Effects of empty bins on image upscaling in capsule endoscopy

NASA Astrophysics Data System (ADS)

Rukundo, Olivier

2017-07-01

This paper presents a preliminary study of the effect of empty bins on image upscaling in capsule endoscopy. The presented study was conducted based on results of existing contrast enhancement and interpolation methods. A low contrast enhancement method based on pixels consecutiveness and modified bilinear weighting scheme has been developed to distinguish between necessary empty bins and unnecessary empty bins in the effort to minimize the number of empty bins in the input image, before further processing. Linear interpolation methods have been used for upscaling input images with stretched histograms. Upscaling error differences and similarity indices between pairs of interpolation methods have been quantified using the mean squared error and feature similarity index techniques. Simulation results demonstrated more promising effects using the developed method than other contrast enhancement methods mentioned.

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

Correlation-based motion vector processing with adaptive interpolation scheme for motion-compensated frame interpolation.

PubMed

Huang, Ai-Mei; Nguyen, Truong

2009-04-01

In this paper, we address the problems of unreliable motion vectors that cause visual artifacts but cannot be detected by high residual energy or bidirectional prediction difference in motion-compensated frame interpolation. A correlation-based motion vector processing method is proposed to detect and correct those unreliable motion vectors by explicitly considering motion vector correlation in the motion vector reliability classification, motion vector correction, and frame interpolation stages. Since our method gradually corrects unreliable motion vectors based on their reliability, we can effectively discover the areas where no motion is reliable to be used, such as occlusions and deformed structures. We also propose an adaptive frame interpolation scheme for the occlusion areas based on the analysis of their surrounding motion distribution. As a result, the interpolated frames using the proposed scheme have clearer structure edges and ghost artifacts are also greatly reduced. Experimental results show that our interpolated results have better visual quality than other methods. In addition, the proposed scheme is robust even for those video sequences that contain multiple and fast motions.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

The Linear Bicharacteristic Scheme for Computational Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Chan, Siew-Loong

2000-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on electromagnetic wave propagation problems. This paper extends the Linear Bicharacteristic Scheme for computational electromagnetics to treat lossy dielectric and magnetic materials and perfect electrical conductors. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media, and treatment of perfect electrical conductors (PECs) are shown to follow directly in the limit of high conductivity. Heterogeneous media are treated through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for one-dimensional model problems on both uniform and nonuniform grids, and the FDTD algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has approximately one-third the phase velocity error. The LBS is also more accurate on nonuniform grids.

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

High-Fidelity Real-Time Trajectory Optimization for Reusable Launch Vehicles

DTIC Science & Technology

2006-12-01

6.20 Max DR Yawing Moment History. ...............................................................270 Figure 6.21 Snapshot from MATLAB “Profile...Propagation using “ode45” (Euler Angles)...........................................330 Figure 6.114 Interpolated Elevon Controls using Various MATLAB ...Schemes.................332 Figure 6.115 Interpolated Flap Controls using Various MATLAB Schemes.....................333 Figure 6.116 Interpolated

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Debojyoti; Baeder, James D.

2014-01-21

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed inmore » the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows« less

Quadratic trigonometric B-spline for image interpolation using GA

PubMed Central

Abbas, Samreen; Irshad, Misbah

2017-01-01

In this article, a new quadratic trigonometric B-spline with control parameters is constructed to address the problems related to two dimensional digital image interpolation. The newly constructed spline is then used to design an image interpolation scheme together with one of the soft computing techniques named as Genetic Algorithm (GA). The idea of GA has been formed to optimize the control parameters in the description of newly constructed spline. The Feature SIMilarity (FSIM), Structure SIMilarity (SSIM) and Multi-Scale Structure SIMilarity (MS-SSIM) indices along with traditional Peak Signal-to-Noise Ratio (PSNR) are employed as image quality metrics to analyze and compare the outcomes of approach offered in this work, with three of the present digital image interpolation schemes. The upshots show that the proposed scheme is better choice to deal with the problems associated to image interpolation. PMID:28640906

Quadratic trigonometric B-spline for image interpolation using GA.

PubMed

Hussain, Malik Zawwar; Abbas, Samreen; Irshad, Misbah

2017-01-01

In this article, a new quadratic trigonometric B-spline with control parameters is constructed to address the problems related to two dimensional digital image interpolation. The newly constructed spline is then used to design an image interpolation scheme together with one of the soft computing techniques named as Genetic Algorithm (GA). The idea of GA has been formed to optimize the control parameters in the description of newly constructed spline. The Feature SIMilarity (FSIM), Structure SIMilarity (SSIM) and Multi-Scale Structure SIMilarity (MS-SSIM) indices along with traditional Peak Signal-to-Noise Ratio (PSNR) are employed as image quality metrics to analyze and compare the outcomes of approach offered in this work, with three of the present digital image interpolation schemes. The upshots show that the proposed scheme is better choice to deal with the problems associated to image interpolation.

On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids

NASA Astrophysics Data System (ADS)

Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.

2017-03-01

The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.

Multilevel Green's function interpolation method for scattering from composite metallic and dielectric objects.

PubMed

Shi, Yan; Wang, Hao Gang; Li, Long; Chan, Chi Hou

2008-10-01

A multilevel Green's function interpolation method based on two kinds of multilevel partitioning schemes--the quasi-2D and the hybrid partitioning scheme--is proposed for analyzing electromagnetic scattering from objects comprising both conducting and dielectric parts. The problem is formulated using the surface integral equation for homogeneous dielectric and conducting bodies. A quasi-2D multilevel partitioning scheme is devised to improve the efficiency of the Green's function interpolation. In contrast to previous multilevel partitioning schemes, noncubic groups are introduced to discretize the whole EM structure in this quasi-2D multilevel partitioning scheme. Based on the detailed analysis of the dimension of the group in this partitioning scheme, a hybrid quasi-2D/3D multilevel partitioning scheme is proposed to effectively handle objects with fine local structures. Selection criteria for some key parameters relating to the interpolation technique are given. The proposed algorithm is ideal for the solution of problems involving objects such as missiles, microstrip antenna arrays, photonic bandgap structures, etc. Numerical examples are presented to show that CPU time is between O(N) and O(N log N) while the computer memory requirement is O(N).

Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations

DTIC Science & Technology

2008-02-01

Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing...interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms ...congruences), and linear diophantine disequations. We show the utility of the proposed interpolation algorithms for discovering modular/divisibility predicates

Medical image enhancement using resolution synthesis

NASA Astrophysics Data System (ADS)

Wong, Tak-Shing; Bouman, Charles A.; Thibault, Jean-Baptiste; Sauer, Ken D.

2011-03-01

We introduce a post-processing approach to improve the quality of CT reconstructed images. The scheme is adapted from the resolution-synthesis (RS)1 interpolation algorithm. In this approach, we consider the input image, scanned at a particular dose level, as a degraded version of a high quality image scanned at a high dose level. Image enhancement is achieved by predicting the high quality image by classification based linear regression. To improve the robustness of our scheme, we also apply the minimum description length principle to determine the optimal number of predictors to use in the scheme, and the ridge regression to regularize the design of the predictors. Experimental results show that our scheme is effective in reducing the noise in images reconstructed from filtered back projection without significant loss of image details. Alternatively, our scheme can also be applied to reduce dose while maintaining image quality at an acceptable level.

Distributed optical fiber-based monitoring approach of spatial seepage behavior in dike engineering

NASA Astrophysics Data System (ADS)

Su, Huaizhi; Ou, Bin; Yang, Lifu; Wen, Zhiping

2018-07-01

The failure caused by seepage is the most common one in dike engineering. As to the characteristics of seepage in dike, such as longitudinal extension engineering, the randomness, strong concealment and small initial quantity order, by means of distributed fiber temperature sensor system (DTS), adopting an improved optical fiber layer layout scheme, the location of initial interpolation point of the saturation line is obtained. With the barycentric Lagrange interpolation collocation method (BLICM), the infiltrated surface of dike full-section is generated. Combined with linear optical fiber monitoring seepage method, BLICM is applied in an engineering case, which shows that a real-time seepage monitoring technique is presented in full-section of dike based on the combination method.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals

PubMed Central

Husser, Edgar; Bargmann, Swantje

2017-01-01

The mechanical behavior of single crystalline, micro-sized copper is investigated in the context of cantilever beam bending experiments. Particular focus is on the role of geometrically necessary dislocations (GNDs) during bending-dominated load conditions and their impact on the characteristic bending size effect. Three different sample sizes are considered in this work with main variation in thickness. A gradient extended crystal plasticity model is presented and applied in a three-dimensional finite-element (FE) framework considering slip system-based edge and screw components of the dislocation density vector. The underlying mathematical model contains non-standard evolution equations for GNDs, crystal-specific interaction relations, and higher-order boundary conditions. Moreover, two element formulations are examined and compared with respect to size-independent as well as size-dependent bending behavior. The first formulation is based on a linear interpolation of the displacement and the GND density field together with a full integration scheme whereas the second is based on a mixed interpolation scheme. While the GND density fields are treated equivalently, the displacement field is interpolated quadratically in combination with a reduced integration scheme. Computational results indicate that GND storage in small cantilever beams strongly influences the evolution of statistically stored dislocations (SSDs) and, hence, the distribution of the total dislocation density. As a particular example, the mechanical bending behavior in the case of a physically motivated limitation of GND storage is studied. The resulting impact on the mechanical bending response as well as on the predicted size effect is analyzed. Obtained results are discussed and related to experimental findings from the literature. PMID:28772657

A Novel Multi-Receiver Signcryption Scheme with Complete Anonymity.

PubMed

Pang, Liaojun; Yan, Xuxia; Zhao, Huiyang; Hu, Yufei; Li, Huixian

2016-01-01

Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating polynomial was proposed. To ensure the sender's anonymity, the concept of the ring signature was proposed in 2005, but afterwards, this scheme was proven to has some weakness and at the same time, a completely anonymous multi-receiver signcryption scheme is proposed. In this completely anonymous scheme, the sender anonymity is achieved by improving the ring signature, and the receiver anonymity is achieved by also using the Lagrange interpolating polynomial. Unfortunately, the Lagrange interpolation method was proven a failure to protect the anonymity of receivers, because each authorized receiver could judge whether anyone else is authorized or not. Therefore, the completely anonymous multi-receiver signcryption mentioned above can only protect the sender anonymity. In this paper, we propose a new completely anonymous multi-receiver signcryption scheme with a new polynomial technology used to replace the Lagrange interpolating polynomial, which can mix the identity information of receivers to save it as a ciphertext element and prevent the authorized receivers from verifying others. With the receiver anonymity, the proposed scheme also owns the anonymity of the sender at the same time. Meanwhile, the decryption fairness and public verification are also provided.

Poisson Coordinates.

PubMed

Li, Xian-Ying; Hu, Shi-Min

2013-02-01

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

Numerical simulation of supersonic and hypersonic inlet flow fields

NASA Technical Reports Server (NTRS)

Mcrae, D. Scott; Kontinos, Dean A.

