A clustering-based graph Laplacian framework for value function approximation in reinforcement learning.

PubMed

Xu, Xin; Huang, Zhenhua; Graves, Daniel; Pedrycz, Witold

2014-12-01

In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a major research topic in reinforcement learning (RL). In this paper, a clustering-based graph Laplacian framework is presented for feature representation and value function approximation (VFA) in RL. By making use of clustering-based techniques, that is, K-means clustering or fuzzy C-means clustering, a graph Laplacian is constructed by subsampling in Markov decision processes (MDPs) with continuous state spaces. The basis functions for VFA can be automatically generated from spectral analysis of the graph Laplacian. The clustering-based graph Laplacian is integrated with a class of approximation policy iteration algorithms called representation policy iteration (RPI) for RL in MDPs with continuous state spaces. Simulation and experimental results show that, compared with previous RPI methods, the proposed approach needs fewer sample points to compute an efficient set of basis functions and the learning control performance can be improved for a variety of parameter settings.

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

NASA Technical Reports Server (NTRS)

Li, Wesley Waisang; Pak, Chan-Gi

2010-01-01

A technique for approximating the modal aerodynamic influence coefficients [AIC] matrices by using basis functions has been developed and validated. An application of the resulting approximated modal AIC matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO(TradeMark) flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing [ATW] 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

NASA Technical Reports Server (NTRS)

Li, Wesley W.; Pak, Chan-gi

2011-01-01

A technique for approximating the modal aerodynamic influence coefficients matrices by using basis functions has been developed and validated. An application of the resulting approximated modal aerodynamic influence coefficients matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle.

Exact exchange-correlation potentials of singlet two-electron systems

NASA Astrophysics Data System (ADS)

Ryabinkin, Ilya G.; Ospadov, Egor; Staroverov, Viktor N.

2017-10-01

We suggest a non-iterative analytic method for constructing the exchange-correlation potential, v XC ( r ) , of any singlet ground-state two-electron system. The method is based on a convenient formula for v XC ( r ) in terms of quantities determined only by the system's electronic wave function, exact or approximate, and is essentially different from the Kohn-Sham inversion technique. When applied to Gaussian-basis-set wave functions, the method yields finite-basis-set approximations to the corresponding basis-set-limit v XC ( r ) , whereas the Kohn-Sham inversion produces physically inappropriate (oscillatory and divergent) potentials. The effectiveness of the procedure is demonstrated by computing accurate exchange-correlation potentials of several two-electron systems (helium isoelectronic series, H2, H3 + ) using common ab initio methods and Gaussian basis sets.

A Parallel Product-Convolution approach for representing the depth varying Point Spread Functions in 3D widefield microscopy based on principal component analysis.

PubMed

Arigovindan, Muthuvel; Shaevitz, Joshua; McGowan, John; Sedat, John W; Agard, David A

2010-03-29

We address the problem of computational representation of image formation in 3D widefield fluorescence microscopy with depth varying spherical aberrations. We first represent 3D depth-dependent point spread functions (PSFs) as a weighted sum of basis functions that are obtained by principal component analysis (PCA) of experimental data. This representation is then used to derive an approximating structure that compactly expresses the depth variant response as a sum of few depth invariant convolutions pre-multiplied by a set of 1D depth functions, where the convolving functions are the PCA-derived basis functions. The model offers an efficient and convenient trade-off between complexity and accuracy. For a given number of approximating PSFs, the proposed method results in a much better accuracy than the strata based approximation scheme that is currently used in the literature. In addition to yielding better accuracy, the proposed methods automatically eliminate the noise in the measured PSFs.

Exponentially accurate approximations to piece-wise smooth periodic functions

NASA Technical Reports Server (NTRS)

Greer, James; Banerjee, Saheb

1995-01-01

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Optimization of selected molecular orbitals in group basis sets.

PubMed

Ferenczy, György G; Adams, William H

2009-04-07

We derive a local basis equation which may be used to determine the orbitals of a group of electrons in a system when the orbitals of that group are represented by a group basis set, i.e., not the basis set one would normally use but a subset suited to a specific electronic group. The group orbitals determined by the local basis equation minimize the energy of a system when a group basis set is used and the orbitals of other groups are frozen. In contrast, under the constraint of a group basis set, the group orbitals satisfying the Huzinaga equation do not minimize the energy. In a test of the local basis equation on HCl, the group basis set included only 12 of the 21 functions in a basis set one might ordinarily use, but the calculated active orbital energies were within 0.001 hartree of the values obtained by solving the Hartree-Fock-Roothaan (HFR) equation using all 21 basis functions. The total energy found was just 0.003 hartree higher than the HFR value. The errors with the group basis set approximation to the Huzinaga equation were larger by over two orders of magnitude. Similar results were obtained for PCl(3) with the group basis approximation. Retaining more basis functions allows an even higher accuracy as shown by the perfect reproduction of the HFR energy of HCl with 16 out of 21 basis functions in the valence basis set. When the core basis set was also truncated then no additional error was introduced in the calculations performed for HCl with various basis sets. The same calculations with fixed core orbitals taken from isolated heavy atoms added a small error of about 10(-4) hartree. This offers a practical way to calculate wave functions with predetermined fixed core and reduced base valence orbitals at reduced computational costs. The local basis equation can also be used to combine the above approximations with the assignment of local basis sets to groups of localized valence molecular orbitals and to derive a priori localized orbitals. An appropriately chosen localization and basis set assignment allowed a reproduction of the energy of n-hexane with an error of 10(-5) hartree, while the energy difference between its two conformers was reproduced with a similar accuracy for several combinations of localizations and basis set assignments. These calculations include localized orbitals extending to 4-5 heavy atoms and thus they require to solve reduced dimension secular equations. The dimensions are not expected to increase with increasing system size and thus the local basis equation may find use in linear scaling electronic structure calculations.

Validity of virial theorem in all-electron mixed basis density functional, Hartree–Fock, and GW calculations

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

Kuwahara, Riichi; Accelrys K. K., Kasumigaseki Tokyu Building 17F, 3-7-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-0013; Tadokoro, Yoichi

In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree–Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is inmore » excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.« less

Resolution of identity approximation for the Coulomb term in molecular and periodic systems.

PubMed

Burow, Asbjörn M; Sierka, Marek; Mohamed, Fawzi

2009-12-07

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 muhartree per atom, for both molecular and periodic systems.

Resolution of identity approximation for the Coulomb term in molecular and periodic systems

NASA Astrophysics Data System (ADS)

Burow, Asbjörn M.; Sierka, Marek; Mohamed, Fawzi

2009-12-01

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 μhartree per atom, for both molecular and periodic systems.

Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions

NASA Technical Reports Server (NTRS)

Schwenke, David W.; Truhlar, Donald G.

1990-01-01

The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.

Scalar relativistic computations of nuclear magnetic shielding and g-shifts with the zeroth-order regular approximation and range-separated hybrid density functionals

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

Aquino, Fredy W.; Govind, Niranjan; Autschbach, Jochen

2011-10-01

Density functional theory (DFT) calculations of NMR chemical shifts and molecular g-tensors with Gaussian-type orbitals are implemented via second-order energy derivatives within the scalar relativistic zeroth order regular approximation (ZORA) framework. Nonhybrid functionals, standard (global) hybrids, and range-separated (Coulomb-attenuated, long-range corrected) hybrid functionals are tested. Origin invariance of the results is ensured by use of gauge-including atomic orbital (GIAO) basis functions. The new implementation in the NWChem quantum chemistry package is verified by calculations of nuclear shielding constants for the heavy atoms in HX (X=F, Cl, Br, I, At) and H2X (X = O, S, Se, Te, Po), and Temore » chemical shifts in a number of tellurium compounds. The basis set and functional dependence of g-shifts is investigated for 14 radicals with light and heavy atoms. The problem of accurately predicting F NMR shielding in UF6-nCln, n = 1 to 6, is revisited. The results are sensitive to approximations in the density functionals, indicating a delicate balance of DFT self-interaction vs. correlation. For the uranium halides, the results with the range-separated functionals are mixed.« less

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

Makhov, Dmitry V.; Shalashilin, Dmitrii V.; Glover, William J.

We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as “cloning,” in analogy to the “spawning” procedure in AIMS. This synthesis of AIMS and MCEmore » allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, “trains,” as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.« less

A systematic way for the cost reduction of density fitting methods

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

Kállay, Mihály, E-mail: kallay@mail.bme.hu

2014-12-28

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of themore » computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.« less

Variational treatment of electron-polyatomic-molecule scattering calculations using adaptive overset grids

NASA Astrophysics Data System (ADS)

Greenman, Loren; Lucchese, Robert R.; McCurdy, C. William

2017-11-01

The complex Kohn variational method for electron-polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential Ĝ0+V ̂ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

A function approximation approach to anomaly detection in propulsion system test data

NASA Technical Reports Server (NTRS)

Whitehead, Bruce A.; Hoyt, W. A.

1993-01-01

Ground test data from propulsion systems such as the Space Shuttle Main Engine (SSME) can be automatically screened for anomalies by a neural network. The neural network screens data after being trained with nominal data only. Given the values of 14 measurements reflecting external influences on the SSME at a given time, the neural network predicts the expected nominal value of a desired engine parameter at that time. We compared the ability of three different function-approximation techniques to perform this nominal value prediction: a novel neural network architecture based on Gaussian bar basis functions, a conventional back propagation neural network, and linear regression. These three techniques were tested with real data from six SSME ground tests containing two anomalies. The basis function network trained more rapidly than back propagation. It yielded nominal predictions with, a tight enough confidence interval to distinguish anomalous deviations from the nominal fluctuations in an engine parameter. Since the function-approximation approach requires nominal training data only, it is capable of detecting unknown classes of anomalies for which training data is not available.

Computational tests of quantum chemical models for excited and ionized states of molecules with phosphorus and sulfur atoms.

PubMed

Hahn, David K; RaghuVeer, Krishans; Ortiz, J V

2014-05-15

Time-dependent density functional theory (TD-DFT) and electron propagator theory (EPT) are used to calculate the electronic transition energies and ionization energies, respectively, of species containing phosphorus or sulfur. The accuracy of TD-DFT and EPT, in conjunction with various basis sets, is assessed with data from gas-phase spectroscopy. TD-DFT is tested using 11 prominent exchange-correlation functionals on a set of 37 vertical and 19 adiabatic transitions. For vertical transitions, TD-CAM-B3LYP calculations performed with the MG3S basis set are lowest in overall error, having a mean absolute deviation from experiment of 0.22 eV, or 0.23 eV over valence transitions and 0.21 eV over Rydberg transitions. Using a larger basis set, aug-pc3, improves accuracy over the valence transitions via hybrid functionals, but improved accuracy over the Rydberg transitions is only obtained via the BMK functional. For adiabatic transitions, all hybrid functionals paired with the MG3S basis set perform well, and B98 is best, with a mean absolute deviation from experiment of 0.09 eV. The testing of EPT used the Outer Valence Green's Function (OVGF) approximation and the Partial Third Order (P3) approximation on 37 vertical first ionization energies. It is found that OVGF outperforms P3 when basis sets of at least triple-ζ quality in the polarization functions are used. The largest basis set used in this study, aug-pc3, obtained the best mean absolute error from both methods -0.08 eV for OVGF and 0.18 eV for P3. The OVGF/6-31+G(2df,p) level of theory is particularly cost-effective, yielding a mean absolute error of 0.11 eV.

DFT benchmark study for the oxidative addition of CH 4 to Pd. Performance of various density functionals

NASA Astrophysics Data System (ADS)

de Jong, G. Theodoor; Geerke, Daan P.; Diefenbach, Axel; Matthias Bickelhaupt, F.

2005-06-01

We have evaluated the performance of 24 popular density functionals for describing the potential energy surface (PES) of the archetypal oxidative addition reaction of the methane C-H bond to the palladium atom by comparing the results with our recent ab initio [CCSD(T)] benchmark study of this reaction. The density functionals examined cover the local density approximation (LDA), the generalized gradient approximation (GGA), meta-GGAs as well as hybrid density functional theory. Relativistic effects are accounted for through the zeroth-order regular approximation (ZORA). The basis-set dependence of the density-functional-theory (DFT) results is assessed for the Becke-Lee-Yang-Parr (BLYP) functional using a hierarchical series of Slater-type orbital (STO) basis sets ranging from unpolarized double-ζ (DZ) to quadruply polarized quadruple-ζ quality (QZ4P). Stationary points on the reaction surface have been optimized using various GGA functionals, all of which yield geometries that differ only marginally. Counterpoise-corrected relative energies of stationary points are converged to within a few tenths of a kcal/mol if one uses the doubly polarized triple-ζ (TZ2P) basis set and the basis-set superposition error (BSSE) drops to 0.0 kcal/mol for our largest basis set (QZ4P). Best overall agreement with the ab initio benchmark PES is achieved by functionals of the GGA, meta-GGA, and hybrid-DFT type, with mean absolute errors of 1.3-1.4 kcal/mol and errors in activation energies ranging from +0.8 to -1.4 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with an only slightly larger mean absolute error of 2.5 kcal/mol and an underestimation by -1.9 kcal/mol of the overall barrier (i.e., the difference in energy between the TS and the separate reactants). For comparison, with B3LYP we arrive at a mean absolute error of 3.8 kcal/mol and an overestimation of the overall barrier by 4.5 kcal/mol.

Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

NASA Astrophysics Data System (ADS)

Viswanathan, K. K.; Karthik, K.; Sanyasiraju, Y. V. S. S.; Aziz, Z. A.

2016-11-01

Two type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

Approximating the Helium Wavefunction in Positronium-Helium Scattering

NASA Technical Reports Server (NTRS)

DiRienzi, Joseph; Drachman, Richard J.

2003-01-01

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

Adaptive critic autopilot design of bank-to-turn missiles using fuzzy basis function networks.

PubMed

Lin, Chuan-Kai

2005-04-01

A new adaptive critic autopilot design for bank-to-turn missiles is presented. In this paper, the architecture of adaptive critic learning scheme contains a fuzzy-basis-function-network based associative search element (ASE), which is employed to approximate nonlinear and complex functions of bank-to-turn missiles, and an adaptive critic element (ACE) generating the reinforcement signal to tune the associative search element. In the design of the adaptive critic autopilot, the control law receives signals from a fixed gain controller, an ASE and an adaptive robust element, which can eliminate approximation errors and disturbances. Traditional adaptive critic reinforcement learning is the problem faced by an agent that must learn behavior through trial-and-error interactions with a dynamic environment, however, the proposed tuning algorithm can significantly shorten the learning time by online tuning all parameters of fuzzy basis functions and weights of ASE and ACE. Moreover, the weight updating law derived from the Lyapunov stability theory is capable of guaranteeing both tracking performance and stability. Computer simulation results confirm the effectiveness of the proposed adaptive critic autopilot.

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.

Limitations of the method of complex basis functions

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

Baumel, R.T.; Crocker, M.C.; Nuttall, J.

1975-08-01

The method of complex basis functions proposed by Rescigno and Reinhardt is applied to the calculation of the amplitude in a model problem which can be treated analytically. It is found for an important class of potentials, including some of infinite range and also the square well, that the method does not provide a converging sequence of approximations. However, in some cases, approximations of relatively low order might be close to the correct result. The method is also applied to S-wave e-H elastic scattering above the ionization threshold, and spurious ''convergence'' to the wrong result is found. A procedure whichmore » might overcome the difficulties of the method is proposed.« less

Min-Max Spaces and Complexity Reduction in Min-Max Expansions

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

Gaubert, Stephane, E-mail: Stephane.Gaubert@inria.fr; McEneaney, William M., E-mail: wmceneaney@ucsd.edu

2012-06-15

Idempotent methods have been found to be extremely helpful in the numerical solution of certain classes of nonlinear control problems. In those methods, one uses the fact that the value function lies in the space of semiconvex functions (in the case of maximizing controllers), and approximates this value using a truncated max-plus basis expansion. In some classes, the value function is actually convex, and then one specifically approximates with suprema (i.e., max-plus sums) of affine functions. Note that the space of convex functions is a max-plus linear space, or moduloid. In extending those concepts to game problems, one finds amore » different function space, and different algebra, to be appropriate. Here we consider functions which may be represented using infima (i.e., min-max sums) of max-plus affine functions. It is natural to refer to the class of functions so represented as the min-max linear space (or moduloid) of max-plus hypo-convex functions. We examine this space, the associated notion of duality and min-max basis expansions. In using these methods for solution of control problems, and now games, a critical step is complexity-reduction. In particular, one needs to find reduced-complexity expansions which approximate the function as well as possible. We obtain a solution to this complexity-reduction problem in the case of min-max expansions.« less

The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Nikpour, Ahmad

2013-09-01

In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

Novel transform for image description and compression with implementation by neural architectures

NASA Astrophysics Data System (ADS)

Ben-Arie, Jezekiel; Rao, Raghunath K.

1991-10-01

A general method for signal representation using nonorthogonal basis functions that are composed of Gaussians are described. The Gaussians can be combined into groups with predetermined configuration that can approximate any desired basis function. The same configuration at different scales forms a set of self-similar wavelets. The general scheme is demonstrated by representing a natural signal employing an arbitrary basis function. The basic methodology is demonstrated by two novel schemes for efficient representation of 1-D and 2- D signals using Gaussian basis functions (BFs). Special methods are required here since the Gaussian functions are nonorthogonal. The first method employs a paradigm of maximum energy reduction interlaced with the A* heuristic search. The second method uses an adaptive lattice system to find the minimum-squared error of the BFs onto the signal, and a lateral-vertical suppression network to select the most efficient representation in terms of data compression.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

PubMed

Roper, Ian P E; Besley, Nicholas A

2016-03-21

The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

Density functional theory calculations of the lowest energy quintet and triplet states of model hemes: role of functional, basis set, and zero-point energy corrections.

PubMed

Khvostichenko, Daria; Choi, Andrew; Boulatov, Roman

2008-04-24

We investigated the effect of several computational variables, including the choice of the basis set, application of symmetry constraints, and zero-point energy (ZPE) corrections, on the structural parameters and predicted ground electronic state of model 5-coordinate hemes (iron(II) porphines axially coordinated by a single imidazole or 2-methylimidazole). We studied the performance of B3LYP and B3PW91 with eight Pople-style basis sets (up to 6-311+G*) and B97-1, OLYP, and TPSS functionals with 6-31G and 6-31G* basis sets. Only hybrid functionals B3LYP, B3PW91, and B97-1 reproduced the quintet ground state of the model hemes. With a given functional, the choice of the basis set caused up to 2.7 kcal/mol variation of the quintet-triplet electronic energy gap (DeltaEel), in several cases, resulting in the inversion of the sign of DeltaEel. Single-point energy calculations with triple-zeta basis sets of the Pople (up to 6-311G++(2d,2p)), Ahlrichs (TZVP and TZVPP), and Dunning (cc-pVTZ) families showed the same trend. The zero-point energy of the quintet state was approximately 1 kcal/mol lower than that of the triplet, and accounting for ZPE corrections was crucial for establishing the ground state if the electronic energy of the triplet state was approximately 1 kcal/mol less than that of the quintet. Within a given model chemistry, effects of symmetry constraints and of a "tense" structure of the iron porphine fragment coordinated to 2-methylimidazole on DeltaEel were limited to 0.3 kcal/mol. For both model hemes the best agreement with crystallographic structural data was achieved with small 6-31G and 6-31G* basis sets. Deviation of the computed frequency of the Fe-Im stretching mode from the experimental value with the basis set decreased in the order: nonaugmented basis sets, basis sets with polarization functions, and basis sets with polarization and diffuse functions. Contraction of Pople-style basis sets (double-zeta or triple-zeta) affected the results insignificantly for iron(II) porphyrin coordinated with imidazole. Poor performance of a "locally dense" basis set with a large number of basis functions on the Fe center was observed in calculation of quintet-triplet gaps. Our results lead to a series of suggestions for density functional theory calculations of quintet-triplet energy gaps in ferrohemes with a single axial imidazole; these suggestions are potentially applicable for other transition-metal complexes.

Orbital dependent functionals: An atom projector augmented wave method implementation

NASA Astrophysics Data System (ADS)

Xu, Xiao

This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.

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.

Weak solution concept and Galerkin's matrix for the exterior of an oblate ellipsoid of revolution in the representation of the Earth's gravity potential by buried masses

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The paper is motivated by the role of boundary value problems in Earth's gravity field studies. The discussion focuses on Neumann's problem formulated for the exterior of an oblate ellipsoid of revolution as this is considered a basis for an iteration solution of the linear gravimetric boundary value problem in the determination of the disturbing potential. The approach follows the concept of the weak solution and Galerkin's approximations are applied. This means that the solution of the problem is approximated by linear combinations of basis functions with scalar coefficients. The construction of Galerkin's matrix for basis functions generated by elementary potentials (point masses) is discussed. Ellipsoidal harmonics are used as a natural tool and the elementary potentials are expressed by means of series of ellipsoidal harmonics. The problem, however, is the summation of the series that represent the entries of Galerkin's matrix. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Therefore, the straightforward application of series of ellipsoidal harmonics is complemented by deeper relations contained in the theory of ordinary differential equations of second order and in the theory of Legendre's functions. Subsequently, also hypergeometric functions and series are used. Moreover, within some approximations the entries are split into parts. Some of the resulting series may be summed relatively easily, apart from technical tricks. For the remaining series the summation was converted to elliptic integrals. The approach made it possible to deduce a closed (though approximate) form representation of the entries in Galerkin's matrix. The result rests on concepts and methods of mathematical analysis. In the paper it is confronted with a direct numerical approach applied for the implementation of Legendre's functions. The computation of the entries is more demanding in this case, but conceptually it avoids approximations. Finally, some specific features associated with function bases generated by elementary potentials in case the ellipsoidal solution domain are illustrated and discussed.

Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral approximations.

PubMed

Giese, Timothy J; York, Darrin M

2010-12-28

We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.

Point Set Denoising Using Bootstrap-Based Radial Basis Function.

PubMed

Liew, Khang Jie; Ramli, Ahmad; Abd Majid, Ahmad

2016-01-01

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities.

PubMed

Zhu, Xiaolei; Yarkony, David R

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.

Highly efficient implementation of pseudospectral time-dependent density-functional theory for the calculation of excitation energies of large molecules.

PubMed

Cao, Yixiang; Hughes, Thomas; Giesen, Dave; Halls, Mathew D; Goldberg, Alexander; Vadicherla, Tati Reddy; Sastry, Madhavi; Patel, Bhargav; Sherman, Woody; Weisman, Andrew L; Friesner, Richard A

2016-06-15

We have developed and implemented pseudospectral time-dependent density-functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm-Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time-dependent density-functional theory with full linear response (PS-FLR-TDDFT) and within the Tamm-Dancoff approximation (PS-TDA-TDDFT) for G2 set molecules using B3LYP/6-31G*(*) show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS-FLR-TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS-FLR-TDDFT and best estimations demonstrate that the accuracy of both PS-FLR-TDDFT and PS-TDA-TDDFT. Calculations for a set of medium-sized molecules, including Cn fullerenes and nanotubes, using the B3LYP functional and 6-31G(**) basis set show PS-TDA-TDDFT provides 19- to 34-fold speedups for Cn fullerenes with 450-1470 basis functions, 11- to 32-fold speedups for nanotubes with 660-3180 basis functions, and 9- to 16-fold speedups for organic molecules with 540-1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46-residue crambin protein, fullerenes up to C540 and nanotubes up to 14×(6,6), using the B3LYP functional and 6-31G(**) basis set with up to 8100 basis functions show that PS-FLR-TDDFT CPU time scales as N(2.05) with the number of basis functions. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation.

PubMed

Kühn, Michael; Weigend, Florian

2015-01-21

We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition.

Hamiltonian lattice field theory: Computer calculations using variational methods

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

Zako, Robert L.

1991-12-03

I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato`s generalizations of Temple`s formula. The algorithm could bemore » adapted to systems such as atoms and molecules. I show how to compute Green`s functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green`s functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems.« less

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

Polarization functions for the modified m6-31G basis sets for atoms Ga through Kr.

PubMed

Mitin, Alexander V

2013-09-05

The 2df polarization functions for the modified m6-31G basis sets of the third-row atoms Ga through Kr (Int J Quantum Chem, 2007, 107, 3028; Int J. Quantum Chem, 2009, 109, 1158) are proposed. The performances of the m6-31G, m6-31G(d,p), and m6-31G(2df,p) basis sets were examined in molecular calculations carried out by the density functional theory (DFT) method with B3LYP hybrid functional, Møller-Plesset perturbation theory of the second order (MP2), quadratic configuration interaction method with single and double substitutions and were compared with those for the known 6-31G basis sets as well as with the other similar 641 and 6-311G basis sets with and without polarization functions. Obtained results have shown that the performances of the m6-31G, m6-31G(d,p), and m6-31G(2df,p) basis sets are better in comparison with the performances of the known 6-31G, 6-31G(d,p) and 6-31G(2df,p) basis sets. These improvements are mainly reached due to better approximations of different electrons belonging to the different atomic shells in the modified basis sets. Applicability of the modified basis sets in thermochemical calculations is also discussed. © 2013 Wiley Periodicals, Inc.

Development and characterization of rice mutants for functional genomic studies and breeding

USDA-ARS?s Scientific Manuscript database

Mutagenesis is a powerful tool for creating genetic materials for studying functional genomics, breeding, and understanding the molecular basis of disease resistance. Approximately 100,000 putative mutants of rice (Oryza sativa L.) have been generated with mutagens. Numerous mutant genes involved in...

Genome duplication events and functional reduction of ploidy levels in sturgeon (Acipenser, Huso and Scaphirhynchus).

PubMed

Ludwig, A; Belfiore, N M; Pitra, C; Svirsky, V; Jenneckens, I

2001-07-01

Sturgeon (order Acipenserformes) provide an ideal taxonomic context for examination of genome duplication events. Multiple levels of ploidy exist among these fish. In a novel microsatellite approach, data from 962 fish from 20 sturgeon species were used for analysis of ploidy in sturgeon. Allele numbers in a sample of individuals were assessed at six microsatellite loci. Species with approximately 120 chromosomes are classified as functional diploid species, species with approximately 250 chromosomes as functional tetraploid species, and with approximately 500 chromosomes as functional octaploids. A molecular phylogeny of the sturgeon was determined on the basis of sequences of the entire mitochondrial cytochrome b gene. By mapping the estimated levels of ploidy on this proposed phylogeny we demonstrate that (I) polyploidization events independently occurred in the acipenseriform radiation; (II) the process of functional genome reduction is nearly finished in species with approximately 120 chromosomes and more active in species with approximately 250 chromosomes and approximately 500 chromosomes; and (III) species with approximately 250 and approximately 500 chromosomes arose more recently than those with approximately 120 chromosomes. These results suggest that gene silencing, chromosomal rearrangements, and transposition events played an important role in the acipenseriform genome formation. Furthermore, this phylogeny is broadly consistent with previous hypotheses but reveals a highly supported oceanic (Atlantic-Pacific) subdivision within the Acipenser/Huso complex.

Genome duplication events and functional reduction of ploidy levels in sturgeon (Acipenser, Huso and Scaphirhynchus).

PubMed Central

Ludwig, A; Belfiore, N M; Pitra, C; Svirsky, V; Jenneckens, I

2001-01-01

Sturgeon (order Acipenserformes) provide an ideal taxonomic context for examination of genome duplication events. Multiple levels of ploidy exist among these fish. In a novel microsatellite approach, data from 962 fish from 20 sturgeon species were used for analysis of ploidy in sturgeon. Allele numbers in a sample of individuals were assessed at six microsatellite loci. Species with approximately 120 chromosomes are classified as functional diploid species, species with approximately 250 chromosomes as functional tetraploid species, and with approximately 500 chromosomes as functional octaploids. A molecular phylogeny of the sturgeon was determined on the basis of sequences of the entire mitochondrial cytochrome b gene. By mapping the estimated levels of ploidy on this proposed phylogeny we demonstrate that (I) polyploidization events independently occurred in the acipenseriform radiation; (II) the process of functional genome reduction is nearly finished in species with approximately 120 chromosomes and more active in species with approximately 250 chromosomes and approximately 500 chromosomes; and (III) species with approximately 250 and approximately 500 chromosomes arose more recently than those with approximately 120 chromosomes. These results suggest that gene silencing, chromosomal rearrangements, and transposition events played an important role in the acipenseriform genome formation. Furthermore, this phylogeny is broadly consistent with previous hypotheses but reveals a highly supported oceanic (Atlantic-Pacific) subdivision within the Acipenser/Huso complex. PMID:11454768

An efficient basis set representation for calculating electrons in molecules

DOE PAGES

Jones, Jeremiah R.; Rouet, Francois -Henry; Lawler, Keith V.; ...

2016-04-27

The method of McCurdy, Baertschy, and Rescigno, is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. Themore » calculation of contracted two-electron matrix elements among orbitals requires only O( Nlog (N)) multiplication operations, not O( N 4), where N is the number of basis functions; N = n 3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionisation potentials are reported for 1- (He +, H + 2), 2- (H 2, He), 10- (CH 4), and 56-electron (C 8H 8) systems.« less

Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities

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

Zhu, Xiaolei, E-mail: virtualzx@gmail.com; Yarkony, David R., E-mail: yarkony@jhu.edu

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility,more » has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.« less

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

PubMed

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Benchmarking Hydrogen and Carbon NMR Chemical Shifts at HF, DFT, and MP2 Levels.

PubMed

Flaig, Denis; Maurer, Marina; Hanni, Matti; Braunger, Katharina; Kick, Leonhard; Thubauville, Matthias; Ochsenfeld, Christian

2014-02-11

An extensive study of error distributions for calculating hydrogen and carbon NMR chemical shifts at Hartree-Fock (HF), density functional theory (DFT), and Møller-Plesset second-order perturbation theory (MP2) levels is presented. Our investigation employs accurate CCSD(T)/cc-pVQZ calculations for providing reference data for 48 hydrogen and 40 carbon nuclei within an extended set of chemical compounds covering a broad range of the NMR scale with high relevance to chemical applications, especially in organic chemistry. Besides the approximations of HF, a variety of DFT functionals, and conventional MP2, we also present results with respect to a spin component-scaled MP2 (GIAO-SCS-MP2) approach. For each method, the accuracy is analyzed in detail for various basis sets, allowing identification of efficient combinations of method and basis set approximations.

Combining Density Functional Theory and Green's Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional.

PubMed

Kananenka, Alexei A; Zgid, Dominika

2017-11-14

We present a rigorous framework which combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short- and long-range components. Short-range contribution to the total energy and exchange-correlation potential is provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Green's function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Green's function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Green's function theory. We illustrate that similarly to density functional approximations, the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamic correlation. The many-body contribution to the functional mitigates the many-electron self-interaction error present in many density functional approximations and provides a better description of molecular properties. Additionally, we illustrate that the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.

Non-additive non-interacting kinetic energy of rare gas dimers

NASA Astrophysics Data System (ADS)

Jiang, Kaili; Nafziger, Jonathan; Wasserman, Adam

2018-03-01

Approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within partition density functional theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare-gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint Perdew-Burke-Ernzerhof (PBE) functional. The second is a simple, physically motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.

Application of Approximate Unsteady Aerodynamics for Flutter Analysis

NASA Technical Reports Server (NTRS)

Pak, Chan-gi; Li, Wesley W.

2010-01-01

A technique for approximating the modal aerodynamic influence coefficient (AIC) matrices by using basis functions has been developed. A process for using the resulting approximated modal AIC matrix in aeroelastic analysis has also been developed. The method requires the unsteady aerodynamics in frequency domain, and this methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root locus et cetera. The unsteady aeroelastic analysis using unsteady subsonic aerodynamic approximation is demonstrated herein. The technique presented is shown to offer consistent flutter speed prediction on an aerostructures test wing (ATW) 2 and a hybrid wing body (HWB) type of vehicle configuration with negligible loss in precision. This method computes AICs that are functions of the changing parameters being studied and are generated within minutes of CPU time instead of hours. These results may have practical application in parametric flutter analyses as well as more efficient multidisciplinary design and optimization studies.

Approximating a retarded-advanced differential equation that models human phonation

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2017-11-01

In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; ...

2016-08-04

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computationalmore » cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.« less

Quantitative molecular orbital energies within a G0W0 approximation

NASA Astrophysics Data System (ADS)

Sharifzadeh, S.; Tamblyn, I.; Doak, P.; Darancet, P. T.; Neaton, J. B.

2012-09-01

Using many-body perturbation theory within a G 0 W 0 approximation, with a plane wave basis set and using a starting point based on density functional theory within the generalized gradient approximation, we explore routes for computing the ionization potential (IP), electron affinity (EA), and fundamental gap of three gas-phase molecules — benzene, thiophene, and (1,4) diamino-benzene — and compare with experiments. We examine the dependence of the IP and fundamental gap on the number of unoccupied states used to represent the dielectric function and the self energy, as well as the dielectric function plane-wave cutoff. We find that with an effective completion strategy for approximating the unoccupied subspace, and a well converged dielectric function kinetic energy cutoff, the computed IPs and EAs are in excellent quantitative agreement with available experiment (within 0.2 eV), indicating that a one-shot G 0 W 0 approach can be very accurate for calculating addition/removal energies of small organic molecules.

Sparse regularization for force identification using dictionaries

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Wang, Chenxi; Zhang, Hang; Chen, Xuefeng

2016-04-01

The classical function expansion method based on minimizing l2-norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l1-norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases.

Data approximation using a blending type spline construction

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

Dalmo, Rune; Bratlie, Jostein

2014-11-18

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

The two-electron atomic systems. S-states

NASA Astrophysics Data System (ADS)

Liverts, Evgeny Z.; Barnea, Nir

2010-01-01

A simple Mathematica program for computing the S-state energies and wave functions of two-electron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computation time depend on the basis size. The precise energy values of 7-8 significant figures along with the corresponding wave functions can be computed on a single processor within a few minutes. The resultant wave functions have a simple analytical form consisting of elementary functions, that enables one to calculate the expectation values of arbitrary physical operators without any difficulties. Program summaryProgram title: TwoElAtom-S Catalogue identifier: AEFK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 185 No. of bytes in distributed program, including test data, etc.: 495 164 Distribution format: tar.gz Programming language: Mathematica 6.0; 7.0 Computer: Any PC Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0 RAM:⩾10 bytes Classification: 2.1, 2.2, 2.7, 2.9 Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations. Solution method: The S-wave function is expanded into a triple basis set in three perimetric coordinates. Method of projecting the two-electron Schrödinger equation (for atoms/ions) onto a subspace of the basis functions enables one to obtain the set of homogeneous linear equations F.C=0 for the coefficients C of the above expansion. The roots of equation det(F)=0 yield the bound energies. Restrictions: First, the too large length of expansion (basis size) takes the too large computation time giving no perceptible improvement in accuracy. Second, the order of polynomial Ω (input parameter) in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive. Additional comments: The CPC Program Library includes "A program to calculate the eigenfunctions of the random phase approximation for two electron systems" (AAJD). It should be emphasized that this fortran code realizes a very rough approximation describing only the averaged electron density of the two electron systems. It does not characterize the properties of the individual electrons and has a number of input parameters including the Roothaan orbitals. Running time: ˜10 minutes (depends on basis size and computer speed)

Application of ab initio many-body perturbation theory with Gaussian basis sets to the singlet and triplet excitations of organic molecules

NASA Astrophysics Data System (ADS)

Hamed, Samia; Rangel, Tonatiuh; Bruneval, Fabien; Neaton, Jeffrey B.

Quantitative understanding of charged and neutral excitations of organic molecules is critical in diverse areas of study that include astrophysics and the development of energy technologies that are clean and efficient. The recent use of local basis sets with ab initio many-body perturbation theory in the GW approximation and the Bethe-Saltpeter equation approach (BSE), methods traditionally applied to periodic condensed phases with a plane-wave basis, has opened the door to detailed study of such excitations for molecules, as well as accurate numerical benchmarks. Here, through a series of systematic benchmarks with a Gaussian basis, we report on the extent to which the predictive power and utility of this approach depend critically on interdependent underlying approximations and choices for molecules, including the mean-field starting point (eg optimally-tuned range separated hybrids, pure DFT functionals, and untuned hybrids), the GW scheme, and the Tamm Dancoff approximation. We demonstrate the effects of these choices in the context of Thiels' set while drawing analogies to linear-response time-dependent DFT and making comparisons to best theoretical estimates from higher-order wavefunction-based theories.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Affordable and accurate large-scale hybrid-functional calculations on GPU-accelerated supercomputers

NASA Astrophysics Data System (ADS)

Ratcliff, Laura E.; Degomme, A.; Flores-Livas, José A.; Goedecker, Stefan; Genovese, Luigi

2018-03-01

Performing high accuracy hybrid functional calculations for condensed matter systems containing a large number of atoms is at present computationally very demanding or even out of reach if high quality basis sets are used. We present a highly optimized multiple graphics processing unit implementation of the exact exchange operator which allows one to perform fast hybrid functional density-functional theory (DFT) calculations with systematic basis sets without additional approximations for up to a thousand atoms. With this method hybrid DFT calculations of high quality become accessible on state-of-the-art supercomputers within a time-to-solution that is of the same order of magnitude as traditional semilocal-GGA functionals. The method is implemented in a portable open-source library.

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition.

