (2009), 10.1103/PhysRevLett.102.226401], for electronic, magnetic, and density-related properties is presented. It is shown that for the band gap, GLLB-SC does not perform as well as mBJ for systems with a small band gap and strongly correlated systems, but is on average of similar accuracy as hybrid functionals. The results on itinerant metals indicate that GLLB-SC overestimates significantly the magnetic moment (much more than mBJ does), but leads to excellent results for the electric field gradient, for which mBJ is in general not recommended. In the aim of improving the results, variants of the GLLB-SC potential are also tested.

Bin Packing, Number Balancing, and Rescaling Linear Programs

NASA Astrophysics Data System (ADS)

Hoberg, Rebecca

This thesis deals with several important algorithmic questions using techniques from diverse areas including discrepancy theory, machine learning and lattice theory. In Chapter 2, we construct an improved approximation algorithm for a classical NP-complete problem, the bin packing problem. In this problem, the goal is to pack items of sizes si ∈ [0,1] into as few bins as possible, where a set of items fits into a bin provided the sum of the item sizes is at most one. We give a polynomial-time rounding scheme for a standard linear programming relaxation of the problem, yielding a packing that uses at most OPT + O(log OPT) bins. This makes progress towards one of the "10 open problems in approximation algorithms" stated in the book of Shmoys and Williamson. In fact, based on related combinatorial lower bounds, Rothvoss conjectures that theta(logOPT) may be a tight bound on the additive integrality gap of this LP relaxation. In Chapter 3, we give a new polynomial-time algorithm for linear programming. Our algorithm is based on the multiplicative weights update (MWU) method, which is a general framework that is currently of great interest in theoretical computer science. An algorithm for linear programming based on MWU was known previously, but was not polynomial time--we remedy this by alternating between a MWU phase and a rescaling phase. The rescaling methods we introduce improve upon previous methods by reducing the number of iterations needed until one can rescale, and they can be used for any algorithm with a similar rescaling structure. Finally, we note that the MWU phase of the algorithm has a simple interpretation as gradient descent of a particular potential function, and we show we can speed up this phase by walking in a direction that decreases both the potential function and its gradient. In Chapter 4, we show that an approximate oracle for Minkowski's Theorem gives an approximate oracle for the number balancing problem, and conversely. Number balancing is the problem of minimizing | 〈a,x〉 | over x ∈ {-1,0,1}n \\ { 0}, given a ∈ [0,1]n. While an application of the pigeonhole principle shows that there always exists x with | 〈a,x〉| ≤ O(√ n/2n), the best known algorithm only guarantees |〈a,x〉| ≤ 2-ntheta(log n). We show that an oracle for Minkowski's Theorem with approximation factor rho would give an algorithm for NBP that guarantees | 〈a,x〉 | ≤ 2-ntheta(1/rho). In particular, this would beat the bound of Karmarkar and Karp provided rho ≤ O(logn/loglogn). In the other direction, we prove that any polynomial time algorithm for NBP that guarantees a solution of difference at most 2√n/2 n would give a polynomial approximation for Minkowski as well as a polynomial factor approximation algorithm for the Shortest Vector Problem.

Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.

PubMed

Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M

2015-09-08

We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.

Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths.

PubMed

Tsai, Yu-Ju; Larouche, Stéphane; Tyler, Talmage; Lipworth, Guy; Jokerst, Nan M; Smith, David R

2011-11-21

We demonstrate the design, fabrication and characterization of an artificially structured, gradient index metamaterial with a linear index variation of Δn ~ 3.0. The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61 μm. The grating, which operates at a wavelength of 10.6 μm, is composed of non-resonant, progressively modified "I-beam" metamaterial elements and approximates a linear phase shift gradient using 61 distinguishable phase levels. The grating structure consists of four layers of lithographically patterned metallic I-beam elements separated by dielectric layers of SiO(2). The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations incorporating all material properties of the metals and dielectrics of the structures. The large index gradient has the potential to enable compact infrared diffractive and gradient index optics, as well as more exotic transformation optical media. © 2011 Optical Society of America

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Full-Potential Calculation of Structural, Electronic, and Thermodynamic Properties of Fluoroperovskite { CsMF}3 (M = Be and Mg)

NASA Astrophysics Data System (ADS)

Harmel, M.; Khachai, H.; Ameri, A.; Baki, N.; Haddou, A.; Khalfa, M.; Abbar, B.; Omran, S. Bin; Uğur, G.; Uğur, Ş.; Khenata, R.

2012-12-01

The structural and electronic properties of the cubic fluoroperoveskite { CsBeF}3 and { CsMgF}3 have been investigated using the full-potential-linearized augmented plane wave method within the density functional theory. The exchange-correlation potential was treated with the local density approximation and the generalized gradient approximation. The calculations of the electronic band structures show that { CsBeF}_{3 } has an indirect bandgap, whereas { CsMgF}3 has a direct bandgap. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the effect of pressure P and temperature T on the lattice parameter, bulk modulus, thermal expansion coefficient, Debye temperature, and the heat capacity for { CsBeF}3 and { CsMgF}3 compounds are investigated for the first time.

Redundant interferometric calibration as a complex optimization problem

NASA Astrophysics Data System (ADS)

Grobler, T. L.; Bernardi, G.; Kenyon, J. S.; Parsons, A. R.; Smirnov, O. M.

2018-05-01

Observations of the redshifted 21 cm line from the epoch of reionization have recently motivated the construction of low-frequency radio arrays with highly redundant configurations. These configurations provide an alternative calibration strategy - `redundant calibration' - and boost sensitivity on specific spatial scales. In this paper, we formulate calibration of redundant interferometric arrays as a complex optimization problem. We solve this optimization problem via the Levenberg-Marquardt algorithm. This calibration approach is more robust to initial conditions than current algorithms and, by leveraging an approximate matrix inversion, allows for further optimization and an efficient implementation (`redundant STEFCAL'). We also investigated using the preconditioned conjugate gradient method as an alternative to the approximate matrix inverse, but found that its computational performance is not competitive with respect to `redundant STEFCAL'. The efficient implementation of this new algorithm is made publicly available.

Roof planes detection via a second-order variational model

NASA Astrophysics Data System (ADS)

Benciolini, Battista; Ruggiero, Valeria; Vitti, Alfonso; Zanetti, Massimo

2018-04-01

The paper describes a unified automatic procedure for the detection of roof planes in gridded height data. The procedure exploits the Blake-Zisserman (BZ) model for segmentation in both 2D and 1D, and aims to detect, to model and to label roof planes. The BZ model relies on the minimization of a functional that depends on first- and second-order derivatives, free discontinuities and free gradient discontinuities. During the minimization, the relative strength of each competitor is controlled by a set of weight parameters. By finding the minimum of the approximated BZ functional, one obtains: (1) an approximation of the data that is smoothed solely within regions of homogeneous gradient, and (2) an explicit detection of the discontinuities and gradient discontinuities of the approximation. Firstly, input data is segmented using the 2D BZ. The maps of data and gradient discontinuities are used to isolate building candidates and planar patches (i.e. regions with homogeneous gradient) that correspond to roof planes. Connected regions that can not be considered as buildings are filtered according to both patch dimension and distribution of the directions of the normals to the boundary. The 1D BZ model is applied to the curvilinear coordinates of boundary points of building candidates in order to reduce the effect of data granularity when the normals are evaluated. In particular, corners are preserved and can be detected by means of gradient discontinuity. Lastly, a total least squares model is applied to estimate the parameters of the plane that best fits the points of each planar patch (orthogonal regression with planar model). Refinement of planar patches is performed by assigning those points that are close to the boundaries to the planar patch for which a given proximity measure assumes the smallest value. The proximity measure is defined to account for the variance of a fitting plane and a weighted distance of a point from the plane. The effectiveness of the proposed procedure is demonstrated by means of its application to urban digital surface models characterized by different spatial resolutions. Results are presented and discussed along with some promising developments.

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.

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2006-01-01

A DJOINT 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. 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 (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. 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). In previous work on Cartesian adjoint solvers, Melvin et al. 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 two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, 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 were 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 accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying 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.

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

NASA Technical Reports Server (NTRS)

Gray, Justin; Chin, Jeffrey; Hearn, Tristan; Hendricks, Eric; Lavelle, Thomas; Martins, Joaquim R. R. A.

2016-01-01

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

Computational alternatives to obtain time optimal jet engine control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Basso, R. J.; Leake, R. J.

1976-01-01

Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

Development, evaluation and application of a modified micrometeorological gradient method for long-term estimation of gaseous dry deposition over forest canopies.

EPA Science Inventory

Small pollutant concentration gradients between levels above a plant canopy result in large uncertainties in estimated air–surface exchange fluxes when using existing micrometeorological gradient methods, including the aerodynamic gradient method (AGM) and the modified Bowen rati...

Adaptive Discrete Hypergraph Matching.

PubMed

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Putting Priors in Mixture Density Mercer Kernels

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd

2004-01-01

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Agarose and Polyacrylamide Gel Electrophoresis Methods for Molecular Mass Analysis of 5–500 kDa Hyaluronan

PubMed Central

Bhilocha, Shardul; Amin, Ripal; Pandya, Monika; Yuan, Han; Tank, Mihir; LoBello, Jaclyn; Shytuhina, Anastasia; Wang, Wenlan; Wisniewski, Hans-Georg; de la Motte, Carol; Cowman, Mary K.

2011-01-01

Agarose and polyacrylamide gel electrophoresis systems for the molecular mass-dependent separation of hyaluronan (HA) in the size range of approximately 5–500 kDa have been investigated. For agarose-based systems, the suitability of different agarose types, agarose concentrations, and buffers systems were determined. Using chemoenzymatically synthesized HA standards of low polydispersity, the molecular mass range was determined for each gel composition, over which the relationship between HA mobility and logarithm of the molecular mass was linear. Excellent linear calibration was obtained for HA molecular mass as low as approximately 9 kDa in agarose gels. For higher resolution separation, and for extension to molecular masses as low as approximately 5 kDa, gradient polyacrylamide gels were superior. Densitometric scanning of stained gels allowed analysis of the range of molecular masses present in a sample, and calculation of weight-average and number-average values. The methods were validated for polydisperse HA samples with viscosity-average molecular masses of 112, 59, 37, and 22 kDa, at sample loads of 0.5 µg (for polyacrylamide) to 2.5 µg (for agarose). Use of the methods for electrophoretic mobility shift assays was demonstrated for binding of the HA-binding region of aggrecan (recombinant human aggrecan G1-IGD-G2 domains) to a 150 kDa HA standard. PMID:21684248

Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime.

PubMed

Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E

2010-11-08

Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.

Comment on "the one dimensional acoustic field with arbitrary mean axial temperature gradient and mean flow" (J.Li and A.S.Morgans, Journal of Sound and Vibration 400 (2017) 248-269)

NASA Astrophysics Data System (ADS)

Dokumaci, Erkan

2017-12-01

In a recent study, Li and Morgans [1] present an ingenious WKB approximation for the acoustic plane wave field in a straight uniform duct with mean temperature gradient and mean flow. The authors state that the previous solutions are limited to small linear mean temperature gradients and low mean flow Mach numbers and claim that their solution applies for arbitrary mean temperature profiles and moderate-to-large mean flow velocity Mach numbers at both low and high frequencies.

Insulator edge voltage gradient effects in spacecraft charging phenomena

NASA Technical Reports Server (NTRS)

Stevens, N. J.; Purvis, C. K.; Staskus, J. V.

1978-01-01

Insulating surfaces on geosynchronous satellites were charged by geomagnetic substorms to a point where discharges occur. The electromagnetic pulses from these discharges couple into satellite electronic systems disrupting operations are examined. Laboratory tests conducted on insulator charging have indicated that discharges appear to be initiated at insulator edges where voltage gradients can exist. An experimental investigation was conducted to measure edge voltage gradients on silvered Teflon samples as they are charged by monoenergetic electron beams. It was found that the surface voltage at insulator edges can be approximated by an exponential expression based on an electron current density balance.

Temperature gradient measurements by using thermoelectric effect in CNTs-silicone adhesive composite.

PubMed

Chani, Muhammad Tariq Saeed; Karimov, Kh S; Asiri, Abdullah M; Ahmed, Nisar; Bashir, Muhammad Mehran; Khan, Sher Bahadar; Rub, Malik Abdul; Azum, Naved

2014-01-01

This work presents the fabrication and investigation of thermoelectric cells based on composite of carbon nanotubes (CNT) and silicone adhesive. The composite contains CNT and silicon adhesive 1∶1 by weight. The current-voltage characteristics and dependences of voltage, current and Seebeck coefficient on the temperature gradient of cell were studied. It was observed that with increase in temperature gradient the open circuit voltage, short circuit current and the Seebeck coefficient of the cells increase. Approximately 7 times increase in temperature gradient increases the open circuit voltage and short circuit current up to 40 and 5 times, respectively. The simulation of experimental results is also carried out; the simulated results are well matched with experimental results.

Temperature Gradient Measurements by Using Thermoelectric Effect in CNTs-Silicone Adhesive Composite

PubMed Central

Chani, Muhammad Tariq Saeed; Karimov, Kh. S.; Asiri, Abdullah M.; Ahmed, Nisar; Bashir, Muhammad Mehran; Khan, Sher Bahadar; Rub, Malik Abdul; Azum, Naved

2014-01-01

This work presents the fabrication and investigation of thermoelectric cells based on composite of carbon nanotubes (CNT) and silicone adhesive. The composite contains CNT and silicon adhesive 1∶1 by weight. The current-voltage characteristics and dependences of voltage, current and Seebeck coefficient on the temperature gradient of cell were studied. It was observed that with increase in temperature gradient the open circuit voltage, short circuit current and the Seebeck coefficient of the cells increase. Approximately 7 times increase in temperature gradient increases the open circuit voltage and short circuit current up to 40 and 5 times, respectively. The simulation of experimental results is also carried out; the simulated results are well matched with experimental results. PMID:24748375

Dispersion of acoustic surface waves by velocity gradients

NASA Astrophysics Data System (ADS)

Kwon, S. D.; Kim, H. C.

1987-10-01

The perturbation theory of Auld [Acoustic Fields and Waves in Solids (Wiley, New York, 1973), Vol. II, p. 294], which describes the effect of a subsurface gradient on the velocity dispersion of surface waves, has been modified to a simpler form by an approximation using a newly defined velocity gradient for the case of isotropic materials. The modified theory is applied to nitrogen implantation in AISI 4140 steel with a velocity gradient of Gaussian profile, and compared with dispersion data obtained by the ultrasonic right-angle technique in the frequency range from 2.4 to 14.8 MHz. The good agreement between experiments and our theory suggests that the compound layer in the subsurface region plays a dominant role in causing the dispersion of acoustic surface waves.

An efficient and practical approach to obtain a better optimum solution for structural optimization

NASA Astrophysics Data System (ADS)

Chen, Ting-Yu; Huang, Jyun-Hao

2013-08-01

For many structural optimization problems, it is hard or even impossible to find the global optimum solution owing to unaffordable computational cost. An alternative and practical way of thinking is thus proposed in this research to obtain an optimum design which may not be global but is better than most local optimum solutions that can be found by gradient-based search methods. The way to reach this goal is to find a smaller search space for gradient-based search methods. It is found in this research that data mining can accomplish this goal easily. The activities of classification, association and clustering in data mining are employed to reduce the original design space. For unconstrained optimization problems, the data mining activities are used to find a smaller search region which contains the global or better local solutions. For constrained optimization problems, it is used to find the feasible region or the feasible region with better objective values. Numerical examples show that the optimum solutions found in the reduced design space by sequential quadratic programming (SQP) are indeed much better than those found by SQP in the original design space. The optimum solutions found in a reduced space by SQP sometimes are even better than the solution found using a hybrid global search method with approximate structural analyses.