1995-01-01

This report summarizes the research performed by North Carolina State University and NASA Ames Research Center under Cooperative Agreement NCA2-719, 'Numerical Simulation of Supersonic and Hypersonic Inlet Flow Fields". Four distinct rotated upwind schemes were developed and investigated to determine accuracy and practicality. The scheme found to have the best combination of attributes, including reduction to grid alignment with no rotation, was the cell centered non-orthogonal (CCNO) scheme. In 2D, the CCNO scheme improved rotation when flux interpolation was extended to second order. In 3D, improvements were less dramatic in all cases, with second order flux interpolation showing the least improvement over grid aligned upwinding. The reduction in improvement is attributed to uncertainty in determining optimum rotation angle and difficulty in performing accurate and efficient interpolation of the angle in 3D. The CCNO rotational technique will prove very useful for increasing accuracy when second order interpolation is not appropriate and will materially improve inlet flow solutions.

Boundary Closures for Fourth-order Energy Stable Weighted Essentially Non-Oscillatory Finite Difference Schemes

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.

2009-01-01

A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.

Adapting Better Interpolation Methods to Model Amphibious MT Data Along the Cascadian Subduction Zone.

NASA Astrophysics Data System (ADS)

Parris, B. A.; Egbert, G. D.; Key, K.; Livelybrooks, D.

2016-12-01

Magnetotellurics (MT) is an electromagnetic technique used to model the inner Earth's electrical conductivity structure. MT data can be analyzed using iterative, linearized inversion techniques to generate models imaging, in particular, conductive partial melts and aqueous fluids that play critical roles in subduction zone processes and volcanism. For example, the Magnetotelluric Observations of Cascadia using a Huge Array (MOCHA) experiment provides amphibious data useful for imaging subducted fluids from trench to mantle wedge corner. When using MOD3DEM(Egbert et al. 2012), a finite difference inversion package, we have encountered problems inverting, particularly, sea floor stations due to the strong, nearby conductivity gradients. As a work-around, we have found that denser, finer model grids near the land-sea interface produce better inversions, as characterized by reduced data residuals. This is partly to be due to our ability to more accurately capture topography and bathymetry. We are experimenting with improved interpolation schemes that more accurately track EM fields across cell boundaries, with an eye to enhancing the accuracy of the simulated responses and, thus, inversion results. We are adapting how MOD3DEM interpolates EM fields in two ways. The first seeks to improve weighting functions for interpolants to better address current continuity across grid boundaries. Electric fields are interpolated using a tri-linear spline technique, where the eight nearest electrical field estimates are each given weights determined by the technique, a kind of weighted average. We are modifying these weights to include cross-boundary conductivity ratios to better model current continuity. We are also adapting some of the techniques discussed in Shantsev et al (2014) to enhance the accuracy of the interpolated fields calculated by our forward solver, as well as to better approximate the sensitivities passed to the software's Jacobian that are used to generate a new forward model during each iteration of the inversion.

Conical intersection seams in polyenes derived from their chemical composition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nenov, Artur; Vivie-Riedle, Regina de

2012-08-21

The knowledge of conical intersection seams is important to predict and explain the outcome of ultrafast reactions in photochemistry and photobiology. They define the energetic low-lying reachable regions that allow for the ultrafast non-radiative transitions. In complex molecules it is not straightforward to locate them. We present a systematic approach to predict conical intersection seams in multifunctionalized polyenes and their sensitivity to substituent effects. Included are seams that facilitate the photoreaction of interest as well as seams that open competing loss channels. The method is based on the extended two-electron two-orbital method [A. Nenov and R. de Vivie-Riedle, J. Chem.more » Phys. 135, 034304 (2011)]. It allows to extract the low-lying regions for non-radiative transitions, which are then divided into small linear segments. Rules of thumb are introduced to find the support points for these segments, which are then used in a linear interpolation scheme for a first estimation of the intersection seams. Quantum chemical optimization of the linear interpolated structures yields the final energetic position. We demonstrate our method for the example of the electrocyclic isomerization of trifluoromethyl-pyrrolylfulgide.« less

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

Wavelet-Smoothed Interpolation of Masked Scientific Data for JPEG 2000 Compression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brislawn, Christopher M.

2012-08-13

How should we manage scientific data with 'holes'? Some applications, like JPEG 2000, expect logically rectangular data, but some sources, like the Parallel Ocean Program (POP), generate data that isn't defined on certain subsets. We refer to grid points that lack well-defined, scientifically meaningful sample values as 'masked' samples. Wavelet-smoothing is a highly scalable interpolation scheme for regions with complex boundaries on logically rectangular grids. Computation is based on forward/inverse discrete wavelet transforms, so runtime complexity and memory scale linearly with respect to sample count. Efficient state-of-the-art minimal realizations yield small constants (O(10)) for arithmetic complexity scaling, and in-situ implementationmore » techniques make optimal use of memory. Implementation in two dimensions using tensor product filter banks is straighsorward and should generalize routinely to higher dimensions. No hand-tuning required when the interpolation mask changes, making the method aeractive for problems with time-varying masks. Well-suited for interpolating undefined samples prior to JPEG 2000 encoding. The method outperforms global mean interpolation, as judged by both SNR rate-distortion performance and low-rate artifact mitigation, for data distributions whose histograms do not take the form of sharply peaked, symmetric, unimodal probability density functions. These performance advantages can hold even for data whose distribution differs only moderately from the peaked unimodal case, as demonstrated by POP salinity data. The interpolation method is very general and is not tied to any particular class of applications, could be used for more generic smooth interpolation.« less

Thickness Gauging of Single-Layer Conductive Materials with Two-Point Non Linear Calibration Algorithm

NASA Technical Reports Server (NTRS)

Fulton, James P. (Inventor); Namkung, Min (Inventor); Simpson, John W. (Inventor); Wincheski, Russell A. (Inventor); Nath, Shridhar C. (Inventor)

1998-01-01

A thickness gauging instrument uses a flux focusing eddy current probe and two-point nonlinear calibration algorithm. The instrument is small and portable due to the simple interpretation and operational characteristics of the probe. A nonlinear interpolation scheme incorporated into the instrument enables a user to make highly accurate thickness measurements over a fairly wide calibration range from a single side of nonferromagnetic conductive metals. The instrument is very easy to use and can be calibrated quickly.

Edge directed image interpolation with Bamberger pyramids

NASA Astrophysics Data System (ADS)

Rosiles, Jose Gerardo

2005-08-01

Image interpolation is a standard feature in digital image editing software, digital camera systems and printers. Classical methods for resizing produce blurred images with unacceptable quality. Bamberger Pyramids and filter banks have been successfully used for texture and image analysis. They provide excellent multiresolution and directional selectivity. In this paper we present an edge-directed image interpolation algorithm which takes advantage of the simultaneous spatial-directional edge localization at the subband level. The proposed algorithm outperform classical schemes like bilinear and bicubic schemes from the visual and numerical point of views.

High Order Semi-Lagrangian Advection Scheme

NASA Astrophysics Data System (ADS)

Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

2014-11-01

In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

A Linear Algebraic Approach to Teaching Interpolation

ERIC Educational Resources Information Center

Tassa, Tamir

2007-01-01

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2017-01-01

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2??-1, which is higher than the expected order of ??.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr; Department of Chemistry, Pohang University of Science and Technology

2014-04-28

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabaticmore » transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.« less

A rational interpolation method to compute frequency response

NASA Technical Reports Server (NTRS)

Kenney, Charles; Stubberud, Stephen; Laub, Alan J.

1993-01-01

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

Mutual information estimation for irregularly sampled time series

NASA Astrophysics Data System (ADS)

Rehfeld, K.; Marwan, N.; Heitzig, J.; Kurths, J.

2012-04-01

For the automated, objective and joint analysis of time series, similarity measures are crucial. Used in the analysis of climate records, they allow for a complimentary, unbiased view onto sparse datasets. The irregular sampling of many of these time series, however, makes it necessary to either perform signal reconstruction (e.g. interpolation) or to develop and use adapted measures. Standard linear interpolation comes with an inevitable loss of information and bias effects. We have recently developed a Gaussian kernel-based correlation algorithm with which the interpolation error can be substantially lowered, but this would not work should the functional relationship in a bivariate setting be non-linear. We therefore propose an algorithm to estimate lagged auto and cross mutual information from irregularly sampled time series. We have extended the standard and adaptive binning histogram estimators and use Gaussian distributed weights in the estimation of the (joint) probabilities. To test our method we have simulated linear and nonlinear auto-regressive processes with Gamma-distributed inter-sampling intervals. We have then performed a sensitivity analysis for the estimation of actual coupling length, the lag of coupling and the decorrelation time in the synthetic time series and contrast our results to the performance of a signal reconstruction scheme. Finally we applied our estimator to speleothem records. We compare the estimated memory (or decorrelation time) to that from a least-squares estimator based on fitting an auto-regressive process of order 1. The calculated (cross) mutual information results are compared for the different estimators (standard or adaptive binning) and contrasted with results from signal reconstruction. We find that the kernel-based estimator has a significantly lower root mean square error and less systematic sampling bias than the interpolation-based method. It is possible that these encouraging results could be further improved by using non-histogram mutual information estimators, like k-Nearest Neighbor or Kernel-Density estimators, but for short (<1000 points) and irregularly sampled datasets the proposed algorithm is already a great improvement.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Quantitative Tomography for Continuous Variable Quantum Systems

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

2018-03-01

We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

High order cell-centered scheme totally based on cell average

NASA Astrophysics Data System (ADS)

Liu, Ze-Yu; Cai, Qing-Dong

2018-05-01

This work clarifies the concept of cell average by pointing out the differences between cell average and cell centroid value, which are averaged cell-centered value and pointwise cell-centered value, respectively. Interpolation based on cell averages is constructed and high order QUICK-like numerical scheme is designed for such interpolation. A new approach of error analysis is introduced in this work, which is similar to Taylor’s expansion.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Moore, J.; Nicholson, S.; Moore, J. G.

1985-01-01

Research at NASA Lewis Research Center gave the opportunity to incorporate new control volumes in the Denton 3-D finite-volume time marching code. For duct flows, the new control volumes require no transverse smoothing and this allows calculations with large transverse gradients in properties without significant numerical total pressure losses. Possibilities for improving the Denton code to obtain better distributions of properties through shocks were demonstrated. Much better total pressure distributions through shocks are obtained when the interpolated effective pressure, needed to stabilize the solution procedure, is used to calculate the total pressure. This simple change largely eliminates the undershoot in total pressure down-stream of a shock. Overshoots and undershoots in total pressure can then be further reduced by a factor of 10 by adopting the effective density method, rather than the effective pressure method. Use of a Mach number dependent interpolation scheme for pressure then removes the overshoot in static pressure downstream of a shock. The stability of interpolation schemes used for the calculation of effective density is analyzed and a Mach number dependent scheme is developed, combining the advantages of the correct perfect gas equation for subsonic flow with the stability of 2-point and 3-point interpolation schemes for supersonic flow.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

Higher-dimensional Wannier functions of multiparameter Hamiltonians

NASA Astrophysics Data System (ADS)

Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy

2015-05-01

When using Wannier functions to study the electronic structure of multiparameter Hamiltonians H(k ,λ ) carrying a dependence on crystal momentum k and an additional periodic parameter λ , one usually constructs several sets of Wannier functions for a set of values of λ . We present the concept of higher-dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multiparameter Hamiltonians based on a single set of HDWFs. The obstacle of nonorthogonality of Bloch functions at different λ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter λ . We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of λ : (i) the spin-spiral vector q and (ii) the direction of the ferromagnetic magnetization m ̂. Using the generalized interpolation of the energy, we extract the corresponding values of magnetocrystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization, and spin torques.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slattery, Stuart R.