PubMed

Čársky, Petr; Čurík, Roman; Varga, Štefan

2012-03-21

The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k(1)(1)k(2)(1)|g(1)(2)g(2)(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion. © 2012 American Institute of Physics

Recovery of sparse translation-invariant signals with continuous basis pursuit

PubMed Central

Ekanadham, Chaitanya; Tranchina, Daniel; Simoncelli, Eero

2013-01-01

We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coefficients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients. We formulate a constrained convex optimization problem, in which the full set of dictionary coefficients represents a linear approximation of the signal, the auxiliary coefficients are constrained so as to only represent translated features, and sparsity is imposed on the primary coefficients using an L1 penalty. The basis pursuit denoising (BP) method may be seen as a special case, in which the auxiliary interpolation functions are omitted, and we thus refer to our methodology as continuous basis pursuit (CBP). We develop two implementations of CBP for a one-dimensional translation-invariant source, one using a first-order Taylor approximation, and another using a form of trigonometric spline. We examine the tradeoff between sparsity and signal reconstruction accuracy in these methods, demonstrating empirically that trigonometric CBP substantially outperforms Taylor CBP, which in turn offers substantial gains over ordinary BP. In addition, the CBP bases can generally achieve equally good or better approximations with much coarser sampling than BP, leading to a reduction in dictionary dimensionality. PMID:24352562

Materials Data on BaSi3SnO9 (SG:188) by Materials Project

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

Kristin Persson

2014-11-02

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

Materials Data on BaSi4O9 (SG:188) by Materials Project

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

Kristin Persson

2014-07-09

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

Basis convergence of range-separated density-functional theory.

PubMed

Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien

2015-02-21

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

Achieving accuracy in first-principles calculations for EOS: basis completeness at high temperatures

NASA Astrophysics Data System (ADS)

Wills, John; Mattsson, Ann

2013-06-01

First-principles electronic structure calculations can provide EOS data in regimes of pressure and temperature where accurate experimental data is difficult or impossible to obtain. This lack, however, also precludes validation of calculations in those regimes. Factors that influence the accuracy of first-principles data include (1) theoretical approximations and (2) computational approximations used in implementing and solving the underlying equations. In the first category are the approximate exchange/correlation functionals and approximate wave equations approximating the Dirac equation; in the second are basis completeness, series convergence, and truncation errors. We are using two rather different electronic structure methods (VASP and RSPt) to make definitive the requirements for accuracy of the second type, common to both. In this talk, we discuss requirements for converged calculation at high temperature and moderated pressure. At convergence we show that both methods give identical results. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit

NASA Astrophysics Data System (ADS)

Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias

2007-11-01

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Møller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit.

PubMed

Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias

2007-11-14

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments.

PubMed

Choi, Ji Yeh; Hwang, Heungsun; Timmerman, Marieke E

2018-03-01

Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.

Composite fermion basis for two-component Bose gases

NASA Astrophysics Data System (ADS)

Meyer, Marius; Liabotro, Ola

The composite fermion (CF) construction is known to produce wave functions that are not necessarily orthogonal, or even linearly independent, after projection. While usually not a practical issue in the quantum Hall regime, we have previously shown that it presents a technical challenge for rotating Bose gases with low angular momentum. These are systems where the CF approach yield surprisingly good approximations to the exact eigenstates of weak short-range interactions, and so solving the problem of linearly dependent wave functions is of interest. It can also be useful for studying CF excitations for fermions. Here we present several ways of constructing a basis for the space of ``simple CF states'' for two-component rotating Bose gases in the lowest Landau level, and prove that they all give a basis. Using the basis, we study the structure of the lowest-lying state using so-called restricted wave functions. We also examine the scaling of the overlap between the exact and CF wave functions at the maximal possible angular momentum for simple states. This work was financially supported by the Research Council of Norway.

A minimization method on the basis of embedding the feasible set and the epigraph

NASA Astrophysics Data System (ADS)

Zabotin, I. Ya; Shulgina, O. N.; Yarullin, R. S.

2016-11-01

We propose a conditional minimization method of the convex nonsmooth function which belongs to the class of cutting-plane methods. During constructing iteration points a feasible set and an epigraph of the objective function are approximated by the polyhedral sets. In this connection, auxiliary problems of constructing iteration points are linear programming problems. In optimization process there is some opportunity of updating sets which approximate the epigraph. These updates are performed by periodically dropping of cutting planes which form embedding sets. Convergence of the proposed method is proved, some realizations of the method are discussed.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

The calculations of small molecular conformation energy differences by density functional method

NASA Astrophysics Data System (ADS)

Topol, I. A.; Burt, S. K.

1993-03-01

The differences in the conformational energies for the gauche (G) and trans(T) conformers of 1,2-difluoroethane and for myo-and scyllo-conformer of inositol have been calculated by local density functional method (LDF approximation) with geometry optimization using different sets of calculation parameters. It is shown that in the contrast to Hartree—Fock methods, density functional calculations reproduce the correct sign and value of the gauche effect for 1,2-difluoroethane and energy difference for both conformers of inositol. The results of normal vibrational analysis for1,2-difluoroethane showed that harmonic frequencies calculated in LDF approximation agree with experimental data with the accuracy typical for scaled large basis set Hartree—Fock calculations.

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

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.

Approximate Dynamic Programming Algorithms for United States Air Force Officer Sustainment

DTIC Science & Technology

2015-03-26

level of correction needed. While paying bonuses has an easily calculable cost, RIFs have more subtle costs. Mone (1994) discovered that in a steady...a regression is performed utilizing instrumental variables to minimize Bellman error. This algorithm uses a set of basis functions to approximate the...transitioned to an all-volunteer force. Charnes et al. (1972) utilize a goal programming model for General Schedule civilian manpower management in the

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.

Self-organizing radial basis function networks for adaptive flight control and aircraft engine state estimation

NASA Astrophysics Data System (ADS)

Shankar, Praveen

The performance of nonlinear control algorithms such as feedback linearization and dynamic inversion is heavily dependent on the fidelity of the dynamic model being inverted. Incomplete or incorrect knowledge of the dynamics results in reduced performance and may lead to instability. Augmenting the baseline controller with approximators which utilize a parametrization structure that is adapted online reduces the effect of this error between the design model and actual dynamics. However, currently existing parameterizations employ a fixed set of basis functions that do not guarantee arbitrary tracking error performance. To address this problem, we develop a self-organizing parametrization structure that is proven to be stable and can guarantee arbitrary tracking error performance. The training algorithm to grow the network and adapt the parameters is derived from Lyapunov theory. In addition to growing the network of basis functions, a pruning strategy is incorporated to keep the size of the network as small as possible. This algorithm is implemented on a high performance flight vehicle such as F-15 military aircraft. The baseline dynamic inversion controller is augmented with a Self-Organizing Radial Basis Function Network (SORBFN) to minimize the effect of the inversion error which may occur due to imperfect modeling, approximate inversion or sudden changes in aircraft dynamics. The dynamic inversion controller is simulated for different situations including control surface failures, modeling errors and external disturbances with and without the adaptive network. A performance measure of maximum tracking error is specified for both the controllers a priori. Excellent tracking error minimization to a pre-specified level using the adaptive approximation based controller was achieved while the baseline dynamic inversion controller failed to meet this performance specification. The performance of the SORBFN based controller is also compared to a fixed RBF network based adaptive controller. While the fixed RBF network based controller which is tuned to compensate for control surface failures fails to achieve the same performance under modeling uncertainty and disturbances, the SORBFN is able to achieve good tracking convergence under all error conditions.

Reinforcement learning solution for HJB equation arising in constrained optimal control problem.

PubMed

Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong

2015-11-01

The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

PubMed

Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan

2012-01-01

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. © 2012 Acoustical Society of America.

Projected Hybrid Orbitals: A General QM/MM Method

PubMed Central

2015-01-01

A projected hybrid orbital (PHO) method was described to model the covalent boundary in a hybrid quantum mechanical and molecular mechanical (QM/MM) system. The PHO approach can be used in ab initio wave function theory and in density functional theory with any basis set without introducing system-dependent parameters. In this method, a secondary basis set on the boundary atom is introduced to formulate a set of hybrid atomic orbtials. The primary basis set on the boundary atom used for the QM subsystem is projected onto the secondary basis to yield a representation that provides a good approximation to the electron-withdrawing power of the primary basis set to balance electronic interactions between QM and MM subsystems. The PHO method has been tested on a range of molecules and properties. Comparison with results obtained from QM calculations on the entire system shows that the present PHO method is a robust and balanced QM/MM scheme that preserves the structural and electronic properties of the QM region. PMID:25317748

The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images.

PubMed

Loxley, P N

2017-10-01

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Basis convergence of range-separated density-functional theory

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

Franck, Odile, E-mail: odile.franck@etu.upmc.fr; Mussard, Bastien, E-mail: bastien.mussard@upmc.fr; CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris

2015-02-21

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. Wemore » study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N{sub 2}, and H{sub 2}O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.« less

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-01-01

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction.

PubMed

Song, Chenchen; Martínez, Todd J

2017-01-21

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N 2.5 ) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Stable computations with flat radial basis functions using vector-valued rational approximations

NASA Astrophysics Data System (ADS)

Wright, Grady B.; Fornberg, Bengt

2017-02-01

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Continuous and Discontinuous Galerkin Methods for a Scalable Three-Dimensional Nonhydrostatic Atmospheric Model: Limited-Area Mode

DTIC Science & Technology

2012-03-09

guides/ ranger-user-guide. [3] T . Davies, M. J . P. Cullen, A. J . Malcolm, M. H. Mawson , A. Staniforth, A. A. White, and N. Wood. A new dynamical core...element Ωe, a finite-dimensional approximation qN is formed by expanding q(x, t ) in basis functions ψj (x) such that q (e) N (x, t ) = MN ∑ j =1 ψj(x)q (e... j ( t ) (14) where MN = (N + 1) 3 is the number of nodes per element, N is the order of the basis functions, and the superscript (e) denotes element

Lanczos algorithm with matrix product states for dynamical correlation functions

NASA Astrophysics Data System (ADS)

Dargel, P. E.; Wöllert, A.; Honecker, A.; McCulloch, I. P.; Schollwöck, U.; Pruschke, T.

2012-05-01

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex post reorthogonalization method allows us to avoid several shortcomings of the original approach, namely the multitargeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.

Gaussian functional regression for output prediction: Model assimilation and experimental design

NASA Astrophysics Data System (ADS)

Nguyen, N. C.; Peraire, J.

2016-03-01

In this paper, we introduce a Gaussian functional regression (GFR) technique that integrates multi-fidelity models with model reduction to efficiently predict the input-output relationship of a high-fidelity model. The GFR method combines the high-fidelity model with a low-fidelity model to provide an estimate of the output of the high-fidelity model in the form of a posterior distribution that can characterize uncertainty in the prediction. A reduced basis approximation is constructed upon the low-fidelity model and incorporated into the GFR method to yield an inexpensive posterior distribution of the output estimate. As this posterior distribution depends crucially on a set of training inputs at which the high-fidelity models are simulated, we develop a greedy sampling algorithm to select the training inputs. Our approach results in an output prediction model that inherits the fidelity of the high-fidelity model and has the computational complexity of the reduced basis approximation. Numerical results are presented to demonstrate the proposed approach.

Neural network representation and learning of mappings and their derivatives

NASA Technical Reports Server (NTRS)

White, Halbert; Hornik, Kurt; Stinchcombe, Maxwell; Gallant, A. Ronald

1991-01-01

Discussed here are recent theorems proving that artificial neural networks are capable of approximating an arbitrary mapping and its derivatives as accurately as desired. This fact forms the basis for further results establishing the learnability of the desired approximations, using results from non-parametric statistics. These results have potential applications in robotics, chaotic dynamics, control, and sensitivity analysis. An example involving learning the transfer function and its derivatives for a chaotic map is discussed.

Level Density in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Myo, T.; Katō, K.

2005-06-01

It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of L(2) basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.

Approaching the theoretical limit in periodic local MP2 calculations with atomic-orbital basis sets: the case of LiH.

PubMed

Usvyat, Denis; Civalleri, Bartolomeo; Maschio, Lorenzo; Dovesi, Roberto; Pisani, Cesare; Schütz, Martin

2011-06-07

The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Møller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing "bond"-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids. © 2011 American Institute of Physics

An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling

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

Li, Weixuan, E-mail: weixuan.li@usc.edu; Lin, Guang, E-mail: guang.lin@pnnl.gov; Zhang, Dongxiao, E-mail: dxz@pku.edu.cn

2014-02-01

The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect—except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos basis functions in the expansion helps to capture uncertainty more accurately but increases computational cost. Selection of basis functionsmore » is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE basis functions are pre-set based on users' experience. Also, for sequential data assimilation problems, the basis functions kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE basis functions for different problems and automatically adjusts the number of basis functions in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm was tested with different examples and demonstrated great effectiveness in comparison with non-adaptive PCKF and EnKF algorithms.« less

Auxiliary basis expansions for large-scale electronic structure calculations.

PubMed

Jung, Yousung; Sodt, Alex; Gill, Peter M W; Head-Gordon, Martin

2005-05-10

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.

Diffusion Forecasting Model with Basis Functions from QR-Decomposition

NASA Astrophysics Data System (ADS)

Harlim, John; Yang, Haizhao

2018-06-01

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

Diffusion Forecasting Model with Basis Functions from QR-Decomposition

NASA Astrophysics Data System (ADS)

Harlim, John; Yang, Haizhao

2017-12-01

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method

NASA Astrophysics Data System (ADS)

Fu, Shubin; Gao, Kai

2017-11-01

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.

The luminosity function of quasars

NASA Technical Reports Server (NTRS)

Pei, Yichuan C.

1995-01-01

We propose a new evolutionary model for the optical luminosity function of quasars. Our analytical model is derived from fits to the empirical luminosity function estimated by Hartwick and Schade and Warren, Hewett, and Osmer on the basis of more than 1200 quasars over the range of redshifts 0 approximately less than z approximately less than 4.5. We find that the evolution of quasars over this entire redshift range can be well fitted by a Gaussian distribution, while the shape of the luminosity function can be well fitted by either a double power law or an exponential L(exp 1/4) law. The predicted number counts of quasars, as a function of either apparent magnitude or redshift, are fully consistent with the observed ones. Our model indicates that the evolution of quasars reaches its maximum at z approximately = 2.8 and declines at higher redshifts. An extrapolation of the evolution to z approximately greater than 4.5 implies that quasars may have started their cosmic fireworks at z(sub f) approximately = 5.2-5.5. Forthcoming surveys of quasars at these redshifts will be critical to constrain the epoch of quasar formation. All the results we derived are based on observed quasars and are therefore subject to the bias of obscuration by dust in damped Ly alpha systems. Future surveys of these absorption systems at z approximately greater than 3 will also be important if the formation epoch of quasars is to be known unambiguously.

The ‘prediction imperative’ as the basis for self-awareness

PubMed Central

Llinás, Rodolfo R.; Roy, Sisir

2009-01-01

Here, we propose that global brain function is geared towards the implementation of intelligent motricity. Motricity is the only possible external manifestation of nervous system function (other than endocrine and exocrine secretion and the control of vascular tone). The intelligence component of motricity requires, for its successful wheeling, a prediction imperative to approximate the consequences of the impending motion. We address how such predictive function may originate from the dynamic properties of neuronal networks. PMID:19528011

Practical auxiliary basis implementation of Rung 3.5 functionals

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

Janesko, Benjamin G., E-mail: b.janesko@tcu.edu; Scalmani, Giovanni; Frisch, Michael J.

2014-07-21

Approximate exchange-correlation functionals for Kohn-Sham density functional theory often benefit from incorporating exact exchange. Exact exchange is constructed from the noninteracting reference system's nonlocal one-particle density matrix γ(r{sup -vector},r{sup -vector}′). Rung 3.5 functionals attempt to balance the strengths and limitations of exact exchange using a new ingredient, a projection of γ(r{sup -vector},r{sup -vector} ′) onto a semilocal model density matrix γ{sub SL}(ρ(r{sup -vector}),∇ρ(r{sup -vector}),r{sup -vector}−r{sup -vector} ′). γ{sub SL} depends on the electron density ρ(r{sup -vector}) at reference point r{sup -vector}, and is closely related to semilocal model exchange holes. We present a practical implementation of Rung 3.5 functionals, expandingmore » the r{sup -vector}−r{sup -vector} ′ dependence of γ{sub SL} in an auxiliary basis set. Energies and energy derivatives are obtained from 3D numerical integration as in standard semilocal functionals. We also present numerical tests of a range of properties, including molecular thermochemistry and kinetics, geometries and vibrational frequencies, and bandgaps and excitation energies. Rung 3.5 functionals typically provide accuracy intermediate between semilocal and hybrid approximations. Nonlocal potential contributions from γ{sub SL} yield interesting successes and failures for band structures and excitation energies. The results enable and motivate continued exploration of Rung 3.5 functional forms.« less

Analysis of STM images with pure and CO-functionalized tips: A first-principles and experimental study

NASA Astrophysics Data System (ADS)

Gustafsson, Alexander; Okabayashi, Norio; Peronio, Angelo; Giessibl, Franz J.; Paulsson, Magnus

2017-08-01

We describe a first-principles method to calculate scanning tunneling microscopy (STM) images, and compare the results to well-characterized experiments combining STM with atomic force microscopy (AFM). The theory is based on density functional theory with a localized basis set, where the wave functions in the vacuum gap are computed by propagating the localized-basis wave functions into the gap using a real-space grid. Constant-height STM images are computed using Bardeen's approximation method, including averaging over the reciprocal space. We consider copper adatoms and single CO molecules adsorbed on Cu(111), scanned with a single-atom copper tip with and without CO functionalization. The calculated images agree with state-of-the-art experiments, where the atomic structure of the tip apex is determined by AFM. The comparison further allows for detailed interpretation of the STM images.

Slater-type geminals in explicitly-correlated perturbation theory: application to n-alkanols and analysis of errors and basis-set requirements.

PubMed

Höfener, Sebastian; Bischoff, Florian A; Glöss, Andreas; Klopper, Wim

2008-06-21

In the recent years, Slater-type geminals (STGs) have been used with great success to expand the first-order wave function in an explicitly-correlated perturbation theory. The present work reports on this theory's implementation in the framework of the Turbomole suite of programs. A formalism is presented for evaluating all of the necessary molecular two-electron integrals by means of the Obara-Saika recurrence relations, which can be applied when the STG is expressed as a linear combination of a small number (n) of Gaussians (STG-nG geminal basis). In the Turbomole implementation of the theory, density fitting is employed and a complementary auxiliary basis set (CABS) is used for the resolution-of-the-identity (RI) approximation of explicitly-correlated theory. By virtue of this RI approximation, the calculation of molecular three- and four-electron integrals is avoided. An approximation is invoked to avoid the two-electron integrals over the commutator between the operators of kinetic energy and the STG. This approximation consists of computing commutators between matrices in place of operators. Integrals over commutators between operators would have occurred if the theory had been formulated and implemented as proposed originally. The new implementation in Turbomole was tested by performing a series of calculations on rotational conformers of the alkanols n-propanol through n-pentanol. Basis-set requirements concerning the orbital basis, the auxiliary basis set for density fitting and the CABS were investigated. Furthermore, various (constrained) optimizations of the amplitudes of the explicitly-correlated double excitations were studied. These amplitudes can be optimized in orbital-variant and orbital-invariant manners, or they can be kept fixed at the values governed by the rational generator approach, that is, by the electron cusp conditions. Electron-correlation effects beyond the level of second-order perturbation theory were accounted for by conventional coupled-cluster calculations with single, double and perturbative triple excitations [CCSD(T)]. The explicitly-correlated perturbation theory results were combined with CCSD(T) results and compared with literature data obtained by basis-set extrapolation.

Variable Neural Adaptive Robust Control: A Switched System Approach

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

Lian, Jianming; Hu, Jianghai; Zak, Stanislaw H.

2015-05-01

Variable neural adaptive robust control strategies are proposed for the output tracking control of a class of multi-input multi-output uncertain systems. The controllers incorporate a variable-structure radial basis function (RBF) network as the self-organizing approximator for unknown system dynamics. The variable-structure RBF network solves the problem of structure determination associated with fixed-structure RBF networks. It can determine the network structure on-line dynamically by adding or removing radial basis functions according to the tracking performance. The structure variation is taken into account in the stability analysis of the closed-loop system using a switched system approach with the aid of the piecewisemore » quadratic Lyapunov function. The performance of the proposed variable neural adaptive robust controllers is illustrated with simulations.« less

Pair production in low-energy collisions of uranium nuclei beyond the monopole approximation

NASA Astrophysics Data System (ADS)

Maltsev, I. A.; Shabaev, V. M.; Tupitsyn, I. I.; Kozhedub, Y. S.; Plunien, G.; Stöhlker, Th.

2017-10-01

A method for calculation of electron-positron pair production in low-energy heavy-ion collisions beyond the monopole approximation is presented. The method is based on the numerical solving of the time-dependent Dirac equation with the full two-center potential. The one-electron wave functions are expanded in the finite basis set constructed on the two-dimensional spatial grid. Employing the developed approach the probabilities of bound-free pair production are calculated for collisions of bare uranium nuclei at the energy near the Coulomb barrier. The obtained results are compared with the corresponding values calculated in the monopole approximation.

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

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

A. T. Till; M. Hanuš; J. Lou

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basismore » function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.« less

Analytical approximation of the InGaZnO thin-film transistors surface potential

NASA Astrophysics Data System (ADS)

Colalongo, Luigi

2016-10-01

Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

NASA Astrophysics Data System (ADS)

Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.

2018-06-01

The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.

Auxiliary basis expansions for large-scale electronic structure calculations

PubMed Central

Jung, Yousung; Sodt, Alex; Gill, Peter M. W.; Head-Gordon, Martin

2005-01-01

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems. PMID:15845767

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.

Magnetic exchange couplings from noncollinear perturbation theory: dinuclear CuII complexes.

PubMed

Phillips, Jordan J; Peralta, Juan E

2014-08-07

To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.

Vibrational spectroscopic study of fluticasone propionate

NASA Astrophysics Data System (ADS)

Ali, H. R. H.; Edwards, H. G. M.; Kendrick, J.; Scowen, I. J.

2009-03-01

Fluticasone propionate is a synthetic glucocorticoid with potent anti-inflammatory activity that has been used effectively in the treatment of chronic asthma. The present work reports a vibrational spectroscopic study of fluticasone propionate and gives proposed molecular assignments on the basis of ab initio calculations using BLYP density functional theory with a 6-31G* basis set and vibrational frequencies predicted within the quasi-harmonic approximation. Several spectral features and band intensities are explained. This study generated a library of information that can be employed to aid the process monitoring of fluticasone propionate.

An efficient method for quantum transport simulations in the time domain

NASA Astrophysics Data System (ADS)

Wang, Y.; Yam, C.-Y.; Frauenheim, Th.; Chen, G. H.; Niehaus, T. A.

2011-11-01

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. The density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier ab initio implementations of this formalism, the Hamiltonian is here approximated in the spirit of the density functional based tight-binding (DFTB) method. Results are presented for two prototypical molecular devices and compared to full TDDFT calculations. The temporal profile of the current traces is qualitatively well captured by the DFTB scheme. Steady state currents show considerable variations, both in comparison of approximate and full TDDFT, but also among TDDFT calculations with different basis sets.

Extended polarization in 3rd order SCC-DFTB from chemical potential equilization

PubMed Central

Kaminski, Steve; Giese, Timothy J.; Gaus, Michael; York, Darrin M.; Elstner, Marcus

2012-01-01

In this work we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical potential equilization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for NDDO type methods by Giese and York, has been shown to emend minimal basis methods wrt response properties significantly, and has been applied to SCC-DFTB recently. CPE allows to overcome this inherent limitation of minimal basis methods by supplying an additional response density. The systematic underestimation is thereby corrected quantitatively without the need to extend the atomic orbital basis, i.e. without increasing the overall computational cost significantly. Especially the dependency of polarizability as a function of molecular charge state was significantly improved from the CPE extension of DFTB3. The empirical parameters introduced by the CPE approach were optimized for 172 organic molecules in order to match the results from density functional methods (DFT) methods using large basis sets. However, the first order derivatives of molecular polarizabilities, as e.g. required to compute Raman activities, are not improved by the current CPE implementation, i.e. Raman spectra are not improved. PMID:22894819

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form.

PubMed

Chen, Bing; Zhang, Huaguang; Lin, Chong

2016-01-01

This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict-feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first proposed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficulties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approximation capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Many-body calculations with deuteron based single-particle bases and their associated natural orbits

NASA Astrophysics Data System (ADS)

Puddu, G.

2018-06-01

We use the recently introduced single-particle states obtained from localized deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits (NOs) obtained from this basis are used. We use this modified basis for {}10{{B}}, {}16{{O}} and {}24{{Mg}} employing the bare NNLOopt nucleon–nucleon interaction. The lowering of the energies increases with the mass. Although in principle NOs require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

NASA Astrophysics Data System (ADS)

Oberhofer, Harald; Blumberger, Jochen

2010-12-01

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( {< {| {H_ab } |^2 } > } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.

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.

Tracking control of a closed-chain five-bar robot with two degrees of freedom by integration of an approximation-based approach and mechanical design.

PubMed

Cheng, Long; Hou, Zeng-Guang; Tan, Min; Zhang, W J

2012-10-01

The trajectory tracking problem of a closed-chain five-bar robot is studied in this paper. Based on an error transformation function and the backstepping technique, an approximation-based tracking algorithm is proposed, which can guarantee the control performance of the robotic system in both the stable and transient phases. In particular, the overshoot, settling time, and final tracking error of the robotic system can be all adjusted by properly setting the parameters in the error transformation function. The radial basis function neural network (RBFNN) is used to compensate the complicated nonlinear terms in the closed-loop dynamics of the robotic system. The approximation error of the RBFNN is only required to be bounded, which simplifies the initial "trail-and-error" configuration of the neural network. Illustrative examples are given to verify the theoretical analysis and illustrate the effectiveness of the proposed algorithm. Finally, it is also shown that the proposed approximation-based controller can be simplified by a smart mechanical design of the closed-chain robot, which demonstrates the promise of the integrated design and control philosophy.

High-temperature electronic structure with the Korringa-Kohn-Rostoker Green's function method

NASA Astrophysics Data System (ADS)

Starrett, C. E.

2018-05-01

Modeling high-temperature (tens or hundreds of eV), dense plasmas is challenging due to the multitude of non-negligible physical effects including significant partial ionization and multisite effects. These effects cause the breakdown or intractability of common methods and approximations used at low temperatures, such as pseudopotentials or plane-wave basis sets. Here we explore the Korringa-Kohn-Rostoker Green's function method at these high-temperature conditions. The method is all electron, does not rely on pseudopotentials, and uses a spherical harmonic basis set, and so avoids the aforementioned limitations. It is found to be accurate for solid density aluminum and iron plasmas when compared to a plane-wave method at low temperature, while being able to access high temperatures.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Quantum corrections of the truncated Wigner approximation applied to an exciton transport model.

PubMed

Ivanov, Anton; Breuer, Heinz-Peter

2017-04-01

We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time evolution of the system observables is obtained by calculating the average of a stochastic difference equation which is weighted with a product of pseudoprobability density functions. From the exact equation of motion one can clearly identify the terms that are also present if we apply the truncated Wigner approximation. This description of the problem is used as a basis for the derivation of a new approximation, whose validity goes beyond the truncated Wigner approximation. To demonstrate this we apply the formalism to a donor-acceptor transport model.

A heuristic neural network initialization scheme for modeling nonlinear functions in engineering mechanics: continuous development

NASA Astrophysics Data System (ADS)

Pei, Jin-Song; Mai, Eric C.

2007-04-01

This paper introduces a continuous effort towards the development of a heuristic initialization methodology for constructing multilayer feedforward neural networks to model nonlinear functions. In this and previous studies that this work is built upon, including the one presented at SPIE 2006, the authors do not presume to provide a universal method to approximate arbitrary functions, rather the focus is given to the development of a rational and unambiguous initialization procedure that applies to the approximation of nonlinear functions in the specific domain of engineering mechanics. The applications of this exploratory work can be numerous including those associated with potential correlation and interpretation of the inner workings of neural networks, such as damage detection. The goal of this study is fulfilled by utilizing the governing physics and mathematics of nonlinear functions and the strength of the sigmoidal basis function. A step-by-step graphical procedure utilizing a few neural network prototypes as "templates" to approximate commonly seen memoryless nonlinear functions of one or two variables is further developed in this study. Decomposition of complex nonlinear functions into a summation of some simpler nonlinear functions is utilized to exploit this prototype-based initialization methodology. Training examples are presented to demonstrate the rationality and effciency of the proposed methodology when compared with the popular Nguyen-Widrow initialization algorithm. Future work is also identfied.

On the origin independence of the Verdet tensor†

NASA Astrophysics Data System (ADS)

Caputo, M. C.; Coriani, S.; Pelloni, S.; Lazzeretti, P.

2013-07-01

The condition for invariance under a translation of the coordinate system of the Verdet tensor and the Verdet constant, calculated via quantum chemical methods using gaugeless basis sets, is expressed by a vanishing sum rule involving a third-rank polar tensor. The sum rule is, in principle, satisfied only in the ideal case of optimal variational electronic wavefunctions. In general, it is not fulfilled in non-variational calculations and variational calculations allowing for the algebraic approximation, but it can be satisfied for reasons of molecular symmetry. Group-theoretical procedures have been used to determine (i) the total number of non-vanishing components and (ii) the unique components of both the polar tensor appearing in the sum rule and the axial Verdet tensor, for a series of symmetry groups. Test calculations at the random-phase approximation level of accuracy for water, hydrogen peroxide and ammonia molecules, using basis sets of increasing quality, show a smooth convergence to zero of the sum rule. Verdet tensor components calculated for the same molecules converge to limit values, estimated via large basis sets of gaugeless Gaussian functions and London orbitals.

Model's sparse representation based on reduced mixed GMsFE basis methods

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

Model's sparse representation based on reduced mixed GMsFE basis methods

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

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Qiuqi, E-mail: qiuqili@hnu.edu.cn

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a largemore » number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.« less

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

An Exospheric Temperature Model Based On CHAMP Observations and TIEGCM Simulations

NASA Astrophysics Data System (ADS)

Ruan, Haibing; Lei, Jiuhou; Dou, Xiankang; Liu, Siqing; Aa, Ercha

2018-02-01

In this work, thermospheric densities from the accelerometer measurement on board the CHAMP satellite during 2002-2009 and the simulations from the National Center for Atmospheric Research Thermosphere Ionosphere Electrodynamics General Circulation Model (NCAR-TIEGCM) are employed to develop an empirical exospheric temperature model (ETM). The two-dimensional basis functions of the ETM are first provided from the principal component analysis of the TIEGCM simulations. Based on the exospheric temperatures derived from CHAMP thermospheric densities, a global distribution of the exospheric temperatures is reconstructed. A parameterization is conducted for each basis function amplitude as a function of solar-geophysical and seasonal conditions. Thus, the ETM can be utilized to model the thermospheric temperature and mass density under a specified condition. Our results showed that the averaged standard deviation of the ETM is generally less than 10% than approximately 30% in the MSIS model. Besides, the ETM reproduces the global thermospheric evolutions including the equatorial thermosphere anomaly.

Comparing two Bayes methods based on the free energy functions in Bernoulli mixtures.

PubMed

Yamazaki, Keisuke; Kaji, Daisuke

2013-08-01

Hierarchical learning models are ubiquitously employed in information science and data engineering. The structure makes the posterior distribution complicated in the Bayes method. Then, the prediction including construction of the posterior is not tractable though advantages of the method are empirically well known. The variational Bayes method is widely used as an approximation method for application; it has the tractable posterior on the basis of the variational free energy function. The asymptotic behavior has been studied in many hierarchical models and a phase transition is observed. The exact form of the asymptotic variational Bayes energy is derived in Bernoulli mixture models and the phase diagram shows that there are three types of parameter learning. However, the approximation accuracy or interpretation of the transition point has not been clarified yet. The present paper precisely analyzes the Bayes free energy function of the Bernoulli mixtures. Comparing free energy functions in these two Bayes methods, we can determine the approximation accuracy and elucidate behavior of the parameter learning. Our results claim that the Bayes free energy has the same learning types while the transition points are different. Copyright © 2013 Elsevier Ltd. All rights reserved.

Numerically Exact Calculation of Rovibrational Levels of Cl^-H_2O

NASA Astrophysics Data System (ADS)

Wang, Xiao-Gang; Carrington, Tucker

2014-06-01

Large amplitude vibrations of Van der Waals clusters are important because they reveal large regions of a potential energy surface (PES). To calculate spectra of Van der Waals clusters it is common to use an adiabatic approximation. When coupling between intra- and inter-molecular coordinates is important non-adiabatic coupling cannot be neglected and it is therefore critical to develop and test theoretical methods that couple both types of coordinates. We have developed new product basis and contracted basis Lanczos methods for Van der Waals complexes and tested them by computing rovibrational energy levels of Cl^-H_2O. The new product basis is made of functions of the inter-monomer distance, Wigner functions that depend on Euler angles specifying the orientation of H_2O with respect to a frame attached to the inter-monomer Jacobi vector, basis functions for H_2O vibration, and Wigner functions that depend on Euler angles specifying the orientation of the inter-monomer Jacobi vector with respect to a space-fixed frame. An advantage of this product basis is that it can be used to make an efficient contracted basis by replacing the vibrational basis functions for the monomer with monomer vibrational wavefunctions. Due to weak coupling between intra- and inter-molecular coordinates, only a few tens of monomer vibrational wavefunctions are necessary. The validity of the two new methods is established by comparing energy levels with benchmark rovibrational levels obtained with polyspherical coordinates and spherical harmonic type basis functions. For all bases, product structure is exploited to calculate eigenvalues with the Lanczos algorithm. For Cl^-H_2O, we are able, for the first time, to compute accurate splittings due to tunnelling between the two equivalent C_s minima. We use the PES of Rheinecker and Bowman (RB). Our results are in good agreement with experiment for the five fundamental bands observed. J. Rheinecker and J. M. Bowman, J. Chem. Phys. 124 131102 (2006) J. Rheinecker and J. M. Bowman, J. Chem. Phys. 125 133206 (2006)} S. Horvath, A. B. McCoy, B. M. Elliott, G. H. Weddle, J. R. Roscioli, and M. A. Johnson J. Phys. Chem. A 114 1556 (2010)

A Comparison of the Pencil-of-Function Method with Prony’s Method, Wiener Filters and Other Identification Techniques,

DTIC Science & Technology

1977-12-01

exponentials encountered are complex and zhey are approximately at harmonic frequencies. Moreover, the real parts of the complex exponencials are much...functions as a basis for expanding the current distribution on an antenna by the method of moments results in a regularized ill-posed problem with respect...to the current distribution on the antenna structure. However, the problem is not regularized with respect to chaoge because the chaPge distribution

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction

DOE PAGES

Tencer, John; Carlberg, Kevin; Larsen, Marvin; ...

2017-06-17

Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat-transfer applications, a quasi-steady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite numbermore » of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projection-based model-reduction approach to make high-order quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model constructed from the reduced basis. Finally, this results in a much more accurate solution than might have been achieved using only the ordinate directions used to compute the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.« less

Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction

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

Tencer, John; Carlberg, Kevin; Larsen, Marvin

Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat-transfer applications, a quasi-steady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite numbermore » of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projection-based model-reduction approach to make high-order quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model constructed from the reduced basis. Finally, this results in a much more accurate solution than might have been achieved using only the ordinate directions used to compute the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.« less

Benchmarking the GW Approximation and Bethe–Salpeter Equation for Groups IB and IIB Atoms and Monoxides

DOE PAGES

Hung, Linda; Bruneval, Fabien; Baishya, Kopinjol; ...

2017-04-07

Energies from the GW approximation and the Bethe–Salpeter equation (BSE) are benchmarked against the excitation energies of transition-metal (Cu, Zn, Ag, and Cd) single atoms and monoxide anions. We demonstrate that best estimates of GW quasiparticle energies at the complete basis set limit should be obtained via extrapolation or closure relations, while numerically converged GW-BSE eigenvalues can be obtained on a finite basis set. Calculations using real-space wave functions and pseudopotentials are shown to give best-estimate GW energies that agree (up to the extrapolation error) with calculations using all-electron Gaussian basis sets. We benchmark the effects of a vertex approximationmore » (ΓLDA) and the mean-field starting point in GW and the BSE, performing computations using a real-space, transition-space basis and scalar-relativistic pseudopotentials. Here, while no variant of GW improves on perturbative G0W0 at predicting ionization energies, G0W0Γ LDA-BSE computations give excellent agreement with experimental absorption spectra as long as off-diagonal self-energy terms are included. We also present G0W0 quasiparticle energies for the CuO –, ZnO –, AgO –, and CdO – anions, in comparison to available anion photoelectron spectra.« less

Benchmarking the GW Approximation and Bethe–Salpeter Equation for Groups IB and IIB Atoms and Monoxides

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

Hung, Linda; Bruneval, Fabien; Baishya, Kopinjol

Energies from the GW approximation and the Bethe–Salpeter equation (BSE) are benchmarked against the excitation energies of transition-metal (Cu, Zn, Ag, and Cd) single atoms and monoxide anions. We demonstrate that best estimates of GW quasiparticle energies at the complete basis set limit should be obtained via extrapolation or closure relations, while numerically converged GW-BSE eigenvalues can be obtained on a finite basis set. Calculations using real-space wave functions and pseudopotentials are shown to give best-estimate GW energies that agree (up to the extrapolation error) with calculations using all-electron Gaussian basis sets. We benchmark the effects of a vertex approximationmore » (ΓLDA) and the mean-field starting point in GW and the BSE, performing computations using a real-space, transition-space basis and scalar-relativistic pseudopotentials. Here, while no variant of GW improves on perturbative G0W0 at predicting ionization energies, G0W0Γ LDA-BSE computations give excellent agreement with experimental absorption spectra as long as off-diagonal self-energy terms are included. We also present G0W0 quasiparticle energies for the CuO –, ZnO –, AgO –, and CdO – anions, in comparison to available anion photoelectron spectra.« less

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules

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

Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

2000-05-08

The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin-orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin-orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation,more » the generalized gradient approximation and Hartree-Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin-orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work. (c) 2000 American Institute of Physics.« less

Ab-initio calculation for cation vacancy formation energy in anti-fluorite structure

NASA Astrophysics Data System (ADS)

Saleel, V. P. Saleel Ahammad; Chitra, D.; Veluraja, K.; Eithiraj, R. D.

