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Scalar Field (scalar + 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] Discrete Distortion in Triangulated 3-ManifoldsCOMPUTER GRAPHICS FORUM, Issue 5 2008Mohammed Mostefa Mesmoudi Abstract We introduce a novel notion, that we call discrete distortion, for a triangulated 3-manifold. Discrete distortion naturally generalizes the notion of concentrated curvature defined for triangulated surfaces and provides a powerful tool to understand the local geometry and topology of 3-manifolds. Discrete distortion can be viewed as a discrete approach to Ricci curvature for singular flat manifolds. We distinguish between two kinds of distortion, namely, vertex distortion, which is associated with the vertices of the tetrahedral mesh decomposing the 3-manifold, and bond distortion, which is associated with the edges of the tetrahedral mesh. We investigate properties of vertex and bond distortions. As an example, we visualize vertex distortion on manifold hypersurfaces in R4 defined by a scalar field on a 3D mesh. distance fields. [source] Out-of-core compression and decompression of large n -dimensional scalar fieldsCOMPUTER GRAPHICS FORUM, Issue 3 2003Lawrence Ibarria We present a simple method for compressing very large and regularly sampled scalar fields. Our method is particularlyattractive when the entire data set does not fit in memory and when the sampling rate is high relative to thefeature size of the scalar field in all dimensions. Although we report results foranddata sets, the proposedapproach may be applied to higher dimensions. The method is based on the new Lorenzo predictor, introducedhere, which estimates the value of the scalar field at each sample from the values at processed neighbors. The predictedvalues are exact when the n-dimensional scalar field is an implicit polynomial of degreen, 1. Surprisingly,when the residuals (differences between the actual and predicted values) are encoded using arithmetic coding,the proposed method often outperforms wavelet compression in anL,sense. The proposed approach may beused both for lossy and lossless compression and is well suited for out-of-core compression and decompression,because a trivial implementation, which sweeps through the data set reading it once, requires maintaining only asmall buffer in core memory, whose size barely exceeds a single (n,1)- dimensional slice of the data. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Compression, scalar fields,out-of-core. [source] Spatiotemporal Analysis of Surface Changes by TessellationsGEOGRAPHICAL ANALYSIS, Issue 4 2001Yukio Sadahiro This paper develops a method for analyzing the change of surface, a continuous function defined over the two-dimensional space. The surface change is represented by a scalar field in a spatiotemporal region. The region is divided into subregions called hills and waves which are based on the local form of the surface. They are both three-dimensional tessellations of the spatiotemporal region, and provide an overview of the surface change. To summarize the tessellations, four operations are proposed: section, projection, merging, and graph representation. They extract useful information from tessellations to describe the structure of surface change. To test the validity of the method, the change of a retail cluster in Shinjuku and Shibuya area in Tokyo is analyzed. The empirical study yields some interesting findings that help us understand changes in the spatial structure of retailing. [source] Large eddy simulation (2D) of spatially developing mixing layer using vortex-in-cell for flow field and filtered probability density function for scalar fieldINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2006J. K. Wang Abstract A large eddy simulation based on filtered vorticity transport equation has been coupled with filtered probability density function transport equation for scalar field, to predict the velocity and passive scalar fields. The filtered vorticity transport has been formulated using diffusion-velocity method and then solved using the vortex method. The methodology has been tested on a spatially growing mixing layer using the two-dimensional vortex-in-cell method in conjunction with both Smagorinsky and dynamic eddy viscosity subgrid scale models for an anisotropic flow. The transport equation for filtered probability density function is solved using the Lagrangian Monte-Carlo method. The unresolved subgrid scale convective term in filtered density function transport is modelled using the gradient diffusion model. The unresolved subgrid scale mixing term is modelled using the modified Curl model. The effects of subgrid scale models on the vorticity contours, mean streamwise velocity profiles, root-mean-square velocity and vorticity fluctuations profiles and negative cross-stream correlations are discussed. Also the characteristics of the passive scalar, i.e. mean concentration profiles, root-mean-square concentration fluctuations profiles and filtered probability density function are presented and compared with previous