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-08-01

In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.

On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids

NASA Astrophysics Data System (ADS)

Kaus, B.; Pusok, A. E.; Popov, A.

2015-12-01

The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation reduces the dispersion or clustering of markers and that the density of markers remains steady over time without the need of additional marker control. Jenny et al. (2001, J Comp Phys, 166, 218-252 Meyer and Jenny (2004), Proc Appl Math Mech, 4, 466-467 Wang et al. (2015), G3, Vol.16 Funding was provided by the ERC Starting Grant #258830.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-06-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-04-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Two-argument total scatter factor for small fields simultaneously collimated by MLC and jaws: application to stereotactic radiosurgery and radiotherapy

NASA Astrophysics Data System (ADS)

Han, Zhaohui; Friesen, Scott; Hacker, Fred; Zygmanski, Piotr

2018-01-01

Direct use of the total scatter factor (S tot) for independent monitor unit (MU) calculations can be a good alternative approach to the traditional separate treatment of head/collimator scatter (S c) and phantom scatter (S p), especially for stereotactic small fields under the simultaneous collimation of secondary jaws and tertiary multileaf collimators (MLC). We have carried out the measurement of S tot in water for field sizes down to 0.5  ×  0.5 cm2 on a Varian TrueBeam STx medical linear accelerator (linac) equipped with high definition MLCs. Both the jaw field size (c) and MLC field size (s) significantly impact the linac output factors, especially when c \\gg s and s is small (e.g. s  <  5 cm). The combined influence of MLC and jaws gives rise to a two-argument dependence of the total scatter factor, S tot(c,s), which is difficult to functionally decouple. The (c,s) dependence can be conceived as a set of s-dependent functions (‘branches’) defined on domain [s min, s max  =  c] for a given jaw size of c. We have also developed a heuristic model of S tot to assist the clinical implementation of the measured S tot data for small field dosimetry. The model has two components: (i) empirical fit formula for the s-dependent branches and (ii) interpolation scheme between the branches. The interpolation scheme preserves the characteristic shape of the measured branches and effectively transforms the measured trapezoidal domain in (c,s) plane to a rectangular domain to facilitate easier two-dimensional interpolation to determine S tot for arbitrary (c,s) combinations. Both the empirical fit and interpolation showed good agreement with experimental validation data.

Interpolation Hermite Polynomials For Finite Element Method

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

NASA Astrophysics Data System (ADS)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals

PubMed Central

Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G.

2016-01-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors’ previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp–p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat. PMID:27382478

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.

PubMed

Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G

2016-06-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.

Use of shape-preserving interpolation methods in surface modeling

NASA Technical Reports Server (NTRS)

Ftitsch, F. N.

1984-01-01

In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.

Application of artificial neural networks in nonlinear analysis of trusses

NASA Technical Reports Server (NTRS)

Alam, J.; Berke, L.

1991-01-01

A method is developed to incorporate neural network model based upon the Backpropagation algorithm for material response into nonlinear elastic truss analysis using the initial stiffness method. Different network configurations are developed to assess the accuracy of neural network modeling of nonlinear material response. In addition to this, a scheme based upon linear interpolation for material data, is also implemented for comparison purposes. It is found that neural network approach can yield very accurate results if used with care. For the type of problems under consideration, it offers a viable alternative to other material modeling methods.

Weighted cubic and biharmonic splines

NASA Astrophysics Data System (ADS)

Kvasov, Boris; Kim, Tae-Wan

2017-01-01

In this paper we discuss the design of algorithms for interpolating discrete data by using weighted cubic and biharmonic splines in such a way that the monotonicity and convexity of the data are preserved. We formulate the problem as a differential multipoint boundary value problem and consider its finite-difference approximation. Two algorithms for automatic selection of shape control parameters (weights) are presented. For weighted biharmonic splines the resulting system of linear equations can be efficiently solved by combining Gaussian elimination with successive over-relaxation method or finite-difference schemes in fractional steps. We consider basic computational aspects and illustrate main features of this original approach.

Kernel reconstruction methods for Doppler broadening - Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

NASA Astrophysics Data System (ADS)

Ducru, Pablo; Josey, Colin; Dibert, Karia; Sobes, Vladimir; Forget, Benoit; Smith, Kord

2017-04-01

This article establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (Tj). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T0 to a higher temperature T - namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (Tj). The choice of the L2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (Tj) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [Tmin ,Tmax ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [ 300 K , 3000 K ] with only 9 reference temperatures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schreiner, S.; Paschal, C.B.; Galloway, R.L.

Four methods of producing maximum intensity projection (MIP) images were studied and compared. Three of the projection methods differ in the interpolation kernel used for ray tracing. The interpolation kernels include nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation. The fourth projection method is a voxel projection method that is not explicitly a ray-tracing technique. The four algorithms` performance was evaluated using a computer-generated model of a vessel and using real MR angiography data. The evaluation centered around how well an algorithm transferred an object`s width to the projection plane. The voxel projection algorithm does not suffer from artifactsmore » associated with the nearest neighbor algorithm. Also, a speed-up in the calculation of the projection is seen with the voxel projection method. Linear interpolation dramatically improves the transfer of width information from the 3D MRA data set over both nearest neighbor and voxel projection methods. Even though the cubic convolution interpolation kernel is theoretically superior to the linear kernel, it did not project widths more accurately than linear interpolation. A possible advantage to the nearest neighbor interpolation is that the size of small vessels tends to be exaggerated in the projection plane, thereby increasing their visibility. The results confirm that the way in which an MIP image is constructed has a dramatic effect on information contained in the projection. The construction method must be chosen with the knowledge that the clinical information in the 2D projections in general will be different from that contained in the original 3D data volume. 27 refs., 16 figs., 2 tabs.« less

Comparison of Optimum Interpolation and Cressman Analyses

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1984-01-01

The objective of this investigation is to develop a state-of-the-art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies. A three-dimensional multivariate O/I analysis scheme has been developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Comparison of Optimum Interpolation and Cressman Analyses

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1985-01-01

The development of a state of the art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies was investigated. A three dimensional multivariate O/I analysis scheme was developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Thicke, Kyle

2017-12-01

We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in χ0 by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

DOE PAGES

Slattery, Stuart R.

2015-12-02

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

2002-01-01

We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

Structure-preserving interpolation of temporal and spatial image sequences using an optical flow-based method.

PubMed

Ehrhardt, J; Säring, D; Handels, H

2007-01-01

Modern tomographic imaging devices enable the acquisition of spatial and temporal image sequences. But, the spatial and temporal resolution of such devices is limited and therefore image interpolation techniques are needed to represent images at a desired level of discretization. This paper presents a method for structure-preserving interpolation between neighboring slices in temporal or spatial image sequences. In a first step, the spatiotemporal velocity field between image slices is determined using an optical flow-based registration method in order to establish spatial correspondence between adjacent slices. An iterative algorithm is applied using the spatial and temporal image derivatives and a spatiotemporal smoothing step. Afterwards, the calculated velocity field is used to generate an interpolated image at the desired time by averaging intensities between corresponding points. Three quantitative measures are defined to evaluate the performance of the interpolation method. The behavior and capability of the algorithm is demonstrated by synthetic images. A population of 17 temporal and spatial image sequences are utilized to compare the optical flow-based interpolation method to linear and shape-based interpolation. The quantitative results show that the optical flow-based method outperforms the linear and shape-based interpolation statistically significantly. The interpolation method presented is able to generate image sequences with appropriate spatial or temporal resolution needed for image comparison, analysis or visualization tasks. Quantitative and qualitative measures extracted from synthetic phantoms and medical image data show that the new method definitely has advantages over linear and shape-based interpolation.

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

DOE PAGES

Ducru, Pablo; Josey, Colin; Dibert, Karia; ...

2017-01-25

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernelmore » of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T min,T max]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.« less

Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories

NASA Astrophysics Data System (ADS)

Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques

2013-03-01

In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields.

Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks.

PubMed

Shelley, M J; Tao, L

2001-01-01

To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of Delta(t) = 0.5 x 10(-3) seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10(-5) seconds or 10(-9) seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

SU-F-I-08: CT Image Ring Artifact Reduction Based On Prior Image

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, C; Qi, H; Chen, Z

Purpose: In computed tomography (CT) system, CT images with ring artifacts will be reconstructed when some adjacent bins of detector don’t work. The ring artifacts severely degrade CT image quality. We present a useful CT ring artifacts reduction based on projection data correction, aiming at estimating the missing data of projection data accurately, thus removing the ring artifacts of CT images. Methods: The method consists of ten steps: 1) Identification of abnormal pixel line in projection sinogram; 2) Linear interpolation within the pixel line of projection sinogram; 3) FBP reconstruction using interpolated projection data; 4) Filtering FBP image using meanmore » filter; 5) Forwarding projection of filtered FBP image; 6) Subtraction forwarded projection from original projection; 7) Linear interpolation of abnormal pixel line area in the subtraction projection; 8) Adding the interpolated subtraction projection on the forwarded projection; 9) FBP reconstruction using corrected projection data; 10) Return to step 4 until the pre-set iteration number is reached. The method is validated on simulated and real data to restore missing projection data and reconstruct ring artifact-free CT images. Results: We have studied impact of amount of dead bins of CT detector on the accuracy of missing data estimation in projection sinogram. For the simulated case with a resolution of 256 by 256 Shepp-Logan phantom, three iterations are sufficient to restore projection data and reconstruct ring artifact-free images when the dead bins rating is under 30%. The dead-bin-induced artifacts are substantially reduced. More iteration number is needed to reconstruct satisfactory images while the rating of dead bins increases. Similar results were found for a real head phantom case. Conclusion: A practical CT image ring artifact correction scheme based on projection data is developed. This method can produce ring artifact-free CT images feasibly and effectively.« less

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

NASA Technical Reports Server (NTRS)

Todling, Ricardo; Cohn, Stephen E.

1994-01-01

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Tri-linear interpolation-based cerebral white matter fiber imaging

PubMed Central

Jiang, Shan; Zhang, Pengfei; Han, Tong; Liu, Weihua; Liu, Meixia

2013-01-01

Diffusion tensor imaging is a unique method to visualize white matter fibers three-dimensionally, non-invasively and in vivo, and therefore it is an important tool for observing and researching neural regeneration. Different diffusion tensor imaging-based fiber tracking methods have been already investigated, but making the computing faster, fiber tracking longer and smoother and the details shown clearer are needed to be improved for clinical applications. This study proposed a new fiber tracking strategy based on tri-linear interpolation. We selected a patient with acute infarction of the right basal ganglia and designed experiments based on either the tri-linear interpolation algorithm or tensorline algorithm. Fiber tracking in the same regions of interest (genu of the corpus callosum) was performed separately. The validity of the tri-linear interpolation algorithm was verified by quantitative analysis, and its feasibility in clinical diagnosis was confirmed by the contrast between tracking results and the disease condition of the patient as well as the actual brain anatomy. Statistical results showed that the maximum length and average length of the white matter fibers tracked by the tri-linear interpolation algorithm were significantly longer. The tracking images of the fibers indicated that this method can obtain smoother tracked fibers, more obvious orientation and clearer details. Tracking fiber abnormalities are in good agreement with the actual condition of patients, and tracking displayed fibers that passed though the corpus callosum, which was consistent with the anatomical structures of the brain. Therefore, the tri-linear interpolation algorithm can achieve a clear, anatomically correct and reliable tracking result. PMID:25206524

Incompressibility without tears - How to avoid restrictions of mixed formulation

NASA Technical Reports Server (NTRS)

Zienkiewicz, O. C.; Wu, J.