2018-04-01

Lithium oxide (Li2O) has been suggested as a suitable breeder blanket material for fusion reactors. Li+ vacancies are created by neutron irradiation, forming bulk defect complex whose extra character is experimentally unclear. We present a theoretical study of Li2O using density functional theory (DFT) with a plane-wave basis set. The generalized gradient approximation (GGA) and local-density approximation (LDA) were used for exchange and correlation. Here we address the total energy for defect free, cation defect, cation vacancy and vacancy formation energy in Li2O crystal in anti-fluorite structure.

Steerable Principal Components for Space-Frequency Localized Images*

PubMed Central

Landa, Boris; Shkolnisky, Yoel

2017-01-01

As modern scientific image datasets typically consist of a large number of images of high resolution, devising methods for their accurate and efficient processing is a central research task. In this paper, we consider the problem of obtaining the steerable principal components of a dataset, a procedure termed “steerable PCA” (steerable principal component analysis). The output of the procedure is the set of orthonormal basis functions which best approximate the images in the dataset and all of their planar rotations. To derive such basis functions, we first expand the images in an appropriate basis, for which the steerable PCA reduces to the eigen-decomposition of a block-diagonal matrix. If we assume that the images are well localized in space and frequency, then such an appropriate basis is the prolate spheroidal wave functions (PSWFs). We derive a fast method for computing the PSWFs expansion coefficients from the images' equally spaced samples, via a specialized quadrature integration scheme, and show that the number of required quadrature nodes is similar to the number of pixels in each image. We then establish that our PSWF-based steerable PCA is both faster and more accurate then existing methods, and more importantly, provides us with rigorous error bounds on the entire procedure. PMID:29081879

Vibrations in a moving flexible robot arm

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Wei, Jin-Duo

1987-01-01

The vibration in a flexible robot arm modeled by a moving slender prismatic beam is considered. It is found that the extending and contracting motions have destabilizing and stabilizing effects on the vibratory motions, respectively. The vibration analysis is based on a Galerkin approximation with time-dependent basis functions. Typical numerical results are presented to illustrate the qualitative features of vibrations.

Determination of the temperature distribution in a minichannel using ANSYS CFX and a procedure based on the Trefftz functions

NASA Astrophysics Data System (ADS)

Maciejewska, Beata; Błasiak, Sławomir; Piasecka, Magdalena

This work discusses the mathematical model for laminar-flow heat transfer in a minichannel. The boundary conditions in the form of temperature distributions on the outer sides of the channel walls were determined from experimental data. The data were collected from the experimental stand the essential part of which is a vertical minichannel 1.7 mm deep, 16 mm wide and 180 mm long, asymmetrically heated by a Haynes-230 alloy plate. Infrared thermography allowed determining temperature changes on the outer side of the minichannel walls. The problem was analysed numerically through either ANSYS CFX software or special calculation procedures based on the Finite Element Method and Trefftz functions in the thermal boundary layer. The Trefftz functions were used to construct the basis functions. Solutions to the governing differential equations were approximated with a linear combination of Trefftz-type basis functions. Unknown coefficients of the linear combination were calculated by minimising the functional. The results of the comparative analysis were represented in a graphical form and discussed.

Wave scattering from random sets of closely spaced objects through linear embedding via Green's operators

NASA Astrophysics Data System (ADS)

Lancellotti, V.; de Hon, B. P.; Tijhuis, A. G.

2011-08-01

In this paper we present the application of linear embedding via Green's operators (LEGO) to the solution of the electromagnetic scattering from clusters of arbitrary (both conducting and penetrable) bodies randomly placed in a homogeneous background medium. In the LEGO method the objects are enclosed within simple-shaped bricks described in turn via scattering operators of equivalent surface current densities. Such operators have to be computed only once for a given frequency, and hence they can be re-used to perform the study of many distributions comprising the same objects located in different positions. The surface integral equations of LEGO are solved via the Moments Method combined with Adaptive Cross Approximation (to save memory) and Arnoldi basis functions (to compress the system). By means of purposefully selected numerical experiments we discuss the time requirements with respect to the geometry of a given distribution. Besides, we derive an approximate relationship between the (near-field) accuracy of the computed solution and the number of Arnoldi basis functions used to obtain it. This result endows LEGO with a handy practical criterion for both estimating the error and keeping it in check.

The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

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

Bykov, Dmytro; Kristensen, Kasper; Kjærgaard, Thomas

We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 methodmore » and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.« less

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization.

PubMed

Hilton, Harry H

2012-01-18

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

Superexchange and spin-glass formation in semimagnetic semiconductors

NASA Astrophysics Data System (ADS)

Rusin, Tomasz M.

1996-05-01

The Mn-Mn superexchange interaction in semimagnetic semiconductors A1-xMnxB (where A=Zn, Cd and B=S, Se, Te) is studied within the three-level model of the band structure. We focus on the dependence of the interaction on the interion distance Jdd(r)=J0f(r). In the present work, the function f(r) is obtained analytically. This, only weakly material-dependent function is found to decrease with Mn-Mn distance much slower than its Gaussian approximation derived previously. The exact form of the decay of the superexchange can be approximated by a power law J0r-8.5. This is close to an experimental result, J0r-6.8, determined on the basis of the spin-glass transition temperature on the composition.

Computation of indirect nuclear spin-spin couplings with reduced complexity in pure and hybrid density functional approximations.

PubMed

Luenser, Arne; Kussmann, Jörg; Ochsenfeld, Christian

2016-09-28

We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.

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.

Trends in stratospheric ozone profiles using functional mixed models

NASA Astrophysics Data System (ADS)

Park, A.; Guillas, S.; Petropavlovskikh, I.

2013-11-01

This paper is devoted to the modeling of altitude-dependent patterns of ozone variations over time. Umkehr ozone profiles (quarter of Umkehr layer) from 1978 to 2011 are investigated at two locations: Boulder (USA) and Arosa (Switzerland). The study consists of two statistical stages. First we approximate ozone profiles employing an appropriate basis. To capture primary modes of ozone variations without losing essential information, a functional principal component analysis is performed. It penalizes roughness of the function and smooths excessive variations in the shape of the ozone profiles. As a result, data-driven basis functions (empirical basis functions) are obtained. The coefficients (principal component scores) corresponding to the empirical basis functions represent dominant temporal evolution in the shape of ozone profiles. We use those time series coefficients in the second statistical step to reveal the important sources of the patterns and variations in the profiles. We estimate the effects of covariates - month, year (trend), quasi-biennial oscillation, the solar cycle, the Arctic oscillation, the El Niño/Southern Oscillation cycle and the Eliassen-Palm flux - on the principal component scores of ozone profiles using additive mixed effects models. The effects are represented as smooth functions and the smooth functions are estimated by penalized regression splines. We also impose a heteroscedastic error structure that reflects the observed seasonality in the errors. The more complex error structure enables us to provide more accurate estimates of influences and trends, together with enhanced uncertainty quantification. Also, we are able to capture fine variations in the time evolution of the profiles, such as the semi-annual oscillation. We conclude by showing the trends by altitude over Boulder and Arosa, as well as for total column ozone. There are great variations in the trends across altitudes, which highlights the benefits of modeling ozone profiles.

Comparing fixed and variable-width Gaussian networks.

PubMed

Kůrková, Věra; Kainen, Paul C

2014-09-01

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.

First-principles calculations on the four phases of BaTiO3.

PubMed

Evarestov, Robert A; Bandura, Andrei V

2012-04-30

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO(3) crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange-correlation density functional theory (DFT) functionals for four stable phases of BaTiO(3). A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO(3). The comparative phonon symmetry analysis in BaTiO(3) four phases has been made basing on the site symmetry and irreducible representation indexes for the first time. Copyright © 2012 Wiley Periodicals, Inc.

NMR, MRI, and spectroscopic MRI in inhomogeneous fields

DOEpatents

Demas, Vasiliki; Pines, Alexander; Martin, Rachel W; Franck, John; Reimer, Jeffrey A

2013-12-24

A method for locally creating effectively homogeneous or "clean" magnetic field gradients (of high uniformity) for imaging (with NMR, MRI, or spectroscopic MRI) both in in-situ and ex-situ systems with high degrees of inhomogeneous field strength. THe method of imaging comprises: a) providing a functional approximation of an inhomogeneous static magnetic field strength B.sub.0({right arrow over (r)}) at a spatial position {right arrow over (r)}; b) providing a temporal functional approximation of {right arrow over (G)}.sub.shim(t) with i basis functions and j variables for each basis function, resulting in v.sub.ij variables; c) providing a measured value .OMEGA., which is an temporally accumulated dephasing due to the inhomogeneities of B.sub.0({right arrow over(r)}); and d) minimizing a difference in the local dephasing angle .phi.({right arrow over (r)},t)=.gamma..intg..sub.0.sup.t{square root over (|{right arrow over (B)}.sub.1({right arrow over (r)},t')|.sup.2+({right arrow over (r)}{right arrow over (G)}.sub.shimG.sub.shim(t')+.parallel.{right arrow over (B)}.sub.0({right arrow over (r)}).parallel..DELTA..omega.({right arrow over (r)},t'/.gamma/).sup.2)}dt'-.OMEGA. by varying the v.sub.ij variables to form a set of minimized v.sub.ij variables. The method requires calibration of the static fields prior to minimization, but may thereafter be implemented without such calibration, may be used in open or closed systems, and potentially portable systems.

77 FR 60114 - Agency Information Collection Activities Under OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-02

... approximately 100 entities on a daily basis. The recordkeeping requirement of section 22.5 is expected to apply to approximately 100 entities on an approximately annual basis. Based on experience with analogous... required by section 22.2(g) is expected to require about 100 hours annually per entity, for a total burden...

A vehicle stability control strategy with adaptive neural network sliding mode theory based on system uncertainty approximation

NASA Astrophysics Data System (ADS)

Ji, Xuewu; He, Xiangkun; Lv, Chen; Liu, Yahui; Wu, Jian

2018-06-01

Modelling uncertainty, parameter variation and unknown external disturbance are the major concerns in the development of an advanced controller for vehicle stability at the limits of handling. Sliding mode control (SMC) method has proved to be robust against parameter variation and unknown external disturbance with satisfactory tracking performance. But modelling uncertainty, such as errors caused in model simplification, is inevitable in model-based controller design, resulting in lowered control quality. The adaptive radial basis function network (ARBFN) can effectively improve the control performance against large system uncertainty by learning to approximate arbitrary nonlinear functions and ensure the global asymptotic stability of the closed-loop system. In this paper, a novel vehicle dynamics stability control strategy is proposed using the adaptive radial basis function network sliding mode control (ARBFN-SMC) to learn system uncertainty and eliminate its adverse effects. This strategy adopts a hierarchical control structure which consists of reference model layer, yaw moment control layer, braking torque allocation layer and executive layer. Co-simulation using MATLAB/Simulink and AMESim is conducted on a verified 15-DOF nonlinear vehicle system model with the integrated-electro-hydraulic brake system (I-EHB) actuator in a Sine With Dwell manoeuvre. The simulation results show that ARBFN-SMC scheme exhibits superior stability and tracking performance in different running conditions compared with SMC scheme.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

PubMed

Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek; Faber, Rasmus; Lacerda, Evanildo G; Sauer, Stephan P A

2016-02-05

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.

FDE-vdW: A van der Waals inclusive subsystem density-functional theory.

PubMed

Kevorkyants, Ruslan; Eshuis, Henk; Pavanello, Michele

2014-07-28

We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation-dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method. We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.

FDE-vdW: A van der Waals inclusive subsystem density-functional theory

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

Kevorkyants, Ruslan; Pavanello, Michele, E-mail: m.pavanello@rutgers.edu; Eshuis, Henk

2014-07-28

We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation–dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method.more » We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.« less

Short-term prediction of chaotic time series by using RBF network with regression weights.

PubMed

Rojas, I; Gonzalez, J; Cañas, A; Diaz, A F; Rojas, F J; Rodriguez, M

2000-10-01

We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters sigma are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.

Linear-scaling explicitly correlated treatment of solids: periodic local MP2-F12 method.

PubMed

Usvyat, Denis

2013-11-21

Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.

Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions

DTIC Science & Technology

2007-09-01

C. (2005). Elementary Linear Algebra . New York: John Wiley and Sons. Avitable, Peter (2001, January) Experimental Modal Analysis, A Simple Non...variables under consideration. 3 Frequency sensitivities are the basis for a linear approximation to compute the change in the natural frequencies of a...THEORY The general problem statement for a non- linear constrained optimization problem is: To minimize ( )f x Objective Function Subject to

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Bennett, Floyd V.; Yntema, Robert T.

1959-01-01

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Analysis of the impacts of horizontal translation and scaling on wavefront approximation coefficients with rectangular pupils for Chebyshev and Legendre polynomials.

PubMed

Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong

2013-12-01

Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.

An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

DOE PAGES

Yu, Hua-Gen

2002-01-01

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem ismore » solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.« less

The functional basis for hemophagocytic lymphohistiocytosis in a patient with co-inherited missense mutations in the perforin (PFN1) gene.

PubMed

Voskoboinik, Ilia; Thia, Marie-Claude; De Bono, Annette; Browne, Kylie; Cretney, Erika; Jackson, Jacob T; Darcy, Phillip K; Jane, Stephen M; Smyth, Mark J; Trapani, Joseph A

2004-09-20

About 30% of cases of the autosomal recessive immunodeficiency disorder hemophagocytic lymphohistiocytosis are believed to be caused by inactivating mutations of the perforin gene. We expressed perforin in rat basophil leukemia cells to define the basis of perforin dysfunction associated with two mutations, R225W and G429E, inherited by a compound heterozygote patient. Whereas RBL cells expressing wild-type perforin (67 kD) efficiently killed Jurkat target cells to which they were conjugated, the substitution to tryptophan at position 225 resulted in expression of a truncated ( approximately 45 kD) form of the protein, complete loss of cytotoxicity, and failure to traffic to rat basophil leukemia secretory granules. By contrast, G429E perforin was correctly processed, stored, and released, but the rat basophil leukemia cells possessed reduced cytotoxicity. The defective function of G429E perforin mapped downstream of exocytosis and was due to its reduced ability to bind lipid membranes in a calcium-dependent manner. This study elucidates the cellular basis for perforin dysfunctions in hemophagocytic lymphohistiocytosis and provides the means for studying structure-function relationships for lymphocyte perforin.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: application to SSSH.

PubMed

Kolmann, Stephen J; Jordan, Meredith J T

2010-02-07

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

NASA Astrophysics Data System (ADS)

Kolmann, Stephen J.; Jordan, Meredith J. T.

2010-02-01

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Exponential Approximations Using Fourier Series Partial Sums

NASA Technical Reports Server (NTRS)

Banerjee, Nana S.; Geer, James F.

1997-01-01

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Probability Density Functions of Observed Rainfall in Montana

NASA Technical Reports Server (NTRS)

Larsen, Scott D.; Johnson, L. Ronald; Smith, Paul L.

1995-01-01

The question of whether a rain rate probability density function (PDF) can vary uniformly between precipitation events is examined. Image analysis on large samples of radar echoes is possible because of advances in technology. The data provided by such an analysis easily allow development of radar reflectivity factors (and by extension rain rate) distribution. Finding a PDF becomes a matter of finding a function that describes the curve approximating the resulting distributions. Ideally, one PDF would exist for all cases; or many PDF's that have the same functional form with only systematic variations in parameters (such as size or shape) exist. Satisfying either of theses cases will, validate the theoretical basis of the Area Time Integral (ATI). Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89 percent of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit. Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89% of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit.

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.

First principles investigation of structural, vibrational and thermal properties of black and blue phosphorene

NASA Astrophysics Data System (ADS)

Arif Khalil, R. M.; Ahmad, Javed; Rana, Anwar Manzoor; Bukhari, Syed Hamad; Tufiq Jamil, M.; Tehreem, Tuba; Nissar, Umair

2018-05-01

In this investigation, structural, dynamical and thermal properties of black and blue phosphorene (P) are presented through the first principles calculations based on the density functional theory (DFT). These DFT calculations depict that due to the approximately same values of ground state energy at zero Kelvin and Helmholtz free energy at room-temperature, it is expected that both structures can coexist at transition temperature. Lattice dynamics of both phases were investigated by using the finite displacement supercell approach. It is noticed on the basis of harmonic approximation thermodynamic calculations that the blue phase is thermodynamically more stable than the black phase above 155 K.

Contactless diagnostics of biophysical parameters of skin and blood on the basis of approximating functions for radiation fluxes scattered by skin

NASA Astrophysics Data System (ADS)

Lisenko, S. A.; Kugeiko, M. M.

2014-03-01

Approximating expressions are derived to calculate spectral and spatial characteristics of diffuse reflection of light from a two-layer medium mimicking human skin. The effectiveness of the use of these expressions in the optical diagnosis of skin biophysical parameters (tissue scattering parameters, concentration of melanin in the epidermis, concentration of total haemoglobin and bilirubin in the tissues of the dermis) and content of haemoglobin derivatives in blood (oxy-, deoxy-, met-, carboxy- and sulfhaemoglobin) is analysed numerically. The methods are proposed to determine in realtime these parameters without contact of the measuring instrument with the patient's body.

Methods for converging correlation energies within the dielectric matrix formalism

NASA Astrophysics Data System (ADS)

Dixit, Anant; Claudot, Julien; Gould, Tim; Lebègue, Sébastien; Rocca, Dario

2018-03-01

Within the dielectric matrix formalism, the random-phase approximation (RPA) and analogous methods that include exchange effects are promising approaches to overcome some of the limitations of traditional density functional theory approximations. The RPA-type methods however have a significantly higher computational cost, and, similarly to correlated quantum-chemical methods, are characterized by a slow basis set convergence. In this work we analyzed two different schemes to converge the correlation energy, one based on a more traditional complete basis set extrapolation and one that converges energy differences by accounting for the size-consistency property. These two approaches have been systematically tested on the A24 test set, for six points on the potential-energy surface of the methane-formaldehyde complex, and for reaction energies involving the breaking and formation of covalent bonds. While both methods converge to similar results at similar rates, the computation of size-consistent energy differences has the advantage of not relying on the choice of a specific extrapolation model.

Estimating and Identifying Unspecified Correlation Structure for Longitudinal Data

PubMed Central

Hu, Jianhua; Wang, Peng; Qu, Annie

2014-01-01

Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large size clustered data. In this paper, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We utilize eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies. PMID:26361433

Hartree-Fock theory of the inhomogeneous electron gas at a jellium metal surface: Rigorous upper bounds to the surface energy and accurate work functions

NASA Astrophysics Data System (ADS)

Sahni, V.; Ma, C. Q.

1980-12-01

The inhomogeneous electron gas at a jellium metal surface is studied in the Hartree-Fock approximation by Kohn-Sham density functional theory. Rigorous upper bounds to the surface energy are derived by application of the Rayleigh-Ritz variational principle for the energy, the surface kinetic, electrostatic, and nonlocal exchange energy functionals being determined exactly for the accurate linear-potential model electronic wave functions. The densities obtained by the energy minimization constraint are then employed to determine work-function results via the variationally accurate "displaced-profile change-in-self-consistent-field" expression. The theoretical basis of this non-self-consistent procedure and its demonstrated accuracy for the fully correlated system (as treated within the local-density approximation for exchange and correlation) leads us to conclude these results for the surface energies and work functions to be essentially exact. Work-function values are also determined by the Koopmans'-theorem expression, both for these densities as well as for those obtained by satisfaction of the constraint set on the electrostatic potential by the Budd-Vannimenus theorem. The use of the Hartree-Fock results in the accurate estimation of correlation-effect contributions to these surface properties of the nonuniform electron gas is also indicated. In addition, the original work and approximations made by Bardeen in this attempt at a solution of the Hartree-Fock problem are briefly reviewed in order to contrast with the present work.

B97-3c: A revised low-cost variant of the B97-D density functional method

NASA Astrophysics Data System (ADS)

Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas; Grimme, Stefan

2018-02-01

A revised version of the well-established B97-D density functional approximation with general applicability for chemical properties of large systems is proposed. Like B97-D, it is based on Becke's power-series ansatz from 1997 and is explicitly parametrized by including the standard D3 semi-classical dispersion correction. The orbitals are expanded in a modified valence triple-zeta Gaussian basis set, which is available for all elements up to Rn. Remaining basis set errors are mostly absorbed in the modified B97 parametrization, while an established atom-pairwise short-range potential is applied to correct for the systematically too long bonds of main group elements which are typical for most semi-local density functionals. The new composite scheme (termed B97-3c) completes the hierarchy of "low-cost" electronic structure methods, which are all mainly free of basis set superposition error and account for most interactions in a physically sound and asymptotically correct manner. B97-3c yields excellent molecular and condensed phase geometries, similar to most hybrid functionals evaluated in a larger basis set expansion. Results on the comprehensive GMTKN55 energy database demonstrate its good performance for main group thermochemistry, kinetics, and non-covalent interactions, when compared to functionals of the same class. This also transfers to metal-organic reactions, which is a major area of applicability for semi-local functionals. B97-3c can be routinely applied to hundreds of atoms on a single processor and we suggest it as a robust computational tool, in particular, for more strongly correlated systems where our previously published "3c" schemes might be problematic.

Photosynthetic capacity peaks at intermediate size in temperate deciduous trees.

PubMed

Thomas, Sean C

2010-05-01

Studies of age-related changes in leaf functional biology have generally been based on dichotomous comparisons of young and mature individuals (e.g., saplings and mature canopy trees), with little data available to describe changes through the entire ontogeny of trees, particularly of broadleaf angiosperms. Leaf-level gas-exchange and morphological parameters were quantified in situ in the upper canopy of trees acclimated to high light conditions, spanning a wide range of ontogenetic stages from saplings (approximately 1 cm in stem diameter) to trees >60 cm d.b.h. and nearing their maximum lifespan, in three temperate deciduous tree species in central Ontario, Canada. Traits associated with growth performance, including leaf photosynthetic capacity (expressed on either an area, mass or leaf N basis), stomatal conductance, leaf size and leaf N content, generally showed a unimodal ('hump-shaped') pattern, with peak values at an intermediate ontogenetic stage. In contrast, leaf mass per area (LMA) and related morphological parameters (leaf thickness, leaf tissue density, leaf C content) increased monotonically with tree size, as did water-use efficiency; these monotonic relationships were well described by simple allometric functions of the form Y = aX(b). For traits showing unimodal patterns, tree size corresponding to the trait maximum differed markedly among traits: all three species showed a similar pattern in which the peak for leaf size occurred in trees approximately 2-6 cm d.b.h., followed by leaf chemical traits and photosynthetic capacity on a mass or leaf N basis and finally by photosynthetic capacity on a leaf area basis, which peaked approximately at the size of reproductive onset. It is argued that ontogenetic increases in photosynthetic capacity and related traits early in tree ontogeny are general among relatively shade-tolerant tree species that have a low capacity for leaf-level acclimation, as are declines in this set of traits late in tree ontogeny.

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

The Dynamical Mean Field Study of Competition between Ferromagnetism and Disorder in Ferromagnetic Semiconductors

NASA Astrophysics Data System (ADS)

Aryanpour, Karan

2003-03-01

We employ the Dynamical Mean Field Approximation (DMFA) to study the Janko-Zarand model [1] for the combination of large spin-orbit coupling and spatial disorder effects in GaAs doped with Mn. In this model the electronic dispersion and the spin-orbit coupling are simultaneously diagonalized and therefore, the Hamiltonian for the pure system takes a surprisingly simple form. The price for this simplicity is that the quantization axis for the spin must be rotated along the direction of momentum. This chiral basis greatly complicates the form of the hole-impurity interaction at a single site i. In the DMFA, since all the crossing Feynman diagrams for the hole-impurity interaction vanish, the problem simplifies to the local diagrams for the holes scattering off of a single Mn impurity site only. The diagrammatics for the self-energy reduces to the local Green functions and potentials in the non-chiral basis in which they have very simple forms. We first calculate the initial green function G(k) in the chiral basis and then rotate G(k) back into the non chiral basis and coarse grain it over all the k momenta. The hole-impurity interaction is greatly simplified in the non-chiral basis and can be averaged over all the spin configurations and orientations of the Mn atoms on the lattice.The self energy may be extracted from the averaged Green function, and used to recalculate the initial cluster Green function, etc. completing the DMFA self-consistent loop. We intend to calculate the spin and charge transport coefficients, and spectra such as the AC susceptibility and the ARPES which may be directly compared with experiment. [1] Phys. Rev. Lett.89,047201/1-4 (2002)

Scattering from arbitrarily shaped microstrip patch antennas

NASA Technical Reports Server (NTRS)

Shively, David G.; Deshpande, Manohar D.; Cockrell, Capers R.

1992-01-01

The scattering properties of arbitrarily shaped microstrip patch antennas are examined. The electric field integral equation for a current element on a grounded dielectric slab is developed for a rectangular geometry based on Galerkin's technique with subdomain rooftop basis functions. A shape function is introduced that allows a rectangular grid approximation to the arbitrarily shaped patch. The incident field on the patch is expressed as a function of incidence angle theta(i), phi(i). The resulting system of equations is then solved for the unknown current modes on the patch, and the electromagnetic scattering is calculated for a given angle. Comparisons are made with other calculated results as well as with measurements.

[Functional condition of the spine in female workers in the cotton-processing industry evaluated on the basis of subjective and radiological studies].

PubMed

Split, W; Kotwica, S

1987-01-01

Studies involved 179 weaving and 173 spinning women. All of them underwent functional tests of the spine supported by X-ray tests. In approximately 45% of weavers and 29% of spinners functional disturbances in the lower segment of the spine were found. The incidence of the motorial disturbances of the spine was found to increase with age. The analysis of the impact of employment length upon the rate of motorial disturbances demonstrated that the disturbances occurred within the first years of work and reached the highest level after 10 years.

Vertical spatial coherence model for a transient signal forward-scattered from the sea surface

USGS Publications Warehouse

Yoerger, E.J.; McDaniel, S.T.

1996-01-01

The treatment of acoustic energy forward scattered from the sea surface, which is modeled as a random communications scatter channel, is the basis for developing an expression for the time-dependent coherence function across a vertical receiving array. The derivation of this model uses linear filter theory applied to the Fresnel-corrected Kirchhoff approximation in obtaining an equation for the covariance function for the forward-scattered problem. The resulting formulation is used to study the dependence of the covariance on experimental and environmental factors. The modeled coherence functions are then formed for various geometrical and environmental parameters and compared to experimental data.

Calculation of photoionization differential cross sections using complex Gauss-type orbitals.

PubMed

Matsuzaki, Rei; Yabushita, Satoshi

2017-09-05

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Hyperfine coupling constants of the nitrogen and phosphorus atoms: A challenge for exact-exchange density-functional and post-Hartree-Fock methods

NASA Astrophysics Data System (ADS)

Kaupp, Martin; Arbuznikov, Alexei V.; Heßelmann, Andreas; Görling, Andreas

2010-05-01

The isotropic hyperfine coupling constants of the free N(S4) and P(S4) atoms have been evaluated with high-level post-Hartree-Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree-Fock or numerical OEP data. Results from the localized Hartree-Fock and Krieger-Li-Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(S4) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified.

Macrocell path loss prediction using artificial intelligence techniques

NASA Astrophysics Data System (ADS)

Usman, Abraham U.; Okereke, Okpo U.; Omizegba, Elijah E.

2014-04-01

The prediction of propagation loss is a practical non-linear function approximation problem which linear regression or auto-regression models are limited in their ability to handle. However, some computational Intelligence techniques such as artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs) have been shown to have great ability to handle non-linear function approximation and prediction problems. In this study, the multiple layer perceptron neural network (MLP-NN), radial basis function neural network (RBF-NN) and an ANFIS network were trained using actual signal strength measurement taken at certain suburban areas of Bauchi metropolis, Nigeria. The trained networks were then used to predict propagation losses at the stated areas under differing conditions. The predictions were compared with the prediction accuracy of the popular Hata model. It was observed that ANFIS model gave a better fit in all cases having higher R2 values in each case and on average is more robust than MLP and RBF models as it generalises better to a different data.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory.

PubMed

Sissay, Adonay; Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J; Lopata, Kenneth

2016-09-07

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory

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

Sissay, Adonay; Abanador, Paul; Mauger, François

2016-09-07

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagatingmore » the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.« less

Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory.

PubMed

Simmen, Benjamin; Mátyus, Edit; Reiher, Markus

2014-10-21

This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X (1)Σ(g)(+) and B (1)Σ(u)(+) electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.

Adaptive robust control of a class of non-affine variable-speed variable-pitch wind turbines with unmodeled dynamics.

PubMed

Bagheri, Pedram; Sun, Qiao

2016-07-01

In this paper, a novel synthesis of Nussbaum-type functions, and an adaptive radial-basis function neural network is proposed to design controllers for variable-speed, variable-pitch wind turbines. Dynamic equations of the wind turbine are highly nonlinear, uncertain, and affected by unknown disturbance sources. Furthermore, the dynamic equations are non-affine with respect to the pitch angle, which is a control input. To address these problems, a Nussbaum-type function, along with a dynamic control law are adopted to resolve the non-affine nature of the equations. Moreover, an adaptive radial-basis function neural network is designed to approximate non-parametric uncertainties. Further, the closed-loop system is made robust to unknown disturbance sources, where no prior knowledge of disturbance bound is assumed in advance. Finally, the Lyapunov stability analysis is conducted to show the stability of the entire closed-loop system. In order to verify analytical results, a simulation is presented and the results are compared to both a PI and an existing adaptive controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1997-01-01

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.

PubMed

Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai

2017-11-01

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.

An adaptive trajectory tracking control of four rotor hover vehicle using extended normalized radial basis function network

NASA Astrophysics Data System (ADS)

ul Amin, Rooh; Aijun, Li; Khan, Muhammad Umer; Shamshirband, Shahaboddin; Kamsin, Amirrudin

2017-01-01

In this paper, an adaptive trajectory tracking controller based on extended normalized radial basis function network (ENRBFN) is proposed for 3-degree-of-freedom four rotor hover vehicle subjected to external disturbance i.e. wind turbulence. Mathematical model of four rotor hover system is developed using equations of motions and a new computational intelligence based technique ENRBFN is introduced to approximate the unmodeled dynamics of the hover vehicle. The adaptive controller based on the Lyapunov stability approach is designed to achieve tracking of the desired attitude angles of four rotor hover vehicle in the presence of wind turbulence. The adaptive weight update based on the Levenberg-Marquardt algorithm is used to avoid weight drift in case the system is exposed to external disturbances. The closed-loop system stability is also analyzed using Lyapunov stability theory. Simulations and experimental results are included to validate the effectiveness of the proposed control scheme.

Spectrally-Invariant Approximation Within Atmospheric Radiative Transfer

NASA Technical Reports Server (NTRS)

Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.

2011-01-01

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These "spectrally invariant relationships" are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in clouddominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction. and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with ID radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Ab initio molecular dynamics simulation study of successive hydrogenation reactions of carbon monoxide producing methanol

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

Pham, Thi Nu; Ono, Shota; Ohno, Kaoru, E-mail: ohno@ynu.ac.jp

Doing ab initio molecular dynamics simulations, we demonstrate a possibility of hydrogenation of carbon monoxide producing methanol step by step. At first, the hydrogen atom reacts with the carbon monoxide molecule at the excited state forming the formyl radical. Formaldehyde was formed after adding one more hydrogen atom to the system. Finally, absorption of two hydrogen atoms to formaldehyde produces methanol molecule. This study is performed by using the all-electron mixed basis approach based on the time dependent density functional theory within the adiabatic local density approximation for an electronic ground-state configuration and the one-shot GW approximation for an electronicmore » excited state configuration.« less

Z-dependence of mean excitation energies for second and third row atoms and their ions

NASA Astrophysics Data System (ADS)

Sauer, Stephan P. A.; Sabin, John R.; Oddershede, Jens

2018-05-01

All mean excitation energies for second and third row atoms and their ions are calculated in the random-phase approximation using large basis sets. To a very good approximation, it turns out that mean excitation energies within an isoelectronic series are a quadratic function of the nuclear charge. It is demonstrated that this behavior is linked to the fact that the contributions from continuum electronic states give the dominate contributions to the mean excitation energies and that these contributions for atomic ions appear hydrogen-like. We argue that this finding may present a method to get a first estimate of mean excitation energies also for other non-relativistic atomic ions.

Conformational effect of dicyclo-hexano-18-crown-6 on isotopic fractionation of zinc: DFT approach

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

Boda, A.; Singha Deb, A. K.; Ali, Sk. M.

2014-04-24

Generalized gradient approximated BP86 density functional employing triple zeta valence plus polarization (TZVP) basis set has been used to compute the reduced partition function ratio and isotopic separation factor for zinc isotopes. The isotopic separation factor was found to be in good agreement with the experimental results. The isotopic separation factor was found to depend on the conformation of the crown ether ligand. The trans-trans conformation shows the highest fractionation compared to cis-cis conformer. The present theoretical results can thus be used to plan the isotope separation experiments.

Drift of Phase Fluctuations in the ABC Model

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Buttà, Paolo

2013-07-01

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric function of the three densities. The antisymmetry of the drift can also be inferred from a symmetry property of the underlying microscopic dynamics.

Light-propagation management in coupled waveguide arrays: Quantitative experimental and theoretical assessment from band structures to functional patterns

NASA Astrophysics Data System (ADS)

Moison, Jean-Marie; Belabas, Nadia; Levenson, Juan Ariel; Minot, Christophe

2012-09-01

We assess the band structure of arrays of coupled optical waveguides both by ab initio calculations and by experiments, with an excellent quantitative agreement without any adjustable physical parameter. The band structures we obtain can deviate strongly from the expectations of the standard coupled mode theory approximation, but we describe them efficiently by a few parameters within an extended coupled mode theory. We also demonstrate that this description is in turn a firm and simple basis for accurate beam management in functional patterns of coupled waveguides, in full accordance with their design.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

NASA Astrophysics Data System (ADS)

Schäfer, Tobias; Ramberger, Benjamin; Kresse, Georg

2017-03-01

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O ( N 4 ) , with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2017-09-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

NASA Astrophysics Data System (ADS)

Nourgaliev, Robert

2015-11-01

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and funded by the LDRD at LLNL under project tracking code 13-SI-002.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2018-07-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

NASA Astrophysics Data System (ADS)

Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.

2017-05-01

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

Overset grid implementation of the complex Kohn variational method for electron-polyatomic molecule scattering

NASA Astrophysics Data System (ADS)

McCurdy, C. William; Lucchese, Robert L.; Greenman, Loren

2017-04-01

The complex Kohn variational method, which represents the continuum wave function in each channel using a combination of Gaussians and Bessel or Coulomb functions, has been successful in numerous applications to electron-polyatomic molecule scattering and molecular photoionization. The hybrid basis representation limits it to relatively low energies (< 50 eV) , requires an approximation to exchange matrix elements involving continuum functions, and hampers its coupling to modern electronic structure codes for the description of correlated target states. We describe a successful implementation of the method using completely adaptive overset grids to describe continuum functions, in which spherical subgrids are placed on every atomic center to complement a spherical master grid that describes the behavior at large distances. An accurate method for applying the free-particle Green's function on the grid eliminates the need to operate explicitly with the kinetic energy, enabling a rapidly convergent Arnoldi algorithm for solving linear equations on the grid, and no approximations to exchange operators are made. Results for electron scattering from several polyatomic molecules will be presented. Army Research Office, MURI, WN911NF-14-1-0383 and U. S. DOE DE-SC0012198 (at Texas A&M).

Dimensionality and noise in energy selective x-ray imaging

PubMed Central

Alvarez, Robert E.

2013-01-01

Purpose: To develop and test a method to quantify the effect of dimensionality on the noise in energy selective x-ray imaging. Methods: The Cramèr-Rao lower bound (CRLB), a universal lower limit of the covariance of any unbiased estimator, is used to quantify the noise. It is shown that increasing dimensionality always increases, or at best leaves the same, the variance. An analytic formula for the increase in variance in an energy selective x-ray system is derived. The formula is used to gain insight into the dependence of the increase in variance on the properties of the additional basis functions, the measurement noise covariance, and the source spectrum. The formula is also used with computer simulations to quantify the dependence of the additional variance on these factors. Simulated images of an object with three materials are used to demonstrate the trade-off of increased information with dimensionality and noise. The images are computed from energy selective data with a maximum likelihood estimator. Results: The increase in variance depends most importantly on the dimension and on the properties of the additional basis functions. With the attenuation coefficients of cortical bone, soft tissue, and adipose tissue as the basis functions, the increase in variance of the bone component from two to three dimensions is 1.4 × 103. With the soft tissue component, it is 2.7 × 104. If the attenuation coefficient of a high atomic number contrast agent is used as the third basis function, there is only a slight increase in the variance from two to three basis functions, 1.03 and 7.4 for the bone and soft tissue components, respectively. The changes in spectrum shape with beam hardening also have a substantial effect. They increase the variance by a factor of approximately 200 for the bone component and 220 for the soft tissue component as the soft tissue object thickness increases from 1 to 30 cm. Decreasing the energy resolution of the detectors increases the variance of the bone component markedly with three dimension processing, approximately a factor of 25 as the resolution decreases from 100 to 3 bins. The increase with two dimension processing for adipose tissue is a factor of two and with the contrast agent as the third material for two or three dimensions is also a factor of two for both components. The simulated images show that a maximum likelihood estimator can be used to process energy selective x-ray data to produce images with noise close to the CRLB. Conclusions: The method presented can be used to compute the effects of the object attenuation coefficients and the x-ray system properties on the relationship of dimensionality and noise in energy selective x-ray imaging systems. PMID:24320442

ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy

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

Mardirossian, Narbe; Head-Gordon, Martin

2013-12-18

A 10-parameter, range-separated hybrid (RSH), generalized gradient approximation (GGA) density functional with nonlocal correlation (VV10) is presented in this paper. Instead of truncating the B97-type power series inhomogeneity correction factors (ICF) for the exchange, same-spin correlation, and opposite-spin correlation functionals uniformly, all 16 383 combinations of the linear parameters up to fourth order (m = 4) are considered. These functionals are individually fit to a training set and the resulting parameters are validated on a primary test set in order to identify the 3 optimal ICF expansions. Through this procedure, it is discovered that the functional that performs best onmore » the training and primary test sets has 7 linear parameters, with 3 additional nonlinear parameters from range-separation and nonlocal correlation. The resulting density functional, ωB97X-V, is further assessed on a secondary test set, the parallel-displaced coronene dimer, as well as several geometry datasets. Finally and furthermore, the basis set dependence and integration grid sensitivity of ωB97X-V are analyzed and documented in order to facilitate the use of the functional.« less

Approximation abilities of neuro-fuzzy networks

NASA Astrophysics Data System (ADS)

Mrówczyńska, Maria

2010-01-01

The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.