experimental and numerical works. The sensitivity of the results to the Schmidt number, constant in mixing frequency and inflow boundary conditions are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Hydrodynamical N -body simulations of coupled dark energy cosmologiesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2010Marco Baldi ABSTRACT If the accelerated expansion of the Universe at the present epoch is driven by a dark energy scalar field, there may well be a non-trivial coupling between the dark energy and the cold dark matter (CDM) fluid. Such interactions give rise to new features in cosmological structure growth, like an additional long-range attractive force between CDM particles, or variations of the dark matter particle mass with time. We have implemented these effects in the N -body code gadget-2 and present results of a series of high-resolution N -body simulations where the dark energy component is directly interacting with the CDM. As a consequence of the new physics, CDM and baryon distributions evolve differently both in the linear and in the non-linear regime of structure formation. Already on large scales, a linear bias develops between these two components, which is further enhanced by the non-linear evolution. We also find, in contrast with previous work, that the density profiles of CDM haloes are less concentrated in coupled dark energy cosmologies compared with ,CDM, and that this feature does not depend on the initial conditions setup, but is a specific consequence of the extra physics induced by the coupling. Also, the baryon fraction in haloes in the coupled models is significantly reduced below the universal baryon fraction. These features alleviate tensions between observations and the ,CDM model on small scales. Our methodology is ideally suited to explore the predictions of coupled dark energy models in the fully non-linear regime, which can provide powerful constraints for the viable parameter space of such scenarios. [source] Cosmic momentum field and mass fluctuation power spectrumMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2000Changbom Park We introduce the cosmic momentum field as a new measure of the large-scale peculiar velocity and matter fluctuation fields. The momentum field is defined as the peculiar velocity field traced and weighted by galaxies, and is equal to the velocity field in the linear regime. We show that the radial component of the momentum field can be considered as a scalar field with the power spectrum which is practically one-third of that of the total momentum field. We present a formula for the power spectrum directly calculable from the observed radial peculiar velocity data. The momentum power spectrum is measured for the MAT sample in the Mark III catalogue of peculiar velocities of galaxies. Using the momentum power spectrum we find the amplitude of the matter power spectrum is and at the wavenumbers 0.049 and 0.074 h Mpc,1, respectively, where , is the density parameter. The 68 per cent confidence limits include the cosmic variance. The measured momentum and density power spectra together indicate that the parameter or where bO is the bias factor for optical galaxies. [source] Nonequilibrium quantum anharmonic oscillator and scalar field: high temperature approximationsANNALEN DER PHYSIK, Issue 6 2009R.F. Alvarez-Estrada Abstract We treat a relativistic quantum boson gas, described by a scalar quantum field, with quartic self-interaction (,4) in three spatial dimensions: we review the known equilibrium case and present new proposals off-equilibrium. For high temperature and large spatial scales, the behaviour of the gas at equilibrium simplifies nonperturbatively (equilibrium dimensional reduction or EDR): its thermodynamics is described by classical statistical mechanics with some quantum field effects. By assumption, the initial state of the gas off-equilibrium includes interactions and inhomogeneities and is not far from thermal equilibrium. We employ real-time generating functionals and obtain the free nonequilibrium correlators at non-zero temperature. The nonequilibrium quantum gas appears to simplify nonperturbatively in the regime of high temperature and large temporal and spatial scales (nonequilibrium dimensional reduction or NEDR), its dynamics being described by classical statistical mechanics with some quantum field effects. We outline the renormalization of the ,4 theory, the nonequilibrium statistical mechanics of a quantum anharmonic oscillator and the high temperature simplifications, all of which provide very useful hints for NEDR in the field case. Our main proposals are NEDR and the associated new (renormalized) real-time nonequilibrium generating functionals for the ,4 theory. [source] Non-Gaussian invariant measures for the Majda model of decaying turbulent transportCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2001Eric Vanden Eijnden The problem of turbulent transport of a scalar field by a random velocity field is considered. The scalar field amplitude exhibits rare but very large fluctuations whose typical