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## Coordinate System (coordinate + system)
Kinds of Coordinate System
## Selected Abstracts## Combined compression and simplification of dynamic 3D meshes COMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 4 2009Libor VáAbstract We present a new approach to dynamic mesh compression, which combines compression with simplification to achieve improved compression results, a natural support for incremental transmission and level of detail. The algorithm allows fast progressive transmission of dynamic 3D content. Our scheme exploits both temporal and spatial coherency of the input data, and is especially efficient for the case of highly detailed dynamic meshes. The algorithm can be seen as an ultimate extension of the clustering and local coordinate frame (LCF)-based approaches, where each vertex is expressed within its own specific coordinate system. The presented results show that we have achieved better compression efficiency compared to the state of the art methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Stylized lighting for cartoon shader COMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 2-3 2009Hideki TodoAbstract In the context of non-photorealistic imaging, such as digital cel animation, lighting is symbolic and stylized to depict the scene's mood and the geometric or physical features of the objects in the scene. Stylized light and shade should therefore be intentionally animated rather than rigorously simulated. However, it is difficult to achieve smooth animation of light and shade that are stylized with a user's intention, because such stylization cannot be achieved using just conventional 3D lighting. To address this problem, we propose a 3D stylized lighting method, focusing on several stylized effects including straight lighting, edge lighting, and detail lighting which are important features in hand-drawn cartoon animation. Our method is an extension of the conventional cartoon shader and introduces a light coordinate system for light shape control with smooth animations of light and shade. We also extend a toon mapping process for detailed feature lighting. Having these algorithms in a real-time cartoon shader, our prototype system allows the interactive creation of stylized lighting animations. We show several animation results obtained by our method to illustrate usefulness and effectiveness of our method. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Motion visualization of human left ventricle with a time-varying deformable model for cardiac diagnosis COMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 2 2001Soo-Mi ChoiAbstract We present a time-varying deformable model to visualize and analyze the motion of the left ventricle from a time series of 3-D images. The model is composed of a non-rigid body that deforms around a reference shape obtained from the previous time step. At each time step, the position and orientation of the left ventricle are extracted from the feature points of images. This information gives the position and orientation of the coordinate system attached to the non-rigid body. To compute a dense non-rigid motion field over the entire endocardial wall of the left ventricle, we introduce a 3-D blob finite element and Galerkin interpolants based on 3-D Gaussian, and use a physically based finite element method and a modal analysis. Then, cinematic attributes are visualized in pseudo colors on the reconstructed surface in order to help medical doctors in their interpretation of the data. Using the presented model, we estimate clinically useful quantitative parameters such as regional wall motion and ejection fraction. Experimental results are shown in a time series of X-ray angiographic images. Copyright ©2001 John Wiley & Sons, Ltd. [source] ## Road Infrastructure Data Acquisition Using a Vehicle-Based Mobile Mapping System COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2006Gi-Hong KimThe mobile mapping system that integrates the global positioning system (GPS), the inertial navigation system (INS), and digital cameras has been developed to collect data on position and attributes of road infrastructure. The vehicle-based mobile mapping system works by having the GPS and INS record the position and attitude data, and digital cameras take road images. The stereovision system can determine the position of objects that are visible on the image pair in the global coordinate system with GPS and INS data. As field data acquisition is a very expensive task, a mobile mapping system offers a greatly improved solution. In this study, we successfully created a road infrastructure map with mobile mapping technology and proposed automatic algorithms for detecting and identifying road signs from road images. The proposed detection algorithm includes line and color region extraction processes and uses the Hopfield neural networks. The identification algorithm uses seven invariant moments and parameters that present geometric characteristics. With this combined method, we could successfully detect and identify road signs. [source] ## General Gyrokinetic Equations for Edge Plasmas CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-9 2006H. QinAbstract During the pedestal cycle of H-mode edge plasmas in tokamak experiments, large-amplitude pedestal build-up and destruction coexist with small-amplitude drift wave turbulence. The pedestal dynamics simultaneously includes fast time-scale electromagnetic instabilities, long time-scale turbulence-induced transport processes, and more interestingly the interaction between them. To numerically simulate the pedestal dynamics from first principles, it is desirable to develop an effective algorithm based on the gyrokinetic theory. However, existing gyrokinetic theories cannot treat fully nonlinear electromagnetic perturbations with multi-scale-length structures in spacetime, and therefore do not apply to edge plasmas. A set of generalized gyrokinetic equations valid for the edge plasmas has been derived. