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Function Values (function + value)
Selected AbstractsNumerical study of lid-driven flow in orthogonal and skewed porous cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2008D. Jaya Krishna Abstract Effects of Reynolds number, Darcy number, porosity, aspect ratio and skewness are studied in detail for lid-driven cavity flows filled with fluid-saturated porous medium. A generalized non-Darcy approach has been considered to account for linear and non-linear drag forces. The governing equations are solved by using finite volume method. A quadrilateral cell in a semi-staggered arrangement has been employed and is transformed into a standard square element using local body-fitting co-ordinates by co-ordinate transformation. Details of the flow physics reveal that by the reduction of Darcy number, the primary vortex becomes weaker and tends to move towards the lid. As a measure of volume flow rate maximum stream function value is considered. It is found that, with the reduction in Darcy number and with the increase in Reynolds number and skewness the maximum stream function value reduces. Copyright © 2007 John Wiley & Sons, Ltd. [source] Derivative Free Optimization in Higher DimensionINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 3 2001Shamsuddin Ahmed Non-linear optimizations that do not require explicit or implicit derivative information of an objective function are an alternate search strategy when the derivative of the objective function is not available. In factorial design, the number of trials for experimental identification method in Em is about (m+ 1). These (m+ 1) equally spaced points are allowed to form a geometry that is known as regular simplex. The simplex method is attributed to Spendley, Hext and Himsworth. The method is improved by maintaining a set of (m+ 1) points in m dimensional space to generate a non-regular simplex. This study suggests re-scaling the simplex in higher dimensions for a restart phase. The direction of search is also changed when the simplex degenerates. The performance of this derivative free search method is measured based on the number of function evaluations, number of restart attempts and improvements in function value. An algorithm that describes the improved method is presented and compared with the Nelder and Mead simplex method. The performance of this algorithm is also tested with artificial neural network (ANN) problem. The numbers of function evaluations are about 40 times less with the improved method against the Nelder and Mead (1965) method to train an ANN problem with 36 variables. [source] A systematic evaluation of the benefits and hazards of variable selection in latent variable regression.JOURNAL OF CHEMOMETRICS, Issue 7 2002Part II. Abstract Leave-multiple-out cross-validation (LMO-CV) is compared to leave-one-out cross-validation (LOO-CV) as objective function in variable selection for four real data sets. Two data sets stem from NIR spectroscopy and two from quantitative structure,activity relationships. In all four cases, LMO-CV outperforms LOO-CV with respect to prediction quality, model complexity (number of latent variables) and model size (number of variables). The number of objects left out in LMO-CV has an important effect on the final results. It controls both the number of latent variables in the final model and the prediction quality. The results of variable selection need to be validated carefully with a validation step that is independent of the variable selection. This step needs to be done because the internal figures of merit (i.e. anything that is derived from the objective function value) do not correlate well with the external predictivity of the selected models. This is most obvious for LOO-CV. LOO-CV without further constraints always shows the best internal figures of merit and the worst prediction quality. Copyright © 2002 John Wiley & Sons, Ltd. [source] NONLINEAR CONSTRAINED OPTIMIZATION of THERMAL PROCESSING II.JOURNAL OF FOOD PROCESS ENGINEERING, Issue 3 2003FINITE CYLINDRICAL GEOMETRIES, VARIABLE PROCESS TEMPERATURE PROFILES to REDUCE PROCESS TIME, to IMPROVE NUTRIENT RETENTION IN SPHERICAL ABSTRACT Conventional methods for thermal processing of foods use constant processing temperature profiles (CPTPs) for a prescribed processing time, which is based on achieving a required microbial lethality to comply with public health standards. This also results in degradation of nutrients and quality factors. the variable process temperature profiles (VPTPs) obtained by using optimization methods can reduce quality losses and/or processing time compared to CPTPs. the objective of this research was to evaluate VPTPs using the Complex Method to reduce the processing time and/or improve quality retention for a specified level of lethality in thermal processing of conduction heated foods. the VPTPs were obtained for volume average retention of thiamine considering different sizes of spheres (small and large) and finite cylinders (small and large), and the thiamine retention and processing time results were compared with a conventional method (processing at 121.1C) for a specified lethality level. the use of VPTPs resulted in a 37 and 10% decrease in processing times in spherical and 40 % and 6 % for finite cylindrical shapes, for the same objective function value and specified lethality compared to the CPTP process. For the same processing time, the improvements in thiamine destruction were 3.7 and 2 % for spheres, and 3.9 and 2.2% for finite cylinders. [source] Enhanced stability regions for model predictive control of nonlinear process systemsAICHE JOURNAL, Issue 6 2008Maaz Mahmood Abstract The problem of predictive control of nonlinear process systems subject to input constraints is considered. The key idea in the proposed approach is to use control-law independent characterization of the process dynamics subject to constraints via model predicative controllers to expand on the set of initial conditions for which closed,loop stability can be achieved. An application of this idea is presented to the case of linear process systems for which characterizations of the null controllable region (the set of initial conditions from where closed,loop stability can be achieved subject to input constraints) are available, but not practically implementable control laws that achieve stability from the entire null controllable region. A predictive controller is designed that achieves closed,loop stability for every initial condition in the null controllable region. For nonlinear process systems, while the characterization of the null controllable region remains an open problem, the set of initial conditions for which a (given) Lyapunov function can be made to decay is analytically computed. Constraints are formulated requiring the process to evolve within the region from where continued decay of the Lyapunov function value is achievable and incorporated in the predictive control design, thereby expanding on the set of initial conditions from where closed,loop stability can be achieved. The proposed method is illustrated using a chemical reactor example, and the robustness with respect to parametric uncertainty and disturbances demonstrated via application to a styrene polymerization process. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Function-based flow modeling and animationCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 4 2001Ergun Akleman Abstract This paper summarizes a function-based approach to model and animate 2D and 3D flows. We use periodic functions to create cyclical animations that represent 2D and 3D flows. These periodic functions are constructed with an extremely simple algorithm from a set of oriented lines. The speed and orientation of the flow are described directly by the orientation and the lengths of these oriented lines. The resulting cyclical animations are then obtained by sampling the constructed periodic functions. Our approach is independent of dimension, i.e. for 2D and 3D flow the same types of periodic functions are used. Rendering images for 2D and 3D flows is slightly different. In 2D function values directly are mapped to color values. On the other hand, in 3D function values are first mapped to color and opacity and then the volume is rendered by our volume renderer. Modeled and animated flows are used to improve the visualization of operations of rolling piston and rotary vane compressors. Copyright © 2001 John Wiley & Sons, Ltd. [source] Green's function interpolations for prestack imagingGEOPHYSICAL PROSPECTING, Issue 1 2000Manuela Mendes A new interpolation method is presented to estimate the Green's function values, taking into account the migration/inversion accuracy requirements and the trade-off between resolution and computing costs. The fundamental tool used for this technique is the Dix hyperbolic equation (DHE). The procedure, when applied to evaluate the Green's function for a real source position, uses the DHE to derive the root-mean-square velocity, vRMS, from the precomputed traveltimes for the nearest virtual sources, and by linear interpolation generates vRMS for the real source. Then, by applying the DHE again, the required traveltimes and geometrical spreading can be estimated. The inversion of synthetic data demonstrates that the new interpolation yields excellent results which give a better qualitative and quantitative resolution of the imaging sections, compared with those carried out by conventional linear interpolation. Furthermore, the application to synthetic and real data demonstrates the ability of the technique to interpolate Green's functions from widely spaced virtual sources. Thus the proposed interpolation, besides improving the imaging results, also reduces the overall CPU time and the hard disk space required, hence decreasing the computational effort of the imaging algorithms. [source] A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010G. R. Liu Abstract It is well known that the lower bound to exact solutions in linear fracture problems can be easily obtained by the displacement compatible finite element method (FEM) together with the singular crack tip elements. It is, however, much more difficult to obtain the upper bound solutions for these problems. This paper aims to formulate a novel singular node-based smoothed finite element method (NS-FEM) to obtain the upper bound solutions for fracture problems. In the present singular NS-FEM, the calculation of the system stiffness matrix is performed using the strain smoothing technique over the smoothing domains (SDs) associated with nodes, which leads to the line integrations using only the shape function values along the boundaries of the SDs. A five-node singular crack tip element is used within the framework of NS-FEM to construct singular shape functions via direct point interpolation with proper order of fractional basis. The mix-mode stress intensity factors are evaluated using the domain forms of the interaction integrals. The upper bound solutions of the present singular NS-FEM are demonstrated via benchmark examples for a wide range of material combinations and boundary conditions. Copyright © 2010 John Wiley & Sons, Ltd. [source] A fuzzy-based multimodel system for reasoning about the number of software defectsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2005Marek Reformat Software maintenance engineers need tools to support their work. To make such tools relevant, they should provide engineers with quantitative input, as well as the knowledge needed to understand factors influencing maintenance activities. This article proposes an approach leading to multitechnique knowledge extraction and development of a comprehensive meta-model prediction system in the area of corrective maintenance. It dwells on elements of evidence theory and a number of fuzzy-based models. The models are developed using an evolutionary-based approach with different objectives applied to different subsets of data. Evidence theory,based Transferable Belief Model and belief function values assigned to generated models are used for reasoning purposes. The study comprises a detailed case for estimating the number of defects in a medical imaging system. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1093,1115, 2005. [source] Effect of Pressure on the Miscibility of Polyethylene/Poly(ethylene- alt -propylene) BlendsMACROMOLECULAR THEORY AND SIMULATIONS, Issue 7 2006Phillip Choi Abstract Summary: Effect of density, and hence pressure, on the miscibility of a 50:50 mol/mol PE/PEP blend was studied using a coarse-grained MC simulation approach on a high-coordination lattice, with the conformations of the coarse-grained chains constrained by the RIS model. Interchain pair correlation functions are used to assess the miscibility of the mixtures. Miscibility increases with increasing temperature over the range ,50,150,°C. It is rather insensitive to pressure at high temperatures, but at ,50,°C, the blend miscibility increases with decreasing pressure. The findings are consistent with the fact that the blend is an UCST blend and that the simulation temperatures used, except ,50,°C, were considerably higher than the UCST of the blend. The pressure dependence of the blend miscibility observed near ,50,°C is also in agreement with the experimental observation that the blend exhibits a negative volume change of mixing. The present work demonstrates that the coarse-grained MC approach, when it is used with periodic boundary cells of different sizes filled with the same number of chains, is capable of capturing the pressure dependence of UCST blends. In addition, such a simulation also provides us with insights about the molecular origin of the observed pressure dependence of miscibility. In the present case, the segregation of PE and PEP chains at low temperatures and high pressure simply originates from the fact that fully extended segments of PE chains tend to cluster so that their intermolecular interactions can be maximized. As the temperature increases, there is a decrease in the probability of a trans state at a CC bond in PE, and therefore the attraction between the PE chains is reduced at higher temperatures, promoting miscibility and the UCST behavior. Density (pressure) dependence of the 2nd shell pair correlation function values for a 50/50 PE/PEP blend at ,50,°C. [source] DFT Based Atomic Softness and Its Application in Site SelectivityMOLECULAR INFORMATICS, Issue 8 2003P. Singh Abstract Active site of a complex molecule and mechanism of chemical reaction has been studied with the help of atomic softness values derived from calculation based on Density functional theory. The quantum mechanical equation of Klopman has been solved with the help of AM1 calculation by using Win MOPAC7.21 software. On the basis of chemical potential equalization principle, and Koopmans theorem for frontier orbitals a formalism has been developed for the calculation of electron affinity of an atom in a molecule EA. The reliability of the EA values have been tested with electron density (obtained from AM1 calculation) and Fukui function values taken from literature. [source] Shortest path network interdiction with asymmetric informationNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2008Halil Bayrak Abstract We consider an extension of the shortest path network interdiction problem. In this problem an evader attempts to minimize the length of the shortest path between the origin and the destination in a network, while an interdictor attempts to maximize the length of this shortest path by interdicting network arcs using limited resources. We consider the case where there is asymmetric information, i.e., the evader and the interdictor have different levels of information about the network. We formulate this problem as a nonlinear mixed integer program and show that this formulation can be converted to a linear mixed integer program. Computational results demonstrate improvements in the objective function values over the shortest path network interdiction problem with symmetric information. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008 [source] Consistent interpolation of equidistantly sampled dataNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2009Eike Rietsch Abstract Let u1, u2, ,, uN with un,, denote the values of a function recorded or computed at N real and equidistant abscissa values tn=n,t+t0 for n=1, ,, N. A consistent interpolation operator L, as defined in this paper, interpolates these function values for N new abscissas tn = (n+½),t+t0, the first N,1 of which are halfway between those originally given while the last one is outside of the original abscissa range. Application of L to these interpolated function values produces the last N,1 samples u2, u3, ,, uN of the original data plus one extrapolated function value uN+1. Hence, L2 is essentially a shift operator, but with a prediction component. The difference between various interpolation methods (e.g. polynomials, Fourier series) is now reduced to the way in which uN+1 is determined. This concept not only permits a uniform view at interpolation by quite different classes of functions but also allows the creation of more general interpolation, differentiation, and integration formulas, which can be tailored to particular problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Association of lower airway inflammation with physiologic findings in young children with cystic fibrosis,PEDIATRIC PULMONOLOGY, Issue 5 2009Stacey L. Peterson-Carmichael MD Abstract Background The relationship between lower airway markers of inflammation and infection with physiologic findings is poorly understood in young children with cystic fibrosis (CF). The goal of this study was to evaluate the association of bronchoalveolar lavage fluid (BALF) markers of infection and inflammation, including mediators linked to airway remodeling, to infant lung function values in young children with CF undergoing clinically indicated bronchoscopy. Methods Plethysmography and the raised volume rapid thoracoabdominal compression (RVRTC) technique were performed in 16 sedated infants and young children with CF prior to bronchoscopy. BALF was collected and analyzed for pathogen density, cell count, % neutrophils, transforming growth factor beta 1 (TGF-,1), matrix metalloproteinases (MMP), and interleukin-8 (IL-8). Results There was a significant direct correlation between functional residual capacity (FRC), the ratio of residual volume to total lung capacity (RV/TLC) and FRC/TLC with % neutrophils (P,<,0.05). Forced expiratory flows were inversely correlated to % neutrophils (P,<,0.01). Lung function parameters did not differentiate those with and without lower airway infection; however, pathogen density directly correlated with FRC and inversely correlated with flows (P,<,0.05). In a subset of the population, MMP-2 directly correlated with RV/TLC and inversely correlated with flows (P,<,0.05) and TGF-,1 directly correlated with FRC (P,<,0.05). Conclusions Results from this study suggest that lower airway inflammation as well as mediators linked to airway remodeling play an active role in pulmonary deterioration in CF infants and young children undergoing clinically indicated bronchoscopy. Pediatr Pulmonol. 2009; 44:503,511. © 2009 Wiley-Liss, Inc. [source] | |||||||||||||||||||