1991-01-01

Several time-stepping schemes for incompressibility problems are presented which can be solved directly for steady state or iteratively through the time domain. The difficulty of mixed interpolation is avoided by using these schemes. The schemes are applicable to problems of fluid and solid mechanics.

Maximally Informative Statistics for Localization and Mapping

NASA Technical Reports Server (NTRS)

Deans, Matthew C.

2001-01-01

This paper presents an algorithm for localization and mapping for a mobile robot using monocular vision and odometry as its means of sensing. The approach uses the Variable State Dimension filtering (VSDF) framework to combine aspects of Extended Kalman filtering and nonlinear batch optimization. This paper describes two primary improvements to the VSDF. The first is to use an interpolation scheme based on Gaussian quadrature to linearize measurements rather than relying on analytic Jacobians. The second is to replace the inverse covariance matrix in the VSDF with its Cholesky factor to improve the computational complexity. Results of applying the filter to the problem of localization and mapping with omnidirectional vision are presented.

Interpolation Method Needed for Numerical Uncertainty

NASA Technical Reports Server (NTRS)

Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

NASA Astrophysics Data System (ADS)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Fast digital zooming system using directionally adaptive image interpolation and restoration.

PubMed

Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki

2014-01-01

This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.

Directional view interpolation for compensation of sparse angular sampling in cone-beam CT.

PubMed

Bertram, Matthias; Wiegert, Jens; Schafer, Dirk; Aach, Til; Rose, Georg

2009-07-01

In flat detector cone-beam computed tomography and related applications, sparse angular sampling frequently leads to characteristic streak artifacts. To overcome this problem, it has been suggested to generate additional views by means of interpolation. The practicality of this approach is investigated in combination with a dedicated method for angular interpolation of 3-D sinogram data. For this purpose, a novel dedicated shape-driven directional interpolation algorithm based on a structure tensor approach is developed. Quantitative evaluation shows that this method clearly outperforms conventional scene-based interpolation schemes. Furthermore, the image quality trade-offs associated with the use of interpolated intermediate views are systematically evaluated for simulated and clinical cone-beam computed tomography data sets of the human head. It is found that utilization of directionally interpolated views significantly reduces streak artifacts and noise, at the expense of small introduced image blur.

Accuracy of parameterized proton range models; A comparison

NASA Astrophysics Data System (ADS)

Pettersen, H. E. S.; Chaar, M.; Meric, I.; Odland, O. H.; Sølie, J. R.; Röhrich, D.

2018-03-01

An accurate calculation of proton ranges in phantoms or detector geometries is crucial for decision making in proton therapy and proton imaging. To this end, several parameterizations of the range-energy relationship exist, with different levels of complexity and accuracy. In this study we compare the accuracy of four different parameterizations models for proton range in water: Two analytical models derived from the Bethe equation, and two different interpolation schemes applied to range-energy tables. In conclusion, a spline interpolation scheme yields the highest reproduction accuracy, while the shape of the energy loss-curve is best reproduced with the differentiated Bragg-Kleeman equation.

Pricing and simulation for real estate index options: Radial basis point interpolation

NASA Astrophysics Data System (ADS)

Gong, Pu; Zou, Dong; Wang, Jiayue

2018-06-01

This study employs the meshfree radial basis point interpolation (RBPI) for pricing real estate derivatives contingent on real estate index. This method combines radial and polynomial basis functions, which can guarantee the interpolation scheme with Kronecker property and effectively improve accuracy. An exponential change of variables, a mesh refinement algorithm and the Richardson extrapolation are employed in this study to implement the RBPI. Numerical results are presented to examine the computational efficiency and accuracy of our method.

A fully 3D approach for metal artifact reduction in computed tomography.

PubMed

Kratz, Barbel; Weyers, Imke; Buzug, Thorsten M

2012-11-01

In computed tomography imaging metal objects in the region of interest introduce inconsistencies during data acquisition. Reconstructing these data leads to an image in spatial domain including star-shaped or stripe-like artifacts. In order to enhance the quality of the resulting image the influence of the metal objects can be reduced. Here, a metal artifact reduction (MAR) approach is proposed that is based on a recomputation of the inconsistent projection data using a fully three-dimensional Fourier-based interpolation. The success of the projection space restoration depends sensitively on a sensible continuation of neighboring structures into the recomputed area. Fortunately, structural information of the entire data is inherently included in the Fourier space of the data. This can be used for a reasonable recomputation of the inconsistent projection data. The key step of the proposed MAR strategy is the recomputation of the inconsistent projection data based on an interpolation using nonequispaced fast Fourier transforms (NFFT). The NFFT interpolation can be applied in arbitrary dimension. The approach overcomes the problem of adequate neighborhood definitions on irregular grids, since this is inherently given through the usage of higher dimensional Fourier transforms. Here, applications up to the third interpolation dimension are presented and validated. Furthermore, prior knowledge may be included by an appropriate damping of the transform during the interpolation step. This MAR method is applicable on each angular view of a detector row, on two-dimensional projection data as well as on three-dimensional projection data, e.g., a set of sequential acquisitions at different spatial positions, projection data of a spiral acquisition, or cone-beam projection data. Results of the novel MAR scheme based on one-, two-, and three-dimensional NFFT interpolations are presented. All results are compared in projection data space and spatial domain with the well-known one-dimensional linear interpolation strategy. In conclusion, it is recommended to include as much spatial information into the recomputation step as possible. This is realized by increasing the dimension of the NFFT. The resulting image quality can be enhanced considerably.

The Grand Tour via Geodesic Interpolation of 2-frames

NASA Technical Reports Server (NTRS)

Asimov, Daniel; Buja, Andreas

1994-01-01

Grand tours are a class of methods for visualizing multivariate data, or any finite set of points in n-space. The idea is to create an animation of data projections by moving a 2-dimensional projection plane through n-space. The path of planes used in the animation is chosen so that it becomes dense, that is, it comes arbitrarily close to any plane. One of the original inspirations for the grand tour was the experience of trying to comprehend an abstract sculpture in a museum. One tends to walk around the sculpture, viewing it from many different angles. A useful class of grand tours is based on the idea of continuously interpolating an infinite sequence of randomly chosen planes. Visiting randomly (more precisely: uniformly) distributed planes guarantees denseness of the interpolating path. In computer implementations, 2-dimensional orthogonal projections are specified by two 1-dimensional projections which map to the horizontal and vertical screen dimensions, respectively. Hence, a grand tour is specified by a path of pairs of orthonormal projection vectors. This paper describes an interpolation scheme for smoothly connecting two pairs of orthonormal vectors, and thus for constructing interpolating grand tours. The scheme is optimal in the sense that connecting paths are geodesics in a natural Riemannian geometry.

When Interpolation-Induced Reflection Artifact Meets Time-Frequency Analysis.

PubMed

Lin, Yu-Ting; Flandrin, Patrick; Wu, Hau-Tieng

2016-10-01

While extracting the temporal dynamical features based on the time-frequency analyses, like the reassignment and synchrosqueezing transform, attracts more and more interest in biomedical data analysis, we should be careful about artifacts generated by interpolation schemes, in particular when the sampling rate is not significantly higher than the frequency of the oscillatory component we are interested in. We formulate the problem called the reflection effect and provide a theoretical justification of the statement. We also show examples in the anesthetic depth analysis with clear but undesirable artifacts. The artifact associated with the reflection effect exists not only theoretically but practically as well. Its influence is pronounced when we apply the time-frequency analyses to extract the time-varying dynamics hidden inside the signal. We have to carefully deal with the artifact associated with the reflection effect by choosing a proper interpolation scheme.

Super-resolution convolutional neural network for the improvement of the image quality of magnified images in chest radiographs

NASA Astrophysics Data System (ADS)

Umehara, Kensuke; Ota, Junko; Ishimaru, Naoki; Ohno, Shunsuke; Okamoto, Kentaro; Suzuki, Takanori; Shirai, Naoki; Ishida, Takayuki

2017-02-01

Single image super-resolution (SR) method can generate a high-resolution (HR) image from a low-resolution (LR) image by enhancing image resolution. In medical imaging, HR images are expected to have a potential to provide a more accurate diagnosis with the practical application of HR displays. In recent years, the super-resolution convolutional neural network (SRCNN), which is one of the state-of-the-art deep learning based SR methods, has proposed in computer vision. In this study, we applied and evaluated the SRCNN scheme to improve the image quality of magnified images in chest radiographs. For evaluation, a total of 247 chest X-rays were sampled from the JSRT database. The 247 chest X-rays were divided into 93 training cases with non-nodules and 152 test cases with lung nodules. The SRCNN was trained using the training dataset. With the trained SRCNN, the HR image was reconstructed from the LR one. We compared the image quality of the SRCNN and conventional image interpolation methods, nearest neighbor, bilinear and bicubic interpolations. For quantitative evaluation, we measured two image quality metrics, peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). In the SRCNN scheme, PSNR and SSIM were significantly higher than those of three interpolation methods (p<0.001). Visual assessment confirmed that the SRCNN produced much sharper edge than conventional interpolation methods without any obvious artifacts. These preliminary results indicate that the SRCNN scheme significantly outperforms conventional interpolation algorithms for enhancing image resolution and that the use of the SRCNN can yield substantial improvement of the image quality of magnified images in chest radiographs.

Treatment of Outliers via Interpolation Method with Neural Network Forecast Performances

NASA Astrophysics Data System (ADS)

Wahir, N. A.; Nor, M. E.; Rusiman, M. S.; Gopal, K.

2018-04-01

Outliers often lurk in many datasets, especially in real data. Such anomalous data can negatively affect statistical analyses, primarily normality, variance, and estimation aspects. Hence, handling the occurrences of outliers require special attention. Therefore, it is important to determine the suitable ways in treating outliers so as to ensure that the quality of the analyzed data is indeed high. As such, this paper discusses an alternative method to treat outliers via linear interpolation method. In fact, assuming outlier as a missing value in the dataset allows the application of the interpolation method to interpolate the outliers thus, enabling the comparison of data series using forecast accuracy before and after outlier treatment. With that, the monthly time series of Malaysian tourist arrivals from January 1998 until December 2015 had been used to interpolate the new series. The results indicated that the linear interpolation method, which was comprised of improved time series data, displayed better results, when compared to the original time series data in forecasting from both Box-Jenkins and neural network approaches.

Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy brachytherapy sources.

PubMed

Pujades-Claumarchirant, Ma Carmen; Granero, Domingo; Perez-Calatayud, Jose; Ballester, Facundo; Melhus, Christopher; Rivard, Mark

2010-03-01

The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function g L ( r ) and 2D anisotropy function F ( r , θ ) table entries for radial distance r and polar angle θ . The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive g L ( r ) and F ( r , θ ) from the reported data; 2) to determine the minimum number of entries in g L ( r ) and F ( r , θ ) that allow reproduction of dose distributions with sufficient accuracy. Four high-energy photon-emitting brachytherapy sources were studied: 60 Co model Co0.A86, 137 Cs model CSM-3, 192 Ir model Ir2.A85-2, and 169 Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2-8 (integer steps) and 10 cm. Four different angular steps were evaluated for F ( r , θ ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for g L ( r ). Linear-linear interpolation was used to obtain F ( r , θ ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four sources with the same grid. Linear interpolation of g L ( r ) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F ( r , θ ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60 Co, 192 Ir, and 169 Yb, while 137 Cs agreement was ≤ 1.5% for θ < 15°. The radial mesh studied was adequate for interpolating g L ( r ) for high-energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F ( r , θ ) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.

Exact subthreshold integration with continuous spike times in discrete-time neural network simulations.

PubMed

Morrison, Abigail; Straube, Sirko; Plesser, Hans Ekkehard; Diesmann, Markus

2007-01-01

Very large networks of spiking neurons can be simulated efficiently in parallel under the constraint that spike times are bound to an equidistant time grid. Within this scheme, the subthreshold dynamics of a wide class of integrate-and-fire-type neuron models can be integrated exactly from one grid point to the next. However, the loss in accuracy caused by restricting spike times to the grid can have undesirable consequences, which has led to interest in interpolating spike times between the grid points to retrieve an adequate representation of network dynamics. We demonstrate that the exact integration scheme can be combined naturally with off-grid spike events found by interpolation. We show that by exploiting the existence of a minimal synaptic propagation delay, the need for a central event queue is removed, so that the precision of event-driven simulation on the level of single neurons is combined with the efficiency of time-driven global scheduling. Further, for neuron models with linear subthreshold dynamics, even local event queuing can be avoided, resulting in much greater efficiency on the single-neuron level. These ideas are exemplified by two implementations of a widely used neuron model. We present a measure for the efficiency of network simulations in terms of their integration error and show that for a wide range of input spike rates, the novel techniques we present are both more accurate and faster than standard techniques.

Assignment of boundary conditions in embedded ground water flow models

USGS Publications Warehouse

Leake, S.A.

1998-01-01

Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger-scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger.scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.

Interpolation Method Needed for Numerical Uncertainty Analysis of Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Groves, Curtis; Ilie, Marcel; Schallhorn, Paul

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors in an unstructured grid, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors. Nomenclature

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding.

PubMed

Lai, Hong; Zhang, Jun; Luo, Ming-Xing; Pan, Lei; Pieprzyk, Josef; Xiao, Fuyuan; Orgun, Mehmet A

2016-08-12

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

PubMed Central

Lai, Hong; Zhang, Jun; Luo, Ming-Xing; Pan, Lei; Pieprzyk, Josef; Xiao, Fuyuan; Orgun, Mehmet A.

2016-01-01

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications. PMID:27515908

Interpolation for de-Dopplerisation

NASA Astrophysics Data System (ADS)

Graham, W. R.

2018-05-01

'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.

Differences between measured and linearly interpolated synoptic variables over a 12-h period during AVE 4

NASA Technical Reports Server (NTRS)

Dupuis, L. R.; Scoggins, J. R.

1979-01-01

Results of analyses revealed that nonlinear changes or differences formed centers or systems, that were mesosynoptic in nature. These systems correlated well in space with upper level short waves, frontal zones, and radar observed convection, and were very systematic in time and space. Many of the centers of differences were well established in the vertical, extending up to the tropopause. Statistical analysis showed that on the average nonlinear changes were larger in convective areas than nonconvective regions. Errors often exceeding 100 percent were made by assuming variables to change linearly through a 12-h period in areas of thunderstorms, indicating that these nonlinear changes are important in the development of severe weather. Linear changes, however, accounted for more and more of an observed change as the time interval (within the 12-h interpolation period) increased, implying that the accuracy of linear interpolation increased over larger time intervals.

Catmull-Rom Curve Fitting and Interpolation Equations

ERIC Educational Resources Information Center

Jerome, Lawrence

2010-01-01

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

Multidimensional directional flux weighted upwind scheme for multiphase flow modeling in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Jin, G.

2012-12-01

Multiphase flow modeling is an important numerical tool for a better understanding of transport processes in the fields including, but not limited to, petroleum reservoir engineering, remedy of ground water contamination, and risk evaluation of greenhouse gases such as CO2 injected into deep saline reservoirs. However, accurate numerical modeling for multiphase flow remains many challenges that arise from the inherent tight coupling and strong non-linear nature of the governing equations and the highly heterogeneous media. The existence of counter current flow which is caused by the effect of adverse relative mobility contrast and gravitational and capillary forces will introduce additional numerical instability. Recently multipoint flux approximation (MPFA) has become a subject of extensive research and has been demonstrated with great success in reducing considerable grid orientation effects compared to the conventional single point upstream (SPU) weighting scheme, especially in higher dimensions. However, the present available MPFA schemes are mathematically targeted to certain types of grids in two dimensions, a more general form of MPFA scheme is needed for both 2-D and 3-D problems. In this work a new upstream weighting scheme based on multipoint directional incoming fluxes is proposed which incorporates full permeability tensor to account for the heterogeneity of the porous media. First, the multiphase governing equations are decoupled into an elliptic pressure equation and a hyperbolic or parabolic saturation depends on whether the gravitational and capillary pressures are presented or not. Next, a dual secondary grid (called finite volume grid) is formulated from a primary grid (called finite element grid) to create interaction regions for each grid cell over the entire simulation domain. Such a discretization must ensure the conservation of mass and maintain the continuity of the Darcy velocity across the boundaries between neighboring interaction regions. The pressure field is then implicitly calculated from the pressure equation, which in turn results in the derived velocity field for directional flux calculation at each grid node. Directional flux at the center of each interaction surface is also calculated by interpolation from the element nodal fluxes using shape functions. The MPFA scheme is performed by a specific linear combination of all incoming fluxes into the upstream cell represented by either nodal fluxes or interpolated surface boundary fluxes to produce an upwind directional fluxed weighted relative mobility at the center of the interaction region boundary. Such an upwind weighted relative mobility is then used for calculating the saturations of each fluid phase explicitly. The proposed upwind weighting scheme has been implemented into a mixed finite element-finite volume (FE-FV) method, which allows for handling complex reservoir geometry with second-order accuracies in approximating primary variables. The numerical solver has been tested with several bench mark test problems. The application of the proposed scheme to migration path analysis of CO2 injected into deep saline reservoirs in 3-D has demonstrated its ability and robustness in handling multiphase flow with adverse mobility contrast in highly heterogeneous porous media.

A fast and accurate dihedral interpolation loop subdivision scheme

NASA Astrophysics Data System (ADS)

Shi, Zhuo; An, Yalei; Wang, Zhongshuai; Yu, Ke; Zhong, Si; Lan, Rushi; Luo, Xiaonan

2018-04-01

In this paper, we propose a fast and accurate dihedral interpolation Loop subdivision scheme for subdivision surfaces based on triangular meshes. In order to solve the problem of surface shrinkage, we keep the limit condition unchanged, which is important. Extraordinary vertices are handled using modified Butterfly rules. Subdivision schemes are computationally costly as the number of faces grows exponentially at higher levels of subdivision. To address this problem, our approach is to use local surface information to adaptively refine the model. This is achieved simply by changing the threshold value of the dihedral angle parameter, i.e., the angle between the normals of a triangular face and its adjacent faces. We then demonstrate the effectiveness of the proposed method for various 3D graphic triangular meshes, and extensive experimental results show that it can match or exceed the expected results at lower computational cost.

A Lagrangian particle method with remeshing for tracer transport on the sphere

DOE PAGES

Bosler, Peter Andrew; Kent, James; Krasny, Robert; ...

2017-03-30

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less

A Lagrangian particle method with remeshing for tracer transport on the sphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bosler, Peter Andrew; Kent, James; Krasny, Robert

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

Image processing methods to compensate for IFOV errors in microgrid imaging polarimeters

NASA Astrophysics Data System (ADS)

Ratliff, Bradley M.; Boger, James K.; Fetrow, Matthew P.; Tyo, J. Scott; Black, Wiley T.

2006-05-01

Long-wave infrared imaging Stokes vector polarimeters are used in many remote sensing applications. Imaging polarimeters require that several measurements be made under optically different conditions in order to estimate the polarization signature at a given scene point. This multiple-measurement requirement introduces error in the signature estimates, and the errors differ depending upon the type of measurement scheme used. Here, we investigate a LWIR linear microgrid polarimeter. This type of instrument consists of a mosaic of micropolarizers at different orientations that are masked directly onto a focal plane array sensor. In this scheme, each polarization measurement is acquired spatially and hence each is made at a different point in the scene. This is a significant source of error, as it violates the requirement that each polarization measurement have the same instantaneous field-of-view (IFOV). In this paper, we first study the amount of error introduced by the IFOV handicap in microgrid instruments. We then proceed to investigate means for mitigating the effects of these errors to improve the quality of polarimetric imagery. In particular, we examine different interpolation schemes and gauge their performance. These studies are completed through the use of both real instrumental and modeled data.

The Natural Neighbour Radial Point Interpolation Meshless Method Applied to the Non-Linear Analysis

NASA Astrophysics Data System (ADS)

Dinis, L. M. J. S.; Jorge, R. M. Natal; Belinha, J.

2011-05-01

In this work the Natural Neighbour Radial Point Interpolation Method (NNRPIM), is extended to large deformation analysis of elastic and elasto-plastic structures. The NNPRIM uses the Natural Neighbour concept in order to enforce the nodal connectivity and to create a node-depending background mesh, used in the numerical integration of the NNRPIM interpolation functions. Unlike the FEM, where geometrical restrictions on elements are imposed for the convergence of the method, in the NNRPIM there are no such restrictions, which permits a random node distribution for the discretized problem. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed using the Radial Point Interpolators, with some differences that modify the method performance. In the construction of the NNRPIM interpolation functions no polynomial base is required and the used Radial Basis Function (RBF) is the Multiquadric RBF. The NNRPIM interpolation functions posses the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. One of the scopes of this work is to present the validation the NNRPIM in the large-deformation elasto-plastic analysis, thus the used non-linear solution algorithm is the Newton-Rapson initial stiffness method and the efficient "forward-Euler" procedure is used in order to return the stress state to the yield surface. Several non-linear examples, exhibiting elastic and elasto-plastic material properties, are studied to demonstrate the effectiveness of the method. The numerical results indicated that NNRPIM handles large material distortion effectively and provides an accurate solution under large deformation.

Numerical solution of transport equation for applications in environmental hydraulics and hydrology

NASA Astrophysics Data System (ADS)

Rashidul Islam, M.; Hanif Chaudhry, M.