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. It turns out that the most general gyrokinetic theory can be geometrically formulated. The Poincaré-Cartan-Einstein 1-form on the 7D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinitesimal generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincaré-Cartan-Einstein 1-form. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Because the general gyrokinetic system developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate-independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and phase space volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. As an example, the pullback transformation in the gyrokinetic Poisson equation is explicitly expressed in terms of moments of the gyrocenter distribution function, with the important gyro-orbit squeezing effect due to the large electric field shearing in the edge and the full finite Larmour radius effect for short wavelength fluctuations. The familiar "polarization drift density" in the gyrocenter Poisson equation is replaced by a more general expression. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Extensions of the 3-Dimensional Plasma Transport Code E3D CONTRIBUTIONS TO PLASMA PHYSICS, Issue 1-3 2004A. RunovAbstract One important aspect of modern fusion research is plasma edge physics. Fluid transport codes extending beyond the standard 2-D code packages like B2-Eirene or UEDGE are under development. A 3-dimensional plasma fluid code, E3D, based upon the Multiple Coordinate System Approach and a Monte Carlo integration procedure has been developed for general magnetic configurations including ergodic regions. These local magnetic coordinates lead to a full metric tensor which accurately accounts for all transport terms in the equations. Here, we discuss new computational aspects of the realization of the algorithm. The main limitation to the Monte Carlo code efficiency comes from the restriction on the parallel jump of advancing test particles which must be small compared to the gradient length of the diffusion coefficient. In our problems, the parallel diffusion coefficient depends on both plasma and magnetic field parameters. Usually, the second dependence is much more critical. In order to allow long parallel jumps, this dependence can be eliminated in two steps: first, the longitudinal coordinate x3 of local magnetic coordinates is modified in such a way that in the new coordinate system the metric determinant and contra-variant components of the magnetic field scale along the magnetic field with powers of the magnetic field module (like in Boozer flux coordinates). Second, specific weights of the test particles are introduced. As a result of increased parallel jump length, the efficiency of the code is about two orders of magnitude better. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Three-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetry CRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2007K. BöttcherAbstract A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle , of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Spatial prediction of river channel topography by kriging EARTH SURFACE PROCESSES AND LANDFORMS, Issue 6 2008Carl J. LegleiterAbstract Topographic information is fundamental to geomorphic inquiry, and spatial prediction of bed elevation from irregular survey data is an important component of many reach-scale studies. Kriging is a geostatistical technique for obtaining these predictions along with measures of their reliability, and this paper outlines a specialized framework intended for application to river channels. Our modular approach includes an algorithm for transforming the coordinates of data and prediction locations to a channel-centered coordinate system, several different methods of representing the trend component of topographic variation and search strategies that incorporate geomorphic information to determine which survey data are used to make a prediction at a specific location. For example, a relationship between curvature and the lateral position of maximum depth can be used to include cross-sectional asymmetry in a two-dimensional trend surface model, and topographic breaklines can be used to restrict which data are retained in a local neighborhood around each prediction location. Using survey data from a restored gravel-bed river, we demonstrate how transformation to the channel-centered coordinate system facilitates interpretation of the variogram, a statistical model of reach-scale spatial structure used in kriging, and how the choice of a trend model affects the variogram of the residuals from that trend. Similarly, we show how decomposing kriging predictions into their trend and residual components can yield useful information on channel morphology. Cross-validation analyses involving different data configurations and kriging variants indicate that kriging is quite robust and that survey density is the primary control on the accuracy of bed elevation predictions. The root mean-square error of these predictions is directly proportional to the spacing between surveyed cross-sections, even in a reconfigured channel with a relatively simple morphology; sophisticated methods of spatial prediction are no substitute for field data. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Measurement of the spatial distribution of fluvial bedload transport velocity in both sand and gravel EARTH SURFACE PROCESSES AND LANDFORMS, Issue 10 2004Colin D. RennieAbstract Maps are presented of the spatial distribution of two-dimensional bedload transport velocity vectors. Bedload velocity data were collected using the bottom tracking feature of an acoustic Doppler current pro,ler (aDcp) in both a gravel-bed reach and a sand-bed reach of Fraser River, British Columbia. Block-averaged bedload velocity vectors, and bedload velocity vectors interpolated onto a uniform grid, revealed coherent patterns in the bedload velocity distribution. Concurrent Helley-Smith bedload sampling in the sand-bed reach corroborated the trends observed in the bedload velocity map. Contemporaneous 2D vector maps of near-bed water velocity (velocity in bins centered between 25 cm and 50 cm from the bottom) and depth-averaged water velocity were also generated from the aDcp data. Using a vector correlation coef,cient, which is independent of the choice of coordinate system, the bedload velocity distribution was signi,cantly correlated to the near-bed and depth-averaged water velocity distributions. The bedload velocity distribution also compared favorably with variations in depth and estimates of the spatial distribution of shear stress. Published in 2004 by John Wiley & Sons, Ltd. [source] ## An ellipticity criterion in magnetotelluric tensor analysis GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2004M. BeckenSUMMARY We examine the magnetotelluric (MT) impedance tensor from the viewpoint of polarization states of the electric and magnetic field. In the presence of a regional 2-D conductivity anomaly, a linearly polarized homogeneous external magnetic field will generally produce secondary electromagnetic fields, which are elliptically polarized. If and only if the primary magnetic field vector oscillates parallel or perpendicular to the 2-D structure, will the horizontal components of the secondary fields at any point of the surface also be linearly polarized. When small-scale inhomogeneities galvanically distort the electric field at the surface, only field rotations and amplifications are observed, while the ellipticity remains unchanged. Thus, the regional strike direction can be identified from vanishing ellipticities of electric and magnetic fields even in presence of distortion. In practice, the MT impedance tensor is analysed rather than the fields themselves. It turns out, that a pair of linearly polarized magnetic and electric fields produces linearly polarized columns of the impedance tensor. As the linearly polarized electric field components generally do not constitute an orthogonal basis, the telluric vectors, i.e. the columns of the impedance tensor, will be non-orthogonal. Their linear polarization, however, is manifested in a common phase for the elements of each column of the tensor and is a well-known indication of galvanic distortion. In order to solve the distortion problem, the telluric vectors are fully parametrized in terms of ellipses and subsequently rotated to the coordinate system in which their ellipticities are minimized. If the minimal ellipticities are close to zero, the existence of a (locally distorted) regional 2-D conductivity anomaly may be assumed. Otherwise, the tensor suggests the presence of a strong 3-D conductivity distribution. In the latter case, a coordinate system is often found, in which three elements have a strong amplitude, while the amplitude of the forth, which is one of the main-diagonal elements, is small. In terms of our ellipse parametrization, this means, that one of the ellipticities of the two telluric vectors approximately vanishes, while the other one may not be neglected as a result of the 3-D response. The reason for this particular characteristic is found in an approximate relation between the polarization state of the telluric vector with vanishing ellipticity and the corresponding horizontal electric field vector in the presence of a shallow conductive structure, across which the perpendicular and tangential components of the electric field obey different boundary conditions. [source] ## Three-dimensional elastic earthquake modelling based on integrated seismological and InSAR data: the Mw= 7.2 Nuweiba earthquake, gulf of Elat/Aqaba 1995 November GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2003G. ShamirSUMMARY The Nuweiba earthquake (1995 November 22; Mw= 7.2), the largest seismic event along the Dead Sea Transform (DST) in at least 160 yr, ruptured 45,50 km along the Aragonese segment of the left-stepping strike-slip fault system occupying the gulf of Elat/Aqaba (southern segment of the DST). The rupture initiated in a partly normal, low-slip first subevent near the southern end of the fault and propagated unilaterally north-northeastward as a high-slip, nearly pure sinistral second subevent, which was responsible for over 90 per cent of the total seismic moment. The source mechanism and slip distribution, derived from inversion of teleseismic broad-band