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Vector Field (vector + field)
Selected AbstractsFurstyling on angle-split shell texturesCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 2-3 2009Bin Sheng Abstract This paper presents a new method for modeling and rendering fur with a wide variety of furstyles. We simulate virtual fur using shell textures,a multiple layers of textured slices for its generality and efficiency. As shell textures usually suffer from the inherent visual gap errors due to the uniform discretization nature, we present the angle-split shell textures (ASST) approach, which classifies the shell textures into different types with different numbers of texture layers, by splitting the angle space of the viewing angles between fur orientation and view direction. Our system can render the fur with biological patterns, and utilizes vector field and scalar field on ASST to control the geometric variations of the furry shape. Users can intuitively shape the fur by applying the combing, blowing, and interpolating effects in real time. Our approach is intuitive to implement without using complex data structures, with real-time performance for dynamic fur appearances. Copyright © 2009 John Wiley & Sons, Ltd. [source] Direct Visualization of Deformation in VolumesCOMPUTER GRAPHICS FORUM, Issue 3 2009Stef Busking Abstract Deformation is a topic of interest in many disciplines. In particular in medical research, deformations of surfaces and even entire volumetric structures are of interest. Clear visualization of such deformations can lead to important insight into growth processes and progression of disease. We present new techniques for direct focus+context visualization of deformation fields representing transformations between pairs of volumetric datasets. Typically, such fields are computed by performing a non-rigid registration between two data volumes. Our visualization is based on direct volume rendering and uses the GPU to compute and interactively visualize features of these deformation fields in real-time. We integrate visualization of the deformation field with visualization of the scalar volume affected by the deformations. Furthermore, we present a novel use of texturing in volume rendered visualizations to show additional properties of the vector field on surfaces in the volume. [source] A Parametric Approach to Flexible Nonlinear InferenceECONOMETRICA, Issue 3 2001James D. Hamilton This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt=,(xt)+,t where the functional form of ,(,) is unknown. We propose viewing ,(,) itself as the outcome of a random process. The paper introduces a new stationary random field m(,) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for ,(,). We view the parameters that characterize the relation between a given realization of m(,) and the particular value of ,(,) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions ,(,). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment trade-off may explain the previously reported uneven empirical success of the Phillips Curve. [source] Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading elementGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007E. Pan SUMMARY This study is motivated by a desire to develop a fast numerical algorithm for computing the surface deformation field induced by surface pressure loading on a layered, isotropic, elastic half-space. The approach that we pursue here is based on a circular loading element. That is, an arbitrary surface pressure field applied within a finite surface domain will be represented by a large number of circular loading elements, all with the same radius, in which the applied downwards pressure (normal stress) is piecewise uniform: that is, the load within each individual circle is laterally uniform. The key practical requirement associated with this approach is that we need to be able to solve for the displacement field due to a single circular load, at very large numbers of points (or ,stations'), at very low computational cost. This elemental problem is axisymmetric, and so the displacement vector field consists of radial and vertical components both of which are functions only of the radial coordinate r. We achieve high computational speeds using a novel two-stage approach that we call the sparse evaluation and massive interpolation (SEMI) method. First, we use a high accuracy but computationally expensive method to compute the displacement vectors at a limited number of r values (called control points or knots), and then we use a variety of fast interpolation methods to determine the displacements at much larger numbers of intervening points. The accurate solutions achieved at the control points are framed in terms of cylindrical vector functions, Hankel transforms and propagator matrices. Adaptive Gauss quadrature is used to handle the oscillatory nature of the integrands in an optimal manner. To extend these exact solutions via interpolation we divide the r -axis into three zones, and employ a different interpolation algorithm in each zone. The magnitude of the errors associated with the interpolation is controlled by the number, M, of control points. For M= 54, the maximum RMS relative error associated with the SEMI method is less than 0.2 per cent, and it is possible to evaluate the displacement field at 100 000 stations about 1200 times faster than if the direct (exact) solution was evaluated at each station; for M= 99 which corresponds to a maximum RMS relative error less than 0.03 per cent, the SEMI method is about 700 times faster than the direct solution. [source] Magnetic field annihilators: invisible magnetization at the magnetic equatorGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2003S. Maus SUMMARY Some distributions of magnetization give rise to magnetic fields that vanish everywhere above the surface, rendering these distributions of magnetization completely invisible. They are the annihilators of the magnetic inverse problem. Known examples are the infinite sheet with constant magnetization and the spherical shell of constant susceptibility magnetized by an arbitrary internal field. Here, we