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Higher-order Terms (higher-order + term)
Selected AbstractsSimulating turbulent Dean flow in Cartesian coordinatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009George K. El Khoury Abstract A simplified approach to simulate turbulent flows in curved channels is proposed. A set of governing equations of motion in Cartesian coordinates is derived from the full Navier,Stokes equations in cylindrical coordinates. Terms to first order in the dimensionless curvature parameter are retained, whereas higher-order terms are neglected. The curvature terms are implemented in a conventional Navier,Stokes code using Cartesian coordinates. Direct numerical simulations (DNS) of turbulent flow in weakly curved channels are performed. The pronounced asymmetries in the mean flow and the turbulence statistics observed in earlier DNS studies are faithfully reproduced by the present simplified Navier,Stokes model. It is particularly rewarding that also distinct pairs of counter-rotating streamwise-oriented vortices are embedded in the simulated flow field. Copyright © 2008 John Wiley & Sons, Ltd. [source] Simulation of shockwave propagation with a thermal lattice Boltzmann modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003ShiDe Feng Abstract A two-dimensional 19-velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u4) rather than the usual O(u3) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher-order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13-velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u. Copyright © 2003 John Wiley & Sons, Ltd. [source] Semilocalized approach to investigation of chemical reactivityINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003V. GineityteArticle first published online: 21 JUL 200 Abstract Application of the power series for the one-electron density matrix Gineityte, V., J Mol Struct Theochem 1995, 343, 183 to the case of two interacting molecules is shown to yield a semilocalized approach to investigate chemical reactivity, which is characterized by the following distinctive features: (1) Electron density (ED) redistributions embracing orbitals of the reaction centers of both molecules and of their neighboring fragments are studied instead of the total intermolecular interaction energy; (2) the ED redistributions are expressed directly in the basis of fragmental orbitals (FOs) without passing to the basis of delocalized molecular orbitals (MOs) of initial molecules; (3) terms describing the ED redistributions due to an intermolecular contact arise as additive corrections to the purely monomolecular terms and thereby may be analyzed independently; (4) local ED redistributions only between orbitals of the reaction centers of both molecules are described by lower-order ter s of the power series, whereas those embracing both the reaction centers and their neighborhoods are represented by higher-order terms. As opposed to the standard perturbative methods based on invoking the delocalized (canonical) MOs of isolated molecules, the results of the approach suggested are in-line with the well-known intuition-based concepts of the classic chemistry concerning reactivity, namely, with the assumption about different roles of the reaction center and of its neighborhood in a chemical process, with the expectation about extinction of the indirect influence of a certain fragment (substituent) when its distance from the reaction center grows, etc. Such a parallelism yields quantum chemical analogs for the classic concepts and thereby gives an additional insight into their nature. The scope of validity of these concepts also is discussed. Applicability of the approach suggested to specific chemical problems is illustrated by a brief consideration of the SN2 and AdE2 reactions. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 302,316, 2003 [source] Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic ProgramQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2005Julia C. C. Tsai Abstract This paper presents an automatic and more robust implementation of multivariate adaptive regression splines (MARS) within the orthogonal array (OA)/MARS continuous-state stochastic dynamic programming (SDP) method. MARS is used to estimate the future value functions in each SDP level. The default stopping rule of MARS employs the maximum number of basis functions Mmax, specified by the user. To reduce the computational effort and improve the MARS fit for the wastewater treatment SDP model, two automatic stopping rules, which automatically determine an appropriate value for Mmax, and a robust version of MARS that prefers lower-order terms over higher-order terms are developed. Computational results demonstrate the success of these approaches. Copyright © 2005 John Wiley & Sons, Ltd. [source] Rotation designs: orthogonal first-order designs with higher order projectivityAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2002Dizza Bursztyn Abstract In many factorial experiments, just a few of the experimental factors account for most of the variation in the response, a situation known as factor sparsity. Accurate modelling of the factor,response relationship may require use of higher-order terms in the active factors. In such settings, it may be desirable to use a design that is able, simultaneously, to screen out the important factors and to fit higher-order models in those factors. We derive a useful class of designs by rotating standard two-level fractional factorials. A special class of rotations is developed that has some appealing symmetry properties and can accommodate more factors than the rotation designs in Bursztyn and Steinberg (J. Stat. Plann. Inference 2001;97:399). A comparison of designs based on their projection properties and alias matrices shows that the new designs are better than many other alternatives. Copyright © 2002 John Wiley & Sons, Ltd. [source] A Kharitonov-like theorem for robust stability independent of delay of interval quasipolynomialsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2010Onur Toker Abstract In this paper, a Kharitonov-like theorem is proved for testing robust stability independent of delay of interval quasipolynomials, p(s)+,eqk(s), where p and qk's are interval polynomials with uncertain coefficients. It is shown that the robust stability test of the quasipolynomial basically reduces to the stability test of a set of Kharitonov-like vertex quasipolynomials, where stability is interpreted as stability independent of delay. As discovered in (IEEE Trans. Autom. Control 2008; 53:1219,1234), the well-known vertex-type robust stability result reported in (IMA J. Math. Contr. Info. 1988; 5:117,123) (See also (IEEE Trans. Circ. Syst. 1990; 37(7):969,972; Proc. 34th IEEE Conf. Decision Contr., New Orleans, LA, December 1995; 392,394) does contain a flaw. An alternative approach is proposed in (IEEE Trans. Autom. Control 2008; 53:1219,1234), and both frequency sweeping and vertex type robust stability tests are developed for quasipolynomials with polytopic coefficient uncertainties. Under a specific assumption, it is shown in (IEEE Trans. Autom. Control 2008; 53:1219,1234) that robust stability independent of delay of an interval quasipolynomial can be reduced to stability independent of delay of a set of Kharitonov-like vertex quasipolynomials. In this paper, we show that the assumption made in (IEEE Trans. Autom. Control 2008; 53:1219,1234) is redundant, and the Kharitonov-like result reported in (IEEE Trans. Autom. Control 2008; 53:1219,1234) is true without any additional assumption, and can be applied to all quasipolynomials. The key idea used in (IEEE Trans. Autom. Control 2008; 53:1219,1234) was the equivalence of Hurwitz stability and , -o -stability for interval polynomials with constant term never equal to zero. This simple observation implies that the well-known Kharitonov theorem for Hurwitz stability can be applied for , -o -stability, provided that the constant term of the interval polynomial never vanishes. However, this line of approach is based on a specific assumption, which we call the CNF-assumption. In this paper, we follow a different approach: First, robust , -o -stability problem is studied in a more general framework, including the cases where degree drop is allowed, and the constant term as well as other higher-orders terms can vanish. Then, generalized Kharitonov-like theorems are proved for , -o -stability, and inspired by the techniques used in (IEEE Trans. Autom. Control 2008; 53:1219,1234), it is shown that robust stability independent of delay of an interval quasipolynomial can be reduced to stability independent of delay of a set of Kharitonov-like vertex quasipolynomials, even if the assumption adopted in (IEEE Trans. Autom. Control 2008; 53:1219,1234) is not satisfied. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||