waveforms, are used to construct a 3-D elastic model of the earthquake based on the boundary elements method, resulting in the full 3-D displacement and stress fields induced by the earthquake. In the absence of sufficient Global Positioning System data, the only other constraints on the geometry and slip distribution of the rupture are provided by interferometric synthetic aperture radar (InSAR) measurements spanning the coseismic and early post-seismic period. We calculate simulated interferograms by transforming the calculated surface displacement field into the satellite coordinate system and comparing them with the observed interferograms. The model parameters are then iteratively modified until a best-fitting model is obtained, providing a refined set of static source parameters for the mainshock. This model is then used to calculate the static Coulomb stress changes induced by the mainshock on the step-over faults, suggesting that the major (Mw, 5) aftershocks in the first eight post-seismic months were triggered by small changes (<1 bar) in the left-lateral Coulomb stress, with effective friction coefficient not higher than 0.2. Aftershock distribution and mechanisms indicate that the available Coulomb stress dropped below the frictional strength of the fault but was not complete. [source] ## Traveltime approximation for a reflected wave in a homogeneous anisotropic elastic layer GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002M. ZillmerSummary An approximation to the traveltime field is calculated for an elastic wave that propagates in a homogeneous anisotropic layer and is reflected at a plane boundary. The traveltime is approximated by a Taylor series expansion with the third derivative of the traveltime being taken into account. The coefficients of the series refer to the seismic ray, which is locally the fastest ray. Simple formulae are obtained for orthorhombic media in the crystal coordinate system, which relate the traveltimes of the reflected waves to the elastic constants of the medium. A numerical example is presented for wave propagation in orthorhombic olivine, which is a constituent of the Earth's mantle. A second example is given by an isotropic host rock with a set of parallel cracks, which is an important model for wave propagation in the Earth's crust. The elastic parameters can be determined by measuring the reflection times as a function of source,receiver offset. The approximate traveltime,distance curves are compared with traveltimes obtained from seismic ray tracing. [source] ## Numerical simulation of rime ice accretion process on an airfoil HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2005Zhang Da-linAbstract To simulate the ice accretion on an airfoil, a boundary moving technique is proposed to deal with the distortion of the airfoil surface due to ice accretion on the leading edge. Incorporating the two-phase model of air-supercooled droplets in the Eulerian coordinate system, this technique is applied to simulate the process of the rime ice accretion (the droplets freeze at the instant impinging on the airfoil) on the NACA 0012 airfoil, and the ice profile after ice accretion is achieved successfully. A brief comparison between the results of this paper and the experiment data indicates that the current method is applicable and effective. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 226,234, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20064 [source] ## A numerical study of natural convection in a vertical cylinder bundle HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2003Yuji IsahaiAbstract Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary-fitted coordinate system. Numerical calculations for center-to-center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 108. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nui are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330,341, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10095 [source] ## A structural optimization method based on the level set method using a new geometry-based re-initialization scheme INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010Shintaro YamasakiAbstract Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton,Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. [source] ## Sigma transformation and ALE formulation for three-dimensional free surface flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009A. DecoeneAbstract In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian,Eulerian (ALE) approach. For that purpose we introduce the ALE-sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180-degree turn by algebraic Reynolds stress model INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008Hitoshi SugiyamaAbstract Turbulent flow in a rectangular duct with a sharp 180-degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure-driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large-scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180-degree turn using the algebraic Reynolds stress model. A boundary-fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser-Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log-law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180-degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log-law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## A level set characteristic Galerkin finite element method for free surface flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005Ching-Long LinAbstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Propagation characteristic analysis of ridged circular waveguide using 2D finite-difference frequency-domain method INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 3 2005Qi ZhangAbstract The propagation characteristics of ridged circular waveguides are analyzed by using 2D finite-difference frequency-domain (2D FDFD). Based on the 2D FDFD method in a cylindrical coordinate system, general difference formulas for the ridged circular waveguide are deduced, and modified difference formulas are built at some special points of the ridged circular waveguides. To verify the proposed method, three ridged circular waveguide structures are investigated and the numerical results are compared with available ones obtained by other research methods. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE 15, 2005. [source] ## Generalization of cluster treatment of characteristic roots for robust stability of multiple time-delayed systems INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2008Rifat SipahiAbstract A new perspective is presented for studying the stability robustness of nth order systems with p rationally independent delays. It deploys a holographic mapping procedure over the delay space into a new coordinate system in order to achieve the objective. This mapping collapses the entire set of potential stability switching points on a manageably small number of hypersurfaces, which are explicitly defined in the new domain. This property considerably alleviates the problem, which is otherwise infinite dimensional, and therefore notoriously complex to handle. We further declare some unrecognized features of these switching hypersurfaces, that they are (a) encapsulated within a higher-dimensional cube with edges of length 2,, which we name the ,building block', and (b) the ,offspring' of this building block, which represent the secondary stability switchings, appear within the adjacent and identical building blocks (cubes) stacked up next to each other. The final outlook is an exclusive representation of stability for this general class of systems at any arbitrary point in the delay space. Two example case studies are also provided, which are not possible to analyze using any other methodology known to the authors. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Decentralized nonlinear robust control of UAVs in close formation INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2003Sahjendra N. SinghAbstract This paper treats the design of a decentralized nonlinear robust control system for formation flying of multiple unmanned aerial vehicles (UAVs). In close formation, it is assumed that vortex of any UAV affects the motion of all the UAVs behind it. The forces produced by these vortices are complex functions of relative position co-ordinates of the UAVs. In this paper, these forces are treated as unknown functions, which cannot be parameterized. Since the system is not invertible in the wind axes system, a simplified co-ordinate system obtained from the wind axes system for which the velocity roll (bank angle) is zero, is considered for the design of the control system. A nonlinear robust control system for the separation trajectory control of the wing aircraft in the simplified wind coordinate system is derived. Uncertain functions and unmeasured variables are estimated using a high-gain observer for the synthesis of the control system. Each wing UAV synthesizes its control law using its own state variables and the relative position of the preceding UAV with respect to the wing UAV. Thus the control system is decentralized since each UAV has to communicate (depending on sensors for position measurement) with at most one (preceding) UAV, and no data transmission from the remaining vehicles is required. Simulation results for two UAVs are presented which show precise separation trajectory control of each wing UAV in spite of the presence of unknown and unstructured vortex forces, while the lead aircraft maneuvers. Furthermore, these results confirm that when the wing aircraft is positioned properly in the vortex of the lead aircraft, it experiences reduction in its required flight power. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Transformations for monoclinic crystal symmetry in texture analysis JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2009Siegfried MatthiesMonoclinic crystals can be described in two settings: in the first setting the C2 rotation axis is parallel to the z axis and in the second setting it is parallel to the y axis. Transformations of lattice parameters, Miller and zone indices, and atomic coordinates is straightforward; the situation is far more complex for texture analysis with orientation distributions and corresponding representations. This article gives explicit transformations that need to be applied, not only for texture analysis but also for calculations of physical properties of materials with preferred orientation. In texture research the relationship between the Cartesian crystal coordinate system and the unit cell must be unambiguously defined and a uniform convention is desirable. [source] ## Exploratory orientation data analysis with , sections JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2004K. Gerald Van Den BoogaartSince the domain of crystallographic orientations is three-dimensional and spherical, insightful visualization of them or visualization of related