signature are fatter than Gaussian tails for the probability distribution of the scalar. The existence of such large fluctuations is related to clustering phenomena of the Lagrangian paths within the flow. This suggests an approach to turn the large deviation problem for the scalar field into a small deviation, or small ball, problem for some appropriately defined process measuring the spreading with time of the Lagrangian paths. Here, such a methodology is applied to a model proposed by Majda consisting of a white-in-time linear shear flow and some generalizations of it where the velocity field has finite, or even infinite, correlation time. The non-Gaussian invariant measure for the (reduced) scalar field is derived and, in particular, it is shown that the one-point distribution of the scalar has stretched exponential tails, with a stretching exponent depending of the parameters in the model. Different universality classes for the scalar behavior are identified which, all other parameters being kept fixed, display a one-to-one correspondence with a exponent measuring time persistence effects in the velocity field. © 2001 John Wiley & Sons, Inc. [source] A framework for fusion methods and rendering techniques of multimodal volume dataCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 2 2004Maria Ferre Abstract Many different direct volume rendering methods have been developed to visualize 3D scalar fields on uniform rectilinear grids. However, little work has been done on rendering simultaneously various properties of the same 3D region measured with different registration devices or at different instants of time. The demand for this type of visualization is rapidly increasing in scientific applications such as medicine in which the visual integration of multiple modalities allows a better comprehension of the anatomy and a perception of its relationships with activity. This paper presents different strategies of direct multimodal volume rendering (DMVR). It is restricted to voxel models with a known 3D rigid alignment transformation. The paper evaluates at which steps of the rendering pipeline the data fusion must be realized in order to accomplish the desired visual integration and to provide fast re-renders when some fusion parameters are modified. In addition, it analyses how existing monomodal visualization algorithms can be extended to multiple datasets and it compares their efficiency and their computational cost. Copyright © 2004 John Wiley & Sons, Ltd. [source] Out-of-core compression and decompression of large n -dimensional scalar fieldsCOMPUTER GRAPHICS FORUM, Issue 3 2003Lawrence Ibarria We present a simple method for compressing very large and regularly sampled scalar fields. Our method is particularlyattractive when the entire data set does not fit in memory and when the sampling rate is high relative to thefeature size of the scalar field in all dimensions. Although we report results foranddata sets, the proposedapproach may be applied to higher dimensions. The method is based on the new Lorenzo predictor, introducedhere, which estimates the value of the scalar field at each sample from the values at processed neighbors. The predictedvalues are exact when the n-dimensional scalar field is an implicit polynomial of degreen, 1. Surprisingly,when the residuals (differences between the actual and predicted values) are encoded using arithmetic coding,the proposed method often outperforms wavelet compression in anL,sense. The proposed approach may beused both for lossy and lossless compression and is well suited for out-of-core compression and decompression,because a trivial implementation, which sweeps through the data set reading it once, requires maintaining only asmall buffer in core memory, whose size barely exceeds a single (n,1)- dimensional slice of the data. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Compression, scalar fields,out-of-core. [source] Optimised Dirac operators on the lattice: construction, properties and applicationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2 20082Article first published online: 29 NOV 200, W. Bietenholz Abstract We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p -regime and in the ,-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian , the chiral condensate and the pion decay constant , from QCD simulations with extremely light quarks. [source] Large eddy simulation of passive scalar in complex turbulence with flow impingement and flow separationHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2001Ken-ichi Abe Abstract In order to reveal unknown characteristics of complex turbulent passive scalar fields, large eddy simulations in forced convection regimes have been performed under several strain conditions, including flow impingement and flow separation. By using the simulation results, relations between the dynamic and scalar fields are carefully examined. It is then confirmed that the scalar is transported by a large vortex structure near the examined regions wherever the mean shear vanishes, although in the high-shear regions, the