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Computational Scheme (computational + scheme)
Selected AbstractsOptimization of thermo-elasto-plastic processes using Eulerian sensitivity analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003S. Paul Abstract A computational scheme for the analysis and optimization of quasi-static thermo-mechanical processes is presented in this paper. In order to obtain desirable mechanical transformations in a workpiece using a thermal treatment process, the optimal control parameters need to be determined. The problem is addressed by posing the process as a decoupled thermo-mechanical finite element problem and performing an optimization using gradient methods. The forward problem is solved using the Eulerian formulation since it is computationally more efficient compared to an equivalent Lagrangian formulation. The design sensitivities required for the optimization are developed analytically using direct differentiation. This systematic design approach is applied to optimize a laser forming process. The objective is to maximize the angular distortion of a specimen subject to the constraint that the phase transition temperature is not exceeded at any point in the model. Copyright © 2003 John Wiley & Sons, Ltd. [source] TLM models of waves in moving media: refinements and dispersion analysisINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2003William J O'Connor Abstract Two recent papers about transmission line matrix (TLM) models of waves in moving media used notional diodes to achieve the appropriate direction-dependent wave speeds. Despite the algorithm's demonstrated success, the operation of the diodes might be criticized for being non-physical from a circuit theory perspective. Alternative circuit models are here developed that avoid this objection, being based on wave two-ports and standard circuit theory components. Their operation obeys the same numerical algorithm derived using the diodes, thereby confirming the validity of the original computational scheme. Furthermore these circuits lead more easily to the direction-dependent wave speed expressions and provide exact analytic results for dispersion and attenuation effects, which are here presented and discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Hydrogen-bonding effects on electronic g -tensors of semiquinone anion radicals: Relativistic density functional investigationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002Konstantin M. Neyman Abstract We report results of systematic g -tensor calculations of hydrogen-bonded complexes of two benchmark semiquinone anion radicals, 1,4 -benzoquinone and tetramethyl- 1,4 -benzoquinone (duroquinone), with water and methanol molecules. The calculations have been carried out with the help of a recently developed g -tensor module that is based on a relativistic density functional method that takes spin,orbit interaction self-consistently into account. We demonstrate the applicability of this new computational scheme to describe quantitatively delicate effects of hydrogen bonding on electronic g -tensor values. Also, we explored general trends of how g -tensors depend on the structure and stoichiometry of hydrogen-bonded semiquinone complexes. Complexes exhibiting one hydrogen bond per oxygen atom of the quinones with a linear arrangement of the CO , H moieties were shown to feature g-shifts induced by these hydrogen bonds that are in close agreement with measured electron paramagnetic resonance data. Based on deviations of calculated and measured g-components, we classify all other model complexes studied as less probable under the experimental conditions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Performance of plane-wave-based LDA+U and GGA+U approaches to describe magnetic coupling in molecular systems,JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 14 2009Pablo Rivero Abstract This work explores the performance of periodic plane wave density functional theory calculations with an on-site Coulomb correction to the standard LDA and GGA exchange-correlation potential,commonly used to describe strongly correlated solids,in describing the magnetic coupling constant of a series of molecular compounds representative of dinuclear Cu complexes and of organic diradicals. The resulting LDA+U or GGA+U formalisms, lead to results comparable to experiment and to those obtained by means of standard hybrid functionals provided that the value of the U parameter is adequately chosen. Hence, these methods offer an alternative efficient computational scheme to correct LDA and GGA approaches to adequately describe the electronic structure and magnetic coupling in large molecular magnetic systems, although at the expenses of introducing an empirical (U) parameter. For all investigated copper dinuclear systems, the LDA+U and GGA+U approaches lead to an improvement in the description of magnetic properties over the original LDA and GGA schemes with an accuracy similar to that arising from the hybrid B3LYP functional, by increasing the on-site Coulomb repulsion with a moderate U value. Nevertheless, the introduction of an arbitrary U value in the 0,10 eV range most often provides the correct ground-state spin distribution and the correct sign of the magnetic coupling constant. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] The behavior of transition metal nitrido bonds towards protonation rationalized by means of localized bonding schemes and their weightsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 6 2005Vinzenz Bachler Abstract A new computational scheme is applied to rationalize the different protonation behaviors of the nitrido complexes [L,MnV(N)(acac)]+, [LCrV(N)(acac)]+, and [LVV(N)(acac)]+. L and L, represent the macrocycles 1,4,7-triazacyclononane and its N-methylated derivative, respectively, and acac is the bidentate monoanion pentane-2,4-dionate. The bonds of the complexes are partitioned into bonds to be investigated and bonds of lesser interest. The investigated bonds are the transition metal nitrido bonds MVN| (M = Mn, Cr, and V) and the bonds of lesser interest are located in the ligands. The ligand bonds are described by means of the strongly occupied natural bond orbitals. The electrons in the MVN| nitrido bonds, however, are treated more accurately. A full configuration interaction procedure is applied in the space spanned by the strongly occupied natural bond orbitals and their corresponding antibonding orbitals. Localized bonding schemes and their weights are obtained for the d, -p, bonds of interest. This is achieved by representing the two-center natural bond orbitals for a d, -p, bond by the one-center natural hybrid orbitals localized at the bond atoms. The obtained bonding schemes are close to orthogonal valence bond structures. Their weights indicate that the nitrido nitrogen in [LVV(N)(acac)]+ is more easily protonated than the nitrido nitrogens in [L,MnV(N)(acac)]+ and [LCrV(N)(acac)]+. This result is in good accord with experiment. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 532,551, 2005 [source] Computational analysis of 1-methoxybicyclo[3.2.0]hepta-3,6-dien-2-one and its enantiomeric separationJOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 2 2003Karl Sohlberg Abstract A theoretical analysis of the primary photochemical products of irradiation of ,-tropolone methyl ether is presented. Through this analysis, the fact that only two of the four possible stereoisomers of the product are experimentally observed may be explained. We also present a computational scheme for identifying the enantiomers separated by chiral gas chromatography. Copyright © 2003 John Wiley & Sons, Ltd. [source] Non-empirical calculations of NMR indirect carbon,carbon coupling constants.MAGNETIC RESONANCE IN CHEMISTRY, Issue 6 2003Part 4: Bicycloalkanes Abstract A systematic study of the one-bond and long-range J(C,C), J(C,H) and J(H,H) in the series of nine bicycloalkanes was performed at the SOPPA level with special emphasis on the coupling transmission mechanisms at bridgeheads. Many unknown couplings were predicted with high reliability. Further refinement of SOPPA computational scheme adjusted for better performance was carried out using bicyclo[1.1.1]pentane as a benchmark to investigate the influence of geometry, basis set and electronic correlation. The calculations performed demonstrated that classical ab initio SOPPA applied with the locally dense Dunning's sets augmented with inner core s-functions used for coupled carbons and Sauer's sets augmented with tight s-functions used for coupled hydrogens performs perfectly well in reproducing experimental values of different types of coupling constants (the estimated reliability is ca 1,2 Hz) in relatively large organic molecules of up to 11 carbon atoms. Additive coupling increments were derived for J(C,C), J(C,H) and J(H,H) based on the calculated values of coupling constants within SOPPA in the model bicycloalkanes, in reasonably good agreement with the known values obtained earlier on pure empirical grounds. Most of the bridgehead couplings in all but one bicycloalkane appeared to be essentially additive within ca 2,3 Hz while bicyclo[1.1.1]pentane demonstrated dramatic non-additivity of ,14.5 Hz for J(C,C), +16.6 Hz for J(H,H) and ,5.5 Hz for J(C,H), in line with previous findings. Non-additivity effects in the latter compound established at the SOPPA level should be attributed to the through-space non-bonded interactions at bridgeheads due to the essential overlapping of the bridgehead rear lobes which provides an additional and effective non-bonding coupling path for the bridgehead carbons and their protons in the bicyclopentane framework. Copyright © 2003 John Wiley & Sons, Ltd. [source] Winds from massive stars: implications for the afterglows of , -ray burstsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2001Enrico Ramirez-Ruiz Recent observations suggest that long-duration , -ray bursts (GRBs) and their afterglows are produced by highly relativistic jets emitted in core-collapse explosions. The pre-explosive ambient medium provides a natural test for the most likely progenitors of GRBs. Those stars that shed their envelopes most readily have short jet crossing times and are more likely to produce a GRB. We construct a simple computational scheme to explore the expected contribution of the presupernova ejecta of single Wolf,Rayet (WR) stars to the circumstellar environment. Using detailed stellar tracks for the evolution of massive stars, we discuss the effects that the initial main-sequence mass, metallicity, rotation and membership in a binary system have on the ambient medium. We extend the theory of GRB afterglows in winds to consider the effect of the relativistic fireball propagating through the WR ejecta. Specific predictions are made for the interaction of the relativistic blast wave with the density bumps that arise when the progenitor star rapidly loses a large fraction of its initial mass or when the ejected wind interacts with the external medium and decelerates. A re-brightening of the afterglow with a spectrum redder than the typical synchrotron spectrum (as seen in GRB 970508, GRB 980326 and GRB 000911) is predicted. We also calculate the luminosity of the reflected echo that arises when circumstellar material Compton-scatters the prompt radiation, and examine the spectral signatures expected from the interaction of the GRB afterglow with the ejected medium. [source] On the synthesis of time-varying LQG weights and noises along optimal control and state trajectoriesOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2006L. G. Van