Increasing the utility of regional water table maps: a new method for estimating groundwater recharge

NASA Astrophysics Data System (ADS)

Gilmore, T. E.; Zlotnik, V. A.; Johnson, M.

2017-12-01

Groundwater table elevations are one of the most fundamental measurements used to characterize unconfined aquifers, groundwater flow patterns, and aquifer sustainability over time. In this study, we developed an analytical model that relies on analysis of groundwater elevation contour (equipotential) shape, aquifer transmissivity, and streambed gradient between two parallel, perennial streams. Using two existing regional water table maps, created at different times using different methods, our analysis of groundwater elevation contours, transmissivity and streambed gradient produced groundwater recharge rates (42-218 mm yr-1) that were consistent with previous independent recharge estimates from different methods. The three regions we investigated overly the High Plains Aquifer in Nebraska and included some areas where groundwater is used for irrigation. The three regions ranged from 1,500 to 3,300 km2, with either Sand Hills surficial geology, or Sand Hills transitioning to loess. Based on our results, the approach may be used to increase the value of existing water table maps, and may be useful as a diagnostic tool to evaluate the quality of groundwater table maps, identify areas in need of detailed aquifer characterization and expansion of groundwater monitoring networks, and/or as a first approximation before investing in more complex approaches to groundwater recharge estimation.

Design of A Cyclone Separator Using Approximation Method

NASA Astrophysics Data System (ADS)

Sin, Bong-Su; Choi, Ji-Won; Lee, Kwon-Hee

2017-12-01

A Separator is a device installed in industrial applications to separate mixed objects. The separator of interest in this research is a cyclone type, which is used to separate a steam-brine mixture in a geothermal plant. The most important performance of the cyclone separator is the collection efficiency. The collection efficiency in this study is predicted by performing the CFD (Computational Fluid Dynamics) analysis. This research defines six shape design variables to maximize the collection efficiency. Thus, the collection efficiency is set up as the objective function in optimization process. Since the CFD analysis requires a lot of calculation time, it is impossible to obtain the optimal solution by linking the gradient-based optimization algorithm. Thus, two approximation methods are introduced to obtain an optimum design. In this process, an L18 orthogonal array is adopted as a DOE method, and kriging interpolation method is adopted to generate the metamodel for the collection efficiency. Based on the 18 analysis results, the relative importance of each variable to the collection efficiency is obtained through the ANOVA (analysis of variance). The final design is suggested considering the results obtained from two optimization methods. The fluid flow analysis of the cyclone separator is conducted by using the commercial CFD software, ANSYS-CFX.

Perturbative Out of Equilibrium Quantum Field Theory beyond the Gradient Approximation and Generalized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Ozaki, H.

2004-01-01

Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We employ the derivative expansion and take in up to the second-order term, i.e., one-order higher than the gradient approximation. After constructing self-energy resummed propagator, we formulated two kinds of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the ``bare'' number density function, and the second one is formulated on the basis of ``physical'' number density function. In the course of construction of the second framework, the generalized Boltzmann equations directly come out, which describe the evolution of the system.

Comparison of genetic algorithms with conjugate gradient methods

NASA Technical Reports Server (NTRS)

Bosworth, J. L.; Foo, N. Y.; Zeigler, B. P.

1972-01-01

Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.

Simplified DFT methods for consistent structures and energies of large systems

NASA Astrophysics Data System (ADS)

Caldeweyher, Eike; Gerit Brandenburg, Jan

2018-05-01

Kohn–Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree–Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

Ab-initio study of B{sub 2}-type technetium AB (A=Tc, B=Nb and Ta) intermetallic compounds

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

Acharya, Nikita, E-mail: acharyaniks30@gmail.com; Fatima, Bushra; Sanyal, Sankar P.

2016-05-06

The structural, electronic and elastic properties of AB type (A = Tc, B = Nb and Ta) technetium intermetallic compounds are studied using full potential linearized plane wave (FP-LAPW) method within generalized gradient approximation (GGA). The calculated lattice parameters agree well with the experimental results. The elastic constants obey the stability criteria for cubic system. Ductility for these compounds has been analyzed using the Pugh’s rule and Cauchy’s pressure and found that all the compounds are ductile in nature. Bonding nature is discussed in terms of Fermi surface and band structures.

High-pressure melting of molybdenum.

PubMed

Belonoshko, A B; Simak, S I; Kochetov, A E; Johansson, B; Burakovsky, L; Preston, D L

2004-05-14

The melting curve of the body-centered cubic (bcc) phase of Mo has been determined for a wide pressure range using both direct ab initio molecular dynamics simulations of melting as well as a phenomenological theory of melting. These two methods show very good agreement. The simulations are based on density functional theory within the generalized gradient approximation. Our calculated equation of state of bcc Mo is in excellent agreement with experimental data. However, our melting curve is substantially higher than the one determined in diamond anvil cell experiments up to a pressure of 100 GPa. An explanation is suggested for this discrepancy.

Vibrational and Thermal Properties of Oxyanionic Crystals

NASA Astrophysics Data System (ADS)

Korabel'nikov, D. V.

2018-03-01

The vibrational and thermal properties of dolomite and alkali chlorates and perchlorates were studied in the gradient approximation of density functional theory using the method of a linear combination of atomic orbitals (LCAO). Long-wave vibration frequencies, IR and Raman spectra, and mode Gruneisen parameters were calculated. Equation-of-state parameters, thermodynamic potentials, entropy, heat capacity, and thermal expansion coefficient were also determined. The thermal expansion coefficient of dolomite was established to be much lower than for chlorates and perchlorates. The temperature dependence of the heat capacity at T > 200 K was shown to be generally governed by intramolecular vibrations.

Electrophoretic separation of proteins in space

NASA Technical Reports Server (NTRS)

Brown, R. K.

1976-01-01

Commercially available and synthetic wide range and short range ampholytes used in the isoelectric focusing of proteins was analyzed by ion exchange chromatography. A pH gradient over the pH range 3.8 to 11.0 was used to elute the ampholytes from a column of a sulfonated polystyrene resin. The wide range ampholytes were resolved into some 60 to 70 ninhydrin positive components. The recovery obtained with the method was quantitative. Acid short range ampholytes have approximately 35 components which elute readily from the ion exchange resin. Basic short range ampholytes gave about 50 components, most of which eluted at alkaline pH.

The Effects of Large Wood on Stream Channel Morphology on Three Low-Gradient Stream Reaches in the Coastal Redwood Region

Treesearch

Scott Carroll; E. George Robison

2007-01-01

Several studies have shown that large wood has a prominent role in habitat quality, however there is little research on the role of wood on pool characteristics and other habitat components in low gradient streams (channel slopes less than one percent). Longitudinal profiles are used to analyze general residual pool characteristics of three approximately 1000-meter...

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Characterization of a Dynamic String Method for the Construction of Transition Pathways in Molecular Reactions

PubMed Central

Johnson, Margaret E.; Hummer, Gerhard

2012-01-01

We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion, and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method. PMID:22616575

Pixel-based OPC optimization based on conjugate gradients.

PubMed

Ma, Xu; Arce, Gonzalo R

2011-01-31

Optical proximity correction (OPC) methods are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the mask is divided into small pixels, each of which is modified during the optimization process. Two critical issues in PBOPC are the required computational complexity of the optimization process, and the manufacturability of the optimized mask. Most current OPC optimization methods apply the steepest descent (SD) algorithm to improve image fidelity augmented by regularization penalties to reduce the complexity of the mask. Although simple to implement, the SD algorithm converges slowly. The existing regularization penalties, however, fall short in meeting the mask rule check (MRC) requirements often used in semiconductor manufacturing. This paper focuses on developing OPC optimization algorithms based on the conjugate gradient (CG) method which exhibits much faster convergence than the SD algorithm. The imaging formation process is represented by the Fourier series expansion model which approximates the partially coherent system as a sum of coherent systems. In order to obtain more desirable manufacturability properties of the mask pattern, a MRC penalty is proposed to enlarge the linear size of the sub-resolution assistant features (SRAFs), as well as the distances between the SRAFs and the main body of the mask. Finally, a projection method is developed to further reduce the complexity of the optimized mask pattern.

Geologic and geophysical data for wells drilled at Raft River Valley, Cassia County, Idaho, in 1977-1978 and data for wells drilled previously

USGS Publications Warehouse

Nathenson, Manuel; Urban, Thomas C.; Covington, Harry R.

2014-01-01

For purposes of defining the thermal anomaly for the geothermal system, temperature gradients are calculated over long depth intervals on the basis of the appearance of reasonable linear segments on a temperature versus plot depth.  Temperature versus depth data for some drill holes can be represented by a single gradient, whereas others require multiple gradients to match the data.  Data for some drill holes clearly reflect vertical flows of water in the formation surrounding the drill holes, and water velocities are calculated for these drill holes.  Within The Narrows area, temperature versus depth data show reversals at different depth in different drill holes.  In the main thermal area, temperatures in intermediate-depth drill holes vary approximately linearly but with very high values of temperature gradient.  Temperature gradients on a map of the area can be reasonable divided into a large area of regional gradients and smaller areas defining the thermal anomalies.

Inelastic neutron scattering spectrum of cyclotrimethylenetrinitramine: a comparison with solid-state electronic structure calculations.

PubMed

Ciezak, Jennifer A; Trevino, S F

2006-04-20

Solid-state geometry optimizations and corresponding normal-mode analysis of the widely used energetic material cyclotrimethylenetrinitramine (RDX) were performed using density functional theory with both the generalized gradient approximation (BLYP and BP functionals) and the local density approximation (PWC and VWN functionals). The structural results were found to be in good agreement with experimental neutron diffraction data and previously reported calculations based on the isolated-molecule approximation. The vibrational inelastic neutron scattering (INS) spectrum of polycrystalline RDX was measured and compared with simulated INS constructed from the solid-state calculations. The vibrational frequencies calculated from the solid-state methods had average deviations of 10 cm(-1) or less, whereas previously published frequencies based on an isolated-molecule approximation had deviations of 65 cm(-1) or less, illustrating the importance of including crystalline forces. On the basis of the calculations and analysis, it was possible to assign the normal modes and symmetries, which agree well with previous assignments. Four possible "doorway modes" were found in the energy range defined by the lattice modes, which were all found to contain fundamental contributions from rotation of the nitro groups.

The structural, electronic, magnetic, and mechanical properties of perovskite oxides PbM1/2Nb1/2O3 (M = Fe, Co and Ni)

NASA Astrophysics Data System (ADS)

Erkisi, A.; Surucu, G.; Deligoz, E.

2018-03-01

In this study, the structural, electronic, magnetic, and mechanical properties of perovskite oxides PbM1/2Nb1/2O3 (M = Fe, Co and Ni) are investigated. The systems are treated in ferromagnetic order. The calculations are carried out in the framework of density functional theory (DFT) within the plane-wave pseudopotential method. The exchange-correlation potential is approximated by generalized-gradient spin approach (GGA). The intra-atomic Coulomb repulsion is also taken into account in calculations (GGA + U). We have considered two generalized-gradient spin approximation functionals, which are Perdew-Burke-Ernzerhof (PBE) and PBE for solids (PBEsol) for structural parameter calculations when it included Hubbard potential. Although the spin-polarized electronic band structures of PbCo1/2Nb1/2O3 and PbNi1/2Nb1/2O3 systems exhibit metallic property in ferromagnetic phase, a bandgap is observed in spin-down states of PbFe1/2Nb1/2O3 resulting in half-metallic behavior. The main reason for this behavior is attributed to the hybridization between d-states of transition metal atoms and p-states of oxygen atoms. The stability mechanically and the calculated mechanical properties by using elastic constants show that these compounds are mechanically stable in tetragonal phase and have anisotropic character mechanically.

Present heat flow and paleo-geothermal regime in the Canadian Arctic margin: analysis of industrial thermal data and coalification gradients

NASA Astrophysics Data System (ADS)

Majorowicz, Jacek A.; Embry, Ashton F.

1998-06-01

Calculations of the present geothermal gradient and terrestrial heat flow were made on 156 deep wells of the Canadian Arctic Archipelago. Corrected bottom hole temperature (BHT) data and drill stem test (DST) temperatures were used to determine the thermal gradients for sites for which the quality of data was sufficient. Thermal gradients evaluated for depths below the base of permafrost for the onshore wells and below sea bottom for the offshore wells were combined with the estimates of effective thermal conductivity to approximate heat flow for these sites. The present geothermal gradient is in the 15-50 mK/m range (mean = 31 ± 7 mK/m). Present heat flow is mainly in the 35-90 mW/m 2 range (mean = 53 ± 12 mW/m 2). Maps of the present geothermal gradient and present heat flow have been constructed for the basin. The analysis of vitrinite reflectance profiles and the calculation of logarithmic coalification gradients for 101 boreholes in the Sverdrup Basin showed large variations related in many cases to regional variations of present terrestrial heat flow. Paleo-geothermal gradients estimated from these data are mostly in the range of 15-50 mK/m (mean = 28 ± 9 mK/m) and paleo-heat flow is in the 40-90 mW/m 2 range (mean = 57 ± 18 mW/m 2) related to the time of maximum burial in the Early Tertiary. Mean values of the present heat flow and paleo-heat flow for the Sverdrup Basin are almost identical considering the uncertainties of the methods used (53 ± 12 versus 57 ± 18 mW/m 2, respectively). Present geothermal gradients and paleo-geothermal gradients are also close when means are compared (31 ± 7 versus 28 ± 9 mK/m respectively). A zone of high present heat flow and a paleo-heat flow zone coincide in places with the northeastern-southwestern incipient rift landward of the Arctic margin first described by Balkwill and Fox (1982). Correlation between present heat flow and paleo-heat flow for the time of maximum burial in the earliest Tertiary suggests that the high heat flow zone has prevailed since that time.

Full Gradient Solution to Adaptive Hybrid Control

NASA Technical Reports Server (NTRS)

Bean, Jacob; Schiller, Noah H.; Fuller, Chris

2017-01-01

This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.

Full Gradient Solution to Adaptive Hybrid Control

NASA Technical Reports Server (NTRS)

Bean, Jacob; Schiller, Noah H.; Fuller, Chris

2016-01-01

This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered-reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.

Use of Total Electron Content data to analyze ionosphere electron density gradients

NASA Astrophysics Data System (ADS)

Nava, B.; Radicella, S. M.; Leitinger, R.; Coisson, P.

In presence of electron density gradients the thin shell approximation for the ionosphere used together with a simple mapping function to convert slant Total Electron Content TEC to vertical TEC could lead to TEC conversion errors Therefore these mapping function errors can be used to identify the effects of the electron density gradients in the ionosphere In the present work high precision GPS derived slant TEC data have been used to investigate the effects of the electron density gradients in the middle and low latitude ionosphere under geomagnetic quiet and disturbed conditions In particular the data corresponding to the geographic area of the American sector for the days 5-7 April 2000 have been used to perform a complete analysis of mapping function errors based on the coinciding pierce point technique The results clearly illustrate the electron density gradient effects according to the locations considered and to the actual levels of disturbance of the ionosphere

An efficient method for the creation of tunable optical line traps via control of gradient and scattering forces.

