44 resultados para optimized matrix inversion
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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We present a simple procedure to obtain the maximally localized Wannier function of isolated bands in one-dimensional crystals with or without inversion symmetry. First, we discuss the generality of dealing with real Wannier functions. Next, we use a transfer-matrix technique to obtain nonoptimal Bloch functions which are analytic in the wave number. This produces two classes of real Wannier functions. Then, the minimization of the variance of the Wannier functions is performed, by using the antiderivative of the Berry connection. In the case of centrosymmetric crystals, this procedure leads to the Wannier-Kohn functions. The asymptotic behavior of the Wannier functions is also analyzed. The maximally localized Wannier functions show the expected exponential and power-law decays. Instead, nonoptimal Wannier functions may show reduced exponential and anisotropic power-law decays. The theory is illustrated with numerical calculations of Wannier functions for conduction electrons in semiconductor superlattices.
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The complex reaction between VO2+ ((1)A(1)/(3)A) and C2H4 (Ag-1(g)/(3)A(1)) to yield VO+ ((1)Delta/(3)Sigma) and CH3CHO ('A'/(3)A) has been studied by means of B3LYP/6-31G* and B3LYP/6-311G(2d,p) calculations. The structures of all reactants, products, intermediates, and transition structures of this reaction have been optimized and characterized at the fundamental singlet and first excited triplet electronic states. Crossing points are localized, and possible spin inversion processes are discussed by means of the intrinsic reaction coordinate approach. Relevant stationary points along the most favorable reaction pathways have been studied at the CCSD/6-311G(2d,p)//B3LYP/6-311G(2d,p) calculation level. The theoretical results allow the development of thermodynamic and kinetic arguments about the reaction pathways of the title process. In the singlet state, the first step is the barrierless obtention of a reactant complex associated with the formation of a V-C bond, while in the triplet state a three-membered ring addition complex with the V bonded to the two C atoms is obtained. Similar behavior is found in the exit channels: the product complexes can be formed from isolated products without barriers. The reactant and product complexes are the most stable stationary points in the singlet and triplet electronic states. From the singlet state reactant complex, two reaction pathways are posssible to reach the triplet state product complex. (i) A mechanism in which a hydrogen transfer process is the first and rate limiting step and the second step is an oxygen transfer between vanadium and carbon atoms with a concomitant change in the spin state. The crossing point between singlet and triplet spin states is not kinetically relevant because it takes place at a later stage occurring in the exit channel. (ii) A mechanism in which the first stage renders a four-membered ring between vanadyl cation and the ethylene fragment and an oxygencarbon bond is formed; on going from this minimum to the second transition structure, associated with a carbon-vanadium bond breaking process, the crossing point between singlet and triplet spin states is reached. The final step is the hydrogen transfer between both carbon atoms to yield the product complex. In this case the spin change opens a lower barrier pathway. The transition structures with larger values of relative energies for both reactive channels of VO2+ ((1)A(1)) + C2H4 (Ag-1) --> VO+ ((3)Sigma) + CH3CHO ((1)A') present similar energies, and the two reaction pathways can be considered as competitive.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of J(2). The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10s) and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
A new chart based on sample variances for monitoring the covariance matrix of multivariate processes
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance |S| chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance |S| chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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The main goal in this work is to conduct a quantitative analysis of the mechanical stir casting process for obtaining particulate metal matrix composites. A combined route of stirring at semi-solid state followed by stirring at liquid state is proposed. A fractional factorial design was developed to investigate the influence and interactions of factors as: time, rotation, initial fraction and particle size, on the incorporated fraction. The best incorporations were obtained with all factors at high levels, as well as that very long stirring periods have no strong influence being particle size and rotation the most important factors on the incorporated fraction. Particle wetting occurs during stirring at semisolid state, highlighting the importance of the interactions between particles and the alloy globularized phase. The role of the alloying element Mg as a wettability-promoting agent is discussed. The shear forces resulting from the stirring system is emphasized and understood as the effect of rotation itself added to the propeller blade geometry.
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In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.
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This paper presents a pole placement method using both the augmented Jacobian and the corresponding system transfer function matrices. From the manipulation of these matrices a straightforward approach results to get the coefficients of a non-linear system, whose solution gives the parameters of the stabilizers that can provide a pre-specified minimum damping to the system. (C) 2001 Elsevier B.V. Ltd. All rights reserved.