Willigenburg Abstract A general approach to control non-linear uncertain systems is to apply a pre-computed nominal optimal control, and use a pre-computed LQG compensator to generate control corrections from the on-line measured data. If the non-linear model, on which the optimal control and LQG compensator design is based, is of sufficient quality, and when the LQG compensator is designed appropriately, the closed-loop control system is approximately optimal. This paper contributes to the selection and computation of the time-varying LQG weighting and noise matrices, which determine the LQG compensator design. It is argued that the noise matrices may be taken time-invariant and diagonal. Three very important considerations concerning the selection of the time-varying LQG weighting matrices are turned into a concrete computational scheme. Thereby, the selection of the time-varying LQG weighting matrices is reduced to selecting three scalar design parameters, each one weighting one consideration. Although the three considerations seem straightforward they may oppose one another. Furthermore, they usually result in time-varying weighting matrices that are indefinite, rather than positive (semi) definite as required for the LQG design. The computational scheme presented in this paper addresses and resolves both problems. By two numerical examples the benefits of our optimal closed-loop control system design are demonstrated and evaluated using Monte Carlo simulation. Copyright © 2005 John Wiley & Sons, Ltd. [source] Projected Gradient Flows for BV/Level Set RelaxationPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Martin Burger This paper introduces a new level set method based on projected gradient flows for problems that can be solved by a recently introduced relaxation approach. For the class of problems the relaxation is exact, it can be shown that the solution of the flow converges to a solution of the relaxed problem for large time, and the level sets of the limit are solutions of the original problem. We introduce a simple computational scheme based on explicit time discretization and apply the method to imaging examples. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Group functions approach based on the combination of strictly local geminals and molecular orbitalsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 3 2006A. M. Tokmachev Abstract Thegroup functions technique is a natural way to introduce local description into quantum chemistry. It can also be a basis for construction of numerically effective computational schemes having almost linear growth of computational costs with that of the size of the system. Previously, we constructed a family of computationally efficient semiempirical methods based on the variationally determined strictly local geminals (SLGs). It was implemented with four popular parameterization schemes (MINDO/3, MNDO, AM1, and PM3). Because of construction details, its applicability was restricted only to compounds with well-defined two-electron two-center chemical bonds and lone pairs. We generalize the previous treatment to make the electronic structure calculations possible for a wider class of compounds without loss of computational efficiency. The proposed scheme (SLG/SCF) is based on the general group function approach combining different descriptions for different electron groups: essentially local two-electron ones are described by geminals, while those with other numbers of electrons are described in the one-electron approximation. We implement the RHF, UHF, and ROHF approaches for the groups with delocalized electrons. This approach is tested for a series of radicals and molecules with extended ,-electron systems. It is shown that the SLG/SCF-based methods describe the experimental data not worse than the corresponding SCF procedures and provide a good starting point for calculations of polyatomic molecular systems. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] On the applicability of the HSAB principle through the use of improved computational schemes for chemical hardness evaluationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 7 2004Mihai V. Putz Abstract Finite difference schemes, named Compact Finite Difference Schemes with Spectral-like Resolution, have been used for a less crude approximation of the analytical hardness definition as the second-order derivative of the energy with respect to the electron number. The improved computational schemes, at different levels of theory, have been used to calculate global hardness values of some probe bases, traditionally classified as hard and soft on the basis of their chemical behavior, and to investigate the quantitative applicability of the HSAB principle. Exchange acid-base reactions have been used to test the HSAB principle assuming the reaction energies as a measure of the stabilization of product adducts. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 994,1003, 2004 [source] Alternating direction finite volume element methods for 2D parabolic partial differential equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008Tongke Wang Abstract On the basis of rectangular partition and bilinear interpolation, this article presents alternating direction finite volume element methods for two dimensional parabolic partial differential equations and gives three computational schemes, one is analogous to Douglas finite difference scheme with second order splitting error, the second has third order splitting error, and the third is an extended locally one dimensional scheme. Optimal L2 norm or H1 semi-norm error estimates are obtained for these schemes. Finally, two numerical examples illustrate the effectiveness of the schemes. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source] | |||||||||||||