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Fitting Functions (fitting + function)
Selected AbstractsFLEXMG: A new library of multigrid preconditioners for a spectral/finite element incompressible flow solverINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010M. Rasquin Abstract A new library called FLEXMG has been developed for a spectral/finite element incompressible flow solver called SFELES. FLEXMG allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods. Two families of algebraic multigrid preconditioners have been implemented, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least-square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics, their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in the study. Copyright © 2010 John Wiley & Sons, Ltd. [source] Study of peptide conformation in terms of the ABEEM/MM methodJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2006Zhong-Zhi Yang Abstract The ABEEM/MM model (atom-bond electronegativity equalization method fused into molecular mechanics) is applied to study of the polypeptide conformations. The Lennard,Jones and torsional parameters were optimized to be consistent with the ABEEM/MM fluctuating charge electrostatic potential. The hydrogen bond was specially treated with an electrostatic fitting function. Molecular dipole moments, dimerization energies, and hydrogen bond lengths of complexes are reasonably achieved by our model, compared to ab initio results. The ABEEM/MM fluctuating charge model reproduces both the peptide conformational energies and structures with satisfactory accuracy with low computer cost. The transferability is tested by applying the parameters of our model to the tetrapeptide of alanine and another four dipeptides. The overall RMS deviations in conformational energies and key dihedral angles for four di- or tetrapeptide, is 0.39 kcal/mol and 7.7°. The current results agree well with those by the accurate ab initio method, and are comparable to those from the best existing force fields. The results make us believe that our fluctuating charge model can obtain more promising results in protein and macromolecular modeling with good accuracy but less computer cost. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 1,10, 2006 [source] Measurements by MRI of the settling and packing of solid particles from aqueous suspensionsAICHE JOURNAL, Issue 6 2009Julio Acosta-Cabronero Abstract This study extends the application of existing magnetic resonance imaging methods to measure the settling of solid particles from aqueous suspensions. The acquisition of one-dimensional multiecho projections allowed the direct measurement of initial magnetizations (M0), from which solid volume fractions along the sedimentation column were inferred. For polystyrene beads, it was found that monoexponential curves accurately fitted the transverse relaxation decays. In contrast, for the other four solids investigated (activated carbon, talc, calcium carbonate, and glass beads), the single exponential model did not suffice and additional terms in the fitting function significantly improved the calculation of solid concentrations. Additional information about particle sizes was obtained by comparing volume fractions with the spin,spin relaxation times of the hydrogen protons as a function of the vertical height through the sedimenting suspensions of activated carbon and polystyrene beads. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Model density approach to the Kohn,Sham problem: Efficient extension of the density fitting techniqueINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2005Uwe Birkenheuer Abstract We present a novel procedure for treating the exchange-correlation contributions in the Kohn,Sham procedure. The approach proposed is fully variational and closely related to the so-called "fitting functions" method for the Coulomb Hartree problem; in fact, the method consistently uses this auxiliary representation of the electron density to determine the exchange-correlation contributions. The exchange-correlation potential and its matrix elements in a basis set of localized (atomic) orbitals can be evaluated by reusing the three-center Coulomb integrals involving fitting functions, while the computational cost of the remaining numerical integration is significantly reduced and scales only linearly with the size of the auxiliary basis. We tested the approach extensively for a large set of atoms and small molecules as well as for transition-metal carbonyls and clusters, by comparing total energies, atomization energies, structure parameters, and vibrational frequencies at the local density approximation and generalized gradient approximation levels of theory. The method requires a sufficiently flexible auxiliary basis set. We propose a minimal extension of the conventional auxiliary basis set, which yields essentially the same accuracy for the quantities just mentioned as the standard approach. The new method allows one to achieve substantial savings compared with a fully numerical integration of the exchange-correlation contributions. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Molecular Modeling and Receptor-Dependent (RD) 3D-QSAR Approach to a Set of Antituberculosis DerivativesMOLECULAR INFORMATICS, Issue 11-12 2009Fernanda, Kerly, Mesquita Pasqualoto Abstract In this study, receptor-dependent (RD) 3D-QSAR models were built for a set of thirty-seven isoniazid derivatives bound to the enoyl-acp reductase from M. tuberculosis, called InhA (PDB entry code 1zid). Ligand-receptor (L-R) molecular dynamics (MD) simulations [500,000 steps; the step size was 0.001,ps (1,fs)] were carried out at 310,K (biological assay temperature). The hypothesized active conformations resulting from a previously reported receptor-independent (IR) 4D-QSAR analysis were used as the molecular geometries of each ligand in this structure-based L-R binding research. The dependent variable is the reported MIC values against M. tuberculosis var. bovis. The independent variables (descriptors) are energy terms of a modified first-generation AMBER force field combined with a hydration shell aqueous solvation model. Genetic function approximation (GFA) formalism and partial least squares (PLS) regression were employed as the fitting functions to develop 3D-QSAR models. The bound ligand solvation energy, the sum of electrostatic and hydrogen bonding energies of the unbound ligand, the bending energy of the unbound ligand, the electrostatic intermolecular L-R energy, and the change in hydrogen bonding energy upon binding were found as important energy contributions to the binding process. The 3D-QSAR model at 310,K has good internal and external predictability and may be regarded as representative of the binding process of ligands to InhA. [source] Evolutionary population synthesis for binary stellar population at high spectral resolution: integrated spectral energy distributions and absorption-feature indicesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2005Fenghui Zhang ABSTRACT Using evolutionary population synthesis, we present high-resolution (0.3 Å) integrated spectral energy distributions from 3000 to 7000 Å and absorption-line indices defined by the Lick Observatory Image Dissector Scanner (Lick/IDS) system, for an extensive set of instantaneous-burst binary stellar populations with binary interactions. The ages of the populations are in the range 1,15 Gyr and the metallicities are in the range 0.004,0.03. These high-resolution synthesis results can satisfy the needs of modern spectroscopic galaxy surveys, and are available on request. By comparing the synthetic continuum of populations at high and low resolution, we show that there is good agreement for solar metallicity and tolerable disagreement for non-solar metallicity. The strength of the Balmer lines at high spectral resolution is greater than that at low resolution for all metallicities. The comparison of Lick/IDS absorption-line indices at low and high resolution, both of which are obtained by the fitting functions, shows that the discrepancies in all indices except for TiO1 and TiO2 are insignificant for populations with Z= 0.004 and 0.02. The high-resolution Ca4227, Fe5015 and Mgb indices are redder than the corresponding low-resolution ones for populations with Z= 0.01 and 0.03; this effect lowers the derived age and metallicity of the population. The high-resolution Mg1, Fe5709 and Fe5782 indices are bluer than those at low resolution; this effect raises the age and metallicity. The discrepancy in these six indices is greater for populations with Z= 0.03 in comparison to Z= 0.01. At high resolution we compare the Lick/IDS spectral absorption indices obtained by using the fitting functions with those measured directly from the synthetic spectra. We find that the Ca4455, Fe4668, Mgb and Na D indices obtained by the use of the fitting functions are redder for all metallicities, Fe5709 is redder at Z= 0.03 and becomes bluer at Z= 0.01 and 0.004, and the other indices are bluer for all metallicities than the corresponding values measured directly from the synthetic spectra. [source] Testing stellar population models with star clusters in the Large Magellanic CloudMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2002Michael A. Beasley Abstract We present high signal-to-noise ratio integrated spectra of 24 star clusters in the Large Magellanic Cloud (LMC), obtained using the FLAIR spectrograph at the UK Schmidt telescope. The spectra have been placed on to the Lick/IDS system in order to test the calibration of Simple Stellar Population (SSP) models. We have compared the SSP-predicted metallicities of the clusters with those from the literature, predominantly taken from the Ca-triplet spectroscopy of Olszewski et al. (1991). We find that there is good agreement between the metallicities in the range ,2.10 ,[Fe/H], 0. However, the Mg2 index (and to a lesser degree Mg b) systematically predict higher metallicities (up to +0.5 dex higher) than ,Fe,. Among the possible explanations for this are that the LMC clusters possess [,/Fe] > 0. Metallicities are presented for eleven LMC clusters which have no previous measurements. We compare SSP ages for the clusters, derived from the H,, H, and H, Lick/IDS indices, with the available literature data, and find good agreement for the vast majority. This includes six old globular clusters in our sample, which have ages consistent with their HST colour-magnitude diagram (CMD) ages and/or integrated colours. However, two globular clusters, NGC 1754 and NGC 2005, identified as old (,15 Gyr) on the basis of HST CMDs, have H, line-strengths which lead ages that are too low (,8 and ,6 Gyr respectively). These findings are inconsistent with their CMD-derived values at the 3, level. Comparison between the horizontal branch morphology and the Balmer line strengths of these clusters suggests that the presence of blue horizontal branch stars has increased their Balmer indices by up to ,1.0 Å. We conclude that the Lick/IDS indices, used in conjunction with contemporary SSP models, are able to reproduce the ages and metallicities of the LMC clusters reassuringly well. The required extrapolations of the fitting functions and stellar libraries in the models to lower ages and low metallicities do not lead to serious systematic errors. However, owing to the significant contribution of horizontal branch stars to Balmer indices, SSP model ages derived for metal-poor globular clusters are ambiguous without a priori knowledge of horizontal branch morphology. [source] | ||||||||||