1997-04-01

The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

Optimal Interpolation scheme to generate reference crop evapotranspiration

NASA Astrophysics Data System (ADS)

Tomas-Burguera, Miquel; Beguería, Santiago; Vicente-Serrano, Sergio; Maneta, Marco

2018-05-01

We used an Optimal Interpolation (OI) scheme to generate a reference crop evapotranspiration (ETo) grid, forcing meteorological variables, and their respective error variance in the Iberian Peninsula for the period 1989-2011. To perform the OI we used observational data from the Spanish Meteorological Agency (AEMET) and outputs from a physically-based climate model. To compute ETo we used five OI schemes to generate grids for the five observed climate variables necessary to compute ETo using the FAO-recommended form of the Penman-Monteith equation (FAO-PM). The granularity of the resulting grids are less sensitive to variations in the density and distribution of the observational network than those generated by other interpolation methods. This is because our implementation of the OI method uses a physically-based climate model as prior background information about the spatial distribution of the climatic variables, which is critical for under-observed regions. This provides temporal consistency in the spatial variability of the climatic fields. We also show that increases in the density and improvements in the distribution of the observational network reduces substantially the uncertainty of the climatic and ETo estimates. Finally, a sensitivity analysis of observational uncertainties and network densification suggests the existence of a trade-off between quantity and quality of observations.

Measurement and tricubic interpolation of the magnetic field for the OLYMPUS experiment

NASA Astrophysics Data System (ADS)

Bernauer, J. C.; Diefenbach, J.; Elbakian, G.; Gavrilov, G.; Goerrissen, N.; Hasell, D. K.; Henderson, B. S.; Holler, Y.; Karyan, G.; Ludwig, J.; Marukyan, H.; Naryshkin, Y.; O'Connor, C.; Russell, R. L.; Schmidt, A.; Schneekloth, U.; Suvorov, K.; Veretennikov, D.

2016-07-01

The OLYMPUS experiment used a 0.3 T toroidal magnetic spectrometer to measure the momenta of outgoing charged particles. In order to accurately determine particle trajectories, knowledge of the magnetic field was needed throughout the spectrometer volume. For that purpose, the magnetic field was measured at over 36,000 positions using a three-dimensional Hall probe actuated by a system of translation tables. We used these field data to fit a numerical magnetic field model, which could be employed to calculate the magnetic field at any point in the spectrometer volume. Calculations with this model were computationally intensive; for analysis applications where speed was crucial, we pre-computed the magnetic field and its derivatives on an evenly spaced grid so that the field could be interpolated between grid points. We developed a spline-based interpolation scheme suitable for SIMD implementations, with a memory layout chosen to minimize space and optimize the cache behavior to quickly calculate field values. This scheme requires only one-eighth of the memory needed to store necessary coefficients compared with a previous scheme (Lekien and Marsden, 2005 [1]). This method was accurate for the vast majority of the spectrometer volume, though special fits and representations were needed to improve the accuracy close to the magnet coils and along the toroidal axis.

a Cell Vertex Algorithm for the Incompressible Navier-Stokes Equations on Non-Orthogonal Grids

NASA Astrophysics Data System (ADS)

Jessee, J. P.; Fiveland, W. A.

1996-08-01

The steady, incompressible Navier-Stokes (N-S) equations are discretized using a cell vertex, finite volume method. Quadrilateral and hexahedral meshes are used to represent two- and three-dimensional geometries respectively. The dependent variables include the Cartesian components of velocity and pressure. Advective fluxes are calculated using bounded, high-resolution schemes with a deferred correction procedure to maintain a compact stencil. This treatment insures bounded, non-oscillatory solutions while maintaining low numerical diffusion. The mass and momentum equations are solved with the projection method on a non-staggered grid. The coupling of the pressure and velocity fields is achieved using the Rhie and Chow interpolation scheme modified to provide solutions independent of time steps or relaxation factors. An algebraic multigrid solver is used for the solution of the implicit, linearized equations.A number of test cases are anlaysed and presented. The standard benchmark cases include a lid-driven cavity, flow through a gradual expansion and laminar flow in a three-dimensional curved duct. Predictions are compared with data, results of other workers and with predictions from a structured, cell-centred, control volume algorithm whenever applicable. Sensitivity of results to the advection differencing scheme is investigated by applying a number of higher-order flux limiters: the MINMOD, MUSCL, OSHER, CLAM and SMART schemes. As expected, studies indicate that higher-order schemes largely mitigate the diffusion effects of first-order schemes but also shown no clear preference among the higher-order schemes themselves with respect to accuracy. The effect of the deferred correction procedure on global convergence is discussed.

Ameliorating slice gaps in multislice magnetic resonance images: an interpolation scheme.

PubMed

Kashou, Nasser H; Smith, Mark A; Roberts, Cynthia J

2015-01-01

Standard two-dimension (2D) magnetic resonance imaging (MRI) clinical acquisition protocols utilize orthogonal plane images which contain slice gaps (SG). The purpose of this work is to introduce a novel interpolation method for these orthogonal plane MRI 2D datasets. Three goals can be achieved: (1) increasing the resolution based on a priori knowledge of scanning protocol, (2) ameliorating the loss of data as a result of SG and (3) reconstructing a three-dimension (3D) dataset from 2D images. MRI data was collected using a 3T GE scanner and simulated using Matlab. The procedure for validating the MRI data combination algorithm was performed using a Shepp-Logan and a Gaussian phantom in both 2D and 3D of varying matrix sizes (64-512), as well as on one MRI dataset of a human brain and on an American College of Radiology magnetic resonance accreditation phantom. The squared error and mean squared error were computed in comparing this scheme to common interpolating functions employed in MR consoles and workstations. The mean structure similarity matrix was computed in 2D as a means of qualitative image assessment. Additionally, MRI scans were used for qualitative assessment of the method. This new scheme was consistently more accurate than upsampling each orientation separately and averaging the upsampled data. An efficient new interpolation approach to resolve SG was developed. This scheme effectively fills in the missing data points by using orthogonal plane images. To date, there have been few attempts to combine the information of three MRI plane orientations using brain images. This has specific applications for clinical MRI, functional MRI, diffusion-weighted imaging/diffusion tensor imaging and MR angiography where 2D slice acquisition are used. In these cases, the 2D data can be combined using our method in order to obtain 3D volume.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne E.

2013-01-01

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

The analysis of decimation and interpolation in the linear canonical transform domain.

PubMed

Xu, Shuiqing; Chai, Yi; Hu, Youqiang; Huang, Lei; Feng, Li

2016-01-01

Decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. As the linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing, it is worthwhile and interesting to analyze the decimation and interpolation in the LCT domain. In this paper, the definition of equivalent filter in the LCT domain have been given at first. Then, by applying the definition, the direct implementation structure and polyphase networks for decimator and interpolator in the LCT domain have been proposed. Finally, the perfect reconstruction expressions for differential filters in the LCT domain have been presented as an application. The proposed theorems in this study are the bases for generalizations of the multirate signal processing in the LCT domain, which can advance the filter banks theorems in the LCT domain.

Turning Avatar into Realistic Human Expression Using Linear and Bilinear Interpolations

NASA Astrophysics Data System (ADS)

Hazim Alkawaz, Mohammed; Mohamad, Dzulkifli; Rehman, Amjad; Basori, Ahmad Hoirul

2014-06-01

The facial animation in term of 3D facial data has accurate research support of the laser scan and advance 3D tools for complex facial model production. However, the approach still lacks facial expression based on emotional condition. Though, facial skin colour is required to offers an effect of facial expression improvement, closely related to the human emotion. This paper presents innovative techniques for facial animation transformation using the facial skin colour based on linear interpolation and bilinear interpolation. The generated expressions are almost same to the genuine human expression and also enhance the facial expression of the virtual human.

Sandia Unstructured Triangle Tabular Interpolation Package v 0.1 beta

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-09-24

The software interpolates tabular data, such as for equations of state, provided on an unstructured triangular grid. In particular, interpolation occurs in a two dimensional space by looking up the triangle in which the desired evaluation point resides and then performing a linear interpolation over the n-tuples associated with the nodes of the chosen triangle. The interface to the interpolation routines allows for automated conversion of units from those tabulated to the desired output units. when multiple tables are included in a data file, new tables may be generated by on-the-fly mixing of the provided tables

Local finite element enrichment strategies for 2D contact computations and a corresponding post-processing scheme

NASA Astrophysics Data System (ADS)

Sauer, Roger A.

2013-08-01

Recently an enriched contact finite element formulation has been developed that substantially increases the accuracy of contact computations while keeping the additional numerical effort at a minimum reported by Sauer (Int J Numer Meth Eng, 87: 593-616, 2011). Two enrich-ment strategies were proposed, one based on local p-refinement using Lagrange interpolation and one based on Hermite interpolation that produces C 1-smoothness on the contact surface. Both classes, which were initially considered for the frictionless Signorini problem, are extended here to friction and contact between deformable bodies. For this, a symmetric contact formulation is used that allows the unbiased treatment of both contact partners. This paper also proposes a post-processing scheme for contact quantities like the contact pressure. The scheme, which provides a more accurate representation than the raw data, is based on an averaging procedure that is inspired by mortar formulations. The properties of the enrichment strategies and the corresponding post-processing scheme are illustrated by several numerical examples considering sliding and peeling contact in the presence of large deformations.

Interpolation schemes for peptide rearrangements.

PubMed

Bauer, Marianne S; Strodel, Birgit; Fejer, Szilard N; Koslover, Elena F; Wales, David J

2010-02-07

A variety of methods (in total seven) comprising different combinations of internal and Cartesian coordinates are tested for interpolation and alignment in connection attempts for polypeptide rearrangements. We consider Cartesian coordinates, the internal coordinates used in CHARMM, and natural internal coordinates, each of which has been interfaced to the OPTIM code and compared with the corresponding results for united-atom force fields. We show that aligning the methylene hydrogens to preserve the sign of a local dihedral angle, rather than minimizing a distance metric, provides significant improvements with respect to connection times and failures. We also demonstrate the superiority of natural coordinate methods in conjunction with internal alignment. Checking the potential energy of the interpolated structures can act as a criterion for the choice of the interpolation coordinate system, which reduces failures and connection times significantly.

Numerical Methods for Nonlinear Fokker-Planck Collision Operator in TEMPEST

NASA Astrophysics Data System (ADS)

Kerbel, G.; Xiong, Z.

2006-10-01

Early implementations of Fokker-Planck collision operator and moment computations in TEMPEST used low order polynomial interpolation schemes to reuse conservative operators developed for speed/pitch-angle (v, θ) coordinates. When this approach proved to be too inaccurate we developed an alternative higher order interpolation scheme for the Rosenbluth potentials and a high order finite volume method in TEMPEST (,) coordinates. The collision operator is thus generated by using the expansion technique in (v, θ) coordinates for the diffusion coefficients only, and then the fluxes for the conservative differencing are computed directly in the TEMPEST (,) coordinates. Combined with a cut-cell treatment at the turning-point boundary, this new approach is shown to have much better accuracy and conservation properties.