PubMed

Tietjen, Gregory T; Kong, Yupeng; Parthasarathy, Raghuveer

2008-07-07

Interparticle interaction energies and other useful physical characteristics can be extracted from the statistical properties of the motion of particles confined by an optical line trap. In practice, however, the potential energy landscape, U(x), imposed by the line provides an extra, and in general unknown, influence on particle dynamics. We describe a new class of line traps in which both the optical gradient and scattering forces acting on a trapped particle are designed to be linear functions of the line coordinate and in which their magnitude can be counterbalanced to yield a flat U(x). These traps are formed using approximate solutions to general relations concerning non-conservative optical forces that have been the subject of recent investigations [Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602-4 (2008).]. We implement the lines using holographic optical trapping and measure the forces acting on silica microspheres, demonstrating the tunability of the confining potential energy landscape. Furthermore, we show that our approach efficiently directs available laser power to the trap, in contrast to other methods.

Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations.

PubMed

Cvitaš, Marko T

2018-03-13

The ring-polymer instanton (RPI) method is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. In the RPI method, tunneling splitting is evaluated from the properties of the minimum action path (MAP) connecting the symmetric wells, whereby the extensive sampling of the full potential energy surface of the exact quantum-dynamics methods is avoided. Nevertheless, the search for the MAP is usually the most time-consuming step in the standard numerical procedures. Recently, nudged elastic band (NEB) and string methods, originaly developed for locating minimum energy paths (MEPs), were adapted for the purpose of MAP finding with great efficiency gains [ J. Chem. Theory Comput. 2016 , 12 , 787 ]. In this work, we develop a new quadratic string method for locating instantons. The Euclidean action is minimized by propagating the initial guess (a path connecting two wells) over the quadratic potential energy surface approximated by means of updated Hessians. This allows the algorithm to take many minimization steps between the potential/gradient calls with further reductions in the computational effort, exploiting the smoothness of potential energy surface. The approach is general, as it uses Cartesian coordinates, and widely applicable, with computational effort of finding the instanton usually lower than that of determining the MEP. It can be combined with expensive potential energy surfaces or on-the-fly electronic-structure methods to explore a wide variety of molecular systems.

Accurate critical pressures for structural phase transitions of group IV, III-V, and II-VI compounds from the SCAN density functional

NASA Astrophysics Data System (ADS)

Shahi, Chandra; Sun, Jianwei; Perdew, John P.

2018-03-01

Most of the group IV, III-V, and II-VI compounds crystallize in semiconductor structures under ambient conditions. Upon application of pressure, they undergo structural phase transitions to more closely packed structures, sometimes metallic phases. We have performed density functional calculations using projector augmented wave (PAW) pseudopotentials to determine the transition pressures for these transitions within the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA. LDA underestimates the transition pressure for most of the studied materials. PBE under- or overestimates in many cases. SCAN typically corrects the errors of LDA and PBE for the transition pressure. The accuracy of SCAN is comparable to that of computationally expensive methods like the hybrid functional HSE06, the random phase approximation (RPA), and quantum Monte Carlo (QMC), in cases where calculations with these methods have been reported, but at a more modest computational cost. The improvement from LDA to PBE to SCAN is especially clearcut and dramatic for covalent semiconductor-metal transitions, as for Si and Ge, where it reflects the increasing relative stabilization of the covalent semiconducting phases under increasing functional sophistication.

Band Gap Tuning in 2D Layered Materials by Angular Rotation.

PubMed

Polanco-Gonzalez, Javier; Carranco-Rodríguez, Jesús Alfredo; Enríquez-Carrejo, José L; Mani-Gonzalez, Pierre G; Domínguez-Esquivel, José Manuel; Ramos, Manuel

2017-02-08

We present a series of computer-assisted high-resolution transmission electron (HRTEM) simulations to determine Moiré patters by induced twisting effects between slabs at rotational angles of 3°, 5°, 8°, and 16°, for molybdenum disulfide, graphene, tungsten disulfide, and tungsten selenide layered materials. In order to investigate the electronic structure, a series of numerical simulations using density functional methods (DFT) methods was completed using Cambridge serial total energy package (CASTEP) with a generalized gradient approximation to determine both the band structure and density of states on honeycomb-like new superlattices. Our results indicated metallic transitions when the rotation approached 8° with respect to each other laminates for most of the two-dimensional systems that were analyzed.

Band Gap Tuning in 2D Layered Materials by Angular Rotation

PubMed Central

Polanco-Gonzalez, Javier; Carranco-Rodríguez, Jesús Alfredo; Enríquez-Carrejo, José L.; Mani-Gonzalez, Pierre G.; Domínguez-Esquivel, José Manuel; Ramos, Manuel

2017-01-01

We present a series of computer-assisted high-resolution transmission electron (HRTEM) simulations to determine Moiré patters by induced twisting effects between slabs at rotational angles of 3°, 5°, 8°, and 16°, for molybdenum disulfide, graphene, tungsten disulfide, and tungsten selenide layered materials. In order to investigate the electronic structure, a series of numerical simulations using density functional methods (DFT) methods was completed using Cambridge serial total energy package (CASTEP) with a generalized gradient approximation to determine both the band structure and density of states on honeycomb-like new superlattices. Our results indicated metallic transitions when the rotation approached 8° with respect to each other laminates for most of the two-dimensional systems that were analyzed. PMID:28772507

Electronic structure and properties of lanthanum

NASA Astrophysics Data System (ADS)

Nixon, Lane; Papaconstantopoulos, Dimitrios

2008-03-01

The total energy and electronic structure of lanthanum have been calculated in the bcc, fcc, hcp and dhcp structures for pressures up to 50 GPa. The full potential linearized-augmented-planewave method was used with both the local-density and general-gradient approximations. The correct phase ordering has been found, with lattice parameters and bulk moduli in good agreement with experimental data. The GGA method shows excellent agreement overall while the LDA results show larger discrepancies. The calculated strain energies for the fcc and bcc structures demonstrate the respective stable and unstable configurations at ambient conditions. The calculated superconductivity properties under pressure for the fcc structure are also found to agree well with measurements. Both LDA and GGA, with minor differences, reproduce well the experimental results for Tc.

Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: Comparison of gradient-ascent-pulse-engineering and Krotov optimization schemes

NASA Astrophysics Data System (ADS)

Jäger, Georg; Reich, Daniel M.; Goerz, Michael H.; Koch, Christiane P.; Hohenester, Ulrich

2014-09-01

We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation, and to excite a condensate from the ground state to the first-excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use; namely, gradient-ascent pulse engineering (GRAPE) and Krotov's method. Both approaches are derived from the variational principle but differ in the way the control is updated, additional costs are accounted for, and second-order-derivative information can be included. We find that GRAPE produces smoother control fields and works in a black-box manner, whereas Krotov with a suitably chosen step-size parameter converges faster but can produce sharp features in the control fields.

Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2017-03-01

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.

A constrained-gradient method to control divergence errors in numerical MHD

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2016-10-01

In numerical magnetohydrodynamics (MHD), a major challenge is maintaining nabla \\cdot {B}=0. Constrained transport (CT) schemes achieve this but have been restricted to specific methods. For more general (meshless, moving-mesh, ALE) methods, `divergence-cleaning' schemes reduce the nabla \\cdot {B} errors; however they can still be significant and can lead to systematic errors which converge away slowly. We propose a new constrained gradient (CG) scheme which augments these with a projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. Unlike `locally divergence free' methods, this actually minimizes the numerically unstable nabla \\cdot {B} terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare various test problems. Compared to cleaning schemes, our CG method reduces the maximum nabla \\cdot {B} errors by ˜1-3 orders of magnitude (˜2-5 dex below typical errors if no nabla \\cdot {B} cleaning is used). By preventing large nabla \\cdot {B} at discontinuities, this eliminates systematic errors at jumps. Our CG results are comparable to CT methods; for practical purposes, the nabla \\cdot {B} errors are eliminated. The cost is modest, ˜30 per cent of the hydro algorithm, and the CG correction can be implemented in a range of numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a range of problems where using only Powell or `8-wave' cleaning can produce order-of-magnitude errors.

Use of vertical temperature gradients for prediction of tidal flat sediment characteristics

USGS Publications Warehouse

Miselis, Jennifer L.; Holland, K. Todd; Reed, Allen H.; Abelev, Andrei

2012-01-01

Sediment characteristics largely govern tidal flat morphologic evolution; however, conventional methods of investigating spatial variability in lithology on tidal flats are difficult to employ in these highly dynamic regions. In response, a series of laboratory experiments was designed to investigate the use of temperature diffusion toward sediment characterization. A vertical thermistor array was used to quantify temperature gradients in simulated tidal flat sediments of varying compositions. Thermal conductivity estimates derived from these arrays were similar to measurements from a standard heated needle probe, which substantiates the thermistor methodology. While the thermal diffusivities of dry homogeneous sediments were similar, diffusivities for saturated homogeneous sediments ranged approximately one order of magnitude. The thermal diffusivity of saturated sand was five times the thermal diffusivity of saturated kaolin and more than eight times the thermal diffusivity of saturated bentonite. This suggests that vertical temperature gradients can be used for distinguishing homogeneous saturated sands from homogeneous saturated clays and perhaps even between homogeneous saturated clay types. However, experiments with more realistic tidal flat mixtures were less discriminating. Relationships between thermal diffusivity and percent fines for saturated mixtures varied depending upon clay composition, indicating that clay hydration and/or water content controls thermal gradients. Furthermore, existing models for the bulk conductivity of sediment mixtures were improved only through the use of calibrated estimates of homogeneous end-member conductivity and water content values. Our findings suggest that remotely sensed observations of water content and thermal diffusivity could only be used to qualitatively estimate tidal flat sediment characteristics.

A parametric heat transfer study for cryogenic ball bearings in SSME HPOTP

NASA Technical Reports Server (NTRS)

Chyu, Mingking K.

1989-01-01

A numerical modeling is to examine the effects of coolant convective heat transfer coefficient and frictional heating on the local temperature characteristics of a ball element in Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP) bearing. The present modeling uses a control-volume based, finite-difference method to solve the non-dimensionalized heat conduction equation in spherical coordinate system. The dimensionless temperature is found as a function of Biot number, heat flux ratio between the two race contacts, and location in the ball. The current results show that, for a given cooling capability, the ball temperature generally increases almost linearly with the heat input from the race-contacts. This increase is always very high at one of the two contacts. An increase in heat transfer coefficient generally reduces the ball temperature and alleviates the temperature gradient, except for the regions very close to the race contacts. For a 10-fold increase of heat transfer coefficient, temperature decrease is 35 percent for the average over entire ball, and 10 percent at the inner-race contact. The corresponding change of temperature gradient displays opposing trends between the regions immediately adjacent to the contacts and the remaining portion of the ball. The average temperature gradient in the vicinity of both contacts increases approximately 70 to 100 percent. A higher temperature gradient produces excessive thermal stress locally which may be detrimental to the material integrity. This, however, is the only unfavorable issue for an increase of heat transfer coefficient.

Biological Image-Guided Radiotherapy in Rectal Cancer: Challenges and Pitfalls

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

Roels, Sarah; Slagmolen, Pieter; Nuyts, Johan

2009-11-01

Purpose: To investigate the feasibility of integrating multiple imaging modalities for image-guided radiotherapy in rectal cancer. Patients and Methods: Magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography/computed tomography (FDG-PET/CT) were performed before, during, and after preoperative chemoradiotherapy (CRT) in patients with resectable rectal cancer. The FDG-PET signals were segmented with an adaptive threshold-based and a gradient-based method. Magnetic resonance tumor volumes (TVs) were manually delineated. A nonrigid registration algorithm was applied to register the images, and mismatch analyses were carried out between MR and FDG-PET TVs and between TVs over time. Tumor volumes delineated on the images after CRTmore » were compared with the pathologic TV. Results: Forty-five FDG-PET/CT and 45 MR images were analyzed from 15 patients. The mean MRI and FDG-PET TVs showed a tendency to shrink during and after CRT. In general, MRI showed larger TVs than FDG-PET. There was an approximately 50% mismatch between the FDG-PET TV and the MRI TV at baseline and during CRT. Sixty-one percent of the FDG-PET TV and 76% of the MRI TV obtained after 10 fractions of CRT remained inside the corresponding baseline TV. On MRI, residual tumor was still suspected in all 6 patients with a pathologic complete response, whereas FDG-PET showed a metabolic complete response in 3 of them. The FDG-PET TVs delineated with the gradient-based method matched closest with pathologic findings. Conclusions: Integration of MRI and FDG-PET into radiotherapy seems feasible. Gradient-based segmentation is recommended for FDG-PET. Spatial variance between MRI and FDG-PET TVs should be taken into account for target definition.« less

Policy oscillation is overshooting.

PubMed

Wagner, Paul

2014-04-01

A majority of approximate dynamic programming approaches to the reinforcement learning problem can be categorized into greedy value function methods and value-based policy gradient methods. The former approach, although fast, is well known to be susceptible to the policy oscillation phenomenon. We take a fresh view to this phenomenon by casting, within the context of non-optimistic policy iteration, a considerable subset of the former approach as a limiting special case of the latter. We explain the phenomenon in terms of this view and illustrate the underlying mechanism with artificial examples. We also use it to derive the constrained natural actor-critic algorithm that can interpolate between the aforementioned approaches. In addition, it has been suggested in the literature that the oscillation phenomenon might be subtly connected to the grossly suboptimal performance in the Tetris benchmark problem of all attempted approximate dynamic programming methods. Based on empirical findings, we offer a hypothesis that might explain the inferior performance levels and the associated policy degradation phenomenon, and which would partially support the suggested connection. Finally, we report scores in the Tetris problem that improve on existing dynamic programming based results by an order of magnitude. Copyright © 2014 Elsevier Ltd. All rights reserved.

Phase gradient imaging for positive contrast generation to superparamagnetic iron oxide nanoparticle-labeled targets in magnetic resonance imaging.

PubMed

Zhu, Haitao; Demachi, Kazuyuki; Sekino, Masaki

2011-09-01

Positive contrast imaging methods produce enhanced signal at large magnetic field gradient in magnetic resonance imaging. Several postprocessing algorithms, such as susceptibility gradient mapping and phase gradient mapping methods, have been applied for positive contrast generation to detect the cells targeted by superparamagnetic iron oxide nanoparticles. In the phase gradient mapping methods, smoothness condition has to be satisfied to keep the phase gradient unwrapped. Moreover, there has been no discussion about the truncation artifact associated with the algorithm of differentiation that is performed in k-space by the multiplication with frequency value. In this work, phase gradient methods are discussed by considering the wrapping problem when the smoothness condition is not satisfied. A region-growing unwrapping algorithm is used in the phase gradient image to solve the problem. In order to reduce the truncation artifact, a cosine function is multiplied in the k-space to eliminate the abrupt change at the boundaries. Simulation, phantom and in vivo experimental results demonstrate that the modified phase gradient mapping methods may produce improved positive contrast effects by reducing truncation or wrapping artifacts. Copyright © 2011 Elsevier Inc. All rights reserved.

Recent Advances in 3D Time-Resolved Contrast-Enhanced MR Angiography

PubMed Central

Riederer, Stephen J.; Haider, Clifton R.; Borisch, Eric A.; Weavers, Paul T.; Young, Phillip M.