show that remarkably more interesting annihilators exist for the Earth's dipole-dominated inducing field. Indeed, any susceptibility profile along the magnetic equator can be extended north/south into an annihilator. Consequently, the induced magnetization along the magnetic equator is entirely undetermined by the visible magnetic field. In contrast to the Backus effect, this ambiguity persists even if the full magnetic vector field is known. [source] Four-node semi-EAS element in six-field nonlinear theory of shellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2006J. Chró, cielewski Abstract We propose a new four-node C0 finite element for shell structures undergoing unlimited translations and rotations. The considerations concern the general six-field theory of shells with asymmetric strain measures in geometrically nonlinear static problems. The shell kinematics is of the two-dimensional Cosserat continuum type and is described by two independent fields: the vector field for translations and the proper orthogonal tensor field for rotations. All three rotational parameters are treated here as independent. Hence, as a consequence of the shell theory, the proposed element has naturally six engineering degrees of freedom at each node, with the so-called drilling rotation. This property makes the element suitable for analysis of shell structures containing folds, branches or intersections. To avoid locking phenomena we use the enhanced assumed strain (EAS) concept. We derive and linearize the modified Hu,Washizu principle for six-field theory of shells. What makes the present approach original is the combination of EAS method with asymmetric membrane strain measures. Based on literature, we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry. To gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element, we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches. Copyright © 2006 John Wiley & Sons, Ltd. [source] A smooth switching adaptive controller for linearizable systems with improved transient performanceINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2006Jeng Tze Huang Abstract The certainty equivalent control has achieved asymptotic tracking stability of linearizable systems in the presence of parametric uncertainty. However, two major drawbacks remain to be tackled, namely, the risk of running into singularity for the calculated control input and the poor transient behaviour arising frequently in a general adaptive system. For the first problem, a high gain control is activated in place of the certainty equivalent control until the risk is bypassed. Among others, it requires less control effort by taking advantages of the bounds for the input vector field. Moreover, the switching mechanism is smooth and hence avoids possible chattering behaviour. Next, to solve the second problem, a new type of update algorithm guaranteeing the exponential stability of the overall closed-loop system, on a weaker persistent excitation (PE) condition, is proposed. In particular, it requires no filtering of the regressor and hence is easier to implement. Simulation results demonstrating the validity of the proposed design are given in the final. Copyright © 2006 John Wiley & Sons, Ltd. [source] The reduced scalar potential in regions with permeable materials: Reasons for loss of accuracy and cancellationINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2007S. Balac Abstract Practical three-dimensional magnetic field problems usually involve regions containing current sources as well as regions with magnetic materials. For computational purposes, the use of the reduced scalar potential (RSP) as unknown has the advantage to transform a problem for a vector field throughout the space into a problem for a scalar function, thus reducing the number of degrees of freedom in the discretization. However, in regions with high magnetic permeability the use of the RSP alone usually results in severe loss in accuracy and it is recommended to use both the RSP and the total scalar potential. Using an asymptotic expansion, we investigate theoretically the underlying reasons for this lack of accuracy in permeable regions when using the RSP as a unique potential. Moreover, this investigation leads to an efficient numerical method to compute the magnetic field in regions with high magnetic permeability. Copyright © 2007 John Wiley & Sons, Ltd. [source] Normal form representation of control systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2002Daizhan Cheng Abstract This paper is to investigate the normal form representation of control systems. First, as numerical tools we develop an algorithm for normal form expression and the matrix representation of the Lie derivative of a linear vector field over homogeneous vector fields. The concept of normal form is modified. Necessary and sufficient conditions for a linear transformation to maintain the Brunowsky canonical form are obtained. It is then shown that the shift term can always be linearized up to any degree. Based on this fact, linearization procedure is proposed and the related algorithms are presented. Least square linear approximations are proposed for non-linearizable systems. Finally, the method is applied to the ball and beam example. The efforts are focused on the numerical and computer realization of linearization process. Copyright © 2002 John Wiley & Sons, Ltd. [source] Intramolecular interactions and intramolecular hydrogen bonding in conformers of gaseous glycineJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 7 2001L. F. Pacios Abstract Ab initio calculations at the MP2/6-311++G** level of theory led recently to the identification of 13 stable conformers of gaseous glycine with relative energies within 11 kcal/mol. The stability of every structure depends on subtle intramolecular effects arising from conformational changes. These intramolecular interactions are examined with the tools provided by the Atoms In Molecules (AIM) theory, which allows obtaining a wealth of quantum mechanics information from the molecular electron density ,(r). The analysis of the topological features of ,(r) on one side and the atomic properties integrated in the basins defined by the gradient vector field of the density on the other side makes possible to explore the different intramolecular effects in every conformer. The existence of intramolecular hydrogen bonds on some conformers is demonstrated, while the presence of other stabilizing interactions arising from favorable conformations is shown to explain the stability of other structures in the potential energy surface of glycine. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 702,716, 2001 [source] Optimum fuzzy filters for phase-contrast magnetic resonance imaging segmentationJOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 1 2009Kartik S. Sundareswaran MS Abstract Purpose To develop and validate a multidimensional segmentation and filtering methodology for accurate blood flow velocity field reconstruction from phase-contrast magnetic resonance imaging (PC MRI). Materials and Methods The proposed technique consists of two steps: (1) the boundary of the vessel is automatically segmented using the active contour approach; and (2) the noise embedded within the segmented vector field is selectively removed using a novel fuzzy adaptive vector median filtering (FAVMF) technique. This two-step segmentation process was tested and validated on 111 synthetically generated PC MRI slices and on 10 patients with congenital heart disease. Results The active contour technique was effective for segmenting blood vessels having a sensitivity and specificity of 93.1% and 92.1% using manual segmentation as a reference standard. FAVMF was the superior technique in filtering out noise vectors, when compared with other commonly used filters in PC MRI (P < 0.05). The peak wall shear rate calculated from the PC MRI data (248 ± 39 sec,1), was significantly decreased to (146 ± 26 sec,1) after the filtering process. Conclusion The proposed two-step segmentation and filtering methodology is more accurate compared to a single-step segmentation process for post-processing of PC MRI data. J. Magn. Reson. Imaging 2009;29:155,165. © 2008 Wiley-Liss, Inc. [source] Robust estimation of the normal to a curve using optimal controlOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2008J. Fehrenbach Abstract We propose an optimal control problem whose optimal command approximates the normal vector field to a given curve. This problem is obtained by studying a partial differential equation satisfied by a map that jumps across the given curve. The gradient of the cost function is then estimated by an adjoint method, and an explicit algorithm is proposed to obtain the optimal command. Examples show that this numerical estimation of the normal is robust, in the sense that when the curve is not a simple closed curve, or when it is incomplete (dashed), the solution is still a good approximation of the normal. As applications, we show how the optimal state can help closing discontinuous curves and improve image restoration; it also provides a coloring of simple planar maps. Copyright © 2007 John Wiley & Sons, Ltd. [source] 3D Surface Smoothing for Arbitrary FE-Meshes by Means of an Enhanced Surface DescriptionPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003P. Helnwein Dipl.-Ing. This paper describes a novel approach to the problem of 3D surface smoothing by introducing an enhanced surface description of the structural model. The idea of the enhanced surface model is the introduction of an independent vector field for the description of the surface normal field. It is connected to the discretized surface by means of a weak form of the orthogonality conditions. Surface smoothing then is applied element-by-element using the interpolation of the surface patch and the nodal normal vectors. [source] Applied Geometry:Discrete Differential Calculus for GraphicsCOMPUTER GRAPHICS FORUM, Issue 3 2004Mathieu Desbrun Geometry has been extensively studied for centuries, almost exclusively from a differential point of view. However, with the advent of the digital age, the interest directed to smooth surfaces has now partially shifted due to the growing importance of discrete geometry. From 3D surfaces in graphics to higher dimensional manifolds in mechanics, computational sciences must deal with sampled geometric data on a daily basis-hence our interest in Applied Geometry. In this talk we cover different aspects of Applied Geometry. First, we discuss the problem of Shape Approximation, where an initial surface is accurately discretized (i.e., remeshed) using anisotropic elements through error minimization. Second, once we have a discrete geometry to work with, we briefly show how to develop a full- blown discrete calculus on such discrete manifolds, allowing us to manipulate functions, vector fields, or even tensors while preserving the fundamental structures and invariants of the differential case. We will emphasize the applicability of our discrete variational approach to geometry by showing results on surface parameterization, smoothing, and remeshing, as well as virtual actors and thin-shell simulation. Joint work with: Pierre Alliez (INRIA), David Cohen-Steiner (Duke U.), Eitan Grinspun (NYU), Anil Hirani (Caltech), Jerrold E. Marsden (Caltech), Mark Meyer (Pixar), Fred Pighin (USC), Peter Schröder (Caltech), Yiying Tong (USC). [source] Constraints from F and D supersymmetry breaking in general supergravity theoriesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2008M. Gomez-Reino Abstract We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit vacua with spontaneously broken supersymmetry and realistic cosmological constant. We find that the existence of such viable vacua implies some constraints involving the curvature tensor of the scalar geometry and the charge and mass matrices of the vector fields, and also that the vector of F and D auxiliary fields defining the Goldstino direction is constrained to lie within a certain domain. We illustrate the relevance of these results through some examples and also discuss the implications of our general results on the dynamics of moduli fields in string models. This contribution is based on [1,3]. [source] Computation of unsteady viscous