scalar transport is governed by a coherent structure due to the high shear strain. In addition, a priori explorations are attempted by processing the data, focusing on the derivation of a possible direction for modeling algebraically the passive scalar transport in a complex strain field. The a priori tests suggest that an expanded form of the GGDH model introducing a quadratic product of the Reynolds stresses is promising for general flow cases. © 2001 Scripta Technica, Heat Trans Asian Res, 30(5): 402,418, 2001 [source] Large eddy simulation (2D) of spatially developing mixing layer using vortex-in-cell for flow field and filtered probability density function for scalar fieldINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2006J. K. Wang Abstract A large eddy simulation based on filtered vorticity transport equation has been coupled with filtered probability density function transport equation for scalar field, to predict the velocity and passive scalar fields. The filtered vorticity transport has been formulated using diffusion-velocity method and then solved using the vortex method. The methodology has been tested on a spatially growing mixing layer using the two-dimensional vortex-in-cell method in conjunction with both Smagorinsky and dynamic eddy viscosity subgrid scale models for an anisotropic flow. The transport equation for filtered probability density function is solved using the Lagrangian Monte-Carlo method. The unresolved subgrid scale convective term in filtered density function transport is modelled using the gradient diffusion model. The unresolved subgrid scale mixing term is modelled using the modified Curl model. The effects of subgrid scale models on the vorticity contours, mean streamwise velocity profiles, root-mean-square velocity and vorticity fluctuations profiles and negative cross-stream correlations are discussed. Also the characteristics of the passive scalar, i.e. mean concentration profiles, root-mean-square concentration fluctuations profiles and filtered probability density function are presented and compared with previous experimental and numerical works. The sensitivity of the results to the Schmidt number, constant in mixing frequency and inflow boundary conditions are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Performance of algebraic multi-grid solvers based on unsmoothed and smoothed aggregation schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001R. WebsterArticle first published online: 31 JUL 200 Abstract A comparison is made of the performance of two algebraic multi-grid (AMG0 and AMG1) solvers for the solution of discrete, coupled, elliptic field problems. In AMG0, the basis functions for each coarse grid/level approximation (CGA) are obtained directly by unsmoothed aggregation, an appropriate scaling being applied to each CGA to improve consistency. In AMG1 they are assembled using a smoothed aggregation with a constrained energy optimization method providing the smoothing. Although more costly, smoothed basis functions provide a better (more consistent) CGA. Thus, AMG1 might be viewed as a benchmark for the assessment of the simpler AMG0. Selected test problems for D'Arcy flow in pipe networks, Fick diffusion, plane strain elasticity and Navier,Stokes flow (in a Stokes approximation) are used in making the comparison. They are discretized on the basis of both structured and unstructured finite element meshes. The range of discrete equation sets covers both symmetric positive definite systems and systems that may be non-symmetric and/or indefinite. Both global and local mesh refinements to at least one order of resolving power are examined. Some of these include anisotropic refinements involving elements of large aspect ratio; in some hydrodynamics cases, the anisotropy is extreme, with aspect ratios exceeding two orders. As expected, AMG1 delivers typical multi-grid convergence rates, which for all practical purposes are independent of mesh bandwidth. AMG0 rates are slower. They may also be more discernibly mesh-dependent. However, for the range of mesh bandwidths examined, the overall cost effectiveness of the two solvers is remarkably similar when a full convergence to machine accuracy is demanded. Thus, the shorter solution times for AMG1 do not necessarily compensate for the extra time required for its costly grid generation. This depends on the severity of the problem and the demanded level of convergence. For problems requiring few iterations, where grid generation costs represent a significant penalty, AMG0 has the advantage. For problems requiring a large investment in iterations, AMG1 has the edge. However, for the toughest problems addressed (vector and coupled vector,scalar fields discretized exclusively using finite elements of extreme aspect ratio) AMG1 is more robust: AMG0 has failed on some of these tests. However, but for this deficiency AMG0 would be the preferred linear approximation solver for Navier,Stokes solution algorithms in view of its much lower grid generation costs. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||||||||