2015-01-01

Contrast-enhanced MR angiography (CE-MRA) was first introduced for clinical studies approximately 20 years ago. Early work provided 3 to 4 mm spatial resolution with acquisition times in the 30 sec range. Since that time there has been continuing effort to provide improved spatial resolution with reduced acquisition time, allowing high resolution three-dimensional (3D) time-resolved studies. The purpose of this work is to describe how this has been accomplished. Specific technical enablers have been: improved gradients allowing reduced repetition times, improved k-space sampling and reconstruction methods, parallel acquisition particularly in two directions, and improved and higher count receiver coil arrays. These have collectively made high resolution time-resolved studies readily available for many anatomic regions. Depending on the application, approximate 1 mm isotropic resolution is now possible with frame times of several seconds. Clinical applications of time-resolved CE-MRA are briefly reviewed. PMID:26032598

DFT-BASED AB INITIO STUDY OF THE ELECTRONIC AND OPTICAL PROPERTIES OF CESIUM BASED FLUORO-PEROVSKITE CsMF3 (M = Ca AND Sr)

NASA Astrophysics Data System (ADS)

Harmel, M.; Khachai, H.; Ameri, M.; Khenata, R.; Baki, N.; Haddou, A.; Abbar, B.; UǦUR, Ş.; Omran, S. Bin; Soyalp, F.

2012-12-01

Density functional theory (DFT) is performed to study the structural, electronic and optical properties of cubic fluoroperovskite AMF3 (A = Cs; M = Ca and Sr) compounds. The calculations are based on the total-energy calculations within the full-potential linearized augmented plane wave (FP-LAPW) method. The exchange-correlation potential is treated by local density approximation (LDA) and generalized gradient approximation (GGA). The structural properties, including lattice constants, bulk modulus and their pressure derivatives are in very good agreement with the available experimental and theoretical data. The calculations of the electronic band structure, density of states and charge density reveal that compounds are both ionic insulators. The optical properties (namely: the real and the imaginary parts of the dielectric function ɛ(ω), the refractive index n(ω) and the extinction coefficient k(ω)) were calculated for radiation up to 40.0 eV.

High-pressure structural, elastic, and electronic properties of the scintillator host material KMgF3

NASA Astrophysics Data System (ADS)

Vaitheeswaran, G.; Kanchana, V.; Kumar, Ravhi S.; Cornelius, A. L.; Nicol, M. F.; Svane, A.; Delin, A.; Johansson, B.

2007-07-01

The high-pressure structural behavior of the fluoroperovskite KMgF3 is investigated by theory and experiment. Density functional calculations were performed within the local density approximation and the generalized gradient approximation for exchange and correlation effects, as implemented within the full-potential linear muffin-tin orbital method. In situ high-pressure powder x-ray diffraction experiments were performed up to a maximum pressure of 40GPa using synchrotron radiation. We find that the cubic Pm3¯m crystal symmetry persists throughout the pressure range studied. The calculated ground state properties—the equilibrium lattice constant, bulk modulus, and elastic constants—are in good agreement with experimental results. By analyzing the ratio between the bulk and shear moduli, we conclude that KMgF3 is brittle in nature. Under ambient conditions, KMgF3 is found to be an indirect gap insulator, with the gap increasing under pressure.

Implementation of Two-Component Time-Dependent Density Functional Theory in TURBOMOLE.

PubMed

Kühn, Michael; Weigend, Florian

2013-12-10

We report the efficient implementation of a two-component time-dependent density functional theory proposed by Wang et al. (Wang, F.; Ziegler, T.; van Lenthe, E.; van Gisbergen, S.; Baerends, E. J. J. Chem. Phys. 2005, 122, 204103) that accounts for spin-orbit effects on excitations of closed-shell systems by employing a noncollinear exchange-correlation kernel. In contrast to the aforementioned implementation, our method is based on two-component effective core potentials as well as Gaussian-type basis functions. It is implemented in the TURBOMOLE program suite for functionals of the local density approximation and the generalized gradient approximation. Accuracy is assessed by comparison of two-component vertical excitation energies of heavy atoms and ions (Cd, Hg, Au(+)) and small molecules (I2, TlH) to other two- and four-component approaches. Efficiency is demonstrated by calculating the electronic spectrum of Au20.

Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

NASA Technical Reports Server (NTRS)

Arian, Eyal; Ta'asan, Shlomo

1996-01-01

In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

Orbital relaxation effects on Kohn–Sham frontier orbital energies in density functional theory

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

Zhang, DaDi; Zheng, Xiao, E-mail: xz58@ustc.edu.cn; Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026

2015-04-21

We explore effects of orbital relaxation on Kohn–Sham frontier orbital energies in density functional theory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohn–Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohn–Sham frontier orbital energies by Hartree–Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scalingmore » correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N ± 1)-electron systems.« less

The role of large-scale eddies in the climate equilibrium. Part 2: Variable static stability

NASA Technical Reports Server (NTRS)

Zhou, Shuntai; Stone, Peter H.

1993-01-01

Lorenz's two-level model on a sphere is used to investigate how the results of Part 1 are modified when the interaction of the vertical eddy heat flux and static stability is included. In general, the climate state does not depend very much on whether or not this interaction is included, because the poleward eddy heat transport dominates the eddy forcing of mean temperature and wind fields. However, the climatic sensitivity is significantly affected. Compared to two-level model results with fixed static stability, the poleward eddy heat flux is less sensitive to the meridional temperature gradient and the gradient is more sensitive to the forcing. For example, the logarithmic derivative of the eddy flux with respect to the gradient has a slope that is reduced from approximately 15 on a beta-plane with fixed static stability and approximately 6 on a sphere with fixed static stability, to approximately 3 to 4 in the present model. This last result is more in line with analyses from observations. The present model also has a stronger baroclinic adjustment than that in Part 1, more like that in two-level beta-plane models with fixed static stability, that is, the midlatitude isentropic slope is very insensitive to the forcing, the diabatic heating, and the friction, unless the forcing is very weak.

Dexamethasone levels and base to apex concentration gradients in scala tympani perilymph following intracochlear delivery in the guinea pig

PubMed Central

Hahn, Hartmut; Salt, Alec N.; Biegner, Thorsten; Kammerer, Bernd; Delabar, Ursular; Hartsock, Jared; Plontke, Stefan K.

2012-01-01

Hypothesis To determine whether intracochlearly applied dexamethasone will lead to better control of drug levels, higher peak concentrations and lower base-to apex concentration gradients in scala tympani (ST) of the guinea pig than after intratympanic (round window, RW) application. Background Local application of drugs to the RW results in substantial variation of intracochlear drug levels and significant base-to apex concentration gradients in ST. Methods Two μL of dexamethasone-phosphate (10 mg/mL) were injected into ST either through the RW membrane which was covered with 1% sodium hyaluronate gel or through a cochleostomy with a fluid tight seal of the micropipette. Perilymph was sequentially sampled from the apex at a single time point for each animal, at 20, 80, or 200 min after the injection ended. Results were mathematically interpreted by the means of an established computer model and compared with prior experiments performed by our group with the same experimental techniques but using intratympanic applications. Results Single intracochlear injections over 20 min resulted in approximately ten times higher peak concentrations (on average) than 2-3 hours of intratympanic application to the round window niche. Intracochlear drug levels were less variable and could be measured for at least up to 220 min. Concentration gradients along scala tympani were less pronounced. The remaining variability in intracochlear drug levels was attributable to perilymph and drug leak from the injection site. Conclusion With significantly higher, less variable drug levels and smaller base-to apex concentration gradients, intracochlear applications have advantages to intratympanic injections. For further development of this technique, it is of importance to control leaks of perilymph and drug from the injection site and to evaluate its clinical feasibility and associated risks. PMID:22588238

Water potential gradient in a tall sequoiadendron.

PubMed

Tobiessen, P

1971-09-01

With an elevator installed in a 90-meter tall Sequoiadendron to collect the samples, xylem pressure potential measurements were made approximately every 15 meters along 60 meters of the tree's height. The measured gradient was about -0.8 bar per 10 meters of height, i.e., less than the hydrostatic gradient. Correction of the xylem pressure potential data by calibration against a thermocouple psychrometer confirmed this result. Similar gradients are described in the literature in tall conifers at times of low transpiration, although a different sampling technique was used. If the data in the present study and those supporting it are typical, they imply a re-evaluation of either the use of the pressure chamber to estimate water potential or the present theories describing water transport in tall trees.

Water Potential Gradient in a Tall Sequoiadendron

PubMed Central

Tobiessen, Peter; Rundel, Philip W.; Stecker, R. E.

1971-01-01

With an elevator installed in a 90-meter tall Sequoiadendron to collect the samples, xylem pressure potential measurements were made approximately every 15 meters along 60 meters of the tree's height. The measured gradient was about −0.8 bar per 10 meters of height, i.e., less than the hydrostatic gradient. Correction of the xylem pressure potential data by calibration against a thermocouple psychrometer confirmed this result. Similar gradients are described in the literature in tall conifers at times of low transpiration, although a different sampling technique was used. If the data in the present study and those supporting it are typical, they imply a re-evaluation of either the use of the pressure chamber to estimate water potential or the present theories describing water transport in tall trees. PMID:16657786

Inviscid, nonadiabatic flow fields over blunt, sonic corner bodies for outer planet entry conditions by a method of integral relations

NASA Technical Reports Server (NTRS)

Gnoffo, P. A.

1978-01-01

An investigation has been made into the ability of a method of integral relations to calculate inviscid zero degree angle of attack, radiative heating distributions over blunt, sonic corner bodies for some representative outer planet entry conditions is investigated. Comparisons have been made with a more detailed numerical method, a time asymptotic technique, using the same equilibrium chemistry and radiation transport subroutines. An effort to produce a second order approximation (two-strip) method of integral relations code to aid in this investigation is also described and a modified two-strip routine is presented. Results indicate that the one-strip method of integral relations cannot be used to obtain accurate estimates of the radiative heating distribution because of its inability to resolve thermal gradients near the wall. The two-strip method can sometimes be used to improve these estimates; however, the two-strip method has only a small range of conditions over which it will yield significant improvement over the one-strip method.

Tools for Designing and Analyzing Structures

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Structural Design and Analysis Toolset is a collection of approximately 26 Microsoft Excel spreadsheet programs, each of which performs calculations within a different subdiscipline of structural design and analysis. These programs present input and output data in user-friendly, menu-driven formats. Although these programs cannot solve complex cases like those treated by larger finite element codes, these programs do yield quick solutions to numerous common problems more rapidly than the finite element codes, thereby making it possible to quickly perform multiple preliminary analyses - e.g., to establish approximate limits prior to detailed analyses by the larger finite element codes. These programs perform different types of calculations, as follows: 1. determination of geometric properties for a variety of standard structural components; 2. analysis of static, vibrational, and thermal- gradient loads and deflections in certain structures (mostly beams and, in the case of thermal-gradients, mirrors); 3. kinetic energies of fans; 4. detailed analysis of stress and buckling in beams, plates, columns, and a variety of shell structures; and 5. temperature dependent properties of materials, including figures of merit that characterize strength, stiffness, and deformation response to thermal gradients

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

DOE PAGES

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

2018-02-14

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons inmore » a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.« less

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

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

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons inmore » a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.« less

Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Gritsenko, O. V.; van Gisbergen, S. J. A.; Görling, A.; Baerends, E. J.

2000-11-01

Time-dependent density functional theory (TDDFT) is applied for calculation of the excitation energies of the dissociating H2 molecule. The standard TDDFT method of adiabatic local density approximation (ALDA) totally fails to reproduce the potential curve for the lowest excited singlet 1Σu+ state of H2. Analysis of the eigenvalue problem for the excitation energies as well as direct derivation of the exchange-correlation (xc) kernel fxc(r,r',ω) shows that ALDA fails due to breakdown of its simple spatially local approximation for the kernel. The analysis indicates a complex structure of the function fxc(r,r',ω), which is revealed in a different behavior of the various matrix elements K1c,1cxc (between the highest occupied Kohn-Sham molecular orbital ψ1 and virtual MOs ψc) as a function of the bond distance R(H-H). The effect of nonlocality of fxc(r,r') is modeled by using different expressions for the corresponding matrix elements of different orbitals. Asymptotically corrected ALDA (ALDA-AC) expressions for the matrix elements K12,12xc(στ) are proposed, while for other matrix elements the standard ALDA expressions are retained. This approach provides substantial improvement over the standard ALDA. In particular, the ALDA-AC curve for the lowest singlet excitation qualitatively reproduces the shape of the exact curve. It displays a minimum and approaches a relatively large positive energy at large R(H-H). ALDA-AC also produces a substantial improvement for the calculated lowest triplet excitation, which is known to suffer from the triplet instability problem of the restricted KS ground state. Failure of the ALDA for the excitation energies is related to the failure of the local density as well as generalized gradient approximations to reproduce correctly the polarizability of dissociating H2. The expression for the response function χ is derived to show the origin of the field-counteracting term in the xc potential, which is lacking in the local density and generalized gradient approximations and which is required to obtain a correct polarizability.

Computation of Steady and Unsteady Laminar Flames: Theory

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Radhakrishnan, Krishnan; Zhou, Ruhai

1999-01-01

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Nonuniform discharge currents in active plasma lenses

DOE PAGES

van Tilborg, J.; Barber, S. K.; Tsai, H. -E.; ...

2017-03-24

Active plasma lenses have attracted interest in novel accelerator applications due to their ability to provide large-field-gradient (short focal length), tunable, and radially symmetric focusing for charged particle beams. However, if the discharge current is not flowing uniformly as a function of radius, one can expect a radially varying field gradient as well as potential emittance degradation. We have investigated this experimentally for a 1-mm-diameter active plasma lens. The measured near-axis field gradient is approximately 35% larger than expected for a uniform current distribution, and at overfocusing currents ring-shaped electron beams are observed. These observations are explained by simulations.

Nonuniform discharge currents in active plasma lenses

NASA Astrophysics Data System (ADS)

van Tilborg, J.; Barber, S. K.; Tsai, H.-E.; Swanson, K. K.; Steinke, S.; Geddes, C. G. R.; Gonsalves, A. J.; Schroeder, C. B.; Esarey, E.; Bulanov, S. S.; Bobrova, N. A.; Sasorov, P. V.; Leemans, W. P.

2017-03-01

Active plasma lenses have attracted interest in novel accelerator applications due to their ability to provide large-field-gradient (short focal length), tunable, and radially symmetric focusing for charged particle beams. However, if the discharge current is not flowing uniformly as a function of radius, one can expect a radially varying field gradient as well as potential emittance degradation. We have investigated this experimentally for a 1-mm-diameter active plasma lens. The measured near-axis field gradient is approximately 35% larger than expected for a uniform current distribution, and at overfocusing currents ring-shaped electron beams are observed. These observations are explained by simulations.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frinks, Neal T.