Comparison of interpolation functions to improve a rebinning-free CT-reconstruction algorithm.

PubMed

de las Heras, Hugo; Tischenko, Oleg; Xu, Yuan; Hoeschen, Christoph

2008-01-01

The robust algorithm OPED for the reconstruction of images from Radon data has been recently developed. This reconstructs an image from parallel data within a special scanning geometry that does not need rebinning but only a simple re-ordering, so that the acquired fan data can be used directly for the reconstruction. However, if the number of rays per fan view is increased, there appear empty cells in the sinogram. These cells need to be filled by interpolation before the reconstruction can be carried out. The present paper analyzes linear interpolation, cubic splines and parametric (or "damped") splines for the interpolation task. The reconstruction accuracy in the resulting images was measured by the Normalized Mean Square Error (NMSE), the Hilbert Angle, and the Mean Relative Error. The spatial resolution was measured by the Modulation Transfer Function (MTF). Cubic splines were confirmed to be the most recommendable method. The reconstructed images resulting from cubic spline interpolation show a significantly lower NMSE than the ones from linear interpolation and have the largest MTF for all frequencies. Parametric splines proved to be advantageous only for small sinograms (below 50 fan views).

C1-Continuous relative permeability and hybrid upwind discretization of three phase flow in porous media

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.

2016-10-01

Three-phase flow in a reservoir model has been a major challenge in simulation studies due to slowly convergent iterations in Newton solution of nonlinear transport equations. In this paper, we examine the numerical characteristics of three-phase flow and propose a consistent, "C1-continuous discretization" (to be clarified later) of transport equations that ensures a convergent solution in finite difference approximation. First, we examine three-phase relative permeabilities that are critical in solving nonlinear transport equations. Three-phase relative permeabilities are difficult to measure in the laboratory, and they are often correlated with two-phase relative permeabilities (e.g., oil-gas and water-oil systems). Numerical convergence of non-linear transport equations entails that three-phase relative permeability correlations are a monotonically increasing function of the phase saturation and the consistency conditions of phase transitions are satisfied. The Modified Stone's Method II and the Linear Interpolation Method for three-phase relative permeability are closely examined for their mathematical properties. We show that the Linear Interpolation Method yields C1-continuous three-phase relative permeabilities for smooth solutions if the two phase relative permeabilities are monotonic and continuously differentiable. In the second part of the paper, we extend a Hybrid-Upwinding (HU) method of two-phase flow (Lee, Efendiev and Tchelepi, ADWR 82 (2015) 27-38) to three phase flow. In the HU method, the phase flux is divided into two parts based on the driving forces (in general, it can be divided into several parts): viscous and buoyancy. The viscous-driven and buoyancy-driven fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total velocity. The pure buoyancy-induced flux is shown to be only dependent on saturation distributions and counter-current. In three-phase flow, the buoyancy effect can be expressed as a sum of two buoyancy effects from two-phase flows, i.e., oil-water and oil-gas systems. We propose an upwind scheme for the buoyancy flux term from three-phase flow as a sum of two buoyancy terms from two-phase flows. The upwind direction of the buoyancy flux in two phase flow is always fixed such that the heavier fluid goes downward and the lighter fluid goes upward. It is shown that the Implicit Hybrid-Upwinding (IHU) scheme for three-phase flow is locally conservative and produces physically-consistent numerical solutions. As in two phase flow, the primary advantage of the IHU scheme is that the flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions as a function of time, or (Newton) iterations. This is in contrast to the standard phase-potential-based upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the transition between co-current and counter-current flows.

Computer program documentation for a subcritical wing design code using higher order far-field drag minimization

NASA Technical Reports Server (NTRS)

Kuhlman, J. M.; Shu, J. Y.

1981-01-01

A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).

An adaptive interpolation scheme for molecular potential energy surfaces

NASA Astrophysics Data System (ADS)

Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa

2016-08-01

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.

Spatiotemporal Interpolation Methods for Solar Event Trajectories

NASA Astrophysics Data System (ADS)

Filali Boubrahimi, Soukaina; Aydin, Berkay; Schuh, Michael A.; Kempton, Dustin; Angryk, Rafal A.; Ma, Ruizhe

2018-05-01

This paper introduces four spatiotemporal interpolation methods that enrich complex, evolving region trajectories that are reported from a variety of ground-based and space-based solar observatories every day. Our interpolation module takes an existing solar event trajectory as its input and generates an enriched trajectory with any number of additional time–geometry pairs created by the most appropriate method. To this end, we designed four different interpolation techniques: MBR-Interpolation (Minimum Bounding Rectangle Interpolation), CP-Interpolation (Complex Polygon Interpolation), FI-Interpolation (Filament Polygon Interpolation), and Areal-Interpolation, which are presented here in detail. These techniques leverage k-means clustering, centroid shape signature representation, dynamic time warping, linear interpolation, and shape buffering to generate the additional polygons of an enriched trajectory. Using ground-truth objects, interpolation effectiveness is evaluated through a variety of measures based on several important characteristics that include spatial distance, area overlap, and shape (boundary) similarity. To our knowledge, this is the first research effort of this kind that attempts to address the broad problem of spatiotemporal interpolation of solar event trajectories. We conclude with a brief outline of future research directions and opportunities for related work in this area.

Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales

NASA Astrophysics Data System (ADS)

Cuzzone, Joshua K.; Morlighem, Mathieu; Larour, Eric; Schlegel, Nicole; Seroussi, Helene

2018-05-01

Paleoclimate proxies are being used in conjunction with ice sheet modeling experiments to determine how the Greenland ice sheet responded to past changes, particularly during the last deglaciation. Although these comparisons have been a critical component in our understanding of the Greenland ice sheet sensitivity to past warming, they often rely on modeling experiments that favor minimizing computational expense over increased model physics. Over Paleoclimate timescales, simulating the thermal structure of the ice sheet has large implications on the modeled ice viscosity, which can feedback onto the basal sliding and ice flow. To accurately capture the thermal field, models often require a high number of vertical layers. This is not the case for the stress balance computation, however, where a high vertical resolution is not necessary. Consequently, since stress balance and thermal equations are generally performed on the same mesh, more time is spent on the stress balance computation than is otherwise necessary. For these reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn) over timescales equivalent to the paleoclimate record has not been possible without incurring a large computational expense. To mitigate this issue, we propose a method that can be implemented within ice sheet models, whereby the vertical interpolation along the z axis relies on higher-order polynomials, rather than the traditional linear interpolation. This method is tested within the Ice Sheet System Model (ISSM) using quadratic and cubic finite elements for the vertical interpolation on an idealized case and a realistic Greenland configuration. A transient experiment for the ice thickness evolution of a single-dome ice sheet demonstrates improved accuracy using the higher-order vertical interpolation compared to models using the linear vertical interpolation, despite having fewer degrees of freedom. This method is also shown to improve a model's ability to capture sharp thermal gradients in an ice sheet particularly close to the bed, when compared to models using a linear vertical interpolation. This is corroborated in a thermal steady-state simulation of the Greenland ice sheet using a higher-order model. In general, we find that using a higher-order vertical interpolation decreases the need for a high number of vertical layers, while dramatically reducing model runtime for transient simulations. Results indicate that when using a higher-order vertical interpolation, runtimes for a transient ice sheet relaxation are upwards of 5 to 7 times faster than using a model which has a linear vertical interpolation, and this thus requires a higher number of vertical layers to achieve a similar result in simulated ice volume, basal temperature, and ice divide thickness. The findings suggest that this method will allow higher-order models to be used in studies investigating ice sheet behavior over paleoclimate timescales at a fraction of the computational cost than would otherwise be needed for a model using a linear vertical interpolation.

Investigations of interpolation errors of angle encoders for high precision angle metrology

NASA Astrophysics Data System (ADS)

Yandayan, Tanfer; Geckeler, Ralf D.; Just, Andreas; Krause, Michael; Asli Akgoz, S.; Aksulu, Murat; Grubert, Bernd; Watanabe, Tsukasa

2018-06-01

Interpolation errors at small angular scales are caused by the subdivision of the angular interval between adjacent grating lines into smaller intervals when radial gratings are used in angle encoders. They are often a major error source in precision angle metrology and better approaches for determining them at low levels of uncertainty are needed. Extensive investigations of interpolation errors of different angle encoders with various interpolators and interpolation schemes were carried out by adapting the shearing method to the calibration of autocollimators with angle encoders. The results of the laboratories with advanced angle metrology capabilities are presented which were acquired by the use of four different high precision angle encoders/interpolators/rotary tables. State of the art uncertainties down to 1 milliarcsec (5 nrad) were achieved for the determination of the interpolation errors using the shearing method which provides simultaneous access to the angle deviations of the autocollimator and of the angle encoder. Compared to the calibration and measurement capabilities (CMC) of the participants for autocollimators, the use of the shearing technique represents a substantial improvement in the uncertainty by a factor of up to 5 in addition to the precise determination of interpolation errors or their residuals (when compensated). A discussion of the results is carried out in conjunction with the equipment used.

Quantum realization of the nearest neighbor value interpolation method for INEQR

NASA Astrophysics Data System (ADS)

Zhou, RiGui; Hu, WenWen; Luo, GaoFeng; Liu, XingAo; Fan, Ping

2018-07-01

This paper presents the nearest neighbor value (NNV) interpolation algorithm for the improved novel enhanced quantum representation of digital images (INEQR). It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The difference between the proposed scheme and nearest neighbor interpolation is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. Firstly, a sequence of quantum operations is predefined, such as cyclic shift transformations and the basic arithmetic operations. Then, the feasibility of the nearest neighbor value interpolation method for quantum image of INEQR is proven using the previously designed quantum operations. Furthermore, quantum image scaling algorithm in the form of circuits of the NNV interpolation for INEQR is constructed for the first time. The merit of the proposed INEQR circuit lies in their low complexity, which is achieved by utilizing the unique properties of quantum superposition and entanglement. Finally, simulation-based experimental results involving different classical images and ratios (i.e., conventional or non-quantum) are simulated based on the classical computer's MATLAB 2014b software, which demonstrates that the proposed interpolation method has higher performances in terms of high resolution compared to the nearest neighbor and bilinear interpolation.

Reducing Interpolation Artifacts for Mutual Information Based Image Registration

PubMed Central

Soleimani, H.; Khosravifard, M.A.

2011-01-01

Medical image registration methods which use mutual information as similarity measure have been improved in recent decades. Mutual Information is a basic concept of Information theory which indicates the dependency of two random variables (or two images). In order to evaluate the mutual information of two images their joint probability distribution is required. Several interpolation methods, such as Partial Volume (PV) and bilinear, are used to estimate joint probability distribution. Both of these two methods yield some artifacts on mutual information function. Partial Volume-Hanning window (PVH) and Generalized Partial Volume (GPV) methods are introduced to remove such artifacts. In this paper we show that the acceptable performance of these methods is not due to their kernel function. It's because of the number of pixels which incorporate in interpolation. Since using more pixels requires more complex and time consuming interpolation process, we propose a new interpolation method which uses only four pixels (the same as PV and bilinear interpolations) and removes most of the artifacts. Experimental results of the registration of Computed Tomography (CT) images show superiority of the proposed scheme. PMID:22606673

A novel interpolation approach for the generation of 3D-geometric digital bone models from image stacks

PubMed Central

Mittag, U.; Kriechbaumer, A.; Rittweger, J.