probability density functions requires (i) exploitation of the effect of a given orientation on the crystallographic axes, (ii) consideration of spherical means of the orientation probability density function, in particular with respect to one-dimensional totally geodesic submanifolds, and (iii) application of projections from the two-dimensional unit sphere onto the unit disk . The familiar crystallographic `pole figures' are actually mean values of the spherical Radon transform. The mathematical Radon transform associates a real-valued function f defined on a sphere with its mean values along one-dimensional circles with centre , the origin of the coordinate system, and spanned by two unit vectors. The family of views suggested here defines , sections in terms of simultaneous orientational relationships of two different crystal axes with two different specimen directions, such that their superposition yields a user-specified pole probability density function. Thus, the spherical averaging and the spherical projection onto the unit disk determine the distortion of the display. Commonly, spherical projections preserving either volume or angle are favoured. This rich family displays f completely, i.e. if f is given or can be determined unambiguously, then it is uniquely represented by several subsets of these views. A computer code enables the user to specify and control interactively the display of linked views, which is comprehensible as the user is in control of the display. [source] ## A standard local coordinate system for multipole refinements of the estrogen core structure JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2003Kristin KirschbaumA comparative charge density study on a series of estrogen derivatives has been initiated. The study utilizes the Hansen,Coppens atom-centred multipole model to describe the valence electron density distribution. Direct comparison of the population parameters for each estrogen after the respective multipole refinements requires standardization of the atom-centred local coordinate systems. Such a standard coordinate system for the common estrogen core is reported, taking advantage of the shape of those multipoles which have the spatial characteristics of sp2 and sp3 hybrid orbitals. Additionally, populating these principal multipoles at the beginning stage of the refinements improves the stability of these large highly correlated calculations. [source] ## Perspectives of data analysis of enzyme inhibition and activation, Part 1: Use of the three-dimensional Km, V,I coordinate system for data analysis of enzyme inhibition and activation JOURNAL OF BIOCHEMICAL AND MOLECULAR TOXICOLOGY, Issue 2 2009Vladimir I. KrupyankoAbstract The possibility of construction of the three-dimensional (unfolded and folded) Km, V,I rectangular coordinate systems convenient for vector representation of inhibited and activated enzymatic reactions as well as of a two-dimensional Km, V, scalar rectangular coordinate system convenient for diagrammatic representation of enzymatic reactions is considered. The perspectives of using the properties of the three-dimensional L vectors and their scalar L projections for data analysis of enzyme inhibition and activation are analyzed. © 2009 Wiley Periodicals, Inc. J Biochem Mol Toxicol 23:97,100, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jbt.20273 [source] ## Characterization of molecular orbitals by counting nodal regions JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 4 2005Yasuyo HatanoAbstract The number of nodal regions can be used as an index for characterizing molecular orbitals. A computer program has been developed to count the number of nodal regions, based on the labeling and contraction algorithms. This program is applied to the water molecule, the hydrogen sulfide molecule, the hydrogen atomic orbitals, the Rydberg excited states of ethylene, dissociation of carbon monoxide, and CASSCF calculations of formaldehyde. Because the number of nodal regions is independent of the coordinate system, the method is applicable even when the molecular structure changes drastically as in bond rotation or bond elongation. Changes of nodal regions with bond elongation are investigated for carbon monoxide. A prescription for problems arising with basis set expansion techniques is also given. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 325,333, 2005 [source] ## Localization of mobile robots: Development and comparative evaluation of algorithms based on odometric and inertial sensors JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 12 2005G. IppolitiAn autonomous mobile robot must be able to elaborate the measures provided by the sensor equipment to localize itself with respect to a coordinate system. The precision of the location estimate depends on the sensor accuracy and on the reliability of the measure processing algorithm. The purpose of this article is to propose a low cost positioning system using internal sensors like odometers and optical fiber gyroscopes. Three simple localization algorithms based on different sensor data processing procedures are presented. Two of them operate in a deterministic framework, the third operates in a stochastic framework where the uncertainty is induced by sensing and unmodeled robot dynamics. The performance of the proposed localization algorithms are tested through a wide set of laboratory experiments and compared in terms of localization accuracy and computational cost. © 2005 Wiley