2016-01-01

Several improvements to the mixed-elementUSM3Ddiscretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Evolution of the orbitals Dy-4f in the DyB2 compound using the LDA, PBE approximations, and the PBE0 hybrid functional

NASA Astrophysics Data System (ADS)

Rasero Causil, Diego; Ortega López, César; Espitia Rico, Miguel

2018-04-01

Computational calculations of total energy based on density functional theory were used to investigate the structural, electronic, and magnetic properties of the DyB2 compounds in the hexagonal structure. The calculations were carried out by means of the full-potential linearized augmented plane wave (FP-LAPW) method, employing the computational Wien2k package. The local density approximation (LDA) and the generalized gradient approximation (GGA) were used for the electron-electron interactions. Additionally, we used the functional hybrid PBE0 for a better description the electronic and magnetic properties, because the DyB2 compound is a strongly-correlated system. We found that the calculated lattice constant agrees well with the values reported theoretically and experimentally. The density of states (DOS) calculation shows that the compound exhibits a metallic behavior and has magnetic properties, with a total magnetic moment of 5.47 μ0/cell determined mainly by the 4f states of the rare earth elements. The functional PBE0 shows a strong localization of the Dy-4f orbitals.

Quantum calculations for one-dimensional cooling of helium

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

Vredenbregt, E.; Doery, M.; Bergeman, T.

1993-05-01

We report theoretical velocity distributions for sub-Doppler laser cooling of metastable He*(2{sup 3}S), calculated with the Density Matrix and Monte Carlo Wavefunction approaches. For low-field (B = 50 mG) magnetic-field induced laser cooling on the 2{sup 3}S {yields} (2{sup 3}P, J = 2) transition ({lambda} = 1083 nm), we get a narrow, sub-Doppler structure, consisting of three, {approximately}1 photon recoil wide peaks, spaced {approximately}1 recoil apart. With increasing field, this three-peak structure develops into two velocity-selective resonance (VSR) peaks, each {approximately}2 recoils wide. For the 2{sup 3}S {yields} (3{sup 3}P, J = 2) transition ({lambda} 389 nm), VSR peaks aremore » predicted to appear at low field without the third, central peak, which only develops at higher field (B = 200 mG). Additional computations deal with polarization-gradient cooling. In general, we find that for one-dimensional cooling calculations, the Density Matrix method is more efficient than the Monte Carlo Wavefunction approach. Experiments are currently under way to test the results.« less

An n -material thresholding method for improving integerness of solutions in topology optimization

DOE PAGES

Watts, Seth; Tortorelli, Daniel A.

2016-04-10

It is common in solving topology optimization problems to replace an integer-valued characteristic function design field with the material volume fraction field, a real-valued approximation of the design field that permits "fictitious" mixtures of materials during intermediate iterations in the optimization process. This is reasonable so long as one can interpolate properties for such materials and so long as the final design is integer valued. For this purpose, we present a method for smoothly thresholding the volume fractions of an arbitrary number of material phases which specify the design. This method is trivial for two-material design problems, for example, themore » canonical topology design problem of specifying the presence or absence of a single material within a domain, but it becomes more complex when three or more materials are used, as often occurs in material design problems. We take advantage of the similarity in properties between the volume fractions and the barycentric coordinates on a simplex to derive a thresholding, method which is applicable to an arbitrary number of materials. As we show in a sensitivity analysis, this method has smooth derivatives, allowing it to be used in gradient-based optimization algorithms. Finally, we present results, which show synergistic effects when used with Solid Isotropic Material with Penalty and Rational Approximation of Material Properties material interpolation functions, popular methods of ensuring integerness of solutions.« less

Wellskins and slug tests: where's the bias?

NASA Astrophysics Data System (ADS)

Rovey, C. W.; Niemann, W. L.

2001-03-01

Pumping tests in an outwash sand at the Camp Dodge Site give hydraulic conductivities ( K) approximately seven times greater than conventional slug tests in the same wells. To determine if this difference is caused by skin bias, we slug tested three sets of wells, each in a progressively greater stage of development. Results were analyzed with both the conventional Bouwer-Rice method and the deconvolution method, which quantifies the skin and eliminates its effects. In 12 undeveloped wells the average skin is +4.0, causing underestimation of conventional slug-test K (Bouwer-Rice method) by approximately a factor of 2 relative to the deconvolution method. In seven nominally developed wells the skin averages just +0.34, and the Bouwer-Rice method gives K within 10% of that calculated with the deconvolution method. The Bouwer-Rice K in this group is also within 5% of that measured by natural-gradient tracer tests at the same site. In 12 intensely developed wells the average skin is <-0.82, consistent with an average skin of -1.7 measured during single-well pumping tests. At this site the maximum possible skin bias is much smaller than the difference between slug and pumping-test Ks. Moreover, the difference in K persists even in intensely developed wells with negative skins. Therefore, positive wellskins do not cause the difference in K between pumping and slug tests at this site.

A robust rotation-invariance displacement measurement method for a micro-/nano-positioning system

NASA Astrophysics Data System (ADS)

Zhang, Xiang; Zhang, Xianmin; Wu, Heng; Li, Hai; Gan, Jinqiang

2018-05-01

A robust and high-precision displacement measurement method for a compliant mechanism-based micro-/nano-positioning system is proposed. The method is composed of an integer-pixel and a sub-pixel matching procedure. In the proposed algorithm (Pro-A), an improved ring projection transform (IRPT) and gradient information are used as features for approximating the coarse candidates and fine locations, respectively. Simulations are conducted and the results show that the Pro-A has the ability of rotation-invariance and strong robustness, with a theoretical accuracy of 0.01 pixel. To validate the practical performance, a series of experiments are carried out using a computer micro-vision and laser interferometer system (LIMS). The results demonstrate that both the LIMS and Pro-A can achieve high precision, while the Pro-A has better stability and adaptability.

Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion.

PubMed

Fröhlich, Fabian; Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J; Grima, Ramon; Hasenauer, Jan

2016-07-01

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity.

Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion

PubMed Central

Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J.; Grima, Ramon; Hasenauer, Jan

2016-01-01

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity. PMID:27447730

Perturbational treatment of spin-orbit coupling for generally applicable high-level multi-reference methods

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

Mai, Sebastian; Marquetand, Philipp; González, Leticia

2014-08-21

An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbitmore » coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.« less

Evaluation of an alternate method for sampling benthic macroinvertebrates in low-gradient streams sampled as part of the National Rivers and Streams Assessment.

PubMed

Flotemersch, Joseph E; North, Sheila; Blocksom, Karen A

2014-02-01

Benthic macroinvertebrates are sampled in streams and rivers as one of the assessment elements of the US Environmental Protection Agency's National Rivers and Streams Assessment. In a 2006 report, the recommendation was made that different yet comparable methods be evaluated for different types of streams (e.g., low gradient vs. high gradient). Consequently, a research element was added to the 2008-2009 National Rivers and Streams Assessment to conduct a side-by-side comparison of the standard macroinvertebrate sampling method with an alternate method specifically designed for low-gradient wadeable streams and rivers that focused more on stream edge habitat. Samples were collected using each method at 525 sites in five of nine aggregate ecoregions located in the conterminous USA. Methods were compared using the benthic macroinvertebrate multimetric index developed for the 2006 Wadeable Streams Assessment. Statistical analysis did not reveal any trends that would suggest the overall assessment of low-gradient streams on a regional or national scale would change if the alternate method was used rather than the standard sampling method, regardless of the gradient cutoff used to define low-gradient streams. Based on these results, the National Rivers and Streams Survey should continue to use the standard field method for sampling all streams.

Gravity gradient preprocessing at the GOCE HPF

NASA Astrophysics Data System (ADS)

Bouman, J.; Rispens, S.; Gruber, T.; Schrama, E.; Visser, P.; Tscherning, C. C.; Veicherts, M.

2009-04-01

One of the products derived from the GOCE observations are the gravity gradients. These gravity gradients are provided in the Gradiometer Reference Frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. In order to use these gravity gradients for application in Earth sciences and gravity field analysis, additional pre-processing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and non-tidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10-3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10-2 level with this method.

Preprocessing of gravity gradients at the GOCE high-level processing facility

NASA Astrophysics Data System (ADS)

Bouman, Johannes; Rispens, Sietse; Gruber, Thomas; Koop, Radboud; Schrama, Ernst; Visser, Pieter; Tscherning, Carl Christian; Veicherts, Martin

2009-07-01

One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/ f behaviour for low frequencies. In the outlier detection, the 1/ f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/ f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10-3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10-2 level with this method.

Combining Biomarkers Linearly and Nonlinearly for Classification Using the Area Under the ROC Curve

PubMed Central

Fong, Youyi; Yin, Shuxin; Huang, Ying

2016-01-01

In biomedical studies, it is often of interest to classify/predict a subject’s disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on AUC - Area under the Receiver Operating Characteristic Curve. Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient-based algorithms to find the best marker combination, which often result in sub-optimal local solutions. In this paper, we address these two problems by proposing a new kernel-based AUC optimization method called Ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function, and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data is generated from a semiparametric generalized linear model, just as the Smoothed AUC method (SAUC). Through simulation studies and real data examples, we demonstrate that RAUC out-performs SAUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial. PMID:27058981

Rapid analysis of charge variants of monoclonal antibodies using non-linear salt gradient in cation-exchange high performance liquid chromatography.

PubMed

Joshi, Varsha; Kumar, Vijesh; Rathore, Anurag S

2015-08-07

A method is proposed for rapid development of a short, analytical cation exchange high performance liquid chromatography method for analysis of charge heterogeneity in monoclonal antibody products. The parameters investigated and optimized include pH, shape of elution gradient and length of the column. It is found that the most important parameter for development of a shorter method is the choice of the shape of elution gradient. In this paper, we propose a step by step approach to develop a non-linear sigmoidal shape gradient for analysis of charge heterogeneity for two different monoclonal antibody products. The use of this gradient not only decreases the run time of the method to 4min against the conventional method that takes more than 40min but also the resolution is retained. Superiority of the phosphate gradient over sodium chloride gradient for elution of mAbs is also observed. The method has been successfully evaluated for specificity, sensitivity, linearity, limit of detection, and limit of quantification. Application of this method as a potential at-line process analytical technology tool has been suggested. Copyright © 2015 Elsevier B.V. All rights reserved.

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

DOE PAGES

Jónsson, Elvar Örn; Lehtola, Susi; Jónsson, Hannes

2015-06-01

Results of Perdew–Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, wheremore » the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol for small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F 2 molecule being a notable outlier.« less

Bayesian Inversion of 2D Models from Airborne Transient EM Data

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Key, K.; Ray, A.

2016-12-01

The inherent non-uniqueness in most geophysical inverse problems leads to an infinite number of Earth models that fit observed data to within an adequate tolerance. To resolve this ambiguity, traditional inversion methods based on optimization techniques such as the Gauss-Newton and conjugate gradient methods rely on an additional regularization constraint on the properties that an acceptable model can possess, such as having minimal roughness. While allowing such an inversion scheme to converge on a solution, regularization makes it difficult to estimate the uncertainty associated with the model parameters. This is because regularization biases the inversion process toward certain models that satisfy the regularization constraint and away from others that don't, even when both may suitably fit the data. By contrast, a Bayesian inversion framework aims to produce not a single `most acceptable' model but an estimate of the posterior likelihood of the model parameters, given the observed data. In this work, we develop a 2D Bayesian framework for the inversion of transient electromagnetic (TEM) data. Our method relies on a reversible-jump Markov Chain Monte Carlo (RJ-MCMC) Bayesian inverse method with parallel tempering. Previous gradient-based inversion work in this area used a spatially constrained scheme wherein individual (1D) soundings were inverted together and non-uniqueness was tackled by using lateral and vertical smoothness constraints. By contrast, our work uses a 2D model space of Voronoi cells whose parameterization (including number of cells) is fully data-driven. To make the problem work practically, we approximate the forward solution for each TEM sounding using a local 1D approximation where the model is obtained from the 2D model by retrieving a vertical profile through the Voronoi cells. The implicit parsimony of the Bayesian inversion process leads to the simplest models that adequately explain the data, obviating the need for explicit smoothness constraints. In addition, credible intervals in model space are directly obtained, resolving some of the uncertainty introduced by regularization. An example application shows how the method can be used to quantify the uncertainty in airborne EM soundings for imaging subglacial brine channels and groundwater systems.

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

NASA Technical Reports Server (NTRS)

Mair, R. W.; Sen, P. N.; Hurlimann, M. D.; Patz, S.; Cory, D. G.; Walsworth, R. L.

2002-01-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Pade approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Pade interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Pade length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media.

PubMed

Mair, R W; Sen, P N; Hürlimann, M D; Patz, S; Cory, D G; Walsworth, R L

2002-06-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

Resolving the circumstellar environment of the B[e] star V921 Scorpii in the near-infrared with VLTI/AMBER

NASA Astrophysics Data System (ADS)

Kreplin, A.; Kraus, S.; Hofmann, K.-H.; Schertl, D.; Weigelt, G.; Driebe, T.

2012-01-01

Aims: We study the AU-scale circumstellar environment of the unclassified B[e] star V921 Sco in the near-infrared. For interpreting the observations, we employ temperature-gradient disk models. Methods: Using the near-infrared beam combiner instrument AMBER, we recorded spectrally dispersed (spectral resolution R = 35) interferograms in the H and K bands. To obtain an improved calibration of the visibilities, we developed a method that is able to equalize the histograms of the optical path difference of target and calibrator. We fit temperature-gradient disk models to the visibilities and spectral energy distribution (SED) to analyze the circumstellar dust geometry. Results: We derived a geometric ring-fit radius of 2.10 ± 0.16 mas in the K band. If we adopt the distance of 1150 ± 150 pc reported elsewhere, we obtain a ring-fit radius of 2.4 AU, which is slightly smaller than the 3.5 AU dust sublimation radius predicted by the size-luminosity relation. The fitted H-band radius of 1.61 ± 0.23 mas (1.85 AU) is found to be more compact than the K-band radius. The best-fit temperature-gradient disk model has an inner disk radius of ~1.45 AU, an inner-edge disk temperature T0 = 1533 K, and a temperature-gradient exponent q = 0.46 suggesting a flared disk geometry. Conclusions: The distance and luminosity of V921 Sco are not well known. If we assume a distance of 1150 ± 150 pc, we derive a ring-fit radius of ~2.4 AU, which is approximately consistent with the computed temperature-gradient disk model with inner and outer ring radii of 1.45 and 8.5 AU, respectively. If the inner radius of V921 Sco is more compact than the sublimation radius, this compact observed size can be explained by emitting material (e.g., a gaseous disk) inside the dust sublimation radius, as suggested for several other B[e] stars. Based on observations made with ESO telescopes at Paranal Observatory under program ID (MPG-VISA GTO): 079.C-0212(A).

Velocity Gradient Power Functional for Brownian Dynamics.

PubMed

de Las Heras, Daniel; Schmidt, Matthias

2018-01-12

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

Velocity Gradient Power Functional for Brownian Dynamics

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-01-01

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

Sensor Phenomenology and Feature Development for Improved Sonar-based Detection & Classification of Underwater UXO

DTIC Science & Technology

2009-12-01

the validity of approximating poroelastic media with acoustic or acoustic /elastic models , and to characterize how scattering physics will differ for...elastic buried object (yellow rectangle in the figure) in three types of environments: • (1) Model 1: acoustic layer on top of a poroelastic medium with a...porosity gradient and no viscous damping. • (2) Model 2: acoustic layer on top of a poroelastic medium with a porosity gradient and viscous damping

Performance in the vertical test of the 832 nine-cell 1.3 GHz cavities for the European X-ray Free Electron Laser

NASA Astrophysics Data System (ADS)

Reschke, D.; Gubarev, V.; Schaffran, J.; Steder, L.; Walker, N.; Wenskat, M.; Monaco, L.