Calibration of AIS Data Using Ground-based Spectral Reflectance Measurements

NASA Technical Reports Server (NTRS)

Conel, J. E.

1985-01-01

Present methods of correcting airborne imaging spectrometer (AIS) data for instrumental and atmospheric effects include the flat- or curved-field correction and a deviation-from-the-average adjustment performed on a line-by-line basis throughout the image. Both methods eliminate the atmospheric absorptions, but remove the possibility of studying the atmosphere for its own sake, or of using the atmospheric information present as a possible basis for theoretical modeling. The method discussed here relies on use of ground-based measurements of the surface spectral reflectance in comparison with scanner data to fix in a least-squares sense parameters in a simplified model of the atmosphere on a wavelength-by-wavelength basis. The model parameters (for optically thin conditions) are interpretable in terms of optical depth and scattering phase function, and thus, in principle, provide an approximate description of the atmosphere as a homogeneous body intervening between the sensor and the ground.

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.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters

DOE PAGES

Bruneval, Fabien; Rangel, Tonatiuh; Hamed, Samia M.; ...

2016-07-12

Here, we summarize the MOLGW code that implements density-functional theory and many-body perturbation theory in a Gaussian basis set. The code is dedicated to the calculation of the many-body self-energy within the GW approximation and the solution of the Bethe–Salpeter equation. These two types of calculations allow the user to evaluate physical quantities that can be compared to spectroscopic experiments. Quasiparticle energies, obtained through the calculation of the GW self-energy, can be compared to photoemission or transport experiments, and neutral excitation energies and oscillator strengths, obtained via solution of the Bethe–Salpeter equation, are measurable by optical absorption. The implementation choicesmore » outlined here have aimed at the accuracy and robustness of calculated quantities with respect to measurements. Furthermore, the algorithms implemented in MOLGW allow users to consider molecules or clusters containing up to 100 atoms with rather accurate basis sets, and to choose whether or not to apply the resolution-of-the-identity approximation. Finally, we demonstrate the parallelization efficacy of the MOLGW code over several hundreds of processors.« less

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

NASA Astrophysics Data System (ADS)

Champagne, Benoı̂t; Botek, Edith; Nakano, Masayoshi; Nitta, Tomoshige; Yamaguchi, Kizashi

2005-03-01

The basis set and electron correlation effects on the static polarizability (α) and second hyperpolarizability (γ) are investigated ab initio for two model open-shell π-conjugated systems, the C5H7 radical and the C6H8 radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C6H8 whereas diffuse functions are compulsory for C5H7, in particular, p diffuse functions. In addition to the 6-31G*+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for α and γ of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order Møller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Møller-Plesset method, provide for both compounds γ values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged α and γ values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of α and γ have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.

Hybrid Grid and Basis Set Approach to Quantum Chemistry DMRG

NASA Astrophysics Data System (ADS)

Stoudenmire, Edwin Miles; White, Steven

We present a new approach for using DMRG for quantum chemistry that combines the advantages of a basis set with that of a grid approximation. Because DMRG scales linearly for quasi-one-dimensional systems, it is feasible to approximate the continuum with a fine grid in one direction while using a standard basis set approach for the transverse directions. Compared to standard basis set methods, we reach larger systems and achieve better scaling when approaching the basis set limit. The flexibility and reduced costs of our approach even make it feasible to incoporate advanced DMRG techniques such as simulating real-time dynamics. Supported by the Simons Collaboration on the Many-Electron Problem.

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

Association/Dissociation Processes in Dense Gases.

DTIC Science & Technology

1985-08-16

temperature 0 and generally lies 1 0 ke below the dissociation limit (taken as zero energy). The central block E of highly excited " bound levels is...approximate solution of (1.1) with general V(R) "* a large body of literature (see ref. 7) exists on various schemes based on Green’s function,8...be obtained for general mass systems provided the new basic expression introduced here - for RAD(t) is adopted. A The microscopic basis of the

Valores, Creencias Y Objectivos: Base del programa de la Escuela Experimental P.K. Yonge. (Values, Beliefs and Objectives: The Basis of Experimental Schools P.K. Yonge's Program.)

ERIC Educational Resources Information Center

Florida Univ., Gainesville. Coll. of Education.

The values, beliefs, and objectives that form the core of the program at the Experimental School P.K. Yonge in the University of Florida are presented in this paper which is written in Spanish. This experimental school serves approximately 900 students from grades one through twelve. The function of the school is to conduct research to solve…

The energy spectrum and the optical absorption spectrum of C{sub 60} fullerene within the Hubbard model

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

Silant’ev, A. V., E-mail: kvvant@rambler.ru

2015-10-15

Anticommutator Green’s functions and the energy spectrum of C{sub 60} fullerene are calculated in the approximation of static fluctuations within the Hubbard model. On the basis of this spectrum, an interpretation is proposed for the experimentally observed optical absorption bands of C{sub 60} fullerene. The parameters of C{sub 60} fullerene that characterize it within the Hubbard model are calculated by the optical absorption spectrum.

Retrieval of ammonia abundances and cloud opacities on Jupiter from Voyager IRIS spectra

NASA Technical Reports Server (NTRS)

Conrath, B. J.; Gierasch, P. J.

1986-01-01

Gaseous ammonia abundances and cloud opacities are retrieved from Voyager IRIS 5- and 45-micron data on the basis of a simplified atmospheric model and a two-stream radiative transfer approximation, assuming a single cloud layer with 680-mbar base pressure and 0.14 gas scale height. Brightness temperature measurements obtained as a function of emission angle from selected planetary locations are used to verify the model and constrain a number of its parameters.

Fuzziness In Approximate And Common-Sense Reasoning In Knowledge-Based Robotics Systems

NASA Astrophysics Data System (ADS)

Dodds, David R.

1987-10-01

Fuzzy functions, a major key to inexact reasoning, are described as they are applied to the fuzzification of robot co-ordinate systems. Linguistic-variables, a means of labelling ranges in fuzzy sets, are used as computationally pragmatic means of representing spatialization metaphors, themselves an extraordinarily rich basis for understanding concepts in orientational terms. Complex plans may be abstracted and simplified in a system which promotes conceptual planning by means of the orientational representation.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

NASA Astrophysics Data System (ADS)

Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

2013-06-01

We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the transformed harmonic oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single- particle basis to expand quasi-particle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogoliubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions until a self-consistent solution is found. A previous version of the program was presented in: M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Reasons for new version: Version 2.00d of HFBTHO provides a number of new options such as the optional breaking of reflection symmetry, the calculation of axial multipole moments, the finite temperature formalism for the HFB method, optimized multi-constraint calculations, the treatment of odd-even and odd-odd nuclei in the blocking approximation, and the framework for generalized energy density with arbitrary density-dependences. It is also the first version of HFBTHO to contain threading capabilities. Summary of revisions: The modified Broyden method has been implemented, Optional breaking of reflection symmetry has been implemented, The calculation of all axial multipole moments up to λ=8 has been implemented, The finite temperature formalism for the HFB method has been implemented, The linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations has been implemented, The blocking of quasi-particles in the Equal Filling Approximation (EFA) has been implemented, The framework for generalized energy density functionals with arbitrary density-dependence has been implemented, Shared memory parallelism via OpenMP pragmas has been implemented. Restrictions: Axial- and time-reversal symmetries are assumed. Unusual features: The user must have access to the LAPACK subroutines DSYEVD, DSYTRF and DSYTRI, and their dependences, which compute eigenvalues and eigenfunctions of real symmetric matrices, the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/. Running time: Highly variable, as it depends on the nucleus, size of the basis, requested accuracy, requested configuration, compiler and libraries, and hardware architecture. An order of magnitude would be a few seconds for ground-state configurations in small bases N≈8-12, to a few minutes in very deformed configuration of a heavy nucleus with a large basis N>20.

Gaussian Radial Basis Function for Efficient Computation of Forest Indirect Illumination

NASA Astrophysics Data System (ADS)

Abbas, Fayçal; Babahenini, Mohamed Chaouki

2018-06-01

Global illumination of natural scenes in real time like forests is one of the most complex problems to solve, because the multiple inter-reflections between the light and material of the objects composing the scene. The major problem that arises is the problem of visibility computation. In fact, the computing of visibility is carried out for all the set of leaves visible from the center of a given leaf, given the enormous number of leaves present in a tree, this computation performed for each leaf of the tree which also reduces performance. We describe a new approach that approximates visibility queries, which precede in two steps. The first step is to generate point cloud representing the foliage. We assume that the point cloud is composed of two classes (visible, not-visible) non-linearly separable. The second step is to perform a point cloud classification by applying the Gaussian radial basis function, which measures the similarity in term of distance between each leaf and a landmark leaf. It allows approximating the visibility requests to extract the leaves that will be used to calculate the amount of indirect illumination exchanged between neighbor leaves. Our approach allows efficiently treat the light exchanges in the scene of a forest, it allows a fast computation and produces images of good visual quality, all this takes advantage of the immense power of computation of the GPU.

Robust/optimal temperature profile control of a high-speed aerospace vehicle using neural networks.

PubMed

Yadav, Vivek; Padhi, Radhakant; Balakrishnan, S N

2007-07-01

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A 1-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

The moving-least-squares-particle hydrodynamics method (MLSPH)

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

Dilts, G.

1997-12-31

An enhancement of the smooth-particle hydrodynamics (SPH) method has been developed using the moving-least-squares (MLS) interpolants of Lancaster and Salkauskas which simultaneously relieves the method of several well-known undesirable behaviors, including spurious boundary effects, inaccurate strain and rotation rates, pressure spikes at impact boundaries, and the infamous tension instability. The classical SPH method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of motion for continua using as basis functions the SPH kernel function multiplied by the particle volume. This derivation is then modified by simply substituting the MLS interpolants for themore » SPH Galerkin basis, taking care to redefine the particle volume and mass appropriately. The familiar SPH kernel approximation is now equivalent to a colocation-Galerkin method. Both classical conservative and recent non-conservative formulations of SPH can be derived and emulated. The non-conservative forms can be made conservative by adding terms that are zero within the approximation at the expense of boundary-value considerations. The familiar Monaghan viscosity is used. Test calculations of uniformly expanding fluids, the Swegle example, spinning solid disks, impacting bars, and spherically symmetric flow illustrate the superiority of the technique over SPH. In all cases it is seen that the marvelous ability of the MLS interpolants to add up correctly everywhere civilizes the noisy, unpredictable nature of SPH. Being a relatively minor perturbation of the SPH method, it is easily retrofitted into existing SPH codes. On the down side, computational expense at this point is significant, the Monaghan viscosity undoes the contribution of the MLS interpolants, and one-point quadrature (colocation) is not accurate enough. Solutions to these difficulties are being pursued vigorously.« less

On the nature of interactions in the F2 OXe(…) NCCH3 complex: Is there the Xe(IV)N bond?

PubMed

Makarewicz, Emilia; Lundell, Jan; Gordon, Agnieszka J; Berski, Slawomir

2016-07-01

Nature of the bonding in isolated XeOF2 molecule and F2 OXe(…) NCCH3 complexes have been studied in the gas phase (0 K) using Quantum Chemical Topology methods. The wave functions have been approximated at the MP2 and DFT levels of calculations, using the APFD, B3LYP, M062X, and B2PLYP functionals with the GD3 dispersion correction. The nature of the formal XeO bond in the XeOF2 monomer depends on the basis set used (all-electron vs. the ecp-28 approximation for Xe). Within the all-electron basis set approach the bond is represented by two bonding attractors, Vi = 1,2 (Xe,O), with total population of about 1.06e and highly delocalized electron density in both bonding basins. No bonding basins are observed using the ecp-28 approximation. These results shows that the nature of xenon-oxygen is complicated and may be described with mesomeric equilibrium of the Lewis representations: Xe((+)) O((-)) and Xe((-)) O((+)) . For both the xenon-oxygen and xenon-fluorine interactions the charge-shift model can be applied. The F2 OXe(…) NCCH3 complex exists in two structures: "parallel," stabilized by non-covalent C(…) O and Xe(…) N interactions and "linear" stabilized by the Xe(…) N interaction. Topological analysis of ELF shows that the F2 OXe(…) NCCH3 molecule appears as a weakly bound intermolecular complex. Intermolecular interaction energy components have also been studied using Symmetry Adapted Perturbation Theory. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Attractive electron-electron interactions within robust local fitting approximations.

PubMed

Merlot, Patrick; Kjærgaard, Thomas; Helgaker, Trygve; Lindh, Roland; Aquilante, Francesco; Reine, Simen; Pedersen, Thomas Bondo

2013-06-30

An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree-Fock and Kohn-Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. Copyright © 2013 Wiley Periodicals, Inc.

Adaptive sliding control of non-autonomous active suspension systems with time-varying loadings

NASA Astrophysics Data System (ADS)

Chen, Po-Chang; Huang, An-Chyau

2005-04-01

An adaptive sliding controller is proposed in this paper for controlling a non-autonomous quarter-car suspension system with time-varying loadings. The bound of the car-body loading is assumed to be available. Then, the reference coordinate is placed at the static position under the nominal loading so that the system dynamic equation is derived. Due to spring nonlinearities, the system property becomes asymmetric after coordinate transformation. Besides, in practical cases, system parameters are not easy to be obtained precisely for controller design. Therefore, in this paper, system uncertainties are lumped into two unknown time-varying functions. Since the variation bound of one of the unknown functions is not available, conventional adaptive schemes and robust designs are not applicable. To deal with this problem, the function approximation technique is employed to represent the unknown function as a finite combination of basis functions. The Lyapunov direct method can thus be used to find adaptive laws for updating coefficients in the approximating series and to prove stability of the closed-loop system. Since the position and velocity measurements of the unsprung mass are lumped into the unknown function, there is no need to install sensors on the axle and wheel assembly in the actual implementation. Simulation results are presented to show the performance of the proposed strategy.

Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

NASA Astrophysics Data System (ADS)

Khosravian-Arab, Hassan; Dehghan, Mehdi; Eslahchi, M. R.

2017-06-01

This paper is intended to provide exponentially accurate Galerkin, Petrov-Galerkin and pseudo-spectral methods for fractional differential equations on a semi-infinite interval. We start our discussion by introducing two new non-classical Lagrange basis functions: NLBFs-1 and NLBFs-2 which are based on the two new families of the associated Laguerre polynomials: GALFs-1 and GALFs-2 obtained recently by the authors in [28]. With respect to the NLBFs-1 and NLBFs-2, two new non-classical interpolants based on the associated- Laguerre-Gauss and Laguerre-Gauss-Radau points are introduced and then fractional (pseudo-spectral) differentiation (and integration) matrices are derived. Convergence and stability of the new interpolants are proved in detail. Several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives (and integrals) of some functions. Moreover, the pseudo-spectral, Galerkin and Petrov-Galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones. Some useful comments from the numerical point of view on Galerkin and Petrov-Galerkin methods are listed at the end.

Geometric Mechanics for Continuous Swimmers on Granular Material

NASA Astrophysics Data System (ADS)

Dai, Jin; Faraji, Hossein; Schiebel, Perrin; Gong, Chaohui; Travers, Matthew; Hatton, Ross; Goldman, Daniel; Choset, Howie; Biorobotics Lab Collaboration; LaboratoryRobotics; Applied Mechanics (LRAM) Collaboration; Complex Rheology; Biomechanics Lab Collaboration

Animal experiments have shown that Chionactis occipitalis(N =10) effectively undulating on granular substrates exhibits a particular set of waveforms which can be approximated by a sinusoidal variation in curvature, i.e., a serpenoid wave. Furthermore, all snakes tested used a narrow subset of all available waveform parameters, measured as the relative curvature equal to 5.0+/-0.3, and number of waves on the body equal to1.8+/-0.1. We hypothesize that the serpenoid wave of a particular choice of parameters offers distinct benefit for locomotion on granular material. To test this hypothesis, we used a physical model (snake robot) to empirically explore the space of serpenoid motions, which is linearly spanned with two independent continuous serpenoid basis functions. The empirically derived height function map, which is a geometric mechanics tool for analyzing movements of cyclic gaits, showed that displacement per gait cycle increases with amplitude at small amplitudes, but reaches a peak value of 0.55 body-lengths at relative curvature equal to 6.0. This work signifies that with shape basis functions, geometric mechanics tools can be extended for continuous swimmers.

Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

PubMed

Chen, Zhenhua; Hoffmann, Mark R

2012-07-07

A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4, and BeH(2), are performed in order to test the new methods on problems where full configuration interaction results are available.

Sparsest representations and approximations of an underdetermined linear system

NASA Astrophysics Data System (ADS)

Tardivel, Patrick J. C.; Servien, Rémi; Concordet, Didier

2018-05-01

In an underdetermined linear system of equations, constrained l 1 minimization methods such as the basis pursuit or the lasso are often used to recover one of the sparsest representations or approximations of the system. The null space property is a sufficient and ‘almost’ necessary condition to recover a sparsest representation with the basis pursuit. Unfortunately, this property cannot be easily checked. On the other hand, the mutual coherence is an easily checkable sufficient condition insuring the basis pursuit to recover one of the sparsest representations. Because the mutual coherence condition is too strong, it is hardly met in practice. Even if one of these conditions holds, to our knowledge, there is no theoretical result insuring that the lasso solution is one of the sparsest approximations. In this article, we study a novel constrained problem that gives, without any condition, one of the sparsest representations or approximations. To solve this problem, we provide a numerical method and we prove its convergence. Numerical experiments show that this approach gives better results than both the basis pursuit problem and the reweighted l 1 minimization problem.

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method

NASA Astrophysics Data System (ADS)

Neese, Frank; Wennmohs, Frank; Hansen, Andreas

2009-03-01

Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol-1. Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chemical applications.

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method.

PubMed

Neese, Frank; Wennmohs, Frank; Hansen, Andreas

2009-03-21

Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Moller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol(-1). Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chemical applications.

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions

PubMed Central

Mester, Dávid

2017-01-01

A reduced-cost density fitting (DF) linear-response second-order coupled-cluster (CC2) method has been developed for the evaluation of excitation energies. The method is based on the simultaneous truncation of the molecular orbital (MO) basis and the auxiliary basis set used for the DF approximation. For the reduction of the size of the MO basis, state-specific natural orbitals (NOs) are constructed for each excited state using the average of the second-order Møller–Plesset (MP2) and the corresponding configuration interaction singles with perturbative doubles [CIS(D)] density matrices. After removing the NOs of low occupation number, natural auxiliary functions (NAFs) are constructed [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], and the NAF basis is also truncated. Our results show that, for a triple-zeta basis set, about 60% of the virtual MOs can be dropped, while the size of the fitting basis can be reduced by a factor of five. This results in a dramatic reduction of the computational costs of the solution of the CC2 equations, which are in our approach about as expensive as the evaluation of the MP2 and CIS(D) density matrices. All in all, an average speedup of more than an order of magnitude can be achieved at the expense of a mean absolute error of 0.02 eV in the calculated excitation energies compared to the canonical CC2 results. Our benchmark calculations demonstrate that the new approach enables the efficient computation of CC2 excitation energies for excited states of all types of medium-sized molecules composed of up to 100 atoms with triple-zeta quality basis sets. PMID:28527453

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

Neural network approach to quantum-chemistry data: accurate prediction of density functional theory energies.

PubMed

Balabin, Roman M; Lomakina, Ekaterina I

2009-08-21

Artificial neural network (ANN) approach has been applied to estimate the density functional theory (DFT) energy with large basis set using lower-level energy values and molecular descriptors. A total of 208 different molecules were used for the ANN training, cross validation, and testing by applying BLYP, B3LYP, and BMK density functionals. Hartree-Fock results were reported for comparison. Furthermore, constitutional molecular descriptor (CD) and quantum-chemical molecular descriptor (QD) were used for building the calibration model. The neural network structure optimization, leading to four to five hidden neurons, was also carried out. The usage of several low-level energy values was found to greatly reduce the prediction error. An expected error, mean absolute deviation, for ANN approximation to DFT energies was 0.6+/-0.2 kcal mol(-1). In addition, the comparison of the different density functionals with the basis sets and the comparison of multiple linear regression results were also provided. The CDs were found to overcome limitation of the QD. Furthermore, the effective ANN model for DFT/6-311G(3df,3pd) and DFT/6-311G(2df,2pd) energy estimation was developed, and the benchmark results were provided.

Ionic structures and transport properties of hot dense W and U plasmas

NASA Astrophysics Data System (ADS)

Hou, Yong; Yuan, Jianmin

2016-10-01

We have combined the average-atom model with the hyper-netted chain approximation (AAHNC) to describe the electronic and ionic structure of uranium and tungsten in the hot dense matter regime. When the electronic structure is described within the average-atom model, the effects of others ions on the electronic structure are considered by the correlation functions. And the ionic structure is calculated though using the hyper-netted chain (HNC) approximation. The ion-ion pair potential is calculated using the modified Gordon-Kim model based on the electronic density distribution in the temperature-depended density functional theory. And electronic and ionic structures are determined self-consistently. On the basis of the ion-ion pair potential, we perform the classical (CMD) and Langevin (LMD) molecular dynamics to simulate the ionic transport properties, such as ionic self-diffusion and shear viscosity coefficients, through the ionic velocity correlation functions. Due that the free electrons become more and more with increasing the plasma temperature, the influence of the electron-ion collisions on the transport properties become more and more important.

Blending Velocities In Task Space In Computing Robot Motions

NASA Technical Reports Server (NTRS)

Volpe, Richard A.

1995-01-01

Blending of linear and angular velocities between sequential specified points in task space constitutes theoretical basis of improved method of computing trajectories followed by robotic manipulators. In method, generalized velocity-vector-blending technique provides relatively simple, common conceptual framework for blending linear, angular, and other parametric velocities. Velocity vectors originate from straight-line segments connecting specified task-space points, called "via frames" and represent specified robot poses. Linear-velocity-blending functions chosen from among first-order, third-order-polynomial, and cycloidal options. Angular velocities blended by use of first-order approximation of previous orientation-matrix-blending formulation. Angular-velocity approximation yields small residual error, quantified and corrected. Method offers both relative simplicity and speed needed for generation of robot-manipulator trajectories in real time.

Stimulated neutrino transformation through turbulence

DOE PAGES

Patton, Kelly M.; Kneller, James P.; McLaughlin, Gail C.

2014-04-30

We derive an analytical solution for the flavor evolution of a neutrino through a turbulent density profile which is found to accurately predict the amplitude and transition wavelength of numerical solutions on a case-by-case basis. The evolution is seen to strongly depend upon those Fourier modes in the turbulence which are approximately the same as the splitting between neutrino eigenvalues. Transitions are strongly enhanced by those Fourier modes in the turbulence which are approximately the same as the splitting between neutrino eigenvalues. Lastly, we also find a suppression of transitions due to the long wavelength modes when the ratio ofmore » their amplitude and the wavenumber is of order, or greater than, the first root of the Bessel function J 0.« less

Approximate techniques of structural reanalysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lowder, H. E.

1974-01-01

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Significance tests for functional data with complex dependence structure.

PubMed

Staicu, Ana-Maria; Lahiri, Soumen N; Carroll, Raymond J

2015-01-01

We propose an L 2 -norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups-clusters or subjects-units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients. The asymptotic null distribution of the test statistic is developed, under mild regularity conditions. To our knowledge this is the first work that studies hypothesis testing, when data have such complex multilevel functional and spatial structure. Two small-sample alternatives, including a novel block bootstrap for functional data, are proposed, and their performance is examined in simulation studies. The paper concludes with an illustration of a motivating experiment.

Jacob's Ladder as Sketched by Escher: Assessing the Performance of Broadly Used Density Functionals on Transition Metal Surface Properties.

PubMed

Vega, Lorena; Ruvireta, Judit; Viñes, Francesc; Illas, Francesc

2018-01-09

The present work surveys the performance of various widely used density functional theory exchange-correlation (xc) functionals in describing observable surface properties of a total of 27 transition metals with face-centered cubic (fcc), body-centered cubic (bcc), or hexagonal close-packed (hcp) crystallographic structures. A total of 81 low Miller index surfaces were considered employing slab models. Exemplary xc functionals within the three first rungs of Jacob's ladder were considered, including the Vosko-Wilk-Nusair xc functional within the local density approximation, the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria functional as a meta-GGA functional. Hybrids were excluded in the survey because they are known to fail in properly describing metallic systems. In addition, two variants of PBE were considered, PBE adapted for solids (PBEsol) and revised PBE (RPBE), aimed at improving adsorption energies. Interlayer atomic distances, surface energies, and surface work functions were chosen as the scrutinized properties. A comparison with available experimental data, including single-crystal and polycrystalline values, shows that no xc functional is best at describing all of the surface properties. However, in statistical mean terms the PBEsol xc functional is advised, while PBE is recommended when considering both bulk and surface properties. On the basis of the present results, a discussion of adapting GGA functionals to the treatment of metallic surfaces in an alternative way to meta-GGA or hybrids is provided.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Grid-free density functional calculations on periodic systems.

PubMed

Varga, Stefan

2007-09-21

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xalpha exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

Grid-free density functional calculations on periodic systems

NASA Astrophysics Data System (ADS)

Varga, Štefan

2007-09-01

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xα exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V

NASA Astrophysics Data System (ADS)

Mardirossian, Narbe; Head-Gordon, Martin

2015-02-01

A meta-generalized gradient approximation density functional paired with the VV10 nonlocal correlation functional is presented. The functional form is selected from more than 1010 choices carved out of a functional space of almost 1040 possibilities. Raw data come from training a vast number of candidate functional forms on a comprehensive training set of 1095 data points and testing the resulting fits on a comprehensive primary test set of 1153 data points. Functional forms are ranked based on their ability to reproduce the data in both the training and primary test sets with minimum empiricism, and filtered based on a set of physical constraints and an often-overlooked condition of satisfactory numerical precision with medium-sized integration grids. The resulting optimal functional form has 4 linear exchange parameters, 4 linear same-spin correlation parameters, and 4 linear opposite-spin correlation parameters, for a total of 12 fitted parameters. The final density functional, B97M-V, is further assessed on a secondary test set of 212 data points, applied to several large systems including the coronene dimer and water clusters, tested for the accurate prediction of intramolecular and intermolecular geometries, verified to have a readily attainable basis set limit, and checked for grid sensitivity. Compared to existing density functionals, B97M-V is remarkably accurate for non-bonded interactions and very satisfactory for thermochemical quantities such as atomization energies, but inherits the demonstrable limitations of existing local density functionals for barrier heights.

Probabilistic objective functions for sensor management

NASA Astrophysics Data System (ADS)

Mahler, Ronald P. S.; Zajic, Tim R.

2004-08-01

This paper continues the investigation of a foundational and yet potentially practical basis for control-theoretic sensor management, using a comprehensive, intuitive, system-level Bayesian paradigm based on finite-set statistics (FISST). In this paper we report our most recent progress, focusing on multistep look-ahead -- i.e., allocation of sensor resources throughout an entire future time-window. We determine future sensor states in the time-window using a "probabilistically natural" sensor management objective function, the posterior expected number of targets (PENT). This objective function is constructed using a new "maxi-PIMS" optimization strategy that hedges against unknowable future observation-collections. PENT is used in conjuction with approximate multitarget filters: the probability hypothesis density (PHD) filter or the multi-hypothesis correlator (MHC) filter.

Five- and six-electron harmonium atoms: Highly accurate electronic properties and their application to benchmarking of approximate 1-matrix functionals

NASA Astrophysics Data System (ADS)

Cioslowski, Jerzy; Strasburger, Krzysztof

2018-04-01

Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.

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

Trevisanutto, Paolo E.; Vignale, Giovanni, E-mail: vignaleg@missouri.edu

Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is “native” to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basicmore » tools of ab initio electronic structure theory — density functional theory, GW approximation and Bethe-Salpeter equation — are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.« less

Ab initio molecular simulations with numeric atom-centered orbitals

NASA Astrophysics Data System (ADS)

Blum, Volker; Gehrke, Ralf; Hanke, Felix; Havu, Paula; Havu, Ville; Ren, Xinguo; Reuter, Karsten; Scheffler, Matthias

2009-11-01

We describe a complete set of algorithms for ab initio molecular simulations based on numerically tabulated atom-centered orbitals (NAOs) to capture a wide range of molecular and materials properties from quantum-mechanical first principles. The full algorithmic framework described here is embodied in the Fritz Haber Institute "ab initio molecular simulations" (FHI-aims) computer program package. Its comprehensive description should be relevant to any other first-principles implementation based on NAOs. The focus here is on density-functional theory (DFT) in the local and semilocal (generalized gradient) approximations, but an extension to hybrid functionals, Hartree-Fock theory, and MP2/GW electron self-energies for total energies and excited states is possible within the same underlying algorithms. An all-electron/full-potential treatment that is both computationally efficient and accurate is achieved for periodic and cluster geometries on equal footing, including relaxation and ab initio molecular dynamics. We demonstrate the construction of transferable, hierarchical basis sets, allowing the calculation to range from qualitative tight-binding like accuracy to meV-level total energy convergence with the basis set. Since all basis functions are strictly localized, the otherwise computationally dominant grid-based operations scale as O(N) with system size N. Together with a scalar-relativistic treatment, the basis sets provide access to all elements from light to heavy. Both low-communication parallelization of all real-space grid based algorithms and a ScaLapack-based, customized handling of the linear algebra for all matrix operations are possible, guaranteeing efficient scaling (CPU time and memory) up to massively parallel computer systems with thousands of CPUs.

High-throughput analysis of spatio-temporal dynamics in Dictyostelium

PubMed Central

Sawai, Satoshi; Guan, Xiao-Juan; Kuspa, Adam; Cox, Edward C

2007-01-01

We demonstrate a time-lapse video approach that allows rapid examination of the spatio-temporal dynamics of Dictyostelium cell populations. Quantitative information was gathered by sampling life histories of more than 2,000 mutant clones from a large mutagenesis collection. Approximately 4% of the clonal lines showed a mutant phenotype at one stage. Many of these could be ordered by clustering into functional groups. The dataset allows one to search and retrieve movies on a gene-by-gene and phenotype-by-phenotype basis. PMID:17659086

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

Nesterov, V. A., E-mail: archerix@ukpost.ua

On the basis of the energy-density method, the effect of simultaneously taking into account the Pauli exclusion principle and the monopole and quadrupole polarizations of interacting nuclei on their interaction potential is considered for the example of the {sup 16}O + {sup 16}O system by using the wave function for the two-center shell model. The calculations performed in the adiabatic approximation reveal that the inclusion of the Pauli exclusion principle and the polarization of interacting nuclei, especially their quadrupole polarization, has a substantial effect on the potential of the nucleus-nucleus interaction.

Spectral and textural processing of ERTS imagery. [Kansas

NASA Technical Reports Server (NTRS)

Haralick, R. M.; Bosley, R. J.

1974-01-01

A procedure is developed to simultaneously extract textural features from all bands of ERTS multispectral scanner imagery for automatic analysis. Multi-images lead to excessively large grey tone N-tuple co-occurrence matrices; therefore, neighboring grey N-tuple differences are measured and an ellipsoidally symmetric functional form is assumed for the co-occurrence distribution of multiimage greytone N-tuple differences. On the basis of past data the ellipsoidally symmetric approximation is shown to be reasonable. Initial evaluation of the procedure is encouraging.

A Separable Insertion Method to Calculate Atomic and Molecular Resonances on a FE-DVR Grid using Exterior Complex Scaling

NASA Astrophysics Data System (ADS)

Abeln, Brant Anthony

The study of metastable electronic resonances, anion or neutral states of finite lifetime, in molecules is an important area of research where currently no theoretical technique is generally applicable. The role of theory is to calculate both the position and width, which is proportional to the inverse of the lifetime, of these resonances and how they vary with respect to nuclear geometry in order to generate potential energy surfaces. These surfaces are the basis of time-dependent models of the molecular dynamics where the system moves towards vibrational excitation or fragmentation. Three fundamental electronic processes that can be modeled this way are dissociative electronic attachment, vibrational excitation through electronic impact and autoionization. Currently, experimental investigation into these processes is being preformed on polyatomic molecules while theoreticians continue their fifty-year-old search for robust methods to calculate them. The separable insertion method, investigated in this thesis, seeks to tackle the problem of calculating metastable resonances by using existing quantum chemistry tools along with a grid-based method employing exterior complex scaling (ECS). Modern quantum chemistry methods are extremely efficient at calculating ground and (bound) excited electronic states of atoms and molecules by utilizing Gaussian basis functions. These functions provide both a numerically fast and analytic solution to the necessary two-electron, six-dimensional integrals required in structure calculations. However, these computer programs, based on analytic Gaussian basis sets, cannot construct solutions that are not square-integrable, such as resonance wavefunctions. ECS, on the other hand, can formally calculate resonance solutions by rotating the asymptotic electronic coordinates into the complex plane. The complex Siegert energies for resonances, Eres = ER - iGamma/2 where ER is the real-valued position of the resonance and Gamma is the width of the resonance, can be found directly as an isolated pole in the complex energy plane. Unlike the straight complex scaling, ECS on the electronic coordinates overcomes the non-analytic behavior of the nuclear attraction potential, as a function of complex [special characters omitted] where the sum is over each nucleus in a molecular system. Discouragingly, the Gaussian basis functions, which are computationally well-suited for bound electronic structure, fail at forming an effective basis set for ECS due to the derivative discontinuity generated by the complex coordinate rotation and the piecewise defined contour. This thesis seeks to explore methods for implementing ECS indirectly without losing the numerical simplicity and power of Gaussian basis sets. The separable insertion method takes advantage of existing software by constructing a N2-term separable potential of the target system using Gaussian functions to be inserted into a finite-element discrete variable representation (FE-DVR) grid that implements ECS. This work reports an exhaustive investigation into this approach for calculating resonances. This thesis shows that this technique is successful at describing an anion shape resonance of a closed-shell atom or molecule in the static-exchange approximation. This method is applied to the 2P Be-, 2pig N2- and 2pi u CO2- shape resonances to calculate their complex Seigert energies. Additionally, many details on the exact construction of the separable potential and of the expansion basis are explored. The future work considers methods for faster convergence of the resonance energy, moving beyond the static-exchange approximation and applying this technique to polyatomic systems of interest.

The organization of human epidermis: functional epidermal units and phi proportionality.

PubMed

Hoath, Steven B; Leahy, D G

2003-12-01

The concept that mammalian epidermis is structurally organized into functional epidermal units has been proposed on the basis of stratum corneum (SC) architecture, proliferation kinetics, melanocyte:keratinocyte ratios (1:36), and, more recently, Langerhans cell: epidermal cell ratios (1:53). This article examines the concept of functional epidermal units in human skin in which the maintenance of phi (1.618034) proportionality provides a central organizing principle. The following empirical measurements were used: 75,346 nucleated epidermal cells per mm2, 1394 Langerhans cells per mm2, 1999 melanocytes per mm2, 16 (SC) layers, 900-microm2 corneocyte surface area, 17,778 corneocytes per mm2, 14-d (SC) turnover time, and 93,124 per mm2 total epidermal cells. Given these empirical data: (1) the number of corneocytes is a mean proportional between the sum of the Langerhans cell + melanocyte populations and the number of epidermal cells, 3393/17,778-17,778/93,124; (2) the ratio of nucleated epidermal cells over corneocytes is phi proportional, 75,346/17,778 approximately phi3; (3) assuming similar 14-d turnover times for the (SC) and Malpighian epidermis, the number of corneocytes results from subtraction of a cellular fraction equal to approximately 2/phi2 x the number of living cells, 75,436 - (2/phi2 x 75,346) approximately 17,778; and (4) if total epidermal turnover time equals (SC) turnover time x the ratio of living/dead cells, then compartmental turnover times are unequal (14 d for (SC) to 45.3 d for nucleated epidermis approximately 1/2phi) and cellular replacement rates are 52.9 corneocytes/69.3 keratinocytes per mm2 per h approximately 2/phi2. These empirically derived equivalences provide logicomathematical support for the presence of functional epidermal units in human skin. Validation of a phi proportional unit architecture in human epidermis will be important for tissue engineering of skin and the design of instruments for skin measurement.

Discrete wavelet transform: a tool in smoothing kinematic data.

PubMed

Ismail, A R; Asfour, S S

1999-03-01

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.

