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Cartesian Coordinates (cartesian + coordinate)
Terms modified by Cartesian Coordinates Selected AbstractsA ,-coordinate three-dimensional numerical model for surface wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002Pengzhi Lin Abstract A three-dimensional numerical model based on the full Navier,Stokes equations (NSE) in , -coordinate is developed in this study. The , -coordinate transformation is first introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial differentiation, a new set of governing equations is derived in the , -coordinate from the original NSE defined in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23: 485,501), which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified NSE. The model is first tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a confined tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two- and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction. Copyright © 2002 John Wiley & Sons, Ltd. [source] Paraxial ray methods for anisotropic inhomogeneous mediaGEOPHYSICAL PROSPECTING, Issue 1 2007Tijmen Jan Moser ABSTRACT A new formalism of surface-to-surface paraxial matrices allows a very general and flexible formulation of the paraxial ray theory, equally valid in anisotropic and isotropic inhomogeneous layered media. The formalism is based on conventional dynamic ray tracing in Cartesian coordinates along a reference ray. At any user-selected pair of points of the reference ray, a pair of surfaces may be defined. These surfaces may be arbitrarily curved and oriented, and may represent structural interfaces, data recording surfaces, or merely formal surfaces. A newly obtained factorization of the interface propagator matrix allows to transform the conventional 6 × 6 propagator matrix in Cartesian coordinates into a 6 × 6 surface-to-surface paraxial matrix. This matrix defines the transformation of paraxial ray quantities from one surface to another. The redundant non-eikonal and ray-tangent solutions of the dynamic ray-tracing system in Cartesian coordinates can be easily eliminated from the 6 × 6 surface-to-surface paraxial matrix, and it can be reduced to 4 × 4 form. Both the 6 × 6 and 4 × 4 surface-to-surface paraxial matrices satisfy useful properties, particularly the symplecticity. In their 4 × 4 reduced form, they can be used to solve important boundary-value problems of a four-parametric system of paraxial rays, connecting the two surfaces, similarly as the well-known surface-to-surface matrices in isotropic media in ray-centred coordinates. Applications of such boundary-value problems include the two-point eikonal, relative geometrical spreading, Fresnel zones, the design of migration operators, and more. [source] Three-dimensional analysis of a driver-passenger vehicle interfaceHUMAN FACTORS AND ERGONOMICS IN MANUFACTURING & SERVICE INDUSTRIES, Issue 3 2004Sung-Jae Chung This article presents a method of analyzing how drivers' anthropometric data are best accommodated by a specific driver-vehicle interface. Three-dimensional (3-D) manikins with 18 links were developed using anthropometric data for the U.S. 95th percentile male and 5th percentile female. In addition, an adjustable seating buck was constructed to control 7 package variables. After the manikins were positioned in each driving environment, 3-D Cartesian coordinates for the manikins' articulations were determined using a coordinate measuring machine. The data were then converted into joint angles to suggest suitable driving environments that consider appropriate driving postures. © 2004 Wiley Periodicals, Inc. Hum Factors Man 14: 269,284, 2004. [source] Simulating 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] Computational study on the comparative synthesis of energetic FOX-7 derivativesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2010Min-Hsien Liu Abstract Ethene and two kinds of nitrating reagents (HNO3 and N2O5) were included in respective molecular systems, which progressed through a two-stage electrophilic and free radical nitrosubstitution, resulting in the corresponding nitroethene compounds. Subsequent halogenation (using Cl2 and Br2) and amination (using ammonia) were then performed, also by electrophilic and radical substitution, to produce the target 1,1-diamino-2,2-dinitroethene (FOX-7) derivatives. All transition state species were identified using a two- or three-structure Synchronous Transit-Guided Quasi-Newton between the Cartesian coordinates of the related molecular systems at specific reaction stages. The modeling results suggest that N2O5 is the better agent for nitration and bromine is suitable for use in halogenation. The comparable activation energies throughout the reaction stages were considered to imply the most feasible pathways of FOX-7 synthesis. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Coriolis coupling on the rotational and vibrational energy transfer in H2O+ Ar collisions: Classical trajectories simulationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2006E. Borges Abstract Classical trajectories studies in Cartesian coordinates are applied to analyze Coriolis coupling for the energy transfer in H2O + Ar process. Vibrational energies equal to 50 kcal/mol and 100 kcal/mol for initial rotational temperatures in the range 298,30,000 K are used as initial conditions. Initial translational temperatures for the incoming atom are selected in the same way. Effects of rotational and translational temperatures at different initial conditions are also investigated in the molecular vibrational relaxation process. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Modeling and predicting binding affinity of phencyclidine-like compounds using machine learning methodsJOURNAL OF CHEMOMETRICS, Issue 1 2010Ozlem Erdas Abstract Machine learning methods have always been promising in the science and engineering fields, and the use of these methods in chemistry and drug design has advanced especially since the 1990s. In this study, molecular electrostatic potential (MEP) surfaces of phencyclidine-like (PCP-like) compounds are modeled and visualized in order to extract features that are useful in predicting binding affinities. In modeling, the Cartesian coordinates of MEP surface points are mapped onto a spherical self-organizing map (SSOM). The resulting maps are visualized using electrostatic potential (ESP) values. These values also provide features for a prediction system. Support vector machines and partial least-squares method are used for predicting binding affinities of compounds. Copyright © 2009 John Wiley & Sons, Ltd. [source] Isomers of C20: An energy profile IIIJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2004Jennifer I. Chavez Abstract Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C20 isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C20 that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require ,15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C20 structures on the potential surface, relative to the ring, bowl, and cage isomers. © 2003 Wiley Periodicals, Inc. J Comput Chem 25: 322,327, 2004 [source] Isomers of C20: An energy profile IIJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2003Kyle A. Beran Abstract Semi-empirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C20 isomers that are predicted to exist in and around the bowl and cage isomers. Using the optimized Cartesian coordinates for the bowl and the cage isomers, a saddle-point calculation was performed. The output file generated, containing energy, distance, and geometry information, is then organized into a graphical format. The resulting graph, which plots the energy of the 20-atom system as a function of the distance from the geometric midpoint, is a two-dimensional energy profile. This profile illustrates an estimation of the contours on the potential energy surface, showing energy minima and maxima that are encountered as the bowl evolves into the cage structure, or vice-versa. To expand the surface into three dimensions, geometry optimizations were performed on the sets of Cartesian coordinates that correspond to energy minima in the bowl-cage profile. Based on these optimizations, eight additional isomers of C20 have been identified and are predicted to be energetically stable. These additional isomers were subsequently subjected to saddle-point calculations in order to identify those isomers that lie adjacent to one another on the three-dimensional surface. Two isomers that are adjacent to each other will exhibit an energy profile that progresses smoothly from the potential well of each isomer up to the saddle point separating them. Consequently, these adjacent pairs of isomers establish a step-wise transformation between the bowl and the cage. This process, which extends out over the three-dimensional surface, is predicted to require less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1287,1290, 2003 [source] Adaptive grid based on geometric conservation law level set method for time dependent PDENUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009Ali R. Soheili Abstract A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103,122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75,98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118,142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Exact integration of the stiffness matrix of an 8-node plane elastic finite element by symbolic computationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008L. Videla Abstract Computer algebra systems (CAS) are powerful tools for obtaining analytical expressions for many engineering applications in both academic and industrial environments. CAS have been used in this paper to generate exact expressions for the stiffness matrix of an 8-node plane elastic finite element. The Maple software system was used to identify six basic formulas from which all the terms of the stiffness matrix could be obtained. The formulas are functions of the Cartesian coordinates of the corner nodes of the element, and elastic parameters Young's modulus and Poisson's ratio. Many algebraic manipulations were performed on the formulas to optimize their efficiency. The redaction in CPU time using the exact expressions as opposed to the classical Gauss,Legendre numerical integration approach was over 50%. In an additional study of accuracy, it was shown that the numerical approach could lead to quite significant errors as compared with the exact approach, especially as element distortion was increased.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source] Designing herbicide formulation characteristics to maximize efficacy and minimize rice injury in paddy environmentsPEST MANAGEMENT SCIENCE (FORMERLY: PESTICIDE SCIENCE), Issue 6 2001Steven A Cryer Abstract Mathematical descriptors, coupled with experimental observations, are used to quantify differential uptake of an experimental herbicide in Japonica and Indica rice (Oryza sativa, non-target) and barnyardgrass (Echinochloa crus-galli, target). Partitioning, degradation, plant uptake and metabolism are described using mass-balance conservation equations in the form of kinetic approximations. Estimated environmental concentrations, governed by the pesticide formulation, are described using superimposed analytical solutions for the one-dimensional diffusion equation in spherical coordinates and by a finite difference representation of the two-dimensional diffusion equation in Cartesian coordinates. Formulation attributes from granules include active ingredient release rates, particle sizes, pesticide loading, and granule spacing. The diffusion model for pesticide transport is coupled with the compartment model to follow the fate and transport of a pesticide from its initial application location to various environmental matrices of interest. Formulation effects, partitioning and degradation in the various environmental matrices, differential plant uptake and metabolism, and dose-response information for plants are accounted for. This novel model provides a mechanism for selecting formulation delivery systems that optimize specific attributes (such as weed control or the therapeutic index) for risk-assessment procedures. In this report we describe how this methodology was used to explore the factors affecting herbicide efficacy and to define an optimal release rate for a granule formulation. © 2001 Society of Chemical Industry [source] Inverse problem in seismic imagingPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Maria Cameron We address the problem of estimating sound speeds (seismic velocities) inside the earth which is necessary for obtaining