2017-04-01

The successful production and associated vertical testing of over 800 superconducting 1.3 GHz accelerating cavities for the European X-ray Free Electron Laser (XFEL) represents the culmination of over 20 years of superconducting radio-frequency R&D. The cavity production took place at two industrial vendors under the shared responsibility of INFN Milano-LASA and DESY. Average vertical testing rates at DESY exceeded 10 cavities per week, peaking at up to 15 cavities per week. The cavities sent for cryomodule assembly at Commissariat à l'énergie atomique (CEA) Saclay achieved an average maximum gradient of approximately 33 MV /m , reducing to ˜30 MV /m when the operational specifications on quality factor (Q) and field emission were included (the so-called usable gradient). Only 16% of the cavities required an additional surface retreatment to recover their low performance (usable gradient less than 20 MV /m ). These cavities were predominantly limited by excessive field emission for which a simple high pressure water rinse (HPR) was sufficient. Approximately 16% of the cavities also received an additional HPR, e.g. due to vacuum problems before or during the tests or other reasons, but these were not directly related to gradient performance. The in-depth statistical analyses presented in this report have revealed several features of the series produced cavities.

Temporal variations of the anomalous oxygen component

NASA Technical Reports Server (NTRS)

Cummings, A. C.; Webber, W. R.

1983-01-01

Data from the cosmic ray experiment on Voyagers 1 and 2 was used to examine anomalous oxygen in the time period from launch in 1977 to the end of 1981. Several time periods were found where large periodic (typically 26 day) temporal variations of the oxygen intensity between approximately 5 - 15 MeV/nuc are present. Variations in intensity by up to a factor of 10 are observed during these periods. Several characteristics of these variations indicate that they are not higher energy extensions of the low energy particle (approximately 1 MeV/nuc) increases found in many corotating interaction regions (CIR's). Many of these periodic temporal variations are correlated with similar, but much smaller, recurrent variations in the 75 MeV proton rate. Voyager 1 and Voyager 2 counting rates were compared to estimate the local radial gradient for both the protons and the oxygen. The proton gradients during periods of both maximum and minumum fluxes are consistent with the overall positive radial gradients reported by others from Pioneer and near-Earth observations, supporting the view that these variations are due to local modulation of a source outside the radial range of project measurements. In contrast, the oxygen gradients during periods of maximum proton flux differ in sign from those during minimum proton fluxes, suggesting that the origin of the oxygen variations is different from that of the protons.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Saccadic spike potentials in gamma-band EEG: characterization, detection and suppression.

PubMed

Keren, Alon S; Yuval-Greenberg, Shlomit; Deouell, Leon Y

2010-02-01

Analysis of high-frequency (gamma-band) neural activity by means of non-invasive EEG is gaining increasing interest. However, we have recently shown that a saccade-related spike potential (SP) seriously confounds the analysis of EEG induced gamma-band responses (iGBR), as the SP eludes traditional EEG artifact rejection methods. Here we provide a comprehensive profile of the SP and evaluate methods for its detection and suppression, aiming to unveil true cerebral gamma-band activity. The SP appears consistently as a sharp biphasic deflection of about 22 ms starting at the saccade onset, with a frequency band of approximately 20-90 Hz. On the average, larger saccades elicit higher SP amplitudes. The SP amplitude gradually changes from the extra-ocular channels towards posterior sites with the steepest gradients around the eyes, indicating its ocular source. Although the amplitude and the sign of the SP depend on the choice of reference channel, the potential gradients remain the same and non-zero for all references. The scalp topography is modulated almost exclusively by the direction of saccades, with steeper gradients ipsilateral to the saccade target. We discuss how the above characteristics impede attempts to remove these SPs from the EEG by common temporal filtering, choice of different references, or rejection of contaminated trials. We examine the extent to which SPs can be reliably detected without an eye tracker, assess the degree to which scalp current density derivation attenuates the effect of the SP, and propose a tailored ICA procedure for minimizing the effect of the SP. Copyright (c) 2009 Elsevier Inc. All rights reserved.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning

NASA Astrophysics Data System (ADS)

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-08-01

{{\\ell }2,1} -minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the {{\\ell }2,1} -based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the {{\\ell }2,1} -minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the {{\\ell }2,1} -minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the {{\\ell }2,1} -minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning.

PubMed

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-07-20

[Formula: see text]-minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the [Formula: see text]-based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the [Formula: see text]-minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the [Formula: see text]-minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the [Formula: see text]-minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

The uses and limitations of the square‐root‐impedance method for computing site amplification

USGS Publications Warehouse

Boore, David

2013-01-01

The square‐root‐impedance (SRI) method is a fast way of computing approximate site amplification that does not depend on the details from velocity models. The SRI method underestimates the peak response of models with large impedance contrasts near their base, but the amplifications for those models is often close to or equal to the root mean square of the theoretical full resonant (FR) response of the higher modes. On the other hand, for velocity models made up of gradients, with no significant impedance changes across small ranges of depth, the SRI method systematically underestimates the theoretical FR response over a wide frequency range. For commonly used gradient models for generic rock sites, the SRI method underestimates the FR response by about 20%–30%. Notwithstanding the persistent underestimation of amplifications from theoretical FR calculations, however, amplifications from the SRI method may often provide more useful estimates of amplifications than the FR method, because the SRI amplifications are not sensitive to details of the models and will not exhibit the many peaks and valleys characteristic of theoretical full resonant amplifications (jaggedness sometimes not seen in amplifications based on averages of site response from multiple recordings at a given site). The lack of sensitivity to details of the velocity models also makes the SRI method useful in comparing the response of various velocity models, in spite of any systematic underestimation of the response. The quarter‐wavelength average velocity, which is fundamental to the SRI method, is useful by itself in site characterization, and as such, is the fundamental parameter used to characterize the site response in a number of recent ground‐motion prediction equations.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

DOE PAGES

Song, Chenchen; Martinez, Todd J.

2017-08-29

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-10-01

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

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

Song, Chenchen; Martinez, Todd J.

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Thermodynamical study of boron doped CeX{sub 3} (X=Pd, Rh)

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

Sharma, Ramesh; Dwivedi, Shalini; Sharma, Yamini, E-mail: sharma.yamini62@gmail.com

2016-05-06

The structural, electronic, thermal, and optical properties of cubic non magnetic CeX{sub 3}(X=Pd, Rh) compounds which crystallize in the Au{sub 3}Cu structure have been studied using the projected augmented wave (PAW) method within the density functional theory (DFT) with generalized gradient approximation (GGA) for exchange correlation potential. In this paper we have calculated the band structure which are interpreted using the density of states. The optical properties such as extinction coefficients clearly illustrate the changes in CeX{sub 3} due to intercalation of boron. Lattice instability is observed in CePd{sub 3}B from the calculated dynamical properties.

Extrapolation of rotating sound fields.

PubMed

Carley, Michael

2018-03-01

A method is presented for the computation of the acoustic field around a tonal circular source, such as a rotor or propeller, based on an exact formulation which is valid in the near and far fields. The only input data required are the pressure field sampled on a cylindrical surface surrounding the source, with no requirement for acoustic velocity or pressure gradient information. The formulation is approximated with exponentially small errors and appears to require input data at a theoretically minimal number of points. The approach is tested numerically, with and without added noise, and demonstrates excellent performance, especially when compared to extrapolation using a far-field assumption.

Approximate Separability of Green’s Function for High Frequency Helmholtz Equations

DTIC Science & Technology

2014-09-01

is highly separable (Theorem 2.8) for two disjoint domains X,Y based on a key gradient estimate by Caccioppoli inequality . The method and result can be...bounded by (17) 1 ≥< Ĝ(·,y1), Ĝ(·,y2) >X≥ K̃−2, K̃ = C(d, λ, µ) c(d, λ, µ) [ 1 + r ρ ]d−2 . Also Caccioppoli inequality gives a L2 norm bound of the...1− 2) nhk∑ m=1 λm ≥ (1− 2)cnhk . 24 BJÖRN ENGQUIST AND HONGKAI ZHAO Hence inequalities (60) is replaced by the following: (75) nhk∑ m=1 λ2m > N

Surprising performance for vibrational frequencies of the distinguishable clusters with singles and doubles (DCSD) and MP2.5 approximations

NASA Astrophysics Data System (ADS)

Kesharwani, Manoj K.; Sylvetsky, Nitai; Martin, Jan M. L.

2017-11-01

We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive analytical gradients. For systems dominated by a single reference configuration, even MP2.5 is a viable alternative, at MP3 cost. MP2.5 performance for vibrational frequencies is comparable to double hybrids such as DSD-PBEP86-D3BJ, but without resorting to empirical parameters. DCSD is also quite suitable for computing zero-point vibrational energies in computational thermochemistry.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study.

PubMed

Noreen, Saima; Qasim, Muhammad

2015-01-01

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.

Aztec user`s guide. Version 1

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

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1995-10-01

Aztec is an iterative library that greatly simplifies the parallelization process when solving the linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. Aztec is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparsemore » unstructured matrices for parallel solution. Once the distributed matrix is created, computation can be performed on any of the parallel machines running Aztec: nCUBE 2, IBM SP2 and Intel Paragon, MPI platforms as well as standard serial and vector platforms. Aztec includes a number of Krylov iterative methods such as conjugate gradient (CG), generalized minimum residual (GMRES) and stabilized biconjugate gradient (BICGSTAB) to solve systems of equations. These Krylov methods are used in conjunction with various preconditioners such as polynomial or domain decomposition methods using LU or incomplete LU factorizations within subdomains. Although the matrix A can be general, the package has been designed for matrices arising from the approximation of partial differential equations (PDEs). In particular, the Aztec package is oriented toward systems arising from PDE applications.« less

A new gradient shimming method based on undistorted field map of B0 inhomogeneity.

PubMed

Bao, Qingjia; Chen, Fang; Chen, Li; Song, Kan; Liu, Zao; Liu, Chaoyang

2016-04-01

Most existing gradient shimming methods for NMR spectrometers estimate field maps that resolve B0 inhomogeneity spatially from dual gradient-echo (GRE) images acquired at different echo times. However, the distortions induced by B0 inhomogeneity that always exists in the GRE images can result in estimated field maps that are distorted in both geometry and intensity, leading to inaccurate shimming. This work proposes a new gradient shimming method based on undistorted field map of B0 inhomogeneity obtained by a more accurate field map estimation technique. Compared to the traditional field map estimation method, this new method exploits both the positive and negative polarities of the frequency encoded gradients to eliminate the distortions caused by B0 inhomogeneity in the field map. Next, the corresponding automatic post-data procedure is introduced to obtain undistorted B0 field map based on knowledge of the invariant characteristics of the B0 inhomogeneity and the variant polarity of the encoded gradient. The experimental results on both simulated and real gradient shimming tests demonstrate the high performance of this new method. Copyright © 2015 Elsevier Inc. All rights reserved.

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Analysis of separation test for automatic brake adjuster based on linear radon transformation

NASA Astrophysics Data System (ADS)

Luo, Zai; Jiang, Wensong; Guo, Bin; Fan, Weijun; Lu, Yi

2015-01-01

The linear Radon transformation is applied to extract inflection points for online test system under the noise conditions. The linear Radon transformation has a strong ability of anti-noise and anti-interference by fitting the online test curve in several parts, which makes it easy to handle consecutive inflection points. We applied the linear Radon transformation to the separation test system to solve the separating clearance of automatic brake adjuster. The experimental results show that the feature point extraction error of the gradient maximum optimal method is approximately equal to ±0.100, while the feature point extraction error of linear Radon transformation method can reach to ±0.010, which has a lower error than the former one. In addition, the linear Radon transformation is robust.

Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

NASA Astrophysics Data System (ADS)

Kulikov, D. A.; Potapov, A. A.; Rassadin, A. E.; Stepanov, A. V.

2017-10-01

In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

Rapid-gradient HPLC method for measuring drug interactions with immobilized artificial membrane: comparison with other lipophilicity measures.

PubMed

Valko, K; Du, C M; Bevan, C D; Reynolds, D P; Abraham, M H

2000-08-01

A fast-gradient high-performance liquid chromatographic (HPLC) method has been suggested to characterize the interactions of drugs with an immobilized artificial membrane (IAM). With a set of standards, the gradient retention times can be converted to Chromatographic Hydrophobicity Index values referring to IAM chromatography (CHI(IAM)) that approximates an acetonitrile concentration with which the equal distribution of compound can be achieved between the mobile phase and IAM. The CHI(IAM) values are more suitable for interlaboratory comparison and for high throughput screening of new molecular entities than the log k(IAM) values (isocratic retention factor on IAM). The fast-gradient method has been validated against the isocratic log k(IAM) values using the linear free energy relationship solvation equations based on the data from 48 compounds. The compound set was selected to provide a wide range and the least cross-correlation between the molecular descriptors in the solvation equation: (2) where SP is a solute property (e.g., logarithm of partition coefficients, reversed-phase (RP)-HPLC retention parameters, such as log k, log k(w), etc.) and the explanatory variables are solute descriptors as follows: R(2) is an excess molar refraction that can be obtained from the measured refractive index of a compound, pi(2)(H) is the solute dipolarity/polarizability, summation operatoralpha(2)(H) and summation operatorbeta(2)(0) are the solute overall or effective hydrogen-bond acidity and basicity, respectively, and V(x) is the McGowan characteristic volume (in cm(3)/100 mol) that can be calculated for any solute simply from molecular structure using a table of atomic constants. It was found that the relative constants of the solvation equation were very similar for the CHI(IAM) and for the log k(IAM). The IAM lipophilicity scale was quite similar to the octanol/water lipophilicity scale for neutral compounds. The effect of charge on the interaction with IAM was studied by varying the mobile phase pH. Copyright 2000 Wiley-Liss, Inc.

Short Diffusion Time Diffusion-Weighted Imaging With Oscillating Gradient Preparation as an Early Magnetic Resonance Imaging Biomarker for Radiation Therapy Response Monitoring in Glioblastoma: A Preclinical Feasibility Study.

PubMed

Bongers, Andre; Hau, Eric; Shen, Han

2018-01-04

To investigate a novel alternative diffusion-weighted imaging (DWI) approach using oscillating gradients preparation (OGSE) to obtain much shorter effective diffusion times (Δ eff ) for tumor response monitoring by apparent diffusion coefficient (ADC) mapping in a glioblastoma mouse model. Twenty-four BALB/c nude mice inoculated with U87 glioblastoma cells were randomized into a control group and an irradiation group, which underwent a 15-day fractioned radiation therapy (RT) course with 2 Gy/d. Therapy response was assessed by mapping of ADCs at 6 time points using an in-house implementation of a cos-OGSE DWI sequence with Δ eff  = 1.25 ms and compared with a standard pulsed gradient DWI protocol (PGSE) with typical clinical diffusion time Δ eff  = 18 ms. Longitudinal ADC changes in tumor and contralateral white matter (WM) were statistically assessed using repeated-measures analysis of variance and post hoc (Sidak) testing. On short Δ eff OGSE maps tumor ADC was generally 30%-50% higher than in surrounding WM. Areas correlated well with histology. Tumor identification was generally more difficult on PGSE maps owing to nonsignificant WM/tumor contrast. During RT, OGSE maps also showed significant tumor ADC increase (approximately 15%) in response to radiation, consistently seen after 14-Gy RT dose. The clinical reference (PGSE) showed lower sensitivity to radiation changes, and no significant response across the radiation group and time course could be detected. Our short Δ eff DWI method using OGSE better reflected histologically defined tumor areas and enabled more consistent and earlier detection of microstructural radiation changes than conventional methods. Oscillating gradients preparation offers significant potential as a robust microstructural RT response biomarker, potentially helping to shift important therapy decisions to earlier stages in the RT time course. Copyright © 2018 Elsevier Inc. All rights reserved.