Benchmark of Ab Initio Bethe-Salpeter Equation Approach with Numeric Atom-Centered Orbitals

NASA Astrophysics Data System (ADS)

Liu, Chi; Kloppenburg, Jan; Kanai, Yosuke; Blum, Volker

The Bethe-Salpeter equation (BSE) approach based on the GW approximation has been shown to be successful for optical spectra prediction of solids and recently also for small molecules. We here present an all-electron implementation of the BSE using numeric atom-centered orbital (NAO) basis sets. In this work, we present benchmark of BSE implemented in FHI-aims for low-lying excitation energies for a set of small organic molecules, the well-known Thiel's set. The difference between our implementation (using an analytic continuation of the GW self-energy on the real axis) and the results generated by a fully frequency dependent GW treatment on the real axis is on the order of 0.07 eV for the benchmark molecular set. We study the convergence behavior to the complete basis set limit for excitation spectra, using a group of valence correlation consistent NAO basis sets (NAO-VCC-nZ), as well as for standard NAO basis sets for ground state DFT with extended augmentation functions (NAO+aug). The BSE results and convergence behavior are compared to linear-response time-dependent DFT, where excellent numerical convergence is shown for NAO+aug basis sets.

Orientation-dependent integral equation theory for a two-dimensional model of water

NASA Astrophysics Data System (ADS)

Urbič, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

2003-03-01

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein-Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properties; for example, it does not predict liquid water's density maximum with temperature or the negative thermal expansion coefficient.

Stability of Hydrocarbons of the Polyhedrane Family: Convergence of ab Initio Calculations and Corresponding Assessment of DFT Main Approximations.

PubMed

Sancho-García, J C

2011-09-13

Highly accurate coupled-cluster (CC) calculations with large basis sets have been performed to study the binding energy of the (CH)12, (CH)16, (CH)20, and (CH)24 polyhedral hydrocarbons in two, cage-like and planar, forms. We also considered the effect of other minor contributions: core-correlation, relativistic corrections, and extrapolations to the limit of the full CC expansion. Thus, chemically accurate values could be obtained for these complicated systems. These nearly exact results are used to evaluate next the performance of main approximations (i.e., pure, hybrid, and double-hybrid methods) within density functional theory (DFT) in a systematic fashion. Some commonly used functionals, including the B3LYP model, are affected by large errors, and only those having reduced self-interaction error (SIE), which includes the last family of conjectured expressions (double hybrids), are able to achieve reasonable low deviations of 1-2 kcal/mol especially when an estimate for dispersion interactions is also added.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

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

Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis

2013-06-01

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non-Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.« less

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

PubMed Central

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN). In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging. PMID:23227108

Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging.

PubMed

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.

The Interpolation Theory of Radial Basis Functions

NASA Astrophysics Data System (ADS)

Baxter, Brad

2010-06-01

In this dissertation, it is first shown that, when the radial basis function is a p-norm and 1 < p < 2, interpolation is always possible when the points are all different and there are at least two of them. We then show that interpolation is not always possible when p > 2. Specifically, for every p > 2, we construct a set of different points in some Rd for which the interpolation matrix is singular. The greater part of this work investigates the sensitivity of radial basis function interpolants to changes in the function values at the interpolation points. Our early results show that it is possible to recast the work of Ball, Narcowich and Ward in the language of distributional Fourier transforms in an elegant way. We then use this language to study the interpolation matrices generated by subsets of regular grids. In particular, we are able to extend the classical theory of Toeplitz operators to calculate sharp bounds on the spectra of such matrices. Applying our understanding of these spectra, we construct preconditioners for the conjugate gradient solution of the interpolation equations. Our main result is that the number of steps required to achieve solution of the linear system to within a required tolerance can be independent of the number of interpolation points. The Toeplitz structure allows us to use fast Fourier transform techniques, which imp lies that the total number of operations is a multiple of n log n, where n is the number of interpolation points. Finally, we use some of our methods to study the behaviour of the multiquadric when its shape parameter increases to infinity. We find a surprising link with the sinus cardinalis or sinc function of Whittaker. Consequently, it can be highly useful to use a large shape parameter when approximating band-limited functions.

Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO-DFT.

PubMed

Götz, Andreas W; Kollmar, Christian; Hess, Bernd A

2005-09-01

We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by Löwdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods. (c) 2005 Wiley Periodicals, Inc.

Identifying finite-time coherent sets from limited quantities of Lagrangian data.

PubMed

Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W

2015-08-01

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.

Identifying finite-time coherent sets from limited quantities of Lagrangian data

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

Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods basedmore » on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.« less

Dimensionality and noise in energy selective x-ray imaging

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

Alvarez, Robert E.

Purpose: To develop and test a method to quantify the effect of dimensionality on the noise in energy selective x-ray imaging.Methods: The Cramèr-Rao lower bound (CRLB), a universal lower limit of the covariance of any unbiased estimator, is used to quantify the noise. It is shown that increasing dimensionality always increases, or at best leaves the same, the variance. An analytic formula for the increase in variance in an energy selective x-ray system is derived. The formula is used to gain insight into the dependence of the increase in variance on the properties of the additional basis functions, the measurementmore » noise covariance, and the source spectrum. The formula is also used with computer simulations to quantify the dependence of the additional variance on these factors. Simulated images of an object with three materials are used to demonstrate the trade-off of increased information with dimensionality and noise. The images are computed from energy selective data with a maximum likelihood estimator.Results: The increase in variance depends most importantly on the dimension and on the properties of the additional basis functions. With the attenuation coefficients of cortical bone, soft tissue, and adipose tissue as the basis functions, the increase in variance of the bone component from two to three dimensions is 1.4 × 10{sup 3}. With the soft tissue component, it is 2.7 × 10{sup 4}. If the attenuation coefficient of a high atomic number contrast agent is used as the third basis function, there is only a slight increase in the variance from two to three basis functions, 1.03 and 7.4 for the bone and soft tissue components, respectively. The changes in spectrum shape with beam hardening also have a substantial effect. They increase the variance by a factor of approximately 200 for the bone component and 220 for the soft tissue component as the soft tissue object thickness increases from 1 to 30 cm. Decreasing the energy resolution of the detectors increases the variance of the bone component markedly with three dimension processing, approximately a factor of 25 as the resolution decreases from 100 to 3 bins. The increase with two dimension processing for adipose tissue is a factor of two and with the contrast agent as the third material for two or three dimensions is also a factor of two for both components. The simulated images show that a maximum likelihood estimator can be used to process energy selective x-ray data to produce images with noise close to the CRLB.Conclusions: The method presented can be used to compute the effects of the object attenuation coefficients and the x-ray system properties on the relationship of dimensionality and noise in energy selective x-ray imaging systems.« less

Ultra-fast computation of electronic spectra for large systems by tight-binding based simplified Tamm-Dancoff approximation (sTDA-xTB)

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

Grimme, Stefan, E-mail: grimme@thch.uni-bonn.de; Bannwarth, Christoph

2016-08-07

The computational bottleneck of the extremely fast simplified Tamm-Dancoff approximated (sTDA) time-dependent density functional theory procedure [S. Grimme, J. Chem. Phys. 138, 244104 (2013)] for the computation of electronic spectra for large systems is the determination of the ground state Kohn-Sham orbitals and eigenvalues. This limits such treatments to single structures with a few hundred atoms and hence, e.g., sampling along molecular dynamics trajectories for flexible systems or the calculation of chromophore aggregates is often not possible. The aim of this work is to solve this problem by a specifically designed semi-empirical tight binding (TB) procedure similar to the wellmore » established self-consistent-charge density functional TB scheme. The new special purpose method provides orbitals and orbital energies of hybrid density functional character for a subsequent and basically unmodified sTDA procedure. Compared to many previous semi-empirical excited state methods, an advantage of the ansatz is that a general eigenvalue problem in a non-orthogonal, extended atomic orbital basis is solved and therefore correct occupied/virtual orbital energy splittings as well as Rydberg levels are obtained. A key idea for the success of the new model is that the determination of atomic charges (describing an effective electron-electron interaction) and the one-particle spectrum is decoupled and treated by two differently parametrized Hamiltonians/basis sets. The three-diagonalization-step composite procedure can routinely compute broad range electronic spectra (0-8 eV) within minutes of computation time for systems composed of 500-1000 atoms with an accuracy typical of standard time-dependent density functional theory (0.3-0.5 eV average error). An easily extendable parametrization based on coupled-cluster and density functional computed reference data for the elements H–Zn including transition metals is described. The accuracy of the method termed sTDA-xTB is first benchmarked for vertical excitation energies of open- and closed-shell systems in comparison to other semi-empirical methods and applied to exemplary problems in electronic spectroscopy. As side products of the development, a robust and efficient valence electron TB method for the accurate determination of atomic charges as well as a more accurate calculation scheme of dipole rotatory strengths within the Tamm-Dancoff approximation is proposed.« less

An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

2014-09-01

Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the MCPI significantly and will likely be useful for other applications where efficiently computed approximate orbit solutions are needed.

Intelligent robust tracking control for a class of uncertain strict-feedback nonlinear systems.

PubMed

Chang, Yeong-Chan

2009-02-01

This paper addresses the problem of designing robust tracking controls for a large class of strict-feedback nonlinear systems involving plant uncertainties and external disturbances. The input and virtual input weighting matrices are perturbed by bounded time-varying uncertainties. An adaptive fuzzy-based (or neural-network-based) dynamic feedback tracking controller will be developed such that all the states and signals of the closed-loop system are bounded and the trajectory tracking error should be as small as possible. First, the adaptive approximators with linearly parameterized models are designed, and a partitioned procedure with respect to the developed adaptive approximators is proposed such that the implementation of the fuzzy (or neural network) basis functions depends only on the state variables but does not depend on the tuning approximation parameters. Furthermore, we extend to design the nonlinearly parameterized adaptive approximators. Consequently, the intelligent robust tracking control schemes developed in this paper possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.

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

DOE PAGES

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

2017-07-05

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

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory.

PubMed

Saitow, Masaaki; Becker, Ute; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2017-04-28

The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N 6 ) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory

NASA Astrophysics Data System (ADS)

Saitow, Masaaki; Becker, Ute; Riplinger, Christoph; Valeev, Edward F.; Neese, Frank

2017-04-01

The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N6) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

Estimation of spin contamination error in dissociative adsorption of Au2 onto MgO(0 0 1) surface: First application of approximate spin projection (AP) method to plane wave basis

NASA Astrophysics Data System (ADS)

Tada, Kohei; Koga, Hiroaki; Okumura, Mitsutaka; Tanaka, Shingo

2018-06-01

Spin contamination error in the total energy of the Au2/MgO system was estimated using the density functional theory/plane-wave scheme and approximate spin projection methods. This is the first investigation in which the errors in chemical phenomena on a periodic surface are estimated. The spin contamination error of the system was 0.06 eV. This value is smaller than that of the dissociation of Au2 in the gas phase (0.10 eV). This is because of the destabilization of the singlet spin state due to the weakening of the Au-Au interaction caused by the Au-MgO interaction.

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

Coupled-Sturmian and perturbative treatments of electron transfer and ionization in high-energy p-He+ collisions

NASA Astrophysics Data System (ADS)

Winter, Thomas G.; Alston, Steven G.

1992-02-01

Cross sections have been determined for electron transfer and ionization in collisions between protons and He+ ions at proton energies from several hundred kilo-electron-volts to 2 MeV. A coupled-Sturmian approach is taken, extending the work of Winter [Phys. Rev. A 35, 3799 (1987)] and Stodden et al. [Phys. Rev. A 41, 1281 (1990)] to high energies where perturbative approaches are expected to be valid. An explicit connection is made with the first-order Born approximation for ionization and the impulse version of the distorted, strong-potential Born approximation for electron transfer. The capture cross section is shown to be affected by the presence of target basis functions of positive energy near v2/2, corresponding to the Thomas mechanism.

The effects of compressor seventh-stage bleed air extraction on performance of the F100-PW-220 afterburning turbofan engine

NASA Technical Reports Server (NTRS)

Evans, Alison B.

1991-01-01

A study was conducted to determine the effects of seventh-stage compressor bleed on the performance of the F100 afterburning turbofan engine. The effects of bleed on thrust, specific fuel consumption, fan turbine inlet temperature, bleed total pressure, and bleed total temperature were obtained from the engine manufacturer's status deck computer simulation. These effects were determined for power settings of intermediate, partial afterburning, and maximum afterburning for Mach numbers between 0.6 and 2.2 and for altitudes of 30,000, 40,000, and 50,000 ft. It was found that thrust loss and specific fuel consumption increase were approximately linear functions of bleed flow and, based on a percent-thrust change basis, were approximately independent of power setting.

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

Witte, Jonathon; Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720; Neaton, Jeffrey B., E-mail: jbneaton@lbl.gov

Adsorption of gas molecules in metal-organic frameworks is governed by many factors, the most dominant of which are the interaction of the gas with open metal sites, and the interaction of the gas with the ligands. Herein, we examine the latter class of interaction in the context of CO{sub 2} binding to benzene. We begin by clarifying the geometry of the CO{sub 2}–benzene complex. We then generate a benchmark binding curve using a coupled-cluster approach with single, double, and perturbative triple excitations [CCSD(T)] at the complete basis set (CBS) limit. Against this ΔCCSD(T)/CBS standard, we evaluate a plethora of electronicmore » structure approximations: Hartree-Fock, second-order Møller-Plesset perturbation theory (MP2) with the resolution-of-the-identity approximation, attenuated MP2, and a number of density functionals with and without different empirical and nonempirical van der Waals corrections. We find that finite-basis MP2 significantly overbinds the complex. On the other hand, even the simplest empirical correction to standard density functionals is sufficient to bring the binding energies to well within 1 kJ/mol of the benchmark, corresponding to an error of less than 10%; PBE-D in particular performs well. Methods that explicitly include nonlocal correlation kernels, such as VV10, vdW-DF2, and ωB97X-V, perform with similar accuracy for this system, as do ωB97X and M06-L.« less

Eigenvectors of optimal color spectra.

PubMed

Flinkman, Mika; Laamanen, Hannu; Tuomela, Jukka; Vahimaa, Pasi; Hauta-Kasari, Markku

2013-09-01

Principal component analysis (PCA) and weighted PCA were applied to spectra of optimal colors belonging to the outer surface of the object-color solid or to so-called MacAdam limits. The correlation matrix formed from this data is a circulant matrix whose biggest eigenvalue is simple and the corresponding eigenvector is constant. All other eigenvalues are double, and the eigenvectors can be expressed with trigonometric functions. Found trigonometric functions can be used as a general basis to reconstruct all possible smooth reflectance spectra. When the spectral data are weighted with an appropriate weight function, the essential part of the color information is compressed to the first three components and the shapes of the first three eigenvectors correspond to one achromatic response function and to two chromatic response functions, the latter corresponding approximately to Munsell opponent-hue directions 9YR-9B and 2BG-2R.

Small Atomic Orbital Basis Set First‐Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

PubMed Central

Sure, Rebecca; Brandenburg, Jan Gerit

2015-01-01

Abstract In quantum chemical computations the combination of Hartree–Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double‐zeta quality is still widely used, for example, in the popular B3LYP/6‐31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean‐field methods. PMID:27308221

Plato: A localised orbital based density functional theory code

NASA Astrophysics Data System (ADS)

Kenny, S. D.; Horsfield, A. P.

2009-12-01

The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation. Program summaryProgram title: Plato Catalogue identifier: AEFC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 219 974 No. of bytes in distributed program, including test data, etc.: 1 821 493 Distribution format: tar.gz Programming language: C/MPI and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux and Mac OS X Has the code been vectorised or parallelised?: Yes, up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Nature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces. Solution method: Localised orbital based density functional theory. Restrictions: Tight-binding and density functional theory only, no exact exchange. Unusual features: Both atom centred and uniform meshes available. Can deal with arbitrary angular momenta for orbitals, whilst still retaining Slater-Koster tables for accuracy. Running time: Test cases will run in a few minutes, large calculations may run for several days.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Frozen-Orbital and Downfolding Calculations with Auxiliary-Field Quantum Monte Carlo.

PubMed

Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

2013-11-12

We describe the implementation of the frozen-orbital and downfolding approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These approaches can provide significant computational savings, compared to fully correlating all of the electrons. While the many-body wave function is never explicit in AFQMC, its random walkers are Slater determinants, whose orbitals may be expressed in terms of any one-particle orbital basis. It is therefore straightforward to partition the full N-particle Hilbert space into active and inactive parts to implement the frozen-orbital method. In the frozen-core approximation, for example, the core electrons can be eliminated in the correlated part of the calculations, greatly increasing the computational efficiency, especially for heavy atoms. Scalar relativistic effects are easily included using the Douglas-Kroll-Hess theory. Using this method, we obtain a way to effectively eliminate the error due to single-projector, norm-conserving pseudopotentials in AFQMC. We also illustrate a generalization of the frozen-orbital approach that downfolds high-energy basis states to a physically relevant low-energy sector, which allows a systematic approach to produce realistic model Hamiltonians to further increase efficiency for extended systems.

A Semi-Discrete Landweber-Kaczmarz Method for Cone Beam Tomography and Laminography Exploiting Geometric Prior Information

NASA Astrophysics Data System (ADS)

Vogelgesang, Jonas; Schorr, Christian

2016-12-01

We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as non-regular scanning curves e.g. appearing in computed laminography (CL) applications, are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.

Collective Human Mobility Pattern from Taxi Trips in Urban Area

PubMed Central

Peng, Chengbin; Jin, Xiaogang; Wong, Ka-Chun; Shi, Meixia; Liò, Pietro

2012-01-01

We analyze the passengers' traffic pattern for 1.58 million taxi trips of Shanghai, China. By employing the non-negative matrix factorization and optimization methods, we find that, people travel on workdays mainly for three purposes: commuting between home and workplace, traveling from workplace to workplace, and others such as leisure activities. Therefore, traffic flow in one area or between any pair of locations can be approximated by a linear combination of three basis flows, corresponding to the three purposes respectively. We name the coefficients in the linear combination as traffic powers, each of which indicates the strength of each basis flow. The traffic powers on different days are typically different even for the same location, due to the uncertainty of the human motion. Therefore, we provide a probability distribution function for the relative deviation of the traffic power. This distribution function is in terms of a series of functions for normalized binomial distributions. It can be well explained by statistical theories and is verified by empirical data. These findings are applicable in predicting the road traffic, tracing the traffic pattern and diagnosing the traffic related abnormal events. These results can also be used to infer land uses of urban area quite parsimoniously. PMID:22529917

Structure and thermodynamics of a simple fluid

NASA Astrophysics Data System (ADS)

Stell, G.; Weis, J. J.

1980-02-01

Monte Carlo results are found for a simple fluid with a pair potential consisting of a hard-sphere core and a Lennard-Jones attractive tail. They are compared with several of the most promising recent theoretical treatments of simple fluids, all of which involve the decomposition of the pair potential into a hard-sphere-core term and an attractive-tail term. This direct comparison avoids the use of a second perturbation scheme associated with softening the core, which would introduce an ambiguity in the significance of the differences found between the theoretical and Monte Carlo results. The study includes the optimized random-phase approximation (ORPA) and exponential (EXP) approximations of Andersen and Chandler, an extension of the latter approximation to nodal order three (the N3 approximation), the linear-plus-square (LIN + SQ) approximation of Høye and Stell, the renormalized hypernetted chain (RHNC) approximation of Lado, and the quadratic (QUAD) approximation suggested by second-order self-consistent Γ ordering, the lowest order of which is identical to the ORPA. As anticipated on the basis of earlier studies, it is found that the EXP approximation yields radial distribution functions and structure factors of excellent overall accuracy in the liquid state, where the RHNC results are also excellent and the EXP, QUAD, and LIN + SQ results prove to be virtually indistinguishable from one another. For all the approximations, however, the thermodynamics from the compressibility relation are poor and the virial-theorem results are not uniformly reliable. Somewhat more surprisingly, it is found that the EXP results yield a negative structure factor S(k) for very small k in the liquid state and poor radial distribution functions at low densities. The RHNC results are nowhere worse than the EXP results and in some states (e.g., at low densities) much better. In contrast, the N3 results are better in some respects than the EXP results but worse in others. The authors briefly comment on the RHNC and EXP approximations applied to the full Lennard-Jones potential, for which the EXP approximation appears somewhat improved in the liquid state as a result of the softening of the potential core.

Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V

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

Mardirossian, Narbe; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720

2015-02-21

A meta-generalized gradient approximation density functional paired with the VV10 nonlocal correlation functional is presented. The functional form is selected from more than 10{sup 10} choices carved out of a functional space of almost 10{sup 40} possibilities. Raw data come from training a vast number of candidate functional forms on a comprehensive training set of 1095 data points and testing the resulting fits on a comprehensive primary test set of 1153 data points. Functional forms are ranked based on their ability to reproduce the data in both the training and primary test sets with minimum empiricism, and filtered based onmore » a set of physical constraints and an often-overlooked condition of satisfactory numerical precision with medium-sized integration grids. The resulting optimal functional form has 4 linear exchange parameters, 4 linear same-spin correlation parameters, and 4 linear opposite-spin correlation parameters, for a total of 12 fitted parameters. The final density functional, B97M-V, is further assessed on a secondary test set of 212 data points, applied to several large systems including the coronene dimer and water clusters, tested for the accurate prediction of intramolecular and intermolecular geometries, verified to have a readily attainable basis set limit, and checked for grid sensitivity. Compared to existing density functionals, B97M-V is remarkably accurate for non-bonded interactions and very satisfactory for thermochemical quantities such as atomization energies, but inherits the demonstrable limitations of existing local density functionals for barrier heights.« less

Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V

DOE PAGES

Mardirossian, Narbe; Head-Gordon, Martin

2015-02-20

We present a meta-generalized gradient approximation density functional paired with the VV10 nonlocal correlation functional. The functional form is selected from more than 10 10 choices carved out of a functional space of almost 10 40 possibilities. This raw data comes from training a vast number of candidate functional forms on a comprehensive training set of 1095 data points and testing the resulting fits on a comprehensive primary test set of 1153 data points. Functional forms are ranked based on their ability to reproduce the data in both the training and primary test sets with minimum empiricism, and filteredmore » based on a set of physical constraints and an often-overlooked condition of satisfactory numerical precision with medium-sized integration grids. The resulting optimal functional form has 4 linear exchange parameters, 4 linear same-spin correlation parameters, and 4 linear opposite-spin correlation parameters, for a total of 12 fitted parameters. The final density functional, B97M-V, is further assessed on a secondary test set of 212 data points, applied to several large systems including the coronene dimer and water clusters, tested for the accurate prediction of intramolecular and intermolecular geometries, verified to have a readily attainable basis set limit, and checked for grid sensitivity. Compared to existing density functionals, B97M-V is remarkably accurate for non-bonded interactions and very satisfactory for thermochemical quantities such as atomization energies, but inherits the demonstrable limitations of existing local density functionals for barrier heights.« less

Solvatochromic shifts from coupled-cluster theory embedded in density functional theory

NASA Astrophysics Data System (ADS)

Höfener, Sebastian; Gomes, André Severo Pereira; Visscher, Lucas

2013-09-01

Building on the framework recently reported for determining general response properties for frozen-density embedding [S. Höfener, A. S. P. Gomes, and L. Visscher, J. Chem. Phys. 136, 044104 (2012)], 10.1063/1.3675845, in this work we report a first implementation of an embedded coupled-cluster in density-functional theory (CC-in-DFT) scheme for electronic excitations, where only the response of the active subsystem is taken into account. The formalism is applied to the calculation of coupled-cluster excitation energies of water and uracil in aqueous solution. We find that the CC-in-DFT results are in good agreement with reference calculations and experimental results. The accuracy of calculations is mainly sensitive to factors influencing the correlation treatment (basis set quality, truncation of the cluster operator) and to the embedding treatment of the ground-state (choice of density functionals). This allows for efficient approximations at the excited state calculation step without compromising the accuracy. This approximate scheme makes it possible to use a first principles approach to investigate environment effects with specific interactions at coupled-cluster level of theory at a cost comparable to that of calculations of the individual subsystems in vacuum.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analysis And Validation of the Field Coupled Through an Aperture in an Avionics Enclosure

NASA Astrophysics Data System (ADS)

Bakore, Rahul

This work focused on accurately predicting the current response of an equipment under test (EUT) to a random electromagnetic field representing a threat source to model radio frequency directed energy weapons (RFDEWs). The modeled EUT consists of a single wire attached to the interior wall of a shielding enclosure that includes an aperture on one face. An in-house computational electromagnetic (CEM) code based on method of moments (MOM) and accelerated by the multi-level fast multipole algorithm (MLFMA), was enhanced through the implementation of first order vector basis functions that approximates the EUT surface current. The electric field integral equation (EFIE) is solved using MOM/MLFMA. Use of first-order basis functions gives a large savings in computational time over the previous implementation with zero-order Rao-Wilton-Glisson basis functions. A sample EUT was fabricated and tested within an anechoic chamber and a reverberation chamber over a wide frequency band. In the anechoic chamber measurements, the current response on the wire within the EUT due to a single uniform plane wave was found and compared with the numerical simulations. In the reverberation chamber measurements, the mean current magnitude excited on the wire within the EUT by a mechanically stirred random field was measured and compared with the numerical simulations. The measured scattering parameter between the source antenna and the EUT measurement port was used to derive the current response on the wire in both chambers. The numerically simulated currents agree very well with the measurements in both the anechoic and reverberation chambers over the measured frequency band, confirming the validity of the numerical approach for calculating EUT response due to a random field. An artificial neural network (ANN) was trained that can rapidly provide the mean induced current response of an EUT due to a random field under different aperture configurations arbitrarily placed on one face of an EUT. However, ANN proved no better than simple linear interpolation in approximating the induced currents on EUTs that give strong resonances and nulls in the response.

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Fuzzy cluster analysis of simple physicochemical properties of amino acids for recognizing secondary structure in proteins.

PubMed Central

Mocz, G.

1995-01-01

Fuzzy cluster analysis has been applied to the 20 amino acids by using 65 physicochemical properties as a basis for classification. The clustering products, the fuzzy sets (i.e., classical sets with associated membership functions), have provided a new measure of amino acid similarities for use in protein folding studies. This work demonstrates that fuzzy sets of simple molecular attributes, when assigned to amino acid residues in a protein's sequence, can predict the secondary structure of the sequence with reasonable accuracy. An approach is presented for discriminating standard folding states, using near-optimum information splitting in half-overlapping segments of the sequence of assigned membership functions. The method is applied to a nonredundant set of 252 proteins and yields approximately 73% matching for correctly predicted and correctly rejected residues with approximately 60% overall success rate for the correctly recognized ones in three folding states: alpha-helix, beta-strand, and coil. The most useful attributes for discriminating these states appear to be related to size, polarity, and thermodynamic factors. Van der Waals volume, apparent average thickness of surrounding molecular free volume, and a measure of dimensionless surface electron density can explain approximately 95% of prediction results. hydrogen bonding and hydrophobicity induces do not yet enable clear clustering and prediction. PMID:7549882

Estimation of reflectance from camera responses by the regularized local linear model.

PubMed

Zhang, Wei-Feng; Tang, Gongguo; Dai, Dao-Qing; Nehorai, Arye

2011-10-01

Because of the limited approximation capability of using fixed basis functions, the performance of reflectance estimation obtained by traditional linear models will not be optimal. We propose an approach based on the regularized local linear model. Our approach performs efficiently and knowledge of the spectral power distribution of the illuminant and the spectral sensitivities of the camera is not needed. Experimental results show that the proposed method performs better than some well-known methods in terms of both reflectance error and colorimetric error. © 2011 Optical Society of America

Luminance-model-based DCT quantization for color image compression

NASA Technical Reports Server (NTRS)

Ahumada, Albert J., Jr.; Peterson, Heidi A.

1992-01-01

A model is developed to approximate visibility thresholds for discrete cosine transform (DCT) coefficient quantization error based on the peak-to-peak luminance of the error image. Experimentally measured visibility thresholds for R, G, and B DCT basis functions can be predicted by a simple luminance-based detection model. This model allows DCT coefficient quantization matrices to be designed for display conditions other than those of the experimental measurements: other display luminances, other veiling luminances, and other spatial frequencies (different pixel spacings, viewing distances, and aspect ratios).

A simple finite element method for the Stokes equations

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-21

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

A simple finite element method for the Stokes equations

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

Mu, Lin; Ye, Xiu

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

The physiological basis of Glottal electromagnetic micropower sensors (GEMS) and their use in defining an excitation function for the human vocal tract

NASA Astrophysics Data System (ADS)

Burnett, Gregory Clell

1999-10-01

The definition, use, and physiological basis of Glottal Electromagnetic Micropower Sensors (GEMS) is presented. These sensors are a new type of low power (<20 milliwatts radiated) microwave regime (900 MHz to 2.5 GHz) multi-purpose motion sensor developed at the Lawrence Livermore National Laboratory. The GEMS are sensitive to movement in an adjustable field of view (FOV) surrounding the antennae. In this thesis, the GEMS has been utilized for speech research, targeted to receive motion signals from the subglottal region of the trachea. The GEMS signal is analyzed to determine the physiological source of the signal, and this information is used to calculate the subglottal pressure, effectively an excitation function for the human vocal tract. For the first time, an excitation function may be calculated in near real time using a noninvasive procedure. Several experiments and models are presented to demonstrate that the GEMS signal is representative of the motion of the subglottal posterior wall of the trachea as it vibrates in response to the pressure changes caused by the folds as they modulate the airflow supplied by the lungs. The vibrational properties of the tracheal wall are modeled using a lumped-element circuit model. Taking the output of the vocal tract to be the audio pressure captured by a microphone and the input to be the subglottal pressure, the transfer function of the vocal tract (including the nasal cavities) can be approximated every 10-30 milliseconds using an autoregressive moving-average model. Unlike the currently utilized method of transfer function approximation, this new method only involves noninvasive GEMS measurements and digital signal processing and does not demand the difficult task of obtaining precise physical measurements of the tract and subsequent estimation of the transfer function using its cross-sectional area. The ability to measure the physical motion of the trachea enables a significant number of potential applications, ranging from very accurate pitch detection to speech synthesis, speaker verification, and speech recognition.

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods.

PubMed

Antony, Jens; Grimme, Stefan; Liakos, Dimitrios G; Neese, Frank

2011-10-20

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.

Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks.

PubMed

Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang

2010-09-01

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

Extensions to the integral line-beam method for gamma-ray skyshine analyses

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

Shultis, J.K.; Faw, R.E.

1995-08-01

A computationally simple method for estimating gamma-ray skyshine dose rates has been developed on the basis of the line-beam response function. Both Monte Carlo and pointkernel calculations that account for both annihilation and bremsstrahlung were used in the generation of line beam response functions (LBRF) for gamma-ray energies between 10 and 100 MeV. The LBRF is approximated by a three-parameter formula. By combining results with those obtained in an earlier study for gamma energies below 10 MeV, LBRF values are readily and accurately evaluated for source energies between 0.02 and 100 MeV, for source-to-detector distances between 1 and 3000 m,more » and beam angles as great as 180 degrees. Tables of the parameters for the approximate LBRF are presented. The new response functions are then applied to three simple skyshine geometries, an open silo geometry, an infinite wall, and a rectangular four-wall building. Results are compared to those of previous calculations and to benchmark measurements. A new approach is introduced to account for overhead shielding of the skyshine source and compared to the simplistic exponential-attenuation method used in earlier studies. The effect of the air-ground interface, usually neglected in gamma skyshine studies, is also examined and an empirical correction factor is introduced. Finally, a revised code based on the improved LBRF approximations and the treatment of the overhead shielding is presented, and results shown for several benchmark problems.« less

Diagonal Born-Oppenheimer correction for coupled-cluster wave-functions

NASA Astrophysics Data System (ADS)

Shamasundar, K. R.

2018-06-01

We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. This is shown to lead to a biorthogonal version of SOS formula with similar properties. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. One of this agrees with the formula used in the current literature. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified.

Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints.

PubMed

Chen, Weisheng

2009-07-01

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh(.) is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.

[Mathematic concept model of accumulation of functional disorders associated with environmental factors].

PubMed

Zaĭtseva, N V; Trusov, P V; Kir'ianov, D A

2012-01-01

The mathematic concept model presented describes accumulation of functional disorders associated with environmental factors, plays predictive role and is designed for assessments of possible effects caused by heterogenous factors with variable exposures. Considering exposure changes with self-restoration process opens prospects of using the model to evaluate, analyse and manage occupational risks. To develop current theoretic approaches, the authors suggested a model considering age-related body peculiarities, systemic interactions of organs, including neuro-humoral regulation, accumulation of functional disorders due to external factors, rehabilitation of functions during treatment. General objective setting covers defining over a hundred unknow coefficients that characterize speed of various processes within the body. To solve this problem, the authors used iteration approach, successive identification, that starts from the certain primary approximation of the model parameters and processes subsequent updating on the basis of new theoretic and empirical knowledge.

Fast Time-Dependent Density Functional Theory Calculations of the X-ray Absorption Spectroscopy of Large Systems.

PubMed

Besley, Nicholas A

2016-10-11

The computational cost of calculations of K-edge X-ray absorption spectra using time-dependent density functional (TDDFT) within the Tamm-Dancoff approximation is significantly reduced through the introduction of a severe integral screening procedure that includes only integrals that involve the core s basis function of the absorbing atom(s) coupled with a reduced quality numerical quadrature for integrals associated with the exchange and correlation functionals. The memory required for the calculations is reduced through construction of the TDDFT matrix within the absorbing core orbitals excitation space and exploiting further truncation of the virtual orbital space. The resulting method, denoted fTDDFTs, leads to much faster calculations and makes the study of large systems tractable. The capability of the method is demonstrated through calculations of the X-ray absorption spectra at the carbon K-edge of chlorophyll a, C 60 and C 70 .

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

Linear electro-optic effect in semiconductors: Ab initio description of the electronic contribution

NASA Astrophysics Data System (ADS)

Prussel, Lucie; Véniard, Valérie

2018-05-01

We propose an ab initio framework to derive the electronic part of the second-order susceptibility tensor for the electro-optic effect in bulk semiconductors. We find a general expression for χ(2 ) evaluated within time-dependent density-functional theory, including explicitly the band-gap corrections at the level of the scissors approximation. Excitonic effects are accounted for, on the basis of a simple scalar approximation. We apply our formalism to the computation of the electro-optic susceptibilities for several semiconductors, such as GaAs, GaN, and SiC. Taking into account the ionic contribution according to the Faust-Henry coefficient, we obtain a good agreement with experimental results. Finally, using different types of strain to break centrosymmetry, we show that high electro-optic coefficients can be obtained in bulk silicon for a large range of frequencies.

Novel density functional methodology for the computation of accurate electronic and thermodynamic properties of molecular systems and improved long-range behavior

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

Kafafi, S.A.

1998-12-10

A novel general purpose density functional methodology for the computation of accurate electronic and thermodynamic properties of molecules and improved long-range behavior is reported. Assuming the separability of the exchange (E{sub x}) and correlation (E{sub c}) contributions to the total exchange-correlation energy functional (E{sub xc}), the E{sub x} term consists of a hybrid mixture of 37.5% Hartree-Fock exchange and the appropriate local spin density exchange using the adiabatic connection formula. He demonstrated that E{sub x} and its corresponding potential V{sub x} [=dE{sub x}/d{rho}(r)] have the proper asymptotic limits at r = 0 and r {r_arrow} {infinity}, E{sub c} consists ofmore » the Vosko, Wilk, and Nusair formula for the free-electron gas correlation energy and a generalized gradient approximation term with one adjustable parameter. V{sub c} [=dE{sub c}/d{rho}(r)] was shown to obey the r {r_arrow} {infinity} limit of the corresponding potential derived from exact atomic exchange-correlation computations; namely, V{sub c} is proportional to r{sup {minus}4}. Most importantly, he demonstrated that, at r values where dispersion forces are operating, V{sub c} is proportional to 1/r{sup n} (n = 4, 6, 8, {hor_ellipsis}). The reported method was denoted by K2-BVWN because it used two adjustable parameters in its formulation. The K2-BVWN scheme scales as N{sup 3}, where N is the number of basis functions, compared to {approximately}N{sup 7} for Gaussian-2 (G2) ab initio theory and related methods, {approximately}N{sup 5} for Barone`s mPW1,3PW, and {approximately}N{sup 4} for Becke`s three-parameter density functional approaches. The G2 data set complemented by the reported molecular systems investigated in this work was recommended as a critical test for evaluating novel ab initio and density functional methodologies. The K2-BVWN method has been implemented in the Gaussian series of programs.« less

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis.

PubMed

Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg

2016-12-13

We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.

Variational formulation of open-ended coaxial line in contact with layered biological medium.

PubMed

Alanen, E; Lahtinen, T; Nuutinen, J

1998-10-01

An open-ended coaxial probe designed to measure layered biological media is analyzed with a new method. The probe is considered as an electrostatic circuit element whose capacitance is solved using a stationary functional. The fundamental transverse electric and magnetic field (TEM)-mode and the series of evanescent wavemodes in the coaxial cable are used as basis functions. The field outside the probe is solved using a Hankel transform. The capacitance is calculated for homogeneous materials and two-layer structures and the results are compared with values measured with a phantom model. The method can be easily extended for structures with an arbitrary number of layers. A practical approximation for two-layer cases, originally developed to take into account the effect of subcutaneous fat in skin measurements, is presented and its validity for different combinations of dielectric constants and the thickness of the first layer is demonstrated. The static approximation limits the frequency range, but it covers biological measurements up to 500 MHz. The developed method is accurate and easy to adopt in practice.

On the Angular Dependence of the Vicinal Fluorine-Fluorine Coupling Constant in 1,2-Difluoroethane:  Deviation from a Karplus-like Shape.