seismic images in regular Cartesian coordinates. The main goals are to develop algorithms to convert time migration velocities to true seismic velocities, and to convert time-migrated images to depth images in regular Cartesian coordinates. Our main results are three-fold. First, we establish a theoretical relation between the seismic velocities and the time migration velocities using the paraxial ray tracing theory. Second, we formulate an appropriate inverse problem describing the relation between time migration velocities and depth velocities and show that this problem is mathematically ill-posed, i.e., unstable to small perturbations. Third, we develop numerical algorithms to solve regularized versions of these equations which can be used to recover smoothed velocity variations. Our algorithms consist of efficient time-to-depth conversion algorithms based on Dijkstra-like Fast Marching Methods, as well as level set and ray tracing algorithms for transforming Dix velocities into seismic velocities. Our algorithms are applied to both two-dimensional and three-dimensional problems and we test them on a collection of both synthetic examples and field data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Some fundamental aspects of building protein structures from fragment librariesPROTEIN SCIENCE, Issue 6 2004J. Bradley Holmes Abstract We have investigated some of the basic principles that influence generation of protein structures using a fragment-based, random insertion method. We tested buildup methods and fragment library quality for accuracy in constructing a set of known structures. The parameters most influential in the construction procedure are bond and torsion angles with minor inaccuracies in bond angles alone causing >6 Å C,RMSD for a 150-residue protein. Idealization to a standard set of values corrects this problem, but changes the torsion angles and does not work for every structure. Alternatively, we found using Cartesian coordinates instead of torsion angles did not reduce performance and can potentially increase speed and accuracy. Under conditions simulating ab initio structure prediction, fragment library quality can be suboptimal and still produce near-native structures. Using various clustering criteria, we created a number of libraries and used them to predict a set of native structures based on nonnative fragments. Local C,RMSD fit of fragments, library size, and takeoff/landing angle criteria weakly influence the accuracy of the models. Based on a fragment's minimal perturbation upon insertion into a known structure, a seminative fragment library was created that produced more accurate structures with fragments that were less similar to native fragments than the other sets. These results suggest that fragments need only contain native-like subsections, which when correctly overlapped, can recreate a native-like model. For fragment-based, random insertion methods used in protein structure prediction and design, our findings help to define the parameters this method needs to generate near-native structures. [source] A computational study on the characteristics of airflow in bilateral abductor vocal fold immobility,THE LARYNGOSCOPE, Issue 9 2010M. Kür, at Gökcan MD Abstract Objectives/Hypothesis: To evaluate airway sufficiency and airflow dynamics in a group of patients who underwent a posterior transverse laser cordotomy (PTLC) procedure. Study Design: Mixed methods research, university hospital setting. Methods: Sixteen patients who underwent a PTLC procedure volunteered to be involved in this study. Dyspnea levels, voice, and glottic opening in indirect laryngoscopy were evaluated subjectively. The airway was evaluated objectively by pulmonary function tests, and glottic areas were measured from axial computed tomography (CT) images. The control group consisted of 63 subjects from the tomography archive. For computational fluid dynamics (CFD) analyses, two subjects from the study group were chosen on the basis of obstruction level, and a normal female subject was selected from the control group. Cartesian coordinates for airway boundaries were determined from axial CT images, and a three-dimensional computational model of the larynx was constructed. Flow simulations were performed with two different flow conditions during inspiration. Comparison of velocity, static pressure, turbulence intensity, and wall shear stress distribution values were made between selected cases and control. Results: Pulmonary data varied widely and did not correlate with the size of the glottic area or dyspnea level. CFD analyses revealed that in addition to obstruction at the glottic level, aerodynamic properties of the larynx are altered due to loss in muscular tonus. Also, the contour of the glottic opening was found to be very important in determining the character of airflow as laminar or turbulent. Conclusions: Patients have considerable differences in their flow patterns and force distributions during respiration. Patient-specific models may help in evaluation and treatment planning. Laryngoscope, 2010 [source] Best domain for an elliptic problem in cartesian coordinates by means of shape-measureASIAN JOURNAL OF CONTROL, Issue 5 2009Alireza Fakharzadeh Jahromi Abstract In (ZAA J. Anal. Appl., Vol. 16, No. 1, pp. 143,155) we introduced a method to determine the optimal domains for elliptic optimal-shape design problems in polar coordinates. However, the same problem in cartesian coordinates, which are more applicable, is found to be much harder, therefore we had to develop a new approach for these designs. Herein, the unknown domain is divided into a fixed and a variable part and the optimal pair of the domain and its optimal control, is characterized in two stages. Firstly, the optimal control for the each given domain is determined by changing the problem into a measure-theoretical one, replacing this with an infinite dimensional linear programming problem and approximating schemes; then the nearly optimal control function is characterized. Therefore a function that offers the optimal value of the objective function for a given domain, is defined. In the second stage, by applying a standard optimization method, the global minimizer pair will be obtained. Some numerical examples are also given. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] | |||||||||||||