incompressible flows in generalized non-inertial co-ordinate system using Godunov-projection method and overlapping meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002H. Pan Abstract Time-dependent incompressible Navier,Stokes equations are formulated in generalized non-inertial co-ordinate system and numerically solved by using a modified second-order Godunov-projection method on a system of overlapped body-fitted structured grids. The projection method uses a second-order fractional step scheme in which the momentum equation is solved to obtain the intermediate velocity field which is then projected on to the space of divergence-free vector fields. The second-order Godunov method is applied for numerically approximating the non-linear convection terms in order to provide a robust discretization for simulating flows at high Reynolds number. In order to obtain the pressure field, the pressure Poisson equation is solved. Overlapping grids are used to discretize the flow domain so that the moving-boundary problem can be solved economically. Numerical results are then presented to demonstrate the performance of this projection method for a variety of unsteady two- and three-dimensional flow problems formulated in the non-inertial co-ordinate systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Stochastic models for chemically reacting systems using polynomial stochastic hybrid systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2005João Pedro Hespanha Abstract A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial stochastic hybrid system (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinite-dimensional linear ordinary differential equations (ODEs), which can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the Master equation; a decaying,dimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. Copyright © 2005 John Wiley & Sons, Ltd. [source] Normal form representation of control systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2002Daizhan Cheng Abstract This paper is to investigate the normal form representation of control systems. First, as numerical tools we develop an algorithm for normal form expression and the matrix representation of the Lie derivative of a linear vector field over homogeneous vector fields. The concept of normal form is modified. Necessary and sufficient conditions for a linear transformation to maintain the Brunowsky canonical form are obtained. It is then shown that the shift term can always be linearized up to any degree. Based on this fact, linearization procedure is proposed and the related algorithms are presented. Least square linear approximations are proposed for non-linearizable systems. Finally, the method is applied to the ball and beam example. The efforts are focused on the numerical and computer realization of linearization process. Copyright © 2002 John Wiley & Sons, Ltd. [source] On the modelling of over-ocean hurricane surface winds and their uncertaintyTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 642 2009Dr. S. P. Khare Abstract This paper investigates the modelling of over-ocean hurricane surface wind fields and their associated uncertainty. The wind models tested include parameterized balance models, a two-dimensional numerical planetary boundary-layer model and a three-dimensional (3D) linear analytical boundary-layer model. Using a set of archived over-ocean surface wind field reconstructions for validation, a series of cross-validation experiments has been performed for a range of norms. For norms that quantify predictability of vector fields, a particular configuration of the 3D analytical model was found to be superior to the other models tested. Using residual fields derived from fitting the wind models to the validation data, the issue of how to model the uncertainty (in the form of a covariance) in the speed field has also been examined. Covariance models based on truncated empirical orthogonal function representations were found to be optimal. Copyright © 2009 Royal Meteorological Society [source] A supersymmetric extension of quantum gauge theoryANNALEN DER PHYSIK, Issue 1-2 2003D.R. Grigore Abstract We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence. [source] Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance lawsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2009Gui-Qiang Chen We analyze a class of weakly differentiable vector fields F : ,n , ,n with the property that F , L, and div F is a (signed) Radon measure. These fields are called bounded divergence-measure fields. The primary focus of our investigation is to introduce a suitable notion of the normal trace of any divergence-measure field F over the boundary of an arbitrary set of finite perimeter that ensures the validity of the Gauss-Green theorem. To achieve this, we first establish a fundamental approximation theorem which states that, given a (signed) Radon measure , that is absolutely continuous with respect to ,N , 1 on ,N, any set of finite perimeter can be approximated by a family of sets with smooth boundary essentially from the measure-theoretic interior of the set with respect to the measure ||,||, the total variation measure. We employ this approximation theorem to derive the normal trace of F on the boundary of any set of finite perimeter E as the limit of the normal traces of F on the boundaries of the approximate sets with smooth boundary so that the Gauss-Green theorem for F holds on E. With these results, we analyze the Cauchy flux that is bounded by a nonnegative Radon measure over any oriented surface (i.e., an (N , 1)-dimensional surface that is a part of the boundary of a set of finite perimeter) and thereby develop a general mathematical formulation of the physical principle of the balance law through the Cauchy flux. Finally, we apply this framework to the derivation of systems of balance laws with measure-valued source terms from the formulation of the balance law. This framework also allows the recovery of Cauchy entropy flux through the Lax entropy inequality for entropy solutions of hyperbolic conservation laws. © 2008 Wiley Periodicals, Inc. [source] | ||||||||||||||||||||||||||||||||||