Periodicals, Inc. [source] ## An autonomous tracked vehicle with omnidirectional sensing JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 8 2004R. David HamptonOperation of an autonomous vehicle along a marked path, in an obstacle-laden environment, requires path detection, relative position detection and control, and obstacle detection and avoidance. The design solution of the team from the U.S. Military Academy is a tracked vehicle operating open-loop in response to position information from an omnidirectional mirror, and to obstacle-detection input from the mirror and from a scanning laser. The use of a tracked rather than a wheeled vehicle is the team's open-loop solution to the problem of wheeled-vehicle slippage on wet and sandy surfaces. The vehicleresponds to sensor information from (1) a digital camera-mounted parabolic omnidirectional mirror for visual inputs and (2) a scanning laser for detecting obstacles in relief. Raw sensor data is converted synchronously into a global virtual context, which places the vehicle's center at the origin of a 2-D Cartesian coordinate system. A four-phase process is used to convert the camera's inputs into the data structures needed to reason about the vehicle's position relative to the course. Development of the path plan proceeds incrementally, using a space-sweeping algorithm to identify safe paths along waypoints within the course boundaries. An attempt is made to minimize translation errors by favoring paths which exhibit fewer sharp turns. Integration of Intel's OpenCV computer vision library and the Independent JPEG Group's JPEG library allow for very good encapsulation of the low-level functions needed to do most of the image processing. Ada95 is the language of choice for the majority of the team-developed software, except where needed to interface to motors and sensors. Use of an object-oriented high-level language has been invaluable in leveraging the efforts of previous years' development activities, and for maximizing the ability to log or otherwise respond to anomalous behavior. © 2004 Wiley Periodicals, Inc. [source] ## Neural network approach to firm grip in the presence of small slips JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2001A. M. Al-Fahed NuseiratThis paper presents a two stage method for constructing a firm grip that can tolerate small slips of the fingertips. The fingers are assumed to be of frictionless contact type. The first stage was to formulate the interaction in the gripper,object system as a linear complementarity problem (LCP). Then it was solved using a special neural network to find minimal fingers forces. The second stage was to use the obtained results in the first stage as a static mapping in training another neural network. The second neural network training included emulating the slips by random noise in the form of changes in the positions of the contact points relative to the reference coordinate system. This noisy training increased robustness against unexpected changes in fingers positions. Genetic algorithms were used in training the second neural network as global optimization techniques. The resulting neural network is a robust, reliable, and stable controller for rigid bodies that can be handled by a robot gripper. © 2001 John Wiley & Sons, Inc. [source] ## SEISMIC FACIES ANALYSIS BASED ON 3D MULTI-ATTRIBUTE VOLUME CLASSIFICATION, DARIYAN FORMATION, SE PERSIAN GULF JOURNAL OF PETROLEUM GEOLOGY, Issue 2 2006P. FarzadiInterpretation of recently acquired 3D seismic data from the adjacent Sirri C and D oilfields in the SE Persian Gulf indicates that a 3D interpretation of seismic facies is crucial to resolve the internal stratal geometries of the Aptian Dariyan Formation. This carbonate formation passes southward into the Shu'aiba Formation, a prolific reservoir rock of similar facies in the UAE. Lack of exposures and limited cored intervals have forced reliance on the seismic data for evidence of the depositional environment and the internal architecture of potential reservoir rocks. The progradational nature of the Dariyan Formation and the occurrence of carbonate build-ups within it make this stratal geometry complex. The complex internal heterogeneity of the build-ups and presence of seismic noise make mapping of the build-ups in 3D space using conventional seismic interpretation tools difficult, despite the availability of high-quality 3D seismic data covering the area. The high quality seismic and limited well data from this field is one of the few datasets of this kind presented in the literature. A procedure for the hierarchical multi-attribute analysis of seismic facies using Paradigm's Seis Facies software is used in this study to provide a 3D interpretation of the stratal patterns. Principal component analysis reduces the noise and redundant data by representing the main data variances as a few vector components in a transformed coordinate system. Cluster analysis is performed using those components which have the greatest contribution to the maximum spread of the data variability. Six seismic attribute volumes are used in this study and the result is a single 3D classified volume. Important new information obtained from within the Dariyan Formation gives new insights into its stratigraphic distribution and internal variability. This method of processing seismic data is a step towards exploring for subtle stratigraphic traps in the study area, and may help to identify exploration targets. [source] |