Use of total electron content data to analyze ionosphere electron density gradients

NASA Astrophysics Data System (ADS)

Nava, B.; Radicella, S. M.; Leitinger, R.; Coïsson, P.

In the presence of electron density gradients the thin shell approximation for the ionosphere, used together with a simple mapping function to convert slant total electron content (TEC) to vertical TEC, could lead to TEC conversion errors. These "mapping function errors" can therefore be used to detect the electron density gradients in the ionosphere. In the present work GPS derived slant TEC data have been used to investigate the effects of the electron density gradients in the middle and low latitude ionosphere under geomagnetic quiet and disturbed conditions. In particular the data corresponding to the geographic area of the American Sector for the days 5-7 April 2000 have been used to perform a complete analysis of mapping function errors based on the "coinciding pierce point technique". The results clearly illustrate the electron density gradient effects according to the locations considered and to the actual levels of disturbance of the ionosphere. In addition, the possibility to assess an ionospheric shell height able to minimize the mapping function errors has been verified.

Accuracy Assessment of the Precise Point Positioning for Different Troposphere Models

NASA Astrophysics Data System (ADS)

Oguz Selbesoglu, Mahmut; Gurturk, Mert; Soycan, Metin

2016-04-01

This study investigates the accuracy and repeatability of PPP technique at different latitudes by using different troposphere delay models. Nine IGS stations were selected between 00-800 latitudes at northern hemisphere and southern hemisphere. Coordinates were obtained for 7 days at 1 hour intervals in summer and winter. At first, the coordinates were estimated by using Niell troposphere delay model with and without including north and east gradients in order to investigate the contribution of troposphere delay gradients to the positioning . Secondly, Saastamoinen model was used to eliminate troposphere path delays by using standart atmosphere parameters were extrapolated for all station levels. Finally, coordinates were estimated by using RTCA-MOPS empirical troposphere delay model. Results demonstrate that Niell troposphere delay model with horizontal gradients has better mean values of rms errors 0.09 % and 65 % than the Niell troposphere model without horizontal gradients and RTCA-MOPS model, respectively. Saastamoinen model mean values of rms errors were obtained approximately 4 times bigger than the Niell troposphere delay model with horizontal gradients.

Magnetoelectrets prepared by using temperature gradient method

NASA Astrophysics Data System (ADS)

Ojha, Pragya; Qureshi, M. S.; Malik, M. M.

2015-05-01

A novel Temperature Gradient method for preparation of magnetoelectret is proposed. Non uniform magnetic field and temperature gradient are expected to be the main cause for the formation of magnetoelectrets (MEs). Being bad conductors of heat, during their formation, there is a possibility for the existence of a temperature gradient along the dielectric electrode interface. In this condition, the motion of, molecules and charge carriers are dependent on Temperature Gradient in a preferred direction. To increase this temperature gradient on both sides of the sample novel method for the preparation of MEs is developed for the first time. For this method the special sample holders are designed in our laboratory. MEs are prepared in such a way that one surface is cooled and the other is heated, during the process. With the help of XRD analysis using Type-E orientation pattern and surface charge studies on magnetoelectrets, the two main causes Non uniform magnetic field and temperature gradient for the formation of magnetoelectrets (MEs), are authenticated experimentally.

Hand-Portable Gradient Capillary Liquid Chromatography Pumping System.

PubMed

Sharma, Sonika; Plistil, Alex; Barnett, Hal E; Tolley, H Dennis; Farnsworth, Paul B; Stearns, Stanley D; Lee, Milton L

2015-10-20

In this work, a novel splitless nanoflow gradient generator integrated with a stop-flow injector was developed and evaluated using an on-column UV-absorption detector. The gradient pumping system consisted of two nanoflow pumps controlled by micro stepper motors, a mixer connected to a serpentine tube, and a high-pressure valve. The gradient system weighed only 4 kg (9 lbs) and could generate up to 55 MPa (8000 psi) pressure. The system could operate using a 24 V DC battery and required 1.2 A for operation. The total volume capacity of the pump was 74 μL, and a sample volume of 60 nL could be injected. The system provided accurate nanoflow rates as low as 10 nL/min without employing a splitter, making it ideal for capillary column use. The gradient dwell volume was calculated to be 1.3 μL, which created a delay of approximately 4 min with a typical flow rate of 350 nL/min. Gradient performance was evaluated for gradient step accuracy, and excellent reproducibility was obtained in day-to-day experiments (RSD < 1.2%, n = 4). Linear gradient reproducibility was tested by separating a three-component pesticide mixture on a poly(ethylene glycol) diacrylate (PEGDA) monolithic column. The retention time reproducibility was very good in run-to-run experiments (RSD < 1.42%, n = 4). Finally, excellent separation of five phenols was demonstrated using the nanoflow gradient system.

Stability of Gradient Field Corrections for Quantitative Diffusion MRI.

PubMed

Rogers, Baxter P; Blaber, Justin; Welch, E Brian; Ding, Zhaohua; Anderson, Adam W; Landman, Bennett A

2017-02-11

In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fields, we predicted the obtained b-values and applied gradient directions throughout a typical field of view for brain imaging for a typical 32-direction diffusion imaging sequence. We measured the stability of these predictions over time. At 80 mm from scanner isocenter, predicted b-value was 1-6% different than intended due to gradient nonlinearity, and predicted gradient directions were in error by up to 1 degree. Over the course of one month the change in these quantities due to calibration-related factors such as scanner drift and variation in phantom placement was <0.5% for b-values, and <0.5 degrees for angular deviation. The proposed calibration procedure allows the estimation of gradient nonlinearity to correct b-values and gradient directions ahead of advanced diffusion image processing for high angular resolution data, and requires only a five-minute phantom scan that can be included in a weekly or monthly quality assurance protocol.

Applications and assessment of QM:QM electronic embedding using generalized asymmetric Mulliken atomic charges.

PubMed

Parandekar, Priya V; Hratchian, Hrant P; Raghavachari, Krishnan

2008-10-14

Hybrid QM:QM (quantum mechanics:quantum mechanics) and QM:MM (quantum mechanics:molecular mechanics) methods are widely used to calculate the electronic structure of large systems where a full quantum mechanical treatment at a desired high level of theory is computationally prohibitive. The ONIOM (our own N-layer integrated molecular orbital molecular mechanics) approximation is one of the more popular hybrid methods, where the total molecular system is divided into multiple layers, each treated at a different level of theory. In a previous publication, we developed a novel QM:QM electronic embedding scheme within the ONIOM framework, where the model system is embedded in the external Mulliken point charges of the surrounding low-level region to account for the polarization of the model system wave function. Therein, we derived and implemented a rigorous expression for the embedding energy as well as analytic gradients that depend on the derivatives of the external Mulliken point charges. In this work, we demonstrate the applicability of our QM:QM method with point charge embedding and assess its accuracy. We study two challenging systems--zinc metalloenzymes and silicon oxide cages--and demonstrate that electronic embedding shows significant improvement over mechanical embedding. We also develop a modified technique for the energy and analytic gradients using a generalized asymmetric Mulliken embedding method involving an unequal splitting of the Mulliken overlap populations to offer improvement in situations where the Mulliken charges may be deficient.

Impact of a century of climate change on small-mammal communities in Yosemite National Park, USA.

PubMed

Moritz, Craig; Patton, James L; Conroy, Chris J; Parra, Juan L; White, Gary C; Beissinger, Steven R

2008-10-10

We provide a century-scale view of small-mammal responses to global warming, without confounding effects of land-use change, by repeating Grinnell's early-20th century survey across a 3000-meter-elevation gradient that spans Yosemite National Park, California, USA. Using occupancy modeling to control for variation in detectability, we show substantial ( approximately 500 meters on average) upward changes in elevational limits for half of 28 species monitored, consistent with the observed approximately 3 degrees C increase in minimum temperatures. Formerly low-elevation species expanded their ranges and high-elevation species contracted theirs, leading to changed community composition at mid- and high elevations. Elevational replacement among congeners changed because species' responses were idiosyncratic. Though some high-elevation species are threatened, protection of elevation gradients allows other species to respond via migration.

Stacking dependence of carrier transport properties in multilayered black phosphorous

NASA Astrophysics Data System (ADS)

Sengupta, A.; Audiffred, M.; Heine, T.; Niehaus, T. A.

2016-02-01

We present the effect of different stacking orders on carrier transport properties of multi-layer black phosphorous. We consider three different stacking orders AAA, ABA and ACA, with increasing number of layers (from 2 to 6 layers). We employ a hierarchical approach in density functional theory (DFT), with structural simulations performed with generalized gradient approximation (GGA) and the bandstructure, carrier effective masses and optical properties evaluated with the meta-generalized gradient approximation (MGGA). The carrier transmission in the various black phosphorous sheets was carried out with the non-equilibrium green’s function (NEGF) approach. The results show that ACA stacking has the highest electron and hole transmission probabilities. The results show tunability for a wide range of band-gaps, carrier effective masses and transmission with a great promise for lattice engineering (stacking order and layers) in black phosphorous.

An Improved Experimental Method for Simulating Erosion Processes by Concentrated Channel Flow

PubMed Central

Chen, Xiao-Yan; Zhao, Yu; Mo, Bin; Mi, Hong-Xing

2014-01-01

Rill erosion is an important process that occurs on hill slopes, including sloped farmland. Laboratory simulations have been vital to understanding rill erosion. Previous experiments obtained sediment yields using rills of various lengths to get the sedimentation process, which disrupted the continuity of the rill erosion process and was time-consuming. In this study, an improved experimental method was used to measure the rill erosion processes by concentrated channel flow. By using this method, a laboratory platform, 12 m long and 3 m wide, was used to construct rills of 0.1 m wide and 12 m long for experiments under five slope gradients (5, 10, 15, 20, and 25 degrees) and three flow rates (2, 4, and 8 L min−1). Sediment laden water was simultaneously sampled along the rill at locations 0.5 m, 1 m, 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 10 m, and 12 m from the water inlet to determine the sediment concentration distribution. The rill erosion process measured by the method used in this study and that by previous experimental methods are approximately the same. The experimental data indicated that sediment concentrations increase with slope gradient and flow rate, which highlights the hydraulic impact on rill erosion. Sediment concentration increased rapidly at the initial section of the rill, and the rate of increase in sediment concentration reduced with the rill length. Overall, both experimental methods are feasible and applicable. However, the method proposed in this study is more efficient and easier to operate. This improved method will be useful in related research. PMID:24949621

The two-phase method for finding a great number of eigenpairs of the symmetric or weakly non-symmetric large eigenvalue problems

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

Dul, F.A.; Arczewski, K.

1994-03-01

Although it has been stated that [open quotes]an attempt to solve (very large problems) by subspace iterations seems futile[close quotes], we will show that the statement is not true, especially for extremely large eigenproblems. In this paper a new two-phase subspace iteration/Rayleigh quotient/conjugate gradient method for generalized, large, symmetric eigenproblems Ax = [lambda]Bx is presented. It has the ability of solving extremely large eigenproblems, N = 216,000, for example, and finding a large number of leftmost or rightmost eigenpairs, up to 1000 or more. Multiple eigenpairs, even those with multiplicity 100, can be easily found. The use of the proposedmore » method for solving the big full eigenproblems (N [approximately] 10[sup 3]), as well as for large weakly non-symmetric eigenproblems, have been considered also. The proposed method is fully iterative; thus the factorization of matrices ins avoided. The key idea consists in joining two methods: subspace and Rayleigh quotient iterations. The systems of indefinite and almost singular linear equations (a - [sigma]B)x = By are solved by various iterative conjugate gradient method can be used without danger of breaking down due to its property that may be called [open quotes]self-correction towards the eigenvector,[close quotes] discovered recently by us. The use of various preconditioners (SSOR and IC) has also been considered. The main features of the proposed method have been analyzed in detail. Comparisons with other methods, such as, accelerated subspace iteration, Lanczos, Davidson, TLIME, TRACMN, and SRQMCG, are presented. The results of numerical tests for various physical problems (acoustic, vibrations of structures, quantum chemistry) are presented as well. 40 refs., 12 figs., 2 tabs.« less

Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: Local, global hybrid, and range-separated hybrid functionals with and without dispersion corrections

DOE PAGES

Mardirossian, Narbe; Head-Gordon, Martin

2014-03-25

The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored in this paper by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the trainingmore » and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. Finally, the range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.« less

Multiscale modeling and simulation for polymer melt flows between parallel plates.

PubMed

Yasuda, Shugo; Yamamoto, Ryoichi

2010-03-01

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for omegatauR < approximately 1 , and the crossover between the liquidlike and solidlike regime takes place around omegataualpha approximately equal 1 (where omega is the angular frequency of the plate and tauR and taualpha are Rouse and alpha relaxation time, respectively).

Renormalization group methods for the Reynolds stress transport equations

NASA Technical Reports Server (NTRS)

Rubinstein, R.

1992-01-01

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Methods for developing time-series climate surfaces to drive topographically distributed energy- and water-balance models

USGS Publications Warehouse

Susong, D.; Marks, D.; Garen, D.

1999-01-01

Topographically distributed energy- and water-balance models can accurately simulate both the development and melting of a seasonal snowcover in the mountain basins. To do this they require time-series climate surfaces of air temperature, humidity, wind speed, precipitation, and solar and thermal radiation. If data are available, these parameters can be adequately estimated at time steps of one to three hours. Unfortunately, climate monitoring in mountain basins is very limited, and the full range of elevations and exposures that affect climate conditions, snow deposition, and melt is seldom sampled. Detailed time-series climate surfaces have been successfully developed using limited data and relatively simple methods. We present a synopsis of the tools and methods used to combine limited data with simple corrections for the topographic controls to generate high temporal resolution time-series images of these climate parameters. Methods used include simulations, elevational gradients, and detrended kriging. The generated climate surfaces are evaluated at points and spatially to determine if they are reasonable approximations of actual conditions. Recommendations are made for the addition of critical parameters and measurement sites into routine monitoring systems in mountain basins.Topographically distributed energy- and water-balance models can accurately simulate both the development and melting of a seasonal snowcover in the mountain basins. To do this they require time-series climate surfaces of air temperature, humidity, wind speed, precipitation, and solar and thermal radiation. If data are available, these parameters can be adequately estimated at time steps of one to three hours. Unfortunately, climate monitoring in mountain basins is very limited, and the full range of elevations and exposures that affect climate conditions, snow deposition, and melt is seldom sampled. Detailed time-series climate surfaces have been successfully developed using limited data and relatively simple methods. We present a synopsis of the tools and methods used to combine limited data with simple corrections for the topographic controls to generate high temporal resolution time-series images of these climate parameters. Methods used include simulations, elevational gradients, and detrended kriging. The generated climate surfaces are evaluated at points and spatially to determine if they are reasonable approximations of actual conditions. Recommendations are made for the addition of critical parameters and measurement sites into routine monitoring systems in mountain basins.

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

Determination of boundaries between ranges of high and low gradient of beam profile.