PubMed

Provasi, Patricio F; Sauer, Stephan P A

2006-07-01

The angular dependence of the vicinal fluorine-fluorine coupling constant, (3)JFF, for 1,2-difluoroethane has been investigated with several polarization propagator methods. (3)JFF and its four Ramsey contributions were calculated using the random phase approximation (RPA), its multiconfigurational generalization, and both second-order polarization propagator approximations (SOPPA and SOPPA(CCSD)), using locally dense basis sets. The geometries were optimized for each dihedral angle at the level of density functional theory using the B3LYP functional and fourth-order Møller-Plesset perturbation theory. The resulting coupling constant curves were fitted to a cosine series with 8 coefficients. Our results are compared with those obtained previously and values estimated from experiment. It is found that the inclusion of electron correlation in the calculation of (3)JFF reduces the absolute values. This is mainly due to changes in the FC contribution, which for dihedral angles around the trans conformation even changes its sign. This sign change is responsible for the breakdown of the Karplus-like curve.

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.

The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques

NASA Astrophysics Data System (ADS)

Izmaylov, Artur F.; Staroverov, Viktor N.; Scuseria, Gustavo E.; Davidson, Ernest R.; Stoltz, Gabriel; Cancès, Eric

2007-02-01

We have recently formulated a new approach, named the effective local potential (ELP) method, for calculating local exchange-correlation potentials for orbital-dependent functionals based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart [V. N. Staroverov et al., J. Chem. Phys. 125, 081104 (2006)]. Here we show that under a mildly simplifying assumption of frozen molecular orbitals, the equation defining the ELP has a unique analytic solution which is identical with the expression arising in the localized Hartree-Fock (LHF) and common energy denominator approximations (CEDA) to the optimized effective potential. The ELP procedure differs from the CEDA and LHF in that it yields the target potential as an expansion in auxiliary basis functions. We report extensive calculations of atomic and molecular properties using the frozen-orbital ELP method and its iterative generalization to prove that ELP results agree with the corresponding LHF and CEDA values, as they should. Finally, we make the case for extending the iterative frozen-orbital ELP method to full orbital relaxation.

Adaptive Fault-Tolerant Control of Uncertain Nonlinear Large-Scale Systems With Unknown Dead Zone.

PubMed

Chen, Mou; Tao, Gang

2016-08-01

In this paper, an adaptive neural fault-tolerant control scheme is proposed and analyzed for a class of uncertain nonlinear large-scale systems with unknown dead zone and external disturbances. To tackle the unknown nonlinear interaction functions in the large-scale system, the radial basis function neural network (RBFNN) is employed to approximate them. To further handle the unknown approximation errors and the effects of the unknown dead zone and external disturbances, integrated as the compounded disturbances, the corresponding disturbance observers are developed for their estimations. Based on the outputs of the RBFNN and the disturbance observer, the adaptive neural fault-tolerant control scheme is designed for uncertain nonlinear large-scale systems by using a decentralized backstepping technique. The closed-loop stability of the adaptive control system is rigorously proved via Lyapunov analysis and the satisfactory tracking performance is achieved under the integrated effects of unknown dead zone, actuator fault, and unknown external disturbances. Simulation results of a mass-spring-damper system are given to illustrate the effectiveness of the proposed adaptive neural fault-tolerant control scheme for uncertain nonlinear large-scale systems.

Fast neutrons measured in copper from the Hiroshima atomic bomb dome.

PubMed

Marchetti, A A; McAninch, J E; Rugel, G; Rühm, W; Korschinek, G; Martinelli, R E; Faestermann, T; Knie, K; Egbert, S D; Wallner, A; Wallner, C; Tanaka, K; Endo, S; Hoshi, M; Shizuma, K; Fujita, S; Hasai, H; Imanaka, T; Straume, T

2009-01-01

The first measurements of (63)Ni produced by A-bomb fast neutrons (above approximately 1 MeV) in copper samples from Hiroshima encompassed distances from approximately 380 to 5062 m from the hypocenter (the point on the ground directly under the bomb). They included the region of interest to survivor studies (approximately 900 to 1500 m) and provided the first direct validation of fast neutrons in that range. However, a significant measurement gap remained between the hypocenter and 380 m. Measurements close to the hypocenter are important as a high-value anchor for the slope of the curve for neutron activation as a function of distance. Here we report measurements of (63)Ni in copper samples from the historic Hiroshima Atomic Bomb Dome, which is located approximately 150 m from the hypocenter. These measurements extend the range of our previously published data for (63)Ni providing a more comprehensive and consistent A-bomb activation curve. The results are also in good agreement with calculations based on the current dosimetry system (DS02) and give further experimental support to the accuracy of this system that forms the basis for radiation risk estimates worldwide.

Koopmans' analysis of chemical hardness with spectral-like resolution.

PubMed

Putz, Mihai V

2013-01-01

Three approximation levels of Koopmans' theorem are explored and applied: the first referring to the inner quantum behavior of the orbitalic energies that depart from the genuine ones in Fock space when the wave-functions' Hilbert-Banach basis set is specified to solve the many-electronic spectra of spin-orbitals' eigenstates; it is the most subtle issue regarding Koopmans' theorem as it brings many critics and refutation in the last decades, yet it is shown here as an irrefutable "observational" effect through computation, specific to any in silico spectra of an eigenproblem; the second level assumes the "frozen spin-orbitals" approximation during the extracting or adding of electrons to the frontier of the chemical system through the ionization and affinity processes, respectively; this approximation is nevertheless workable for great deal of chemical compounds, especially organic systems, and is justified for chemical reactivity and aromaticity hierarchies in an homologue series; the third and the most severe approximation regards the extension of the second one to superior orders of ionization and affinities, here studied at the level of chemical hardness compact-finite expressions up to spectral-like resolution for a paradigmatic set of aromatic carbohydrates.

Koopmans' Analysis of Chemical Hardness with Spectral-Like Resolution

PubMed Central

2013-01-01

Three approximation levels of Koopmans' theorem are explored and applied: the first referring to the inner quantum behavior of the orbitalic energies that depart from the genuine ones in Fock space when the wave-functions' Hilbert-Banach basis set is specified to solve the many-electronic spectra of spin-orbitals' eigenstates; it is the most subtle issue regarding Koopmans' theorem as it brings many critics and refutation in the last decades, yet it is shown here as an irrefutable “observational” effect through computation, specific to any in silico spectra of an eigenproblem; the second level assumes the “frozen spin-orbitals” approximation during the extracting or adding of electrons to the frontier of the chemical system through the ionization and affinity processes, respectively; this approximation is nevertheless workable for great deal of chemical compounds, especially organic systems, and is justified for chemical reactivity and aromaticity hierarchies in an homologue series; the third and the most severe approximation regards the extension of the second one to superior orders of ionization and affinities, here studied at the level of chemical hardness compact-finite expressions up to spectral-like resolution for a paradigmatic set of aromatic carbohydrates. PMID:23970834

Infinite-order sudden approximation for collisions involving molecules in Pi electronic states: a new derivation and calculations of rotationally inelastic cross sections for NO(x superscript 2 Pi) + He and Ar

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

Corey, G.C.; Alexander, M.H.

1986-11-15

A new derivation is presented of the infinite order sudden (IOS) approximation for rotationally inelastic collisions of a diatomic molecule in a Pi electronic state with a closed shell atom. This derivation clearly demonstrates the connection between the two sudden S functions for scattering off the adiabatic potential surface of A' and A symmetry, which would arise from an ab initio calculation on an atom + Pi-state molecule system, and the S matrix elements in diabatic basis, which are required in the quantum treatment of the collision dynamics. Coupled states and IOS calculations were carried out for collisions of NImore » X 2 Pi with helium and argon, based on a electron gas potential surface at total energies of 63, 150, and 300 meV. The IOS approximation is not reliable for collisions of NO with Ar, even at the highest collision energy considered here. However, for collisions with He at 150 and 300 meV, the IOS approximation is nearly quantitative for transitions both within and between the Omega = 1/2 and Omega = 3/2 manifolds.« less

Observer-Based Adaptive NN Control for a Class of Uncertain Nonlinear Systems With Nonsymmetric Input Saturation.

PubMed

Yong-Feng Gao; Xi-Ming Sun; Changyun Wen; Wei Wang

2017-07-01

This paper is concerned with the problem of adaptive tracking control for a class of uncertain nonlinear systems with nonsymmetric input saturation and immeasurable states. The radial basis function of neural network (NN) is employed to approximate unknown functions, and an NN state observer is designed to estimate the immeasurable states. To analyze the effect of input saturation, an auxiliary system is employed. By the aid of adaptive backstepping technique, an adaptive tracking control approach is developed. Under the proposed adaptive tracking controller, the boundedness of all the signals in the closed-loop system is achieved. Moreover, distinct from most of the existing references, the tracking error can be bounded by an explicit function of design parameters and saturation input error. Finally, an example is given to show the effectiveness of the proposed method.

Formulation of improved basis sets for the study of polymer dynamics through diffusion theory methods.

PubMed

Gaspari, Roberto; Rapallo, Arnaldo

2008-06-28

In this work a new method is proposed for the choice of basis functions in diffusion theory (DT) calculations. This method, named hybrid basis approach (HBA), combines the two previously adopted long time sorting procedure (LTSP) and maximum correlation approximation (MCA) techniques; the first emphasizing contributions from the long time dynamics, the latter being based on the local correlations along the chain. In order to fulfill this task, the HBA procedure employs a first order basis set corresponding to a high order MCA one and generates upper order approximations according to LTSP. A test of the method is made first on a melt of cis-1,4-polyisoprene decamers where HBA and LTSP are compared in terms of efficiency. Both convergence properties and numerical stability are improved by the use of the HBA basis set whose performance is evaluated on local dynamics, by computing the correlation times of selected bond vectors along the chain, and on global ones, through the eigenvalues of the diffusion operator L. Further use of the DT with a HBA basis set has been made on a 71-mer of syndiotactic trans-1,2-polypentadiene in toluene solution, whose dynamical properties have been computed with a high order calculation and compared to the "numerical experiment" provided by the molecular dynamics (MD) simulation in explicit solvent. The necessary equilibrium averages have been obtained by a vacuum trajectory of the chain where solvent effects on conformational properties have been reproduced with a proper screening of the nonbonded interactions, corresponding to a definite value of the mean radius of gyration of the polymer in vacuum. Results show a very good agreement between DT calculations and the MD numerical experiment. This suggests a further use of DT methods with the necessary input quantities obtained by the only knowledge of some experimental values, i.e., the mean radius of gyration of the chain and the viscosity of the solution, and by a suitable vacuum trajectory, with great savings in computational time required. This offers a theoretical bridge between the experimental static and dynamical properties of polymers.

Theory of inhomogeneous quantum systems. III. Variational wave functions for Fermi fluids

NASA Astrophysics Data System (ADS)

Krotscheck, E.

1985-04-01

We develop a general variational theory for inhomogeneous Fermi systems such as the electron gas in a metal surface, the surface of liquid 3He, or simple models of heavy nuclei. The ground-state wave function is expressed in terms of two-body correlations, a one-body attenuation factor, and a model-system Slater determinant. Massive partial summations of cluster expansions are performed by means of Born-Green-Yvon and hypernetted-chain techniques. An optimal single-particle basis is generated by a generalized Hartree-Fock equation in which the two-body correlations screen the bare interparticle interaction. The optimization of the pair correlations leads to a state-averaged random-phase-approximation equation and a strictly microscopic determination of the particle-hole interaction.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

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

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis

NASA Astrophysics Data System (ADS)

Albajar, F.; Bertelli, N.; Bornatici, M.; Engelmann, F.

2007-01-01

On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Bateman's expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas. Presented in part at the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, Greece, 9-12 May 2006.

Ab initio electronic structure calculations for metallic intermediate band formation in photovoltaic materials

NASA Astrophysics Data System (ADS)

Wahnón, P.; Tablero, C.

2002-04-01

A metallic isolated band in the middle of the band gap of several III-V semiconductors has been predicted as photovoltaic materials with the possibility of providing substantially enhanced efficiencies. We have investigated the electronic band structures and lattice constants of GanAsmM and GanPmM with M=Sc, Ti, V, and Cr, to identify whether this isolated band is likely to exist by means of accurate calculations. For this task, we use the SIESTA program, an ab initio periodic density-functional method, fully self consistent in the local-density approximation. Norm-conserving, nonlocal pseudopotentials and confined linear combination of atomic orbitals have been used. We have carried out a case study of GanAsmTi and GanPmTi energy-band structure including analyses of the effect of the basis set, fine k-point mesh to ensure numerical convergence, structural parameters, and generalized gradient approximation for exchange and correlation corrections. We find the isolated intermediate band when one Ti atom replaces the position of one As (or P) atom in the crystal structure. For this kind of compound we show that the intermediate band relative position inside the band gap and width are sensitive to the dynamic relaxation of the crystal and the size of the basis set.

DGDFT: A massively parallel method for large scale density functional theory calculations.

PubMed

Hu, Wei; Lin, Lin; Yang, Chao

2015-09-28

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. By using the pole expansion and selected inversion technique to compute electron density, energy, and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that for the two-dimensional (2D) phosphorene systems studied here, using 37 basis functions per atom allows us to reach an accuracy level of 1.3 × 10(-4) Hartree/atom in terms of the error of energy and 6.2 × 10(-4) Hartree/bohr in terms of the error of atomic force, respectively. DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of 2D phosphorene systems with 3500-14 000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

Function approximation and documentation of sampling data using artificial neural networks.

PubMed

Zhang, Wenjun; Barrion, Albert

2006-11-01

Biodiversity studies in ecology often begin with the fitting and documentation of sampling data. This study is conducted to make function approximation on sampling data and to document the sampling information using artificial neural network algorithms, based on the invertebrate data sampled in the irrigated rice field. Three types of sampling data, i.e., the curve species richness vs. the sample size, the curve rarefaction, and the curve mean abundance of newly sampled species vs.the sample size, are fitted and documented using BP (Backpropagation) network and RBF (Radial Basis Function) network. As the comparisons, The Arrhenius model, and rarefaction model, and power function are tested for their ability to fit these data. The results show that the BP network and RBF network fit the data better than these models with smaller errors. BP network and RBF network can fit non-linear functions (sampling data) with specified accuracy and don't require mathematical assumptions. In addition to the interpolation, BP network is used to extrapolate the functions and the asymptote of the sampling data can be drawn. BP network cost a longer time to train the network and the results are always less stable compared to the RBF network. RBF network require more neurons to fit functions and generally it may not be used to extrapolate the functions. The mathematical function for sampling data can be exactly fitted using artificial neural network algorithms by adjusting the desired accuracy and maximum iterations. The total numbers of functional species of invertebrates in the tropical irrigated rice field are extrapolated as 140 to 149 using trained BP network, which are similar to the observed richness.

Novel silicon-carbon fullerene-like nanostructures: an Ab initio study on the stability of Si54C6 and Si60C6 clusters.

PubMed

Srinivasan, Aravind; Ray, Asok K

2006-01-01

Silicon fullerene like nanostructures with six carbon atoms on the surface of Si60 cages by substitution, as well as inside the cage at various symmetry orientations have been studied within the generalized gradient approximation to density functional theory. Full geometry optimizations have been performed without any symmetry constraints using the Gaussian 03 suite of programs and the LANL2DZ basis set. Thus, for the silicon atom, the Hay-Wadt pseudopotential with the associated basis set are used for the core electrons and the valence electrons, respectively. For the carbon atom, the Dunning/Huzinaga double zeta basis set is employed. Electronic and geometric properties of the nanostructures are presented and discussed in detail. It was found that optimized silicon-carbon fullerene like nanostructures have increased stability compared to bare Si60 cage and the stability depends on the orientation of carbon atoms, as well as on the nature of bonding between silicon and carbon atoms and also on the carbon-carbon bonding.

Cerebellar-inspired algorithm for adaptive control of nonlinear dielectric elastomer-based artificial muscle

PubMed Central

Assaf, Tareq; Rossiter, Jonathan M.; Porrill, John

2016-01-01

Electroactive polymer actuators are important for soft robotics, but can be difficult to control because of compliance, creep and nonlinearities. Because biological control mechanisms have evolved to deal with such problems, we investigated whether a control scheme based on the cerebellum would be useful for controlling a nonlinear dielectric elastomer actuator, a class of artificial muscle. The cerebellum was represented by the adaptive filter model, and acted in parallel with a brainstem, an approximate inverse plant model. The recurrent connections between the two allowed for direct use of sensory error to adjust motor commands. Accurate tracking of a displacement command in the actuator's nonlinear range was achieved by either semi-linear basis functions in the cerebellar model or semi-linear functions in the brainstem corresponding to recruitment in biological muscle. In addition, allowing transfer of training between cerebellum and brainstem as has been observed in the vestibulo-ocular reflex prevented the steady increase in cerebellar output otherwise required to deal with creep. The extensibility and relative simplicity of the cerebellar-based adaptive-inverse control scheme suggests that it is a plausible candidate for controlling this type of actuator. Moreover, its performance highlights important features of biological control, particularly nonlinear basis functions, recruitment and transfer of training. PMID:27655667

Online dimensionality reduction using competitive learning and Radial Basis Function network.

PubMed

Tomenko, Vladimir

2011-06-01

The general purpose dimensionality reduction method should preserve data interrelations at all scales. Additional desired features include online projection of new data, processing nonlinearly embedded manifolds and large amounts of data. The proposed method, called RBF-NDR, combines these features. RBF-NDR is comprised of two modules. The first module learns manifolds by utilizing modified topology representing networks and geodesic distance in data space and approximates sampled or streaming data with a finite set of reference patterns, thus achieving scalability. Using input from the first module, the dimensionality reduction module constructs mappings between observation and target spaces. Introduction of specific loss function and synthesis of the training algorithm for Radial Basis Function network results in global preservation of data structures and online processing of new patterns. The RBF-NDR was applied for feature extraction and visualization and compared with Principal Component Analysis (PCA), neural network for Sammon's projection (SAMANN) and Isomap. With respect to feature extraction, the method outperformed PCA and yielded increased performance of the model describing wastewater treatment process. As for visualization, RBF-NDR produced superior results compared to PCA and SAMANN and matched Isomap. For the Topic Detection and Tracking corpus, the method successfully separated semantically different topics. Copyright © 2011 Elsevier Ltd. All rights reserved.

Efficient construction of exchange and correlation potentials by inverting the Kohn-Sham equations.

PubMed

Kananenka, Alexei A; Kohut, Sviataslau V; Gaiduk, Alex P; Ryabinkin, Ilya G; Staroverov, Viktor N

2013-08-21

Given a set of canonical Kohn-Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn-Sham equations in a single step to obtain the corresponding exchange-correlation potential, vXC(r). For orbitals and orbital energies that are solutions of the Kohn-Sham equations with a multiplicative vXC(r) this procedure recovers vXC(r) (in the basis set limit), but for eigenfunctions of a non-multiplicative one-electron operator it produces an orbital-averaged potential. In particular, substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham inversion formula is a fast way to compute the Slater potential. In the same way, we efficiently construct orbital-averaged exchange and correlation potentials for hybrid and kinetic-energy-density-dependent functionals. We also show how the Kohn-Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbital-dependent functionals.

Variational nonadiabatic dynamics in the moving crude adiabatic representation: Further merging of nuclear dynamics and electronic structure

NASA Astrophysics Data System (ADS)

Joubert-Doriol, Loïc; Izmaylov, Artur F.

2018-03-01

A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new approach is the elimination of any global or local model representation of electronic potential energy surfaces; instead, the electron-nuclear interaction is treated explicitly using the Gaussian integration. As a result, the new scheme does not introduce any uncontrolled approximations. The employed variational principle ensures the energy conservation and leaves the number of electronic and nuclear basis functions as the only parameter determining the accuracy. To assess performance of the approach, a model with two electronic and two nuclear spacial degrees of freedom containing conical intersections between potential energy surfaces has been considered. Dynamical features associated with nonadiabatic transitions and nontrivial geometric (or Berry) phases were successfully reproduced within a limited basis expansion.

Creation of heterogeneous materials on the basis of B4C and Ni powders by the method of cold spraying with subsequent layer-by-layer laser treatment

NASA Astrophysics Data System (ADS)

Fomin, V. M.; Golyshev, A. A.; Kosarev, V. F.; Malikov, A. G.; Orishich, A. M.; Ryashin, N. S.; Filippov, A. A.; Shikalov, V. S.

2017-09-01

A method is proposed for creating principally new functionally graded heterogeneous materials on the basis of B4C ceramic powders with different mass fractions in the original mixture and plastic metallic additive of Ni by a combined method of cold spraying with subsequent layer-by-layer laser treatment. Mechanical properties of the resultant tracks are examined. It is shown that the track microhardness increases with increasing B4C concentration in the original mixture. The track structure is found to depend on the size of ceramic particles in the interval from 3 to 75 μm. Reduction of the B4C particle size (approximately by a factor of 2-3) inside the track owing to fragmentation under the action of the laser beam is observed for the first time.

Uniqueness of thermodynamic projector and kinetic basis of molecular individualism

NASA Astrophysics Data System (ADS)

Gorban, Alexander N.; Karlin, Iliya V.

2004-05-01

Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is proven: There exists only one projector which transforms any vector field equipped with the given Lyapunov function into a vector field with the same Lyapunov function for a given anzatz manifold which is not tangent to the Lyapunov function levels. Second, we use the thermodynamic projector for developing the short memory approximation and coarse-graining for general nonlinear dynamic systems. We prove that in this approximation the entropy production increases. ( The theorem about entropy overproduction.) In example, we apply the thermodynamic projector to derive the equations of reduced kinetics for the Fokker-Planck equation. A new class of closures is developed, the kinetic multipeak polyhedra. Distributions of this type are expected in kinetic models with multidimensional instability as universally as the Gaussian distribution appears for stable systems. The number of possible relatively stable states of a nonequilibrium system grows as 2 m, and the number of macroscopic parameters is in order mn, where n is the dimension of configuration space, and m is the number of independent unstable directions in this space. The elaborated class of closures and equations pretends to describe the effects of “molecular individualism”. This is the third result.

Image reconstruction in higher dimensions: myocardial perfusion imaging of tracer dynamics with cardiac motion due to deformation and respiration

DOE PAGES

Shrestha, Uttam M.; Seo, Youngho; Botvinick, Elias H.; ...

2015-10-09

Myocardial perfusion imaging (MPI) using slow rotating large field of view cameras requires spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration. In vivo, MPI contains additional degrees of freedom involving unavoidable motion of the heart due to quasiperiodic beating and the effects of respiration, which can severely degrade the quality of the images. This work develops a technique for a single photon emission computed tomography (SPECT) that reconstructs the distribution of the radiotracer concentration in the myocardium using a tensor product of different sets of basis functions that approximately describe the spatiotemporal variationmore » of the radiotracer concentration and the motion of the heart. In this study the temporal B-spline basis functions are chosen to reflect the dynamics of the radiotracer, while the intrinsic deformation and the extrinsic motion of the heart are described by a product of a discrete set of Gaussian basis functions. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it deforms due to cardiac beating, and is displaced due to respiratory motion. We find these results are compared with the conventional 4D-spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. The higher dimensional reconstruction method proposed here improves bias, yet the signal-to-noise ratio (SNR) decreases slightly due to redistribution of the counts over the cardiac-respiratory gates. Finally, there is a trade-off between the number of gates and the number of projections per gate to achieve high contrast images.« less

Image reconstruction in higher dimensions: myocardial perfusion imaging of tracer dynamics with cardiac motion due to deformation and respiration

NASA Astrophysics Data System (ADS)

Shrestha, Uttam M.; Seo, Youngho; Botvinick, Elias H.; Gullberg, Grant T.

2015-11-01

Myocardial perfusion imaging (MPI) using slow rotating large field of view cameras requires spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration. In vivo, MPI contains additional degrees of freedom involving unavoidable motion of the heart due to quasiperiodic beating and the effects of respiration, which can severely degrade the quality of the images. This work develops a technique for a single photon emission computed tomography (SPECT) that reconstructs the distribution of the radiotracer concentration in the myocardium using a tensor product of different sets of basis functions that approximately describe the spatiotemporal variation of the radiotracer concentration and the motion of the heart. In this study the temporal B-spline basis functions are chosen to reflect the dynamics of the radiotracer, while the intrinsic deformation and the extrinsic motion of the heart are described by a product of a discrete set of Gaussian basis functions. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it deforms due to cardiac beating, and is displaced due to respiratory motion. These results are compared with the conventional 4D-spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. The higher dimensional reconstruction method proposed here improves bias, yet the signal-to-noise ratio (SNR) decreases slightly due to redistribution of the counts over the cardiac-respiratory gates. Additionally, there is a trade-off between the number of gates and the number of projections per gate to achieve high contrast images.

Image reconstruction in higher dimensions: myocardial perfusion imaging of tracer dynamics with cardiac motion due to deformation and respiration

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

Shrestha, Uttam M.; Seo, Youngho; Botvinick, Elias H.

Myocardial perfusion imaging (MPI) using slow rotating large field of view cameras requires spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration. In vivo, MPI contains additional degrees of freedom involving unavoidable motion of the heart due to quasiperiodic beating and the effects of respiration, which can severely degrade the quality of the images. This work develops a technique for a single photon emission computed tomography (SPECT) that reconstructs the distribution of the radiotracer concentration in the myocardium using a tensor product of different sets of basis functions that approximately describe the spatiotemporal variationmore » of the radiotracer concentration and the motion of the heart. In this study the temporal B-spline basis functions are chosen to reflect the dynamics of the radiotracer, while the intrinsic deformation and the extrinsic motion of the heart are described by a product of a discrete set of Gaussian basis functions. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it deforms due to cardiac beating, and is displaced due to respiratory motion. We find these results are compared with the conventional 4D-spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. The higher dimensional reconstruction method proposed here improves bias, yet the signal-to-noise ratio (SNR) decreases slightly due to redistribution of the counts over the cardiac-respiratory gates. Finally, there is a trade-off between the number of gates and the number of projections per gate to achieve high contrast images.« less

Image reconstruction in higher dimensions: myocardial perfusion imaging of tracer dynamics with cardiac motion due to deformation and respiration.

PubMed

Shrestha, Uttam M; Seo, Youngho; Botvinick, Elias H; Gullberg, Grant T

2015-11-07

Myocardial perfusion imaging (MPI) using slow rotating large field of view cameras requires spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration. In vivo, MPI contains additional degrees of freedom involving unavoidable motion of the heart due to quasiperiodic beating and the effects of respiration, which can severely degrade the quality of the images. This work develops a technique for a single photon emission computed tomography (SPECT) that reconstructs the distribution of the radiotracer concentration in the myocardium using a tensor product of different sets of basis functions that approximately describe the spatiotemporal variation of the radiotracer concentration and the motion of the heart. In this study the temporal B-spline basis functions are chosen to reflect the dynamics of the radiotracer, while the intrinsic deformation and the extrinsic motion of the heart are described by a product of a discrete set of Gaussian basis functions. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it deforms due to cardiac beating, and is displaced due to respiratory motion. These results are compared with the conventional 4D-spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. The higher dimensional reconstruction method proposed here improves bias, yet the signal-to-noise ratio (SNR) decreases slightly due to redistribution of the counts over the cardiac-respiratory gates. Additionally, there is a trade-off between the number of gates and the number of projections per gate to achieve high contrast images.

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium.

PubMed

Yura, H T; Thrane, L; Andersen, P E

2000-12-01

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

Trends in stratospheric ozone profiles using functional mixed models

NASA Astrophysics Data System (ADS)

Park, A. Y.; Guillas, S.; Petropavlovskikh, I.

2013-05-01

This paper is devoted to the modeling of altitude-dependent patterns of ozone variations over time. Umkher ozone profiles (quarter of Umkehr layer) from 1978 to 2011 are investigated at two locations: Boulder (USA) and Arosa (Switzerland). The study consists of two statistical stages. First we approximate ozone profiles employing an appropriate basis. To capture primary modes of ozone variations without losing essential information, a functional principal component analysis is performed as it penalizes roughness of the function and smooths excessive variations in the shape of the ozone profiles. As a result, data driven basis functions are obtained. Secondly we estimate the effects of covariates - month, year (trend), quasi biennial oscillation, the Solar cycle, arctic oscillation and the El Niño/Southern Oscillation cycle - on the principal component scores of ozone profiles over time using generalized additive models. The effects are smooth functions of the covariates, and are represented by knot-based regression cubic splines. Finally we employ generalized additive mixed effects models incorporating a more complex error structure that reflects the observed seasonality in the data. The analysis provides more accurate estimates of influences and trends, together with enhanced uncertainty quantification. We are able to capture fine variations in the time evolution of the profiles such as the semi-annual oscillation. We conclude by showing the trends by altitude over Boulder. The strongly declining trends over 2003-2011 for altitudes of 32-64 hPa show that stratospheric ozone is not yet fully recovering.

Recording from two neurons: second-order stimulus reconstruction from spike trains and population coding.

PubMed

Fernandes, N M; Pinto, B D L; Almeida, L O B; Slaets, J F W; Köberle, R

2010-10-01

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5% of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100% improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)(1-x)(ZnO)(x).

PubMed

Liu, Jian; Pedroza, Luana S; Misch, Carissa; Fernández-Serra, Maria V; Allen, Philip B

2014-07-09

We present total energy and force calculations for the (GaN)1-x(ZnO)x alloy. Site-occupancy configurations are generated from Monte Carlo (MC) simulations, on the basis of a cluster expansion model proposed in a previous study. Local atomic coordinate relaxations of surprisingly large magnitude are found via density-functional calculations using a 432-atom periodic supercell, for three representative configurations at x = 0.5. These are used to generate bond-length distributions. The configurationally averaged composition- and temperature-dependent short-range order (SRO) parameters of the alloys are discussed. The entropy is approximated in terms of pair distribution statistics and thus related to SRO parameters. This approximate entropy is compared with accurate numerical values from MC simulations. An empirical model for the dependence of the bond length on the local chemical environments is proposed.

Approximating high-dimensional dynamics by barycentric coordinates with linear programming

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

Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics ofmore » the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.« less

Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

PubMed

Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

2015-01-01

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

PubMed

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

Fast-match on particle swarm optimization with variant system mechanism

NASA Astrophysics Data System (ADS)

Wang, Yuehuang; Fang, Xin; Chen, Jie

2018-03-01

Fast-Match is a fast and effective algorithm for approximate template matching under 2D affine transformations, which can match the target with maximum similarity without knowing the target gesture. It depends on the minimum Sum-of-Absolute-Differences (SAD) error to obtain the best affine transformation. The algorithm is widely used in the field of matching images because of its fastness and robustness. In this paper, our approach is to search an approximate affine transformation over Particle Swarm Optimization (PSO) algorithm. We treat each potential transformation as a particle that possesses memory function. Each particle is given a random speed and flows throughout the 2D affine transformation space. To accelerate the algorithm and improve the abilities of seeking the global excellent result, we have introduced the variant system mechanism on this basis. The benefit is that we can avoid matching with huge amount of potential transformations and falling into local optimal condition, so that we can use a few transformations to approximate the optimal solution. The experimental results prove that our method has a faster speed and a higher accuracy performance with smaller affine transformation space.

A study of different modeling choices for simulating platelets within the immersed boundary method

PubMed Central

Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.

2012-01-01

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. PMID:23585704

Achieving accuracy in first-principles calculations at extreme temperature and pressure

NASA Astrophysics Data System (ADS)

Mattsson, Ann; Wills, John

2013-06-01

First-principles calculations are increasingly used to provide EOS data at pressures and temperatures where experimental data is difficult or impossible to obtain. The lack of experimental data, however, also precludes validation of the calculations in those regimes. Factors influencing the accuracy of first-principles data include theoretical approximations, and computational approximations used in implementing and solving the underlying equations. The first category includes approximate exchange-correlation functionals and wave equations simplifying the Dirac equation. In the second category are, e.g., basis completeness and pseudo-potentials. While the first category is extremely hard to assess without experimental data, inaccuracies of the second type should be well controlled. We are using two rather different electronic structure methods (VASP and RSPt) to make explicit the requirements for accuracy of the second type. We will discuss the VASP Projector Augmented Wave potentials, with examples for Li and Mo. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Nonlocal screening in metal surfaces

NASA Technical Reports Server (NTRS)

Krotscheck, E.; Kohn, W.

1986-01-01

Due to the effect of the nonuniform environment on the static screening of the Coulomb potential, the local-density approximation for the particle-hole interaction is found to be inadequate to determine the surface energy of simple metals. Use of the same set of single-particle states, and thus the same one-body density and the same work function, has eliminated the single-electron states in favor of the structure of the short-ranged correlations as the basis of this effect. A posteriori simplifications of the Fermi hypernetted-chain theory may be found to allow the same calculational accuracy with simpler computational tools.

Symmetry analysis of trimers rovibrational spectra: the case of Ne3★

NASA Astrophysics Data System (ADS)

Márquez-Mijares, Maykel; Roncero, Octavio; Villarreal, Pablo; González-Lezana, Tomás

2018-05-01

An approximate method to assign the symmetry to the rovibrational spectrum of homonuclear trimers based on the solution of the rotational Hamiltonian by means of a purely vibrational basis combined with standard rotational functions is applied on Ne3. The neon trimer constitutes an ideal test between heavier systems such as Ar3 for which the method proves to be an extremely useful technique and some other previously investigated cases such as H3 + where some limitations were observed. Comparisons of the calculated rovibrational energy levels are established with results from different calculations reported in the literature.

Predictive Behavior of a Computational Foot/Ankle Model through Artificial Neural Networks.

PubMed

Chande, Ruchi D; Hargraves, Rosalyn Hobson; Ortiz-Robinson, Norma; Wayne, Jennifer S

2017-01-01

Computational models are useful tools to study the biomechanics of human joints. Their predictive performance is heavily dependent on bony anatomy and soft tissue properties. Imaging data provides anatomical requirements while approximate tissue properties are implemented from literature data, when available. We sought to improve the predictive capability of a computational foot/ankle model by optimizing its ligament stiffness inputs using feedforward and radial basis function neural networks. While the former demonstrated better performance than the latter per mean square error, both networks provided reasonable stiffness predictions for implementation into the computational model.

First principle investigation of structural and optical properties of cubic titanium dioxide

NASA Astrophysics Data System (ADS)

Dash, Debashish; Chaudhury, Saurabh; Tripathy, Susanta K.

2018-05-01

This paper presents an analysis of structural and optical properties of cubic titanium dioxide (TiO2) using Orthogonalzed Linear Combinations of Atomic Orbitals (OLCAO) basis set under the framework of Density Functional Theory (DFT). The structural property, specially the lattice constant `a' and the optical properties such as refractive index, extinction coefficient, and reflectivity are investigated and discussed in the energy range of 0-16 eV. Further, the results have compared with previous theoretical as well as with experimental results. It was found that DFT based simulation results are approximation to experimental results.

Sample size calculations for comparative clinical trials with over-dispersed Poisson process data.

PubMed

Matsui, Shigeyuki

2005-05-15

This paper develops a new formula for sample size calculations for comparative clinical trials with Poisson or over-dispersed Poisson process data. The criteria for sample size calculations is developed on the basis of asymptotic approximations for a two-sample non-parametric test to compare the empirical event rate function between treatment groups. This formula can accommodate time heterogeneity, inter-patient heterogeneity in event rate, and also, time-varying treatment effects. An application of the formula to a trial for chronic granulomatous disease is provided. Copyright 2004 John Wiley & Sons, Ltd.

Changes in functional construction of bone in rats under conditions of simulated increased gravity.

NASA Technical Reports Server (NTRS)

Amtmann, E.; Oyama, J.

1973-01-01

An investigation was conducted to determine experimentally whether femur bones are altered in cross-sectional area or cross-sectional shape by chronic centrifugation at different G-levels in conformance to Wolff's law. It was found that the centrifuged animals exhibit on the average smaller body masses, femur lengths and femur cross sections, as compared to their corresponding age controls. The mean inhibitory effect of chronic centrifugation upon body and femur growth can be measured in a shortcut approximation by calculating the decrease of body masses and femoral dimensions on a percentage basis.

Quasi-optical grids with thin rectangular patch/aperture elements

NASA Technical Reports Server (NTRS)

Wu, Te-Kao

1993-01-01

Theoretical analysis is presented for an efficient and accurate performance evaluation of quasi-optical grids comprised of thin rectangular patch/aperture elements with/without a dielectric substrate/superstrate. The convergence rate of this efficient technique is improved by an order of magnitude with the approximate edge conditions incorporated in the basis functions of the integral equation solution. Also presented are the interesting applications of this efficient analytical technique to the design and performance evaluation of the coupling grids and beam splitters in the optical systems as well as thermal protection sunshields used in the communication systems of satellites and spacecrafts.

A new operational approach for solving fractional variational problems depending on indefinite integrals

NASA Astrophysics Data System (ADS)

Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

2018-04-01

In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

Interaction of acetone with single wall carbon nanotubes at cryogenic temperatures: a combined temperature programmed desorption and theoretical study.

PubMed

Kazachkin, Dmitry; Nishimura, Yoshifumi; Irle, Stephan; Morokuma, Keiji; Vidic, Radisav D; Borguet, Eric

2008-08-05

The interaction of acetone with single wall carbon nanotubes (SWCNTs) at low temperatures was studied by a combination of temperature programmed desorption (TPD) and dispersion-augmented density-functional-based tight binding (DFTB-D) theoretical simulations. On the basis of the results of the TPD study and theoretical simulations, the desorption peaks of acetone can be assigned to the following adsorption sites: (i) sites with energy of approximately 75 kJ mol (-1) ( T des approximately 300 K)endohedral sites of small diameter nanotubes ( approximately 7.7 A); (ii) sites with energy 40-68 kJ mol (-1) ( T des approximately 240 K)acetone adsorption on accessible interstitial, groove sites, and endohedral sites of larger nanotubes ( approximately 14 A); (iii) sites with energy 25-42 kJ mol (-1) ( T des approximately 140 K)acetone adsorption on external walls of SWCNTs and multilayer adsorption. Oxidatively purified SWCNTs have limited access to endohedral sites due to the presence of oxygen functionalities. Oxygen functionalities can be removed by annealing to elevated temperature (900 K) opening access to endohedral sites of nanotubes. Nonpurified, as-received SWCNTs are characterized by limited access for acetone to endohedral sites even after annealing to elevated temperatures (900 K). Annealing of both purified and as-produced SWCNTs to high temperatures (1400 K) leads to reduction of access for acetone molecules to endohedral sites of small nanotubes, probably due to defect self-healing and cap formation at the ends of SWCNTs. No chemical interaction between acetone and SWCNTs was detected for low temperature adsorption experiments. Theoretical simulations of acetone adsorption on finite pristine SWCNTs of different diameters suggest a clear relationship of the adsorption energy with tube sidewall curvature. Adsorption of acetone is due to dispersion forces, with its C-O bond either parallel to the surface or O pointing away from it. No significant charge transfer or polarization was found. Carbon black was used to model amorphous carbonaceous impurities present in as-produced SWCNTs. Desorption of acetone from carbon black revealed two peaks at approximately 140 and approximately 180-230 K, similar to two acetone desorption peaks from SWCNTs. The characteristic feature of acetone desorption from SWCNTs was peak at approximately 300 K that was not observed for carbon black. Care should be taken when assigning TPD peaks for molecules desorbing from carbon nanotubes as amorphous carbon can interfere.

Calculations of molecular multipole electric moments of a series of exo-insaturated four-membered heterocycles, Y = CCH2CH2X

NASA Astrophysics Data System (ADS)

Romero, Angel H.

2017-10-01

The influence of ring puckering angle on the multipole moments of sixteen four-membered heterocycles (1-16) was theoretically estimated using MP2 and different DFTs in combination with the 6-31+G(d,p) basis set. To obtain an accurate evaluation, CCSD/cc-pVDZ level and, the MP2 and PBE1PBE methods in combination with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were performed on the planar geometries of 1-16. In general, the DFT and MP2 approaches provided an identical dependence of the electrical properties with the puckering angle for 1-16. Quantitatively, the quality of the level of theory and basis sets affects significant the predictions of the multipole moments, in particular for the heterocycles containing C=O and C=S bonds. Convergence basis sets within the MP2 and PBE1PBE approximations are reached in the dipole moment calculations when the aug-cc-pVTZ basis set is used, while the quadrupole and octupole moment computations require a larger basis set than aug-cc-pVTZ. On the other hand, the multipole moments showed a strong dependence with the molecular geometry and the nature of the carbon-heteroatom bonds. Specifically, the C-X bond determines the behavior of the μ(ϕ), θ(ϕ) and Ώ(ϕ) functions, while the C=Y bond plays an important role in the magnitude of the studied properties.

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

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

21 CFR 172.841 - Polydextrose.

Code of Federal Regulations, 2013 CFR

2013-04-01

... consists either of approximately 89 percent D-glucose, 10 percent sorbitol, and 1 percent citric acid or of approximately 90 percent D-glucose, 10 percent sorbitol, and 0.1 percent phosphoric acid, on a weight basis. (2...

21 CFR 172.841 - Polydextrose.

Code of Federal Regulations, 2011 CFR

2011-04-01

... consists either of approximately 89 percent D-glucose, 10 percent sorbitol, and 1 percent citric acid or of approximately 90 percent D-glucose, 10 percent sorbitol, and 0.1 percent phosphoric acid, on a weight basis. (2...

21 CFR 172.841 - Polydextrose.

Code of Federal Regulations, 2012 CFR

2012-04-01

... consists either of approximately 89 percent D-glucose, 10 percent sorbitol, and 1 percent citric acid or of approximately 90 percent D-glucose, 10 percent sorbitol, and 0.1 percent phosphoric acid, on a weight basis. (2...

21 CFR 172.841 - Polydextrose.

Code of Federal Regulations, 2010 CFR

2010-04-01

... consists either of approximately 89 percent D-glucose, 10 percent sorbitol, and 1 percent citric acid or of approximately 90 percent D-glucose, 10 percent sorbitol, and 0.1 percent phosphoric acid, on a weight basis. (2...

Simulated quantum computation of molecular energies.

PubMed

Aspuru-Guzik, Alán; Dutoi, Anthony D; Love, Peter J; Head-Gordon, Martin

2005-09-09

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

A Reconfigurable Readout Integrated Circuit for Heterogeneous Display-Based Multi-Sensor Systems

PubMed Central

Park, Kyeonghwan; Kim, Seung Mok; Eom, Won-Jin; Kim, Jae Joon

2017-01-01

This paper presents a reconfigurable multi-sensor interface and its readout integrated circuit (ROIC) for display-based multi-sensor systems, which builds up multi-sensor functions by utilizing touch screen panels. In addition to inherent touch detection, physiological and environmental sensor interfaces are incorporated. The reconfigurable feature is effectively implemented by proposing two basis readout topologies of amplifier-based and oscillator-based circuits. For noise-immune design against various noises from inherent human-touch operations, an alternate-sampling error-correction scheme is proposed and integrated inside the ROIC, achieving a 12-bit resolution of successive approximation register (SAR) of analog-to-digital conversion without additional calibrations. A ROIC prototype that includes the whole proposed functions and data converters was fabricated in a 0.18 μm complementary metal oxide semiconductor (CMOS) process, and its feasibility was experimentally verified to support multiple heterogeneous sensing functions of touch, electrocardiogram, body impedance, and environmental sensors. PMID:28368355

A Reconfigurable Readout Integrated Circuit for Heterogeneous Display-Based Multi-Sensor Systems.

PubMed

Park, Kyeonghwan; Kim, Seung Mok; Eom, Won-Jin; Kim, Jae Joon

2017-04-03

This paper presents a reconfigurable multi-sensor interface and its readout integrated circuit (ROIC) for display-based multi-sensor systems, which builds up multi-sensor functions by utilizing touch screen panels. In addition to inherent touch detection, physiological and environmental sensor interfaces are incorporated. The reconfigurable feature is effectively implemented by proposing two basis readout topologies of amplifier-based and oscillator-based circuits. For noise-immune design against various noises from inherent human-touch operations, an alternate-sampling error-correction scheme is proposed and integrated inside the ROIC, achieving a 12-bit resolution of successive approximation register (SAR) of analog-to-digital conversion without additional calibrations. A ROIC prototype that includes the whole proposed functions and data converters was fabricated in a 0.18 μm complementary metal oxide semiconductor (CMOS) process, and its feasibility was experimentally verified to support multiple heterogeneous sensing functions of touch, electrocardiogram, body impedance, and environmental sensors.

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.

PubMed

Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David

2013-08-07

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

Diffusion of test particles in stochastic magnetic fields for small Kubo numbers.

PubMed

Neuer, Marcus; Spatschek, Karl H

2006-02-01

Motion of charged particles in a collisional plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. Compared to the previously used A-Langevin model, here finite Larmor radius effects are taken into account. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. The velocity correlation function, being averaged with respect to the stochastic variables including collisions, leads to an implicit differential equation for the mean square displacement. From the latter, different transport regimes, including the well-known Rechester-Rosenbluth diffusion coefficient, are derived. Finite Larmor radius contributions show a decrease of the diffusion coefficient compared to the guiding center limit. The case of small (or vanishing) mean fields is also discussed.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Effects of intervention using a community-based walking program for prevention of mental decline: a randomized controlled trial.

PubMed

Maki, Yohko; Ura, Chiaki; Yamaguchi, Tomoharu; Murai, Tatsuhiko; Isahai, Mikie; Kaiho, Ayumi; Yamagami, Tetsuya; Tanaka, Satoshi; Miyamae, Fumiko; Sugiyama, Mika; Awata, Shuichi; Takahashi, Ryutaro; Yamaguchi, Haruyasu

2012-03-01

To evaluate the efficacy of a municipality-led walking program under the Japanese public Long-Term Care Insurance Act to prevent mental decline. Randomized controlled trial. The city of Takasaki. One hundred fifty community members aged 72.0 ± 4.0 were randomly divided into intervention (n = 75) and control (n = 75) groups. A walking program was conducted once a week for 90 minutes for 3 months. The program encouraged participants to walk on a regular basis and to increase their steps per day gradually. The intervention was conducted in small groups of approximately six, so combined benefits of exercise and social interaction were expected. Cognitive function was evaluated focusing on nine tests in five domains: memory, executive function, word fluency, visuospatial abilities, and sustained attention. Quality of life (QOL), depressive state, functional capacity, range of activities, and social network were assessed using questionnaires, and motor function was evaluated. Significant differences between the intervention and control groups were shown in word fluency related to frontal lobe function (F(1, 128) = 6.833, P = .01), QOL (F(1,128) = 9.751, P = .002), functional capacity including social interaction (F(1,128) = 13.055, P < .001), and motor function (Timed Up and Go Test: F(1,127) = 10.117, P = .002). No significant differences were observed in other cognitive tests. Walking programs may provide benefits in some aspects of cognition, QOL, and functional capacity including social interaction in elderly community members. This study could serve as the basis for implementation of a community-based intervention to prevent mental decline. © 2012, Copyright the Authors Journal compilation © 2012, The American Geriatrics Society.

Constitutive Modelling of Resins in the Stiffness Domain

NASA Astrophysics Data System (ADS)

Klasztorny, M.

2004-09-01

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic. The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.

Non-Born-Oppenheimer calculations of the pure vibrational spectrum of HeH+.

PubMed

Pavanello, Michele; Bubin, Sergiy; Molski, Marcin; Adamowicz, Ludwik

2005-09-08

Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported. The method used does not assume the Born-Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.

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

Scherrer, Arne; UMR 8640 ENS-CNRS-UPMC, Département de Chimie, 24 rue Lhomond, École Normale Supérieure, 75005 Paris; UPMC Université Paris 06, 4, Place Jussieu, 75005 Paris

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similar to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that canmore » be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.« less

Stress and the Hair Growth Cycle: Cortisol-Induced Hair Growth Disruption.

PubMed

Thom, Erling

2016-08-01

The stress hormone, cortisol, is known to affect the function and cyclic regulation of the hair follicle. When cortisol is present at high levels it has been demonstrated to reduce the synthesis and accelerate the degradation of important skin elements, namely hyaluronan and proteoglycans by approximately 40%. The following discussion outlines the relationship between stress, cortisol, and the effect on the normal function of the hair follicle. As a result of this connection, important correlations have been established in the literature to form a basis for novel, effective treatments of stress-related hair growth disorders.
Amongst various treatment methods and substances, oral supplementation with a specific bioavailable proteoglycan stands out as a promising new therapeutic treatment method.

J Drugs Dermatol. 2016;15(8):1001-1004.

Stress-strain state on non-thin plates and shells. Generalized theory (survey)

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

Nemish, Yu.N.; Khoma, I.Yu.

1994-05-01

In the first part of this survey, we examined exact and approximate analytic solutions of specific problems for thick shells and plates obtained on the basis of three-dimensional equations of the mathematical theory of elasticity. The second part of the survey, presented here, is devoted to systematization and analysis of studies made in regard to a generalized theory of plates and shells based on expansion of the sought functions into Fourier series in Legendre polynomials of the thickness coordinate. Methods are described for constructing systems of differential equations in the coefficients of the expansions (as functions of two independent variablesmore » and time), along with the corresponding boundary and initial conditions. Matters relating to substantiation of the given approach and its generalizations are also discussed.« less

Sculpting bespoke mountains: Determining free energies with basis expansions

NASA Astrophysics Data System (ADS)

Whitmer, Jonathan K.; Fluitt, Aaron M.; Antony, Lucas; Qin, Jian; McGovern, Michael; de Pablo, Juan J.

2015-07-01

The intriguing behavior of a wide variety of physical systems, ranging from amorphous solids or glasses to proteins, is a direct manifestation of underlying free energy landscapes riddled with local minima separated by large barriers. Exploring such landscapes has arguably become one of statistical physics's great challenges. A new method is proposed here for uniform sampling of rugged free energy surfaces. The method, which relies on special Green's functions to approximate the Dirac delta function, improves significantly on existing simulation techniques by providing a boundary-agnostic approach that is capable of mapping complex features in multidimensional free energy surfaces. The usefulness of the proposed approach is established in the context of a simple model glass former and model proteins, demonstrating improved convergence and accuracy over existing methods.

Vibrational Properties of Hydrogen-Bonded Systems Using the Multireference Generalization to the "On-the-Fly" Electronic Structure within Quantum Wavepacket ab Initio Molecular Dynamics (QWAIMD).

PubMed

Li, Junjie; Li, Xiaohu; Iyengar, Srinivasan S

2014-06-10

We discuss a multiconfigurational treatment of the "on-the-fly" electronic structure within the quantum wavepacket ab initio molecular dynamics (QWAIMD) method for coupled treatment of quantum nuclear effects with electronic structural effects. Here, multiple single-particle electronic density matrices are simultaneously propagated with a quantum nuclear wavepacket and other classical nuclear degrees of freedom. The multiple density matrices are coupled through a nonorthogonal configuration interaction (NOCI) procedure to construct the instantaneous potential surface. An adaptive-mesh-guided set of basis functions composed of Gaussian primitives are used to simplify the electronic structure calculations. Specifically, with the replacement of the atom-centered basis functions positioned on the centers of the quantum-mechanically treated nuclei by a mesh-guided band of basis functions, the two-electron integrals used to compute the electronic structure potential surface become independent of the quantum nuclear variable and hence reusable along the entire Cartesian grid representing the quantum nuclear coordinates. This reduces the computational complexity involved in obtaining a potential surface and facilitates the interpretation of the individual density matrices as representative diabatic states. The parametric nuclear position dependence of the diabatic states is evaluated at the initial time-step using a Shannon-entropy-based sampling function that depends on an approximation to the quantum nuclear wavepacket and the potential surface. This development is meant as a precursor to an on-the-fly fully multireference electronic structure procedure embedded, on-the-fly, within a quantum nuclear dynamics formalism. We benchmark the current development by computing structural, dynamic, and spectroscopic features for a series of bihalide hydrogen-bonded systems: FHF(-), ClHCl(-), BrHBr(-), and BrHCl(-). We find that the donor-acceptor structural features are in good agreement with experiments. Spectroscopic features are computed using a unified velocity/flux autocorrelation function and include vibrational fundamentals and combination bands. These agree well with experiments and other theories.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Adaptive multiresolution modeling of groundwater flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Malenica, Luka; Gotovac, Hrvoje; Srzic, Veljko; Andric, Ivo

2016-04-01

Proposed methodology was originally developed by our scientific team in Split who designed multiresolution approach for analyzing flow and transport processes in highly heterogeneous porous media. The main properties of the adaptive Fup multi-resolution approach are: 1) computational capabilities of Fup basis functions with compact support capable to resolve all spatial and temporal scales, 2) multi-resolution presentation of heterogeneity as well as all other input and output variables, 3) accurate, adaptive and efficient strategy and 4) semi-analytical properties which increase our understanding of usually complex flow and transport processes in porous media. The main computational idea behind this approach is to separately find the minimum number of basis functions and resolution levels necessary to describe each flow and transport variable with the desired accuracy on a particular adaptive grid. Therefore, each variable is separately analyzed, and the adaptive and multi-scale nature of the methodology enables not only computational efficiency and accuracy, but it also describes subsurface processes closely related to their understood physical interpretation. The methodology inherently supports a mesh-free procedure, avoiding the classical numerical integration, and yields continuous velocity and flux fields, which is vitally important for flow and transport simulations. In this paper, we will show recent improvements within the proposed methodology. Since "state of the art" multiresolution approach usually uses method of lines and only spatial adaptive procedure, temporal approximation was rarely considered as a multiscale. Therefore, novel adaptive implicit Fup integration scheme is developed, resolving all time scales within each global time step. It means that algorithm uses smaller time steps only in lines where solution changes are intensive. Application of Fup basis functions enables continuous time approximation, simple interpolation calculations across different temporal lines and local time stepping control. Critical aspect of time integration accuracy is construction of spatial stencil due to accurate calculation of spatial derivatives. Since common approach applied for wavelets and splines uses a finite difference operator, we developed here collocation one including solution values and differential operator. In this way, new improved algorithm is adaptive in space and time enabling accurate solution for groundwater flow problems, especially in highly heterogeneous porous media with large lnK variances and different correlation length scales. In addition, differences between collocation and finite volume approaches are discussed. Finally, results show application of methodology to the groundwater flow problems in highly heterogeneous confined and unconfined aquifers.

Extraction of temporal information in functional MRI

NASA Astrophysics Data System (ADS)

Singh, M.; Sungkarat, W.; Jeong, Jeong-Won; Zhou, Yongxia

2002-10-01

The temporal resolution of functional MRI (fMRI) is limited by the shape of the haemodynamic response function (hrf) and the vascular architecture underlying the activated regions. Typically, the temporal resolution of fMRI is on the order of 1 s. We have developed a new data processing approach to extract temporal information on a pixel-by-pixel basis at the level of 100 ms from fMRI data. Instead of correlating or fitting the time-course of each pixel to a single reference function, which is the common practice in fMRI, we correlate each pixel's time-course to a series of reference functions that are shifted with respect to each other by 100 ms. The reference function yielding the highest correlation coefficient for a pixel is then used as a time marker for that pixel. A Monte Carlo simulation and experimental study of this approach were performed to estimate the temporal resolution as a function of signal-to-noise ratio (SNR) in the time-course of a pixel. Assuming a known and stationary hrf, the simulation and experimental studies suggest a lower limit in the temporal resolution of approximately 100 ms at an SNR of 3. The multireference function approach was also applied to extract timing information from an event-related motor movement study where the subjects flexed a finger on cue. The event was repeated 19 times with the event's presentation staggered to yield an approximately 100-ms temporal sampling of the haemodynamic response over the entire presentation cycle. The timing differences among different regions of the brain activated by the motor task were clearly visualized and quantified by this method. The results suggest that it is possible to achieve a temporal resolution of /spl sim/200 ms in practice with this approach.

Basis for paraxial surface-plasmon-polariton packets

NASA Astrophysics Data System (ADS)

Martinez-Herrero, Rosario; Manjavacas, Alejandro

2016-12-01

We present a theoretical framework for the study of surface-plasmon polariton (SPP) packets propagating along a lossy metal-dielectric interface within the paraxial approximation. Using a rigorous formulation based on the plane-wave spectrum formalism, we introduce a set of modes that constitute a complete basis set for the solutions of Maxwell's equations for a metal-dielectric interface in the paraxial approximation. The use of this set of modes allows us to fully analyze the evolution of the transversal structure of SPP packets beyond the single plane-wave approximation. As a paradigmatic example, we analyze the case of a Gaussian SPP mode, for which, exploiting the analogy with paraxial optical beams, we introduce a set of parameters that characterize its propagation.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

NASA Astrophysics Data System (ADS)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

[Density functional theory studies on structure and spectrum of Cu3 Ti cluster].

PubMed

Wei, Yong-Hui; Cheng, Jian-Bo; Zhao, Bing; Lombardi, John R

2008-07-01

Bulk intermetallic Ti-Cu compounds have been found to possess special properties, including increased hardness, as well as displaying enhanced sound absorption and e shape memory. Since only one Raman progression is observed, there is not sufficient information to determine the structure of TiCu3. The different structures and vibrational frequencies of the Cu3 Ti cluster were studied by means of the density functional theory with SVWN5, B3LYP and BPW91 methods at basis sets of lanl2dz, 6-31g, 6-311g, 6-311g(d), 6-311 +/- g(2df) and 6-311 +/- g(3d2f). The calculated results show that the ground state of the Cu3 Ti cluster is a e-type structure with the C2v point group symmetry, and the bond lengths and vibrational frequencies of Cu3 T are considerably dependent on the variation of basis sets. We observed only a single Raman progression in approximately 300 cm(-1). This progression is most likely the totally symmetric stretch. The computed and observed Raman spectra were also compared with each other.

Parallel Higher-order Finite Element Method for Accurate Field Computations in Wakefield and PIC Simulations

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

Candel, A.; Kabel, A.; Lee, L.

Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell)more » approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.« less

Accurate, precise, and efficient theoretical methods to calculate anion-π interaction energies in model structures.

PubMed

Mezei, Pál D; Csonka, Gábor I; Ruzsinszky, Adrienn; Sun, Jianwei

2015-01-13

A correct description of the anion-π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion-π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π-anion-π' sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values. We give a detailed explanation of the origin of anion-π interactions, using the permanent quadrupole moments, static dipole polarizabilities, and electrostatic potential maps. We use symmetry-adapted perturbation theory (SAPT) to calculate the components of the anion-π interaction energies. We examine the performance of the direct random phase approximation (dRPA), the second-order screened exchange (SOSEX), local-pair natural-orbital (LPNO) coupled electron pair approximation (CEPA), and several dispersion-corrected density functionals (including generalized gradient approximation (GGA), meta-GGA, and double hybrid density functional). The LPNO-CEPA/1 results show the best agreement with the reference results. The dRPA method is only slightly less accurate and precise than the LPNO-CEPA/1, but it is considerably more efficient (6-17 times faster) for the binary complexes studied in this paper. For 30 ternary π-anion-π' sandwich complexes, we give dRPA interaction energies as reference values. The double hybrid functionals are much more efficient but less accurate and precise than dRPA. The dispersion-corrected double hybrid PWPB95-D3(BJ) and B2PLYP-D3(BJ) functionals perform better than the GGA and meta-GGA functionals for the present test set.

Correlation functions from a unified variational principle: Trial Lie groups

NASA Astrophysics Data System (ADS)

Balian, R.; Vénéroni, M.

2015-11-01

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie-Poisson structure. At second order, the variational expression for two-time correlation functions separates-as does its exact counterpart-the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.

The dimension split element-free Galerkin method for three-dimensional potential problems

NASA Astrophysics Data System (ADS)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-06-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory

NASA Astrophysics Data System (ADS)

Phillips, Jordan J.; Zgid, Dominika

2014-06-01

We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H32 finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism.

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions

NASA Astrophysics Data System (ADS)

Jerke, Jonathan; Poirier, Bill

2018-03-01

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy—i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted—as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions.

PubMed

Jerke, Jonathan; Poirier, Bill

2018-03-14

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy-i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted-as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Wavelet SVM in Reproducing Kernel Hilbert Space for hyperspectral remote sensing image classification

NASA Astrophysics Data System (ADS)

Du, Peijun; Tan, Kun; Xing, Xiaoshi

2010-12-01

Combining Support Vector Machine (SVM) with wavelet analysis, we constructed wavelet SVM (WSVM) classifier based on wavelet kernel functions in Reproducing Kernel Hilbert Space (RKHS). In conventional kernel theory, SVM is faced with the bottleneck of kernel parameter selection which further results in time-consuming and low classification accuracy. The wavelet kernel in RKHS is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. Implications on semiparametric estimation are proposed in this paper. Airborne Operational Modular Imaging Spectrometer II (OMIS II) hyperspectral remote sensing image with 64 bands and Reflective Optics System Imaging Spectrometer (ROSIS) data with 115 bands were used to experiment the performance and accuracy of the proposed WSVM classifier. The experimental results indicate that the WSVM classifier can obtain the highest accuracy when using the Coiflet Kernel function in wavelet transform. In contrast with some traditional classifiers, including Spectral Angle Mapping (SAM) and Minimum Distance Classification (MDC), and SVM classifier using Radial Basis Function kernel, the proposed wavelet SVM classifier using the wavelet kernel function in Reproducing Kernel Hilbert Space is capable of improving classification accuracy obviously.

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction.

PubMed

Wei, Jianming; Zhang, Youan; Sun, Meimei; Geng, Baoliang

2017-09-01

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Reinforcement learning controller design for affine nonlinear discrete-time systems using online approximators.

PubMed

Yang, Qinmin; Jagannathan, Sarangapani

2012-04-01

In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.

Approximate Quantum Dynamics using Ab Initio Classical Separable Potentials: Spectroscopic Applications.

PubMed

Hirshberg, Barak; Sagiv, Lior; Gerber, R Benny

2017-03-14

Algorithms for quantum molecular dynamics simulations that directly use ab initio methods have many potential applications. In this article, the ab initio classical separable potentials (AICSP) method is proposed as the basis for approximate algorithms of this type. The AICSP method assumes separability of the total time-dependent wave function of the nuclei and employs mean-field potentials that govern the dynamics of each degree of freedom. In the proposed approach, the mean-field potentials are determined by classical ab initio molecular dynamics simulations. The nuclear wave function can thus be propagated in time using the effective potentials generated "on the fly". As a test of the method for realistic systems, calculations of the stationary anharmonic frequencies of hydrogen stretching modes were carried out for several polyatomic systems, including three amino acids and the guanine-cytosine pair of nucleobases. Good agreement with experiments was found. The method scales very favorably with the number of vibrational modes and should be applicable for very large molecules, e.g., peptides. The method should also be applicable for properties such as vibrational line widths and line shapes. Work in these directions is underway.

Inelastic transport theory from first principles: Methodology and application to nanoscale devices

NASA Astrophysics Data System (ADS)

Frederiksen, Thomas; Paulsson, Magnus; Brandbyge, Mads; Jauho, Antti-Pekka

2007-05-01

We describe a first-principles method for calculating electronic structure, vibrational modes and frequencies, electron-phonon couplings, and inelastic electron transport properties of an atomic-scale device bridging two metallic contacts under nonequilibrium conditions. The method extends the density-functional codes SIESTA and TRANSIESTA that use atomic basis sets. The inelastic conductance characteristics are calculated using the nonequilibrium Green’s function formalism, and the electron-phonon interaction is addressed with perturbation theory up to the level of the self-consistent Born approximation. While these calculations often are computationally demanding, we show how they can be approximated by a simple and efficient lowest order expansion. Our method also addresses effects of energy dissipation and local heating of the junction via detailed calculations of the power flow. We demonstrate the developed procedures by considering inelastic transport through atomic gold wires of various lengths, thereby extending the results presented in Frederiksen [Phys. Rev. Lett. 93, 256601 (2004)]. To illustrate that the method applies more generally to molecular devices, we also calculate the inelastic current through different hydrocarbon molecules between gold electrodes. Both for the wires and the molecules our theory is in quantitative agreement with experiments, and characterizes the system-specific mode selectivity and local heating.

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

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

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Preliminary investigations into macroscopic attenuated total reflection-fourier transform infrared imaging of intact spherical domains: spatial resolution and image distortion.

PubMed

Everall, Neil J; Priestnall, Ian M; Clarke, Fiona; Jayes, Linda; Poulter, Graham; Coombs, David; George, Michael W

2009-03-01

This paper describes preliminary investigations into the spatial resolution of macro attenuated total reflection (ATR) Fourier transform infrared (FT-IR) imaging and the distortions that arise when imaging intact, convex domains, using spheres as an extreme example. The competing effects of shallow evanescent wave penetration and blurring due to finite spatial resolution meant that spheres within the range 20-140 microm all appeared to be approximately the same size ( approximately 30-35 microm) when imaged with a numerical aperture (NA) of approximately 0.2. A very simple model was developed that predicted this extreme insensitivity to particle size. On the basis of these studies, it is anticipated that ATR imaging at this NA will be insensitive to the size of intact highly convex objects. A higher numerical aperture device should give a better estimate of the size of small spheres, owing to superior spatial resolution, but large spheres should still appear undersized due to the shallow sampling depth. An estimate of the point spread function (PSF) was required in order to develop and apply the model. The PSF was measured by imaging a sharp interface; assuming an Airy profile, the PSF width (distance from central maximum to first minimum) was estimated to be approximately 20 and 30 microm for IR bands at 1600 and 1000 cm(-1), respectively. This work has two significant limitations. First, underestimation of domain size only arises when imaging intact convex objects; if surfaces are prepared that randomly and representatively section through domains, the images can be analyzed to calculate parameters such as domain size, area, and volume. Second, the model ignores reflection and refraction and assumes weak absorption; hence, the predicted intensity profiles are not expected to be accurate; they merely give a rough estimate of the apparent sphere size. Much further work is required to place the field of quantitative ATR-FT-IR imaging on a sound basis.

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

PubMed

Saller, Maximilian A C; Habershon, Scott

2017-07-11

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

Theoretical studies on photoelectron and IR spectral properties of Br2.-(H2O)n clusters.

PubMed

Pathak, A K; Mukherjee, T; Maity, D K

2007-07-28

We report vertical detachment energy (VDE) and IR spectra of Br2.-.(H2O)n clusters (n=1-8) based on first principles electronic structure calculations. Cluster structures and IR spectra are calculated at Becke's half-and-half hybrid exchange-correlation functional (BHHLYP) with a triple split valence basis function, 6-311++G(d,p). VDE for the hydrated clusters is calculated based on second order Moller-Plesset perturbation (MP2) theory with the same set of basis function. On full geometry optimization, it is observed that conformers having interwater hydrogen bonding among solvent water molecules are more stable than the structures having double or single hydrogen bonded structures between the anionic solute, Br2.-, and solvent water molecules. Moreover, a conformer having cyclic interwater hydrogen bonded network is predicted to be more stable for each size hydrated cluster. It is also noticed that up to four solvent H2O units can reside around the solute in a cyclic interwater hydrogen bonded network. The excess electron in these hydrated clusters is localized over the solute atoms. Weighted average VDE is calculated for each size (n) cluster based on statistical population of the conformers at 150 K. A linear relationship is obtained for VDE versus (n+3)(-1/3) and bulk VDE of Br2.- aqueous solution is calculated as 10.01 eV at MP2 level of theory. BHHLYP density functional is seen to make a systematic overestimation in VDE values by approximately 0.5 eV compared to MP2 data in all the hydrated clusters. It is observed that hydration increases VDE of bromine dimer anion system by approximately 6.4 eV. Calculated IR spectra show that the formation of Br2.--water clusters induces large shifts from the normal O-H stretching bands of isolated water keeping bending modes rather insensitive. Hydrated clusters, Br2.-.(H2O)n, show characteristic sharp features of O-H stretching bands of water in the small size clusters.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory.

PubMed

Ismail-Beigi, Sohrab

2017-09-27

The question of which non-interacting Green's function 'best' describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Baym-Kadanoff theory, an approach where one locates the stationary point of a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. For the case of the Klein functional, our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the quasiparticle self-consistent GW (QSGW) (van Schilfgaarde et al 2006 Phys. Rev. Lett. 96 226402-4) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g., the GW approximation for the self-energy. The approach also shows that, when working in the basis of quasiparticle states, solving the diagonal part of the self-consistent Dyson equation is of primary importance while the off-diagonals are of secondary importance, a common observation in the electronic structure literature of self-energy calculations. Finally, numerical tests and analytical arguments show that when the Dyson equation produces multiple quasiparticle solutions corresponding to a single non-interacting state, minimizing the length of the gradient translates into choosing the solution with largest quasiparticle weight.

Excitation spectra of aromatic molecules within a real-space G W -BSE formalism: Role of self-consistency and vertex corrections

DOE PAGES

Hung, Linda; da Jornada, Felipe H.; Souto-Casares, Jaime; ...

2016-08-15

Here, we present first-principles calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the GW and Bethe-Salpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well suited for high-accuracy calculations on molecules, as we show by comparing against G0W0 calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the GW approximation that include a local density approximation (LDA)–derived vertex function (Γ LDA ) andmore » quasiparticle-self-consistent (QS) iterations. We find that Γ LDA and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and the same sign for EAs. G0W0 and QS GWΓ LDA are more accurate for IPs, while G 0W 0Γ LDA and QS GW are best for EAs. For optical excitations, we find that perturbative GW-BSE underestimates the singlet excitation energy, while self-consistent GW-BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, in which G0W0 energies are used for occupied orbitals and G0W0Γ LDA for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.« less

Third-order Douglas-Kroll Relativistic Coupled-Cluster Theory through Connected Single, Double, Triple, and Quadruple Substitutions: Applications to Diatomic and Triatomic Hydrides

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

Hirata, So; Yanai, Takeshi; De Jong, Wibe A.

Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions (CCSD, CCSDT, and CCSDTQ) have been automatically derived and implemented for sequential and parallel executions for use in conjunction with a one-component third-order Douglas-Kroll (DK3) approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths within 0.002 angstroms,more » rotational constants within 0.02 cm-1, vibration-rotation constants within 0.01 cm-1, centrifugal distortion constants within 2 %, harmonic vibration frequencies within 9 cm-1 (0.4 %), anharmonic vibrational constants within 2 cm-1, and dissociation energies within 0.03 eV (0.8 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth periods of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated by the formula which was in turn based on the exponential-Gaussian extrapolation formula of the basis set dependence.« less

Excitation spectra of aromatic molecules within a real-space G W -BSE formalism: Role of self-consistency and vertex corrections

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

Hung, Linda; da Jornada, Felipe H.; Souto-Casares, Jaime

Here, we present first-principles calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the GW and Bethe-Salpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well suited for high-accuracy calculations on molecules, as we show by comparing against G0W0 calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the GW approximation that include a local density approximation (LDA)–derived vertex function (Γ LDA ) andmore » quasiparticle-self-consistent (QS) iterations. We find that Γ LDA and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and the same sign for EAs. G0W0 and QS GWΓ LDA are more accurate for IPs, while G 0W 0Γ LDA and QS GW are best for EAs. For optical excitations, we find that perturbative GW-BSE underestimates the singlet excitation energy, while self-consistent GW-BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, in which G0W0 energies are used for occupied orbitals and G0W0Γ LDA for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.« less

Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation

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

Hou, Thomas; Efendiev, Yalchin; Tchelepi, Hamdi

2016-05-24

Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scalemore » basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics.« less

Multiscale analysis and computation for flows in heterogeneous media

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

Efendiev, Yalchin; Hou, T. Y.; Durlofsky, L. J.

Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scalemore » basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics. Below, we present a brief overview of each of these contributions.« less

Studies of dispersion energy in hydrogen-bonded systems. H2O-HOH, H2O-HF, H3N-HF, HF-HF

NASA Astrophysics Data System (ADS)

Szcześniak, M. M.; Scheiner, Steve

1984-02-01

Dispersion energy is calculated in the systems H2O-HOH, H2O-HF, H3N-HF, and HF-HF as a function of the intermolecular separation using a variety of methods. M≂ller-Plesset perturbation theory to second and third orders is applied in conjunction with polarized basis sets of 6-311G** type and with an extended basis set including a second set of polarization functions (DZ+2P). These results are compared to a multipole expansion of the dispersion energy, based on the Unsöld approximation, carried out to the inverse tenth power of the intermolecular distance. Pairwise evaluation is also carried out using both atom-atom and bond-bond formulations. The MP3/6-311G** results are in generally excellent accord with the leading R-6 term of the multipole expansion. This expansion, if carried out to the R-10 term, reproduces extremely well previously reported dispersion energies calculated via variation-perturbation theory. Little damping of the expansion is required for intermolecular distances equal to or greater than the equilibrium separation. Although the asymptotic behavior of the MP2 dispersion energy is somewhat different than that of the other methods, augmentation of the basis set by a second diffuse set of d functions leads to quite good agreement in the vicinity of the minima. Both the atom-atom and bond-bond parametrization schemes are in good qualitative agreement with the other methods tested. All approaches produce similar dependence of the dispersion energy upon the angular orientation between the two molecules involved in the H bond.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

NASA Astrophysics Data System (ADS)

Wu, Hao; Nüske, Feliks; Paul, Fabian; Klus, Stefan; Koltai, Péter; Noé, Frank

2017-04-01

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization.

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

NASA Astrophysics Data System (ADS)

Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

2017-11-01

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of HFBTHO, the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree-Fock-Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592-1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Additional comments: The user must have access to (i) the LAPACK subroutines DSYEEVR, DSYEVD, DSYTRF and DSYTRI, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices, (ii) the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and (iii) the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

Aldaya, Victor; Guerrero, J.

1995-01-01

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Structure and properties of some chiralanes and chirolanes

NASA Astrophysics Data System (ADS)

Novak, Igor

2018-06-01

The molecular structures, spectra and properties of six chiralanes and chirolanes (approximately spheroidal, saturated, cage hydrocarbons) have been determined by density functional theory (DFT) quantum chemistry calculations. The main features determined are: molecular geometry, partial atomic charges, standard enthalpy of formation, IR, nuclear magnetic resonance (NMR) and circular dichroism (CD) spectra. On the basis of the calculated standard enthalpies of formation and highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps, we suggest that chiralanes/chirolanes are potential synthetic targets. We have calculated the anomalously large downfield 13C-NMR shifts for endohedral carbons in the spectra of [5.5] and [5.7]chiralanes.

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.

Electronic and Piezoelectric properties of half-Heusler compounds: A first principles study

NASA Astrophysics Data System (ADS)

Rai, D. P.; Sandeep; Shankar, A.; Aly, Abeer E.; Patra, P. K.; Thapa, R. K.

2016-10-01

We have investigated the semiconducting and piezoelectric properties of bulk MNiSn (M=Ti, Zr, Hf) type a half-Heusler compound with cubic F-43m symmetry by means of density functional theory (DFT). For electron exchange correlation a generalized gradient approximation (GGA) was used. Special attention was paid to establish a most favourble ground state configuration on magnetic as well as non-magnetic ordering. With fully optimized structure the electronic and ferroelectric calculation was performed. The formation of band gap was discussed on the basis of d-d orbital hybridization. Further we have calculated the spontaneous polarization by means of structural deformation.

Lynch Syndrome: Female Genital Tract Cancer Diagnosis and Screening.

PubMed

Mills, Anne M; Longacre, Teri A

2016-06-01

Lynch syndrome is responsible for approximately 5% of endometrial cancers and 1% of ovarian cancers. The molecular basis for Lynch syndrome is a heritable functional deficiency in the DNA mismatch repair system, typically due to a germline mutation. This review discusses the rationales and relative merits of current Lynch syndrome screening tests for endometrial and ovarian cancers and provides pathologists with an informed algorithmic approach to Lynch syndrome testing in gynecologic cancers. Pitfalls in test interpretation and strategies to resolve discordant test results are presented. The potential role for next-generation sequencing panels in future screening efforts is discussed. Copyright © 2016 Elsevier Inc. All rights reserved.