PubMed

Wendykier, Jacek; Bieniasiewicz, Marcin; Grządziel, Aleksandra; Jedynak, Tadeusz; Kośniewski, Wiktor; Reudelsdorf, Marta; Wendykier, Piotr

2016-01-01

This work addresses the problem of treatment planning system commissioning by introducing a new method of determination of boundaries between high and low gradient in beam profile. The commissioning of a treatment planning system is a very important task in the radiation therapy. One of the main goals of this task is to compare two field profiles: measured and calculated. Applying points of 80% and 120% of nominal field size can lead to the incorrect determination of boundaries, especially for small field sizes. The method that is based on the beam profile gradient allows for proper assignment of boundaries between high and low gradient regions even for small fields. TRS 430 recommendations for commissioning were used. The described method allows a separation between high and low gradient, because it directly uses the value of the gradient of a profile. For small fields, the boundaries determined by the new method allow a commissioning of a treatment planning system according to the TRS 430, while the point of 80% of nominal field size is already in the high gradient region. The method of determining the boundaries by using the beam profile gradient can be extremely helpful during the commissioning of the treatment planning system for Intensity Modulated Radiation Therapy or for other techniques which require very small field sizes.

Pure phase encode magnetic field gradient monitor.

PubMed

Han, Hui; MacGregor, Rodney P; Balcom, Bruce J

2009-12-01

Numerous methods have been developed to measure MRI gradient waveforms and k-space trajectories. The most promising new strategy appears to be magnetic field monitoring with RF microprobes. Multiple RF microprobes may record the magnetic field evolution associated with a wide variety of imaging pulse sequences. The method involves exciting one or more test samples and measuring the time evolution of magnetization through the FIDs. Two critical problems remain. The gradient waveform duration is limited by the sample T(2)*, while the k-space maxima are limited by gradient dephasing. The method presented is based on pure phase encode FIDs and solves the above two problems in addition to permitting high strength gradient measurement. A small doped water phantom (1-3 mm droplet, T(1), T(2), T(2)* < 100 micros) within a microprobe is excited by a series of closely spaced broadband RF pulses each followed by FID single point acquisition. Two trial gradient waveforms have been chosen to illustrate the technique, neither of which could be measured by the conventional RF microprobe measurement. The first is an extended duration gradient waveform while the other illustrates the new method's ability to measure gradient waveforms with large net area and/or high amplitude. The new method is a point monitor with simple implementation and low cost hardware requirements.

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

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

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

High energy X-ray diffraction study of a dental ceramics–titanium functional gradient material prepared by field assisted sintering technique

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

Witte, K., E-mail: kerstin.witte@uni-rostock.de; Bodnar, W.; Schell, N.

A functional gradient material with eleven layers composed of a dental ceramics and titanium was successfully consolidated using field assisted sintering technique in a two-step sintering process. High energy X-ray diffraction studies on the gradient were performed at High Energy Material Science beamline at Desy in Hamburg. Phase composition, crystal unit edges and lattice mismatch along the gradient were determined applying Rietveld refinement procedure. Phase analysis revealed that the main crystalline phase present in the gradient is α-Ti. Crystallinity increases stepwisely along the gradient with a decreasing increment between every next layer, following rather the weight fraction of titanium. Themore » crystal unit edge a of titanium remains approximately constant with a value of 2.9686(1) Å, while c is reduced with increasing amount of titanium. In the layer with pure titanium the crystal unit edge c is constant with a value of 4.7174(2) Å. The lattice mismatch leading to an internal stress was calculated over the whole gradient. It was found that the maximal internal stress in titanium embedded in the studied gradient is significantly smaller than its yield strength, which implies that the structure of titanium along the whole gradient is mechanically stable. - Highlights: • High energy XRD studies of dental ceramics–Ti gradient material consolidated by FAST. • Phase composition, crystallinity and lattice parameters are determined. • Crystallinity increases stepwisely along the gradient following weight fraction of Ti. • Lattice mismatch leading to internal stress is calculated over the whole gradient. • Internal stress in α-Ti embedded in the gradient is smaller than its yield strength.« less

Numerical and experimental validation of a particle Galerkin method for metal grinding simulation

NASA Astrophysics Data System (ADS)

Wu, C. T.; Bui, Tinh Quoc; Wu, Youcai; Luo, Tzui-Liang; Wang, Morris; Liao, Chien-Chih; Chen, Pei-Yin; Lai, Yu-Sheng

2018-03-01

In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach.

Determination of catechins and caffeine in camillia sinensis raw materials, extracts, and dietary supplements by HPLC-uv: single-laboratory validation.

PubMed

Roman, Mark C

2013-01-01

A rapid method has been developed to quantify seven catechins and caffeine in green tea (Camillia sinensis) raw material and powdered extract, and dietary supplements containing green tea extract. The method utilizes RP HPLC with a phenyl-based stationary phase and gradient elution. Detection is by UV absorbance. The total run time, including column re-equilibration, is 13 min. Single-laboratory validation (SLV) has been performed on the method to determine the repeatability, accuracy, selectivity, LOD, LOQ, ruggedness, and linearity for (+)-catechin, (-)-epicatechin, (-)-epicatechin gallate, (-)-epigallocatechin, (-)-gallocatechin gallate, (-)-epigallocatechin gallate, and (+)-gallocatechin, as well as caffeine. Repeatability precision and recovery results met AOAC guidelines for SLV studies for all catechins and caffeine down to a level of approximately 20 mg/g. Finished products containing high concentrations of minerals require the use of EDTA to prevent decomposition of the catechins.

Riemann Solvers in Relativistic Hydrodynamics: Basics and Astrophysical Applications

NASA Astrophysics Data System (ADS)

Ibanez, Jose M.

2001-12-01

My contribution to these proceedings summarizes a general overview on t High Resolution Shock Capturing methods (HRSC) in the field of relativistic hydrodynamics with special emphasis on Riemann solvers. HRSC techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. In the first part I will show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. I will review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several 1D and 2D test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. In the second part I will illustrate the use of HRSC methods in several astrophysical applications where special and general relativistic hydrodynamical processes play a crucial role.

A trust region-based approach to optimize triple response systems

NASA Astrophysics Data System (ADS)

Fan, Shu-Kai S.; Fan, Chihhao; Huang, Chia-Fen

2014-05-01

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke-Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.

Learning and tuning fuzzy logic controllers through reinforcements.

PubMed

Berenji, H R; Khedkar, P

1992-01-01

A method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. It is shown that: the generalized approximate-reasoning-based intelligent control (GARIC) architecture learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Non-Gradient Blue Native Polyacrylamide Gel Electrophoresis.

PubMed

Luo, Xiaoting; Wu, Jinzi; Jin, Zhen; Yan, Liang-Jun

2017-02-02

Gradient blue native polyacrylamide gel electrophoresis (BN-PAGE) is a well established and widely used technique for activity analysis of high-molecular-weight proteins, protein complexes, and protein-protein interactions. Since its inception in the early 1990s, a variety of minor modifications have been made to this gradient gel analytical method. Here we provide a major modification of the method, which we call non-gradient BN-PAGE. The procedure, similar to that of non-gradient SDS-PAGE, is simple because there is no expensive gradient maker involved. The non-gradient BN-PAGE protocols presented herein provide guidelines on the analysis of mitochondrial protein complexes, in particular, dihydrolipoamide dehydrogenase (DLDH) and those in the electron transport chain. Protocols for the analysis of blood esterases or mitochondrial esterases are also presented. The non-gradient BN-PAGE method may be tailored for analysis of specific proteins according to their molecular weight regardless of whether the target proteins are hydrophobic or hydrophilic. © 2017 by John Wiley & Sons, Inc. Copyright © 2017 John Wiley & Sons, Inc.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

A modified micrometeorological gradient method for estimating O3 dry depositions over a forest canopy

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Zhang, L.; Wang, X. M.; Munger, J. W.

2015-07-01

Small pollutant concentration gradients between levels above a plant canopy result in large uncertainties in estimated air-surface exchange fluxes when using existing micrometeorological gradient methods, including the aerodynamic gradient method (AGM) and the modified Bowen ratio method (MBR). A modified micrometeorological gradient method (MGM) is proposed in this study for estimating O3 dry deposition fluxes over a forest canopy using concentration gradients between a level above and a level below the canopy top, taking advantage of relatively large gradients between these levels due to significant pollutant uptake in the top layers of the canopy. The new method is compared with the AGM and MBR methods and is also evaluated using eddy-covariance (EC) flux measurements collected at the Harvard Forest Environmental Measurement Site, Massachusetts, during 1993-2000. All three gradient methods (AGM, MBR, and MGM) produced similar diurnal cycles of O3 dry deposition velocity (Vd(O3)) to the EC measurements, with the MGM method being the closest in magnitude to the EC measurements. The multi-year average Vd(O3) differed significantly between these methods, with the AGM, MBR, and MGM method being 2.28, 1.45, and 1.18 times that of the EC, respectively. Sensitivity experiments identified several input parameters for the MGM method as first-order parameters that affect the estimated Vd(O3). A 10% uncertainty in the wind speed attenuation coefficient or canopy displacement height can cause about 10% uncertainty in the estimated Vd(O3). An unrealistic leaf area density vertical profile can cause an uncertainty of a factor of 2.0 in the estimated Vd(O3). Other input parameters or formulas for stability functions only caused an uncertainly of a few percent. The new method provides an alternative approach to monitoring/estimating long-term deposition fluxes of similar pollutants over tall canopies.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Serpentinite and the dawn of life

PubMed Central

Sleep, Norman H.; Bird, Dennis K.; Pope, Emily C.

2011-01-01

Submarine hydrothermal vents above serpentinite produce chemical potential gradients of aqueous and ionic hydrogen, thus providing a very attractive venue for the origin of life. This environment was most favourable before Earth's massive CO2 atmosphere was subducted into the mantle, which occurred tens to approximately 100 Myr after the moon-forming impact; thermophile to clement conditions persisted for several million years while atmospheric pCO2 dropped from approximately 25 bar to below 1 bar. The ocean was weakly acid (pH ∼ 6), and a large pH gradient existed for nascent life with pH 9–11 fluids venting from serpentinite on the seafloor. Total CO2 in water was significant so the vent environment was not carbon limited. Biologically important phosphate and Fe(II) were somewhat soluble during this period, which occurred well before the earliest record of preserved surface rocks approximately 3.8 billion years ago (Ga) when photosynthetic life teemed on the Earth and the oceanic pH was the modern value of approximately 8. Serpentinite existed by 3.9 Ga, but older rocks that might retain evidence of its presence have not been found. Earth's sequesters extensive evidence of Archaean and younger subducted biological material, but has yet to be exploited for the Hadean record. PMID:21930576

Optimization of viral resuspension methods for carbon-rich soils along a permafrost thaw gradient

DOE PAGES

Trubl, Gareth; Solonenko, Natalie; Chittick, Lauren; ...

2016-05-17

Permafrost stores approximately 50% of global soil carbon (C) in a frozen form; it is thawing rapidly under climate change, and little is known about viral communities in these soils or their roles in C cycling. In permafrost soils, microorganisms contribute significantly to C cycling, and characterizing them has recently been shown to improve prediction of ecosystem function. In other ecosystems, viruses have broad ecosystem and community impacts ranging from host cell mortality and organic matter cycling to horizontal gene transfer and reprogramming of core microbial metabolisms. Here we developed an optimized protocol to extract viruses from three types ofmore » high organic-matter peatland soils across a permafrost thaw gradient (palsa, moss-dominated bog, and sedge-dominated fen). Three separate experiments were used to evaluate the impact of chemical buffers, physical dispersion, storage conditions, and concentration and purification methods on viral yields. The most successful protocol, amended potassium citrate buffer with bead-beating or vortexing and BSA, yielded on average as much as 2-fold more virus-like particles (VLPs) g –1of soil than other methods tested. All method combinations yielded VLPs g –1of soil on the 10 8order of magnitude across all three soil types. The different storage and concentration methods did not yield significantly more VLPs g –1of soil among the soil types. In conclusion, this research provides much-needed guidelines for resuspending viruses from soils, specifically carbon-rich soils, paving the way for incorporating viruses into soil ecology studies.« less

Optimization of viral resuspension methods for carbon-rich soils along a permafrost thaw gradient

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

Trubl, Gareth; Solonenko, Natalie; Chittick, Lauren

Permafrost stores approximately 50% of global soil carbon (C) in a frozen form; it is thawing rapidly under climate change, and little is known about viral communities in these soils or their roles in C cycling. In permafrost soils, microorganisms contribute significantly to C cycling, and characterizing them has recently been shown to improve prediction of ecosystem function. In other ecosystems, viruses have broad ecosystem and community impacts ranging from host cell mortality and organic matter cycling to horizontal gene transfer and reprogramming of core microbial metabolisms. Here we developed an optimized protocol to extract viruses from three types ofmore » high organic-matter peatland soils across a permafrost thaw gradient (palsa, moss-dominated bog, and sedge-dominated fen). Three separate experiments were used to evaluate the impact of chemical buffers, physical dispersion, storage conditions, and concentration and purification methods on viral yields. The most successful protocol, amended potassium citrate buffer with bead-beating or vortexing and BSA, yielded on average as much as 2-fold more virus-like particles (VLPs) g –1of soil than other methods tested. All method combinations yielded VLPs g –1of soil on the 10 8order of magnitude across all three soil types. The different storage and concentration methods did not yield significantly more VLPs g –1of soil among the soil types. In conclusion, this research provides much-needed guidelines for resuspending viruses from soils, specifically carbon-rich soils, paving the way for incorporating viruses into soil ecology studies.« less

The turbulent boundary layer on a porous plate: An experimental study of the heat transfer behavior with adverse pressure gradients

NASA Technical Reports Server (NTRS)

Blackwell, B. F.; Kays, W. M.; Moffat, R. J.

1972-01-01

An experimental investigation of the heat transfer behavior of the near equilibrium transpired turbulent boundary layer with adverse pressure gradient has been carried out. Stanton numbers were measured by an energy balance on electrically heated plates that form the bottom wall of the wind tunnel. Two adverse pressure gradients were studied. Two types of transpiration boundary conditions were investigated. The concept of an equilibrium thermal boundary layer was introduced. It was found that Stanton number as a function of enthalpy thickness Reynolds number is essentially unaffected by adverse pressure gradient with no transpiration. Shear stress, heat flux, and turbulent Prandtl number profiles were computed from mean temperature and velocity profiles. It was concluded that the turbulent Prandtl number is greater than unity in near the wall and decreases continuously to approximately 0.5 at the free stream.

The q-G method : A q-version of the Steepest Descent method for global optimization.

PubMed

Soterroni, Aline C; Galski, Roberto L; Scarabello, Marluce C; Ramos, Fernando M

2015-01-01

In this work, the q-Gradient (q-G) method, a q-version of the Steepest Descent method, is presented. The main idea behind the q-G method is the use of the negative of the q-gradient vector of the objective function as the search direction. The q-gradient vector, or simply the q-gradient, is a generalization of the classical gradient vector based on the concept of Jackson's derivative from the q-calculus. Its use provides the algorithm an effective mechanism for escaping from local minima. The q-G method reduces to the Steepest Descent method when the parameter q tends to 1. The algorithm has three free parameters and it is implemented so that the search process gradually shifts from global exploration in the beginning to local exploitation in the end. We evaluated the q-G method on 34 test functions, and compared its performance with 34 optimization algorithms, including derivative-free algorithms and the Steepest Descent method. Our results show that the q-G method is competitive and has a great potential for solving multimodal optimization problems.