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

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

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

Vibrational excitation and vibrationally resolved electronic excitation cross sections of positron-H2 scattering

NASA Astrophysics Data System (ADS)

Zammit, Mark; Fursa, Dmitry; Savage, Jeremy; Bray, Igor

2016-09-01

Vibrational excitation and vibrationally resolved electronic excitation cross sections of positron-H2 scattering have been calculated using the single-centre molecular convergent close-coupling (CCC) method. The adiabatic-nuclei approximation was utilized to model the above scattering processes and obtain the vibrationally resolved positron-H2 scattering length. As previously demonstrated, the CCC results are converged and accurately account for virtual and physical positronium formation by coupling basis functions with large orbital angular momentum. Here vibrationally resolved integrated and differential cross sections are presented over a wide energy range and compared with previous calculations and available experiments. Los Alamos National Laboratory and Curtin University.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

NASA Astrophysics Data System (ADS)

Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

2017-06-01

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals.

PubMed

Zuehlsdorff, T J; Hine, N D M; Payne, M C; Haynes, P D

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

PubMed

van Meer, R; Gritsenko, O V; Baerends, E J

2014-10-14

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

Sequence polymorphism in candidate genes for differences in winter plumage between Scottish and Scandinavian Willow Grouse (Lagopus lagopus).

PubMed

Skoglund, Pontus; Höglund, Jacob

2010-04-23

Population variation in the degree of seasonal polymorphism is rare in birds, and the genetic basis of this phenomenon remains largely undescribed. Both sexes of Scandinavian and Scottish Willow grouse (Lagopus lagopus) display marked differences in their winter phenotypes, with Scottish grouse retaining a pigmented plumage year-round and Scandinavian Willow grouse molting to a white morph during winter. A widely studied pathway implicated in vertebrate pigmentation is the melanin system, for which functional variation has been characterised in many taxa. We sequenced coding regions from four genes involved in melanin pigmentation (DCT, MC1R, TYR and TYRP1), and an additional control involved in the melanocortin pathway (AGRP), to investigate the genetic basis of winter plumage in Lagopus. Despite the well documented role of the melanin system in animal coloration, we found no plumage-associated polymorphism or evidence for selection in a total of approximately 2.6 kb analysed sequence. Our results indicate that the genetic basis of alternating between pigmented and unpigmented seasonal phenotypes is more likely explained by regulatory changes controlling the expression of these or other loci in the physiological pathway leading to pigmentation.

Basis Expansion Approaches for Regularized Sequential Dictionary Learning Algorithms With Enforced Sparsity for fMRI Data Analysis.

PubMed

Seghouane, Abd-Krim; Iqbal, Asif

2017-09-01

Sequential dictionary learning algorithms have been successfully applied to functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are, however, structured data matrices with the notions of temporal smoothness in the column direction. This prior information, which can be converted into a constraint of smoothness on the learned dictionary atoms, has seldomly been included in classical dictionary learning algorithms when applied to fMRI data analysis. In this paper, we tackle this problem by proposing two new sequential dictionary learning algorithms dedicated to fMRI data analysis by accounting for this prior information. These algorithms differ from the existing ones in their dictionary update stage. The steps of this stage are derived as a variant of the power method for computing the SVD. The proposed algorithms generate regularized dictionary atoms via the solution of a left regularized rank-one matrix approximation problem where temporal smoothness is enforced via regularization through basis expansion and sparse basis expansion in the dictionary update stage. Applications on synthetic data experiments and real fMRI data sets illustrating the performance of the proposed algorithms are provided.

Determination of many-electron basis functions for a quantum Hall ground state using Schur polynomials

NASA Astrophysics Data System (ADS)

Mandal, Sudhansu S.; Mukherjee, Sutirtha; Ray, Koushik

2018-03-01

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the 5/2 quantum Hall state with a few particles. We find that one of the basis functions is precisely the Moore-Read Pfaffian wave function.

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2003-01-01

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

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.

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

The Schwinger Variational Method

NASA Technical Reports Server (NTRS)

Huo, Winifred M.

1995-01-01

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. The application of the Schwinger variational (SV) method to e-molecule collisions and molecular photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions. Since this is not a review of cross section data, cross sections are presented only to server as illustrative examples. In the SV method, the correct boundary condition is automatically incorporated through the use of Green's function. Thus SV calculations can employ basis functions with arbitrary boundary conditions. The iterative Schwinger method has been used extensively to study molecular photoionization. For e-molecule collisions, it is used at the static exchange level to study elastic scattering and coupled with the distorted wave approximation to study electronically inelastic scattering.

Space-Pseudo-Time Method: Application to the One-Dimensional Coulomb Potential and Density Funtional Theory

NASA Astrophysics Data System (ADS)

Weatherford, Charles; Gebremedhin, Daniel

2016-03-01

A new and efficient way of evolving a solution to an ordinary differential equation is presented. A finite element method is used where we expand in a convenient local basis set of functions that enforce both function and first derivative continuity across the boundaries of each element. We also implement an adaptive step size choice for each element that is based on a Taylor series expansion. The method is applied to solve for the eigenpairs of the one-dimensional soft-coulomb potential and the hard-coulomb limit is studied. The method is then used to calculate a numerical solution of the Kohn-Sham differential equation within the local density approximation is presented and is applied to the helium atom. Supported by the National Nuclear Security Agency, the Nuclear Regulatory Commission, and the Defense Threat Reduction Agency.

An RBF-based compression method for image-based relighting.

PubMed

Leung, Chi-Sing; Wong, Tien-Tsin; Lam, Ping-Man; Choy, Kwok-Hung

2006-04-01

In image-based relighting, a pixel is associated with a number of sampled radiance values. This paper presents a two-level compression method. In the first level, the plenoptic property of a pixel is approximated by a spherical radial basis function (SRBF) network. That means that the spherical plenoptic function of each pixel is represented by a number of SRBF weights. In the second level, we apply a wavelet-based method to compress these SRBF weights. To reduce the visual artifact due to quantization noise, we develop a constrained method for estimating the SRBF weights. Our proposed approach is superior to JPEG, JPEG2000, and MPEG. Compared with the spherical harmonics approach, our approach has a lower complexity, while the visual quality is comparable. The real-time rendering method for our SRBF representation is also discussed.

Structure and function of SemiSWEET and SWEET sugar transporters.

PubMed

Feng, Liang; Frommer, Wolf B

2015-08-01

SemiSWEETs and SWEETs have emerged as unique sugar transporters. First discovered in plants with the help of fluorescent biosensors, homologs exist in all kingdoms of life. Bacterial and plant homologs transport hexoses and sucrose, whereas animal SWEETs transport glucose. Prokaryotic SemiSWEETs are small and comprise a parallel homodimer of an approximately 100 amino acid-long triple helix bundle (THB). Duplicated THBs are fused to create eukaryotic SWEETs in a parallel orientation via an inversion linker helix, producing a similar configuration to that of SemiSWEET dimers. Structures of four SemiSWEETs have been resolved in three states: open outside, occluded, and open inside, indicating alternating access. As we discuss here, these atomic structures provide a basis for exploring the evolution of structure-function relations in this new class of transporters. Copyright © 2015 Elsevier Ltd. All rights reserved.

Isgur-Karl model revisited

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

Galeta, Leonardo; Pirjol, Dan; Schat, Carlos

2009-12-01

We show how to match the Isgur-Karl model to the spin-flavor quark operator expansion used in the 1/N{sub c} studies of the nonstrange negative parity L=1 excited baryons. Using the transformation properties of states and interactions under the permutation group S{sub 3} we are able to express the operator coefficients as overlap integrals, without making any assumption on the spatial dependence of the quark wave functions. The general mass operator leads to parameter free mass relations and constraints on the mixing angles that are valid beyond the usual harmonic oscillator approximation. The Isgur-Karl model with harmonic oscillator wave functions providesmore » a simple counterexample that demonstrates explicitly that the alternative operator basis for the 1/N{sub c} expansion for excited baryons recently proposed by Matagne and Stancu is incomplete.« less

A group electronegativity equalization scheme including external potential effects.

PubMed

Leyssens, Tom; Geerlings, Paul; Peeters, Daniel

2006-07-20

By calculating the electron affinity and ionization energy of different functional groups, CCSD electronegativity values are obtained, which implicitly account for the effect of the molecular environment. This latter is approximated using a chemically justified point charge model. On the basis of Sanderson's electronegativity equalization principle, this approach is shown to lead to reliable "group in molecule" electronegativities. Using a slight adjustment of the modeled environment and first-order principles, an electronegativity equalization scheme is obtained, which implicitly accounts for the major part of the external potential effect. This scheme can be applied in a predictive manner to estimate the charge transfer between two functional groups, without having to rely on cumbersome calibrations. A very satisfactory correlation is obtained between these charge transfers and those obtained from an ab initio calculation of the entire molecule.

Candida albicans Agglutinin-Like Sequence (Als) Family Vignettes: A Review of Als Protein Structure and Function

PubMed Central

Hoyer, Lois L.; Cota, Ernesto

2016-01-01

Approximately two decades have passed since the description of the first gene in the Candida albicans ALS (agglutinin-like sequence) family. Since that time, much has been learned about the composition of the family and the function of its encoded cell-surface glycoproteins. Solution of the structure of the Als adhesive domain provides the opportunity to evaluate the molecular basis for protein function. This review article is formatted as a series of fundamental questions and explores the diversity of the Als proteins, as well as their role in ligand binding, aggregative effects, and attachment to abiotic surfaces. Interaction of Als proteins with each other, their functional equivalence, and the effects of protein abundance on phenotypic conclusions are also examined. Structural features of Als proteins that may facilitate invasive function are considered. Conclusions that are firmly supported by the literature are presented while highlighting areas that require additional investigation to reveal basic features of the Als proteins, their relatedness to each other, and their roles in C. albicans biology. PMID:27014205

Derivation of a formula for the resonance integral for a nonorthogonal basis set

PubMed Central

Yim, Yung-Chang; Eyring, Henry

1981-01-01

In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set of parameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the π-electron approximation are transformed to those for an orthogonal basis set by the Löwdin symmetrical orthogonalization. PMID:16593009

Individual differences in long-range time representation.

PubMed

Agostino, Camila S; Caetano, Marcelo S; Balci, Fuat; Claessens, Peter M E; Zana, Yossi

2017-04-01

On the basis of experimental data, long-range time representation has been proposed to follow a highly compressed power function, which has been hypothesized to explain the time inconsistency found in financial discount rate preferences. The aim of this study was to evaluate how well linear and power function models explain empirical data from individual participants tested in different procedural settings. The line paradigm was used in five different procedural variations with 35 adult participants. Data aggregated over the participants showed that fitted linear functions explained more than 98% of the variance in all procedures. A linear regression fit also outperformed a power model fit for the aggregated data. An individual-participant-based analysis showed better fits of a linear model to the data of 14 participants; better fits of a power function with an exponent β > 1 to the data of 12 participants; and better fits of a power function with β < 1 to the data of the remaining nine participants. Of the 35 volunteers, the null hypothesis β = 1 was rejected for 20. The dispersion of the individual β values was approximated well by a normal distribution. These results suggest that, on average, humans perceive long-range time intervals not in a highly compressed, biased manner, but rather in a linear pattern. However, individuals differ considerably in their subjective time scales. This contribution sheds new light on the average and individual psychophysical functions of long-range time representation, and suggests that any attribution of deviation from exponential discount rates in intertemporal choice to the compressed nature of subjective time must entail the characterization of subjective time on an individual-participant basis.

Sparse dynamics for partial differential equations

PubMed Central

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D.; Osher, Stanley

2013-01-01

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms. PMID:23533273

Sparse dynamics for partial differential equations.

PubMed

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

2013-04-23

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles.

PubMed

Nanjo, Daisuke; Hosoi, Haruko; Fujino, Tatsuya; Tahara, Tahei; Korenaga, Takashi

2007-03-22

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles (polyacrylamide, PAAm) was reported. Ultrafast fluorescence dynamics of polymer/water solution was monitored using a fluorescent probe molecule (C153). In the femtosecond time-resolved fluorescence measurement at 480 nm, slowly decay components having lifetimes of tau(1) approximately 53 ps and tau(2) approximately 5 ns were observed in addition to rapid fluorescence decay. Picosecond time-resolved fluorescence spectra of C153/PAAm/H2O solution were also measured. In the time-resolved fluorescence spectra of C153/PAAm/H2O, a peak shift from 490 to 515 nm was measured, which can be assigned to the solvation dynamics of polymer fine particles. The fluorescence peak shift was related to the solvation response function and two time constants were determined (tau(3) approximately 50 ps and tau(4) approximately 467 ps). Therefore, the tau(1) component observed in the femtosecond time-resolved fluorescence measurement was assigned to the solvation dynamics that was observed only in the presence of polymer fine particles. Rotational diffusion measurements were also carried out on the basis of the picosecond time-resolved fluorescence spectra. In the C153/PAAm/H2O solution, anisotropy decay having two different time constants was also derived (tau(6) approximately 76 ps and tau(7) approximately 676 ps), indicating the presence of two different microscopic molecular environments around the polymer surface. Using the Stokes-Einstein-Debye (SED) equation, microscopic viscosity around the polymer surface was evaluated. For the area that gave a rotational diffusion time of tau(6) approximately 76 ps, the calculated viscosity is approximately 1.1 cP and for tau(7) approximately 676 ps, it is approximately 10 cP. The calculated viscosity values clearly revealed that there are two different molecular environments around the polyacrylamide fine particles.

Strong shock waves and nonequilibrium response in a one-dimensional gas: a Boltzmann equation approach.

PubMed

Hurtado, Pablo I

2005-10-01

We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity, and temperature profiles are obtained as a function of the mixture mass ratio mu. We show that temperature overshoots near the shock layer, and that heavy particles are denser, slower, and cooler than light particles in the strong nonequilibrium region around the shock. The shock width omega(mu), which characterizes the size of this region, decreases as omega(mu) approximately mu(1/3) for mu-->0. In this limit, two very different length scales control the fluid structure, with heavy particles equilibrating much faster than light ones. Hydrodynamic fields relax exponentially toward equilibrium: phi(chi) approximately exp[-chi/lambda]. The scale separation is also apparent here, with two typical scales, lambda1 and lambda2, such that lambda1 approximately mu(1/2 as mu-->0, while lambda2, which is the slow scale controlling the fluid's asymptotic relaxation, increases to a constant value in this limit. These results are discussed in light of recent numerical studies on the nonequilibrium behavior of similar one-dimensional binary fluids.

Intelligent model-based OPC

NASA Astrophysics Data System (ADS)

Huang, W. C.; Lai, C. M.; Luo, B.; Tsai, C. K.; Chih, M. H.; Lai, C. W.; Kuo, C. C.; Liu, R. G.; Lin, H. T.

2006-03-01

Optical proximity correction is the technique of pre-distorting mask layouts so that the printed patterns are as close to the desired shapes as possible. For model-based optical proximity correction, a lithographic model to predict the edge position (contour) of patterns on the wafer after lithographic processing is needed. Generally, segmentation of edges is performed prior to the correction. Pattern edges are dissected into several small segments with corresponding target points. During the correction, the edges are moved back and forth from the initial drawn position, assisted by the lithographic model, to finally settle on the proper positions. When the correction converges, the intensity predicted by the model in every target points hits the model-specific threshold value. Several iterations are required to achieve the convergence and the computation time increases with the increase of the required iterations. An artificial neural network is an information-processing paradigm inspired by biological nervous systems, such as how the brain processes information. It is composed of a large number of highly interconnected processing elements (neurons) working in unison to solve specific problems. A neural network can be a powerful data-modeling tool that is able to capture and represent complex input/output relationships. The network can accurately predict the behavior of a system via the learning procedure. A radial basis function network, a variant of artificial neural network, is an efficient function approximator. In this paper, a radial basis function network was used to build a mapping from the segment characteristics to the edge shift from the drawn position. This network can provide a good initial guess for each segment that OPC has carried out. The good initial guess reduces the required iterations. Consequently, cycle time can be shortened effectively. The optimization of the radial basis function network for this system was practiced by genetic algorithm, which is an artificially intelligent optimization method with a high probability to obtain global optimization. From preliminary results, the required iterations were reduced from 5 to 2 for a simple dumbbell-shape layout.

Adaptive Sliding Mode Control of Dynamic Systems Using Double Loop Recurrent Neural Network Structure.

PubMed

Fei, Juntao; Lu, Cheng

2018-04-01

In this paper, an adaptive sliding mode control system using a double loop recurrent neural network (DLRNN) structure is proposed for a class of nonlinear dynamic systems. A new three-layer RNN is proposed to approximate unknown dynamics with two different kinds of feedback loops where the firing weights and output signal calculated in the last step are stored and used as the feedback signals in each feedback loop. Since the new structure has combined the advantages of internal feedback NN and external feedback NN, it can acquire the internal state information while the output signal is also captured, thus the new designed DLRNN can achieve better approximation performance compared with the regular NNs without feedback loops or the regular RNNs with a single feedback loop. The new proposed DLRNN structure is employed in an equivalent controller to approximate the unknown nonlinear system dynamics, and the parameters of the DLRNN are updated online by adaptive laws to get favorable approximation performance. To investigate the effectiveness of the proposed controller, the designed adaptive sliding mode controller with the DLRNN is applied to a -axis microelectromechanical system gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed methodology can achieve good tracking property, and the comparisons of the approximation performance between radial basis function NN, RNN, and DLRNN show that the DLRNN can accurately estimate the unknown dynamics with a fast speed while the internal states of DLRNN are more stable.

Evaluation of liquefaction potential of soil based on standard penetration test using multi-gene genetic programming model

NASA Astrophysics Data System (ADS)

Muduli, Pradyut; Das, Sarat

2014-06-01

This paper discusses the evaluation of liquefaction potential of soil based on standard penetration test (SPT) dataset using evolutionary artificial intelligence technique, multi-gene genetic programming (MGGP). The liquefaction classification accuracy (94.19%) of the developed liquefaction index (LI) model is found to be better than that of available artificial neural network (ANN) model (88.37%) and at par with the available support vector machine (SVM) model (94.19%) on the basis of the testing data. Further, an empirical equation is presented using MGGP to approximate the unknown limit state function representing the cyclic resistance ratio (CRR) of soil based on developed LI model. Using an independent database of 227 cases, the overall rates of successful prediction of occurrence of liquefaction and non-liquefaction are found to be 87, 86, and 84% by the developed MGGP based model, available ANN and the statistical models, respectively, on the basis of calculated factor of safety (F s) against the liquefaction occurrence.

Evaluation of the metabolic rate based on the recording of the heart rate.

PubMed

Malchaire, Jacques; d'AMBROSIO Alfano, Francesca Romana; Palella, Boris Igor

2017-06-08

The assessment of harsh working conditions requires a correct evaluation of the metabolic rate. This paper revises the basis described in the ISO 8996 standard for the evaluation of the metabolic rate at a work station from the recording of the heart rate of a worker during a representative period of time. From a review of the literature, formulas different from those given in the standard are proposed to estimate the maximum working capacity, the maximum heart rate, the heart rate and the metabolic rate at rest and the relation (HR vs. M) at the basis of the estimation of the equivalent metabolic rate, as a function of the age, height and weight of the person. A Monte Carlo simulation is used to determine, from the approximations of these parameters and formulas, the imprecision of the estimated equivalent metabolic rate. The results show that the standard deviation of this estimate varies from 10 to 15%.

Evaluation of the metabolic rate based on the recording of the heart rate

PubMed Central

MALCHAIRE, Jacques; ALFANO, Francesca Romana d’AMBROSIO; PALELLA, Boris Igor

2017-01-01

The assessment of harsh working conditions requires a correct evaluation of the metabolic rate. This paper revises the basis described in the ISO 8996 standard for the evaluation of the metabolic rate at a work station from the recording of the heart rate of a worker during a representative period of time. From a review of the literature, formulas different from those given in the standard are proposed to estimate the maximum working capacity, the maximum heart rate, the heart rate and the metabolic rate at rest and the relation (HR vs. M) at the basis of the estimation of the equivalent metabolic rate, as a function of the age, height and weight of the person. A Monte Carlo simulation is used to determine, from the approximations of these parameters and formulas, the imprecision of the estimated equivalent metabolic rate. The results show that the standard deviation of this estimate varies from 10 to 15%. PMID:28250334

Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems.

PubMed

Angom, D; Ghosh, S; Kota, V K B

2004-01-01

We revisit statistical wave function properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength lambda, the strength functions F(k) (E) are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio xi(2) and the information entropy S(info) during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law lambda(d) approximately 1/sqrt[m] ( m is number of fermions) for the duality point lambda= lambda(d), where F(k) (E), xi(2), and S(info) in both the weak ( lambda=0 ) and strong mixing ( lambda= infinity ) basis coincide. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.

Robust adaptive backstepping neural networks control for spacecraft rendezvous and docking with input saturation.

PubMed

Xia, Kewei; Huo, Wei

2016-05-01

This paper presents a robust adaptive neural networks control strategy for spacecraft rendezvous and docking with the coupled position and attitude dynamics under input saturation. Backstepping technique is applied to design a relative attitude controller and a relative position controller, respectively. The dynamics uncertainties are approximated by radial basis function neural networks (RBFNNs). A novel switching controller consists of an adaptive neural networks controller dominating in its active region combined with an extra robust controller to avoid invalidation of the RBFNNs destroying stability of the system outside the neural active region. An auxiliary signal is introduced to compensate the input saturation with anti-windup technique, and a command filter is employed to approximate derivative of the virtual control in the backstepping procedure. Globally uniformly ultimately bounded of the relative states is proved via Lyapunov theory. Simulation example demonstrates effectiveness of the proposed control scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Implementation of polyatomic MCTDHF capability

NASA Astrophysics Data System (ADS)

Haxton, Daniel; Jones, Jeremiah; Rescigno, Thomas; McCurdy, C. William; Ibrahim, Khaled; Williams, Sam; Vecharynski, Eugene; Rouet, Francois-Henry; Li, Xiaoye; Yang, Chao

2015-05-01

The implementation of the Multiconfiguration Time-Dependent Hartree-Fock method for poly- atomic molecules using a cartesian product grid of sinc basis functions will be discussed. The focus will be on two key components of the method: first, the use of a resolution-of-the-identity approximation; sec- ond, the use of established techniques for triple Toeplitz matrix algebra using fast Fourier transform over distributed memory architectures (MPI 3D FFT). The scaling of two-electron matrix element transformations is converted from O(N4) to O(N log N) by including these components. Here N = n3, with n the number of points on a side. We test the prelim- inary implementation by calculating absorption spectra of small hydro- carbons, using approximately 16-512 points on a side. This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under the Early Career program, and by the offices of BES and Advanced Scientific Computing Research, under the SciDAC program.

Large Deviations for Nonlocal Stochastic Neural Fields

PubMed Central

2014-01-01

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers’ law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations. Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20. PMID:24742297

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

NASA Technical Reports Server (NTRS)

Gnoffo, P. A.

1978-01-01

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling.

PubMed

Grell, Gilbert; Bokarev, Sergey I; Winter, Bernd; Seidel, Robert; Aziz, Emad F; Aziz, Saadullah G; Kühn, Oliver

2015-08-21

X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the restricted active space self-consistent field method including spin-orbit coupling is used to cope with this challenge and to calculate valence- and core-level photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and the sudden approximation. Thereby, we utilize an efficient computational algorithm that is based on a biorthonormal basis transformation. The approach is applied to the valence photoionization of the gas phase water molecule and to the core ionization spectrum of the [Fe(H2O)6](2+) complex. The results show good agreement with the experimental data obtained in this work, whereas the sudden approximation demonstrates distinct deviations from experiments.

Regional seismic wavefield computation on a 3-D heterogeneous Earth model by means of coupled traveling wave synthesis

USGS Publications Warehouse

Pollitz, F.F.

2002-01-01

I present a new algorithm for calculating seismic wave propagation through a three-dimensional heterogeneous medium using the framework of mode coupling theory originally developed to perform very low frequency (f < ???0.01-0.05 Hz) seismic wavefield computation. It is a Greens function approach for multiple scattering within a defined volume and employs a truncated traveling wave basis set using the locked mode approximation. Interactions between incident and scattered wavefields are prescribed by mode coupling theory and account for the coupling among surface waves, body waves, and evanescent waves. The described algorithm is, in principle, applicable to global and regional wave propagation problems, but I focus on higher frequency (typically f ??????0.25 Hz) applications at regional and local distances where the locked mode approximation is best utilized and which involve wavefields strongly shaped by propagation through a highly heterogeneous crust. Synthetic examples are shown for P-SV-wave propagation through a semi-ellipsoidal basin and SH-wave propagation through a fault zone.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed.

PubMed

Weiss, M; Stedtler, C; Roberts, M S

1997-09-01

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximately by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as an alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models.

A new general method for the assessment of the molecular-weight distribution of polydisperse preparations. Its application to an intestinal epithelial glycoprotein and two dextran samples, and comparison with a monodisperse glycoprotein

PubMed Central

Gibbons, Richard A.; Dixon, Stephen N.; Pocock, David H.

1973-01-01

A specimen of intestinal glycoprotein isolated from the pig and two samples of dextran, all of which are polydisperse (that is, the preparations may be regarded as consisting of a continuous distribution of molecular weights), have been examined in the ultracentrifuge under meniscus-depletion conditions at equilibrium. They are compared with each other and with a glycoprotein from Cysticercus tenuicollis cyst fluid which is almost monodisperse. The quantity c−⅓ (c=concentration) is plotted against ξ (the reduced radius); this plot is linear when the molecular-weight distribution approximates to the `most probable', i.e. when Mn:Mw:Mz: M(z+1)....... is as 1:2:3:4: etc. The use of this plot, and related procedures, to evaluate qualitatively and semi-quantitatively molecular-weight distribution functions where they can be realistically approximated to Schulz distributions is discussed. The theoretical basis is given in an Appendix. PMID:4778265

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

Balian, R., E-mail: roger.balian@cea.fr; Vénéroni, M.

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces themore » original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.« less

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

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

Mao, Yuezhi; Horn, Paul R.; Mardirossian, Narbe

2016-07-28

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set producesmore » <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.« less

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J.

2012-07-01

Many approximations have been developed to help deal with the O(N4) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be carried out in O(N4) operations. This should be compared to the usual scaling behavior of O(N5) and O(N6) for MP2 and MP3, respectively. The THC-DF technique can also be applied to other methods in electronic structure theory, such as coupled-cluster and configuration interaction, promising significant gains in computational efficiency and storage reduction.

Employing general fit-bases for construction of potential energy surfaces with an adaptive density-guided approach

NASA Astrophysics Data System (ADS)

Klinting, Emil Lund; Thomsen, Bo; Godtliebsen, Ian Heide; Christiansen, Ove

2018-02-01

We present an approach to treat sets of general fit-basis functions in a single uniform framework, where the functional form is supplied on input, i.e., the use of different functions does not require new code to be written. The fit-basis functions can be used to carry out linear fits to the grid of single points, which are generated with an adaptive density-guided approach (ADGA). A non-linear conjugate gradient method is used to optimize non-linear parameters if such are present in the fit-basis functions. This means that a set of fit-basis functions with the same inherent shape as the potential cuts can be requested and no other choices with regards to the fit-basis functions need to be taken. The general fit-basis framework is explored in relation to anharmonic potentials for model systems, diatomic molecules, water, and imidazole. The behaviour and performance of Morse and double-well fit-basis functions are compared to that of polynomial fit-basis functions for unsymmetrical single-minimum and symmetrical double-well potentials. Furthermore, calculations for water and imidazole were carried out using both normal coordinates and hybrid optimized and localized coordinates (HOLCs). Our results suggest that choosing a suitable set of fit-basis functions can improve the stability of the fitting routine and the overall efficiency of potential construction by lowering the number of single point calculations required for the ADGA. It is possible to reduce the number of terms in the potential by choosing the Morse and double-well fit-basis functions. These effects are substantial for normal coordinates but become even more pronounced if HOLCs are used.

A general range-separated double-hybrid density-functional theory

NASA Astrophysics Data System (ADS)

Kalai, Cairedine; Toulouse, Julien

2018-04-01

A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order Møller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.

The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations

NASA Astrophysics Data System (ADS)

Chen, L.; Cheng, Y. M.

2018-07-01

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.

Dual adaptive dynamic control of mobile robots using neural networks.

PubMed

Bugeja, Marvin K; Fabri, Simon G; Camilleri, Liberato

2009-02-01

This paper proposes two novel dual adaptive neural control schemes for the dynamic control of nonholonomic mobile robots. The two schemes are developed in discrete time, and the robot's nonlinear dynamic functions are assumed to be unknown. Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are used for function approximation. In each scheme, the unknown network parameters are estimated stochastically in real time, and no preliminary offline neural network training is used. In contrast to other adaptive techniques hitherto proposed in the literature on mobile robots, the dual control laws presented in this paper do not rely on the heuristic certainty equivalence property but account for the uncertainty in the estimates. This results in a major improvement in tracking performance, despite the plant uncertainty and unmodeled dynamics. Monte Carlo simulation and statistical hypothesis testing are used to illustrate the effectiveness of the two proposed stochastic controllers as applied to the trajectory-tracking problem of a differentially driven wheeled mobile robot.

A simplified method of evaluating the stress wave environment of internal equipment

NASA Technical Reports Server (NTRS)

Colton, J. D.; Desmond, T. P.

1979-01-01

A simplified method called the transfer function technique (TFT) was devised for evaluating the stress wave environment in a structure containing internal equipment. The TFT consists of following the initial in-plane stress wave that propagates through a structure subjected to a dynamic load and characterizing how the wave is altered as it is transmitted through intersections of structural members. As a basis for evaluating the TFT, impact experiments and detailed stress wave analyses were performed for structures with two or three, or more members. Transfer functions that relate the wave transmitted through an intersection to the incident wave were deduced from the predicted wave response. By sequentially applying these transfer functions to a structure with several intersections, it was found that the environment produced by the initial stress wave propagating through the structure can be approximated well. The TFT can be used as a design tool or as an analytical tool to determine whether a more detailed wave analysis is warranted.

Analysis of nystagmus response to a pseudorandom velocity input

NASA Technical Reports Server (NTRS)

Lessard, C. S.

1986-01-01

Space motion sickness was not reported during the first Apollo missions; however, since Apollo 8 through the current Shuttle and Skylab missions, approximately 50% of the crewmembers have experienced instances of space motion sickness. Space motion sickness, renamed space adaptation syndrome, occurs primarily during the initial period of a mission until habilation takes place. One of NASA's efforts to resolve the space adaptation syndrome is to model the individual's vestibular response for basis knowledge and as a possible predictor of an individual's susceptibility to the disorder. This report describes a method to analyse the vestibular system when subjected to a pseudorandom angular velocity input. A sum of sinusoids (pseudorandom) input lends itself to analysis by linear frequency methods. Resultant horizontal ocular movements were digitized, filtered and transformed into the frequency domain. Programs were developed and evaluated to obtain the (1) auto spectra of input stimulus and resultant ocular resonse, (2) cross spectra, (3) the estimated vestibular-ocular system transfer function gain and phase, and (4) coherence function between stimulus and response functions.

Functional genomics of chlorine-induced acute lung injury in mice.

PubMed

Leikauf, George D; Pope-Varsalona, Hannah; Concel, Vincent J; Liu, Pengyuan; Bein, Kiflai; Brant, Kelly A; Dopico, Richard A; Di, Y Peter; Jang, An-Soo; Dietsch, Maggie; Medvedovic, Mario; Li, Qian; Vuga, Louis J; Kaminski, Naftali; You, Ming; Prows, Daniel R

2010-07-01

Acute lung injury can be induced indirectly (e.g., sepsis) or directly (e.g., chlorine inhalation). Because treatment is still limited to supportive measures, mortality remains high ( approximately 74,500 deaths/yr). In the past, accidental (railroad derailments) and intentional (Iraq terrorism) chlorine exposures have led to deaths and hospitalizations from acute lung injury. To better understand the molecular events controlling chlorine-induced acute lung injury, we have developed a functional genomics approach using inbred mice strains. Various mouse strains were exposed to chlorine (45 ppm x 24 h) and survival was monitored. The most divergent strains varied by more than threefold in mean survival time, supporting the likelihood of an underlying genetic basis of susceptibility. These divergent strains are excellent models for additional genetic analysis to identify critical candidate genes controlling chlorine-induced acute lung injury. Gene-targeted mice then could be used to test the functional significance of susceptibility candidate genes, which could be valuable in revealing novel insights into the biology of acute lung injury.

Global and critical test of the perturbation density-functional theory based on extensive simulation of Lennard-Jones fluid near an interface and in confined systems.

PubMed

Zhou, Shiqi; Jamnik, Andrej

2005-09-22

The structure of a Lennard-Jones (LJ) fluid subjected to diverse external fields maintaining the equilibrium with the bulk LJ fluid is studied on the basis of the third-order+second-order perturbation density-functional approximation (DFA). The chosen density and potential parameters for the bulk fluid correspond to the conditions situated at "dangerous" regions of the phase diagram, i.e., near the critical temperature or close to the gas-liquid coexistence curve. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. It is found that the DFA theory presented in this work performs successfully for the nonuniform LJ fluid only on the condition of high accuracy of the required bulk second-order direct correlation function. The present report further indicates that the proposed perturbation DFA is efficient and suitable for both supercritical and subcritical temperatures.

Binary collision approximations for the memory function for density fluctuations in equilibrium atomic liquids

NASA Astrophysics Data System (ADS)

Noah, Joyce E.

Time correlation functions of density fluctuations of liquids at equilibrium can be used to relate the microscopic dynamics of a liquid to its macroscopic transport properties. Time correlation functions are especially useful since they can be generated in a variety of ways, from scattering experiments to computer simulation to analytic theory. The kinetic theory of fluctuations in equilibrium liquids is an analytic theory for calculating correlation functions using memory functions. In this work, we use a diagrammatic formulation of the kinetic theory to develop a series of binary collision approximations for the collisional part of the memory function. We define binary collisions as collisions between two distinct density fluctuations whose identities are fixed during the duration of a collsion. R approximations are for the short time part of the memory function, and build upon the work of Ranganathan and Andersen. These approximations have purely repulsive interactions between the fluctuations. The second type of approximation, RA approximations, is for the longer time part of the memory function, where the density fluctuations now interact via repulsive and attractive forces. Although RA approximations are a natural extension of R approximations, they permit two density fluctuations to become trapped in the wells of the interaction potential, leading to long-lived oscillatory behavior, which is unphysical. Therefore we consider S approximations which describe binary particles which experience the random effect of the surroundings while interacting via repulsive or repulsive and attractive interactions. For each of these approximations for the memory function we numerically solve the kinetic equation to generate correlation functions. These results are compared to molecular dynamics results for the correlation functions. Comparing the successes and failures of the different approximations, we conclude that R approximations give more accurate intermediate and long time results while RA and S approximations do particularly well at predicting the short time behavior. Lastly, we also develop a series of non-graphically derived approximations and use an optimization procedure to determine the underlying memory function from the simulation data. These approaches provide valuable information about the memory function that will be used in the development of future kinetic theories.

40 CFR 63.2872 - What definitions apply to this subpart?

Code of Federal Regulations, 2010 CFR

2010-07-01

... NESHAP General Provisions. (c) In this section as follows: Accounting month means a time interval defined... consistent and regular basis. An accounting month will consist of approximately 4 to 5 calendar weeks and each accounting month will be of approximate equal duration. An accounting month may not correspond...

The Best m-Term Approximation and Greedy Algorithms

DTIC Science & Technology

1997-01-01

in the paper DKT For a given basis we dene the Greedy Algorithm Gp as follows Let f X I cIf I and cIf p kcIf Ikp Then... DKT RA DeVore SV Konyagin and VV Temlyakov Hyperbolic Wavelet Approximation to appear DL R DeVore GLorentz

Using the Pearson Distribution for Synthesis of the Suboptimal Algorithms for Filtering Multi-Dimensional Markov Processes

NASA Astrophysics Data System (ADS)

Mit'kin, A. S.; Pogorelov, V. A.; Chub, E. G.

2015-08-01

We consider the method of constructing the suboptimal filter on the basis of approximating the a posteriori probability density of the multidimensional Markov process by the Pearson distributions. The proposed method can efficiently be used for approximating asymmetric, excessive, and finite densities.

Multiscale model reduction for shale gas transport in poroelastic fractured media

NASA Astrophysics Data System (ADS)

Akkutlu, I. Yucel; Efendiev, Yalchin; Vasilyeva, Maria; Wang, Yuhe

2018-01-01

Inherently coupled flow and geomechanics processes in fractured shale media have implications for shale gas production. The system involves highly complex geo-textures comprised of a heterogeneous anisotropic fracture network spatially embedded in an ultra-tight matrix. In addition, nonlinearities due to viscous flow, diffusion, and desorption in the matrix and high velocity gas flow in the fractures complicates the transport. In this paper, we develop a multiscale model reduction approach to couple gas flow and geomechanics in fractured shale media. A Discrete Fracture Model (DFM) is used to treat the complex network of fractures on a fine grid. The coupled flow and geomechanics equations are solved using a fixed stress-splitting scheme by solving the pressure equation using a continuous Galerkin method and the displacement equation using an interior penalty discontinuous Galerkin method. We develop a coarse grid approximation and coupling using the Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM constructs the multiscale basis functions in a systematic way to capture the fracture networks and their interactions with the shale matrix. Numerical results and an error analysis is provided showing that the proposed approach accurately captures the coupled process using a few multiscale basis functions, i.e. a small fraction of the degrees of freedom of the fine-scale problem.

Sparse approximation problem: how rapid simulated annealing succeeds and fails

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Kabashima, Yoshiyuki

2016-03-01

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.

Laplace approximation for Bessel functions of matrix argument

NASA Astrophysics Data System (ADS)

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.