2017-01-01

The authors propose a new 3D interpolation algorithm for the generation of digital geometric 3D-models of bones from existing image stacks obtained by peripheral Quantitative Computed Tomography (pQCT) or Magnetic Resonance Imaging (MRI). The technique is based on the interpolation of radial gray value profiles of the pQCT cross sections. The method has been validated by using an ex-vivo human tibia and by comparing interpolated pQCT images with images from scans taken at the same position. A diversity index of <0.4 (1 meaning maximal diversity) even for the structurally complex region of the epiphysis, along with the good agreement of mineral-density-weighted cross-sectional moment of inertia (CSMI), demonstrate the high quality of our interpolation approach. Thus the authors demonstrate that this interpolation scheme can substantially improve the generation of 3D models from sparse scan sets, not only with respect to the outer shape but also with respect to the internal gray-value derived material property distribution. PMID:28574415

Regionalizing nonparametric models of precipitation amounts on different temporal scales

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András

2017-05-01

Parametric distribution functions are commonly used to model precipitation amounts corresponding to different durations. The precipitation amounts themselves are crucial for stochastic rainfall generators and weather generators. Nonparametric kernel density estimates (KDEs) offer a more flexible way to model precipitation amounts. As already stated in their name, these models do not exhibit parameters that can be easily regionalized to run rainfall generators at ungauged locations as well as at gauged locations. To overcome this deficiency, we present a new interpolation scheme for nonparametric models and evaluate it for different temporal resolutions ranging from hourly to monthly. During the evaluation, the nonparametric methods are compared to commonly used parametric models like the two-parameter gamma and the mixed-exponential distribution. As water volume is considered to be an essential parameter for applications like flood modeling, a Lorenz-curve-based criterion is also introduced. To add value to the estimation of data at sub-daily resolutions, we incorporated the plentiful daily measurements in the interpolation scheme, and this idea was evaluated. The study region is the federal state of Baden-Württemberg in the southwest of Germany with more than 500 rain gauges. The validation results show that the newly proposed nonparametric interpolation scheme provides reasonable results and that the incorporation of daily values in the regionalization of sub-daily models is very beneficial.

A characteristics-based method for solving the transport equation and its application to the process of mantle differentiation and continental root growth

NASA Astrophysics Data System (ADS)

de Smet, Jeroen H.; van den Berg, Arie P.; Vlaar, Nico J.; Yuen, David A.

2000-03-01

Purely advective transport of composition is of major importance in the Geosciences, and efficient and accurate solution methods are needed. A characteristics-based method is used to solve the transport equation. We employ a new hybrid interpolation scheme, which allows for the tuning of stability and accuracy through a threshold parameter ɛth. Stability is established by bilinear interpolations, and bicubic splines are used to maintain accuracy. With this scheme, numerical instabilities can be suppressed by allowing numerical diffusion to work in time and locally in space. The scheme can be applied efficiently for preliminary modelling purposes. This can be followed by detailed high-resolution experiments. First, the principal effects of this hybrid interpolation method are illustrated and some tests are presented for numerical solutions of the transport equation. Second, we illustrate that this approach works successfully for a previously developed continental evolution model for the convecting upper mantle. In this model the transport equation contains a source term, which describes the melt production in pressure-released partial melting. In this model, a characteristic phenomenon of small-scale melting diapirs is observed (De Smet et al.1998; De Smet et al. 1999). High-resolution experiments with grid cells down to 700m horizontally and 515m vertically result in highly detailed observations of the diapiric melting phenomenon.

Surface reconstruction and deformation monitoring of stratospheric airship based on laser scanning technology

NASA Astrophysics Data System (ADS)

Guo, Kai; Xie, Yongjie; Ye, Hu; Zhang, Song; Li, Yunfei

2018-04-01

Due to the uncertainty of stratospheric airship's shape and the security problem caused by the uncertainty, surface reconstruction and surface deformation monitoring of airship was conducted based on laser scanning technology and a √3-subdivision scheme based on Shepard interpolation was developed. Then, comparison was conducted between our subdivision scheme and the original √3-subdivision scheme. The result shows our subdivision scheme could reduce the shrinkage of surface and the number of narrow triangles. In addition, our subdivision scheme could keep the sharp features. So, surface reconstruction and surface deformation monitoring of airship could be conducted precisely by our subdivision scheme.

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.; Simms, R. M.

2018-04-01

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

Generalized Reduced Order Modeling of Aeroservoelastic Systems

NASA Astrophysics Data System (ADS)

Gariffo, James Michael

Transonic aeroelastic and aeroservoelastic (ASE) modeling presents a significant technical and computational challenge. Flow fields with a mixture of subsonic and supersonic flow, as well as moving shock waves, can only be captured through high-fidelity CFD analysis. With modern computing power, it is realtively straightforward to determine the flutter boundary for a single structural configuration at a single flight condition, but problems of larger scope remain quite costly. Some such problems include characterizing a vehicle's flutter boundary over its full flight envelope, optimizing its structural weight subject to aeroelastic constraints, and designing control laws for flutter suppression. For all of these applications, reduced-order models (ROMs) offer substantial computational savings. ROM techniques in general have existed for decades, and the methodology presented in this dissertation builds on successful previous techniques to create a powerful new scheme for modeling aeroelastic systems, and predicting and interpolating their transonic flutter boundaries. In this method, linear ASE state-space models are constructed from modal structural and actuator models coupled to state-space models of the linearized aerodynamic forces through feedback loops. Flutter predictions can be made from these models through simple eigenvalue analysis of their state-transition matrices for an appropriate set of dynamic pressures. Moreover, this analysis returns the frequency and damping trend of every aeroelastic branch. In contrast, determining the critical dynamic pressure by direct time-marching CFD requires a separate run for every dynamic pressure being analyzed simply to obtain the trend for the critical branch. The present ROM methodology also includes a new model interpolation technique that greatly enhances the benefits of these ROMs. This enables predictions of the dynamic behavior of the system for flight conditions where CFD analysis has not been explicitly performed, thus making it possible to characterize the overall flutter boundary with far fewer CFD runs. A major challenge of this research is that transonic flutter boundaries can involve multiple unstable modes of different types. Multiple ROM-based studies on the ONERA M6 wing are shown indicating that in addition to classic bending-torsion (BT) flutter modes. which become unstable above a threshold dynamic pressure after two natural modes become aerodynamically coupled, some natural modes are able to extract energy from the air and become unstable by themselves. These single-mode instabilities tend to be weaker than the BT instabilities, but have near-zero flutter boundaries (exactly zero in the absence of structural damping). Examples of hump modes, which behave like natural mode instabilities before stabilizing, are also shown, as are cases where multiple instabilities coexist at a single flight condition. The result of all these instabilities is a highly sensitive flutter boundary, where small changes in Mach number, structural stiffness, and structural damping can substantially alter not only the stability of individual aeroelastic branches, but also which branch is critical. Several studies are shown presenting how the flutter boundary varies with respect to all three of these parameters, as well as the number of structural modes used to construct the ROMs. Finally, an investigation of the effectiveness and limitations of the interpolation scheme is presented. It is found that in regions where the flutter boundary is relatively smooth, the interpolation method produces ROMs that predict the flutter characteristics of the corresponding directly computed models to a high degree of accuracy, even for relatively coarsely spaced data. On the other hand, in the transonic dip region, the interpolated ROMs show significant errors at points where the boundary changes rapidly; however, they still give a good qualitative estimate of where the largest jumps occur.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2013-08-01

We propose a 1D analytical particle mover for the recent charge- and energy-conserving electrostatic particle-in-cell (PIC) algorithm in Ref. [G. Chen, L. Chacón, D.C. Barnes, An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm, Journal of Computational Physics 230 (2011) 7018-7036]. The approach computes particle orbits exactly for a given piece-wise linear electric field. The resulting PIC algorithm maintains the exact charge and energy conservation properties of the original algorithm, but with improved performance (both in efficiency and robustness against the number of particles and timestep). We demonstrate the advantageous properties of the scheme with a challenging multiscale numerical test case, the ion acoustic wave. Using the analytical mover as a reference, we demonstrate that the choice of error estimator in the Crank-Nicolson mover has significant impact on the overall performance of the implicit PIC algorithm. The generalization of the approach to the multi-dimensional case is outlined, based on a novel and simple charge conserving interpolation scheme.

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

NASA Technical Reports Server (NTRS)

Chang, T. S.

1974-01-01

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

The first ANDES elements: 9-DOF plate bending triangles

NASA Technical Reports Server (NTRS)

Militello, Carmelo; Felippa, Carlos A.

1991-01-01

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Computational aeroelasticity using a pressure-based solver

NASA Astrophysics Data System (ADS)

Kamakoti, Ramji

A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.

Probabilistic surface reconstruction from multiple data sets: An example for the Australian Moho

NASA Astrophysics Data System (ADS)

Bodin, T.; Salmon, M.; Kennett, B. L. N.; Sambridge, M.

2012-10-01

Interpolation of spatial data is a widely used technique across the Earth sciences. For example, the thickness of the crust can be estimated by different active and passive seismic source surveys, and seismologists reconstruct the topography of the Moho by interpolating these different estimates. Although much research has been done on improving the quantity and quality of observations, the interpolation algorithms utilized often remain standard linear regression schemes, with three main weaknesses: (1) the level of structure in the surface, or smoothness, has to be predefined by the user; (2) different classes of measurements with varying and often poorly constrained uncertainties are used together, and hence it is difficult to give appropriate weight to different data types with standard algorithms; (3) there is typically no simple way to propagate uncertainties in the data to uncertainty in the estimated surface. Hence the situation can be expressed by Mackenzie (2004): "We use fantastic telescopes, the best physical models, and the best computers. The weak link in this chain is interpreting our data using 100 year old mathematics". Here we use recent developments made in Bayesian statistics and apply them to the problem of surface reconstruction. We show how the reversible jump Markov chain Monte Carlo (rj-McMC) algorithm can be used to let the degree of structure in the surface be directly determined by the data. The solution is described in probabilistic terms, allowing uncertainties to be fully accounted for. The method is illustrated with an application to Moho depth reconstruction in Australia.

An adaptive interpolation scheme for molecular potential energy surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kowalewski, Markus, E-mail: mkowalew@uci.edu; Larsson, Elisabeth; Heryudono, Alfa

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within amore » given accuracy compared to the non-adaptive version.« less

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

Restoring the missing features of the corrupted speech using linear interpolation methods

NASA Astrophysics Data System (ADS)

Rassem, Taha H.; Makbol, Nasrin M.; Hasan, Ali Muttaleb; Zaki, Siti Syazni Mohd; Girija, P. N.

2017-10-01

One of the main challenges in the Automatic Speech Recognition (ASR) is the noise. The performance of the ASR system reduces significantly if the speech is corrupted by noise. In spectrogram representation of a speech signal, after deleting low Signal to Noise Ratio (SNR) elements, the incomplete spectrogram is obtained. In this case, the speech recognizer should make modifications to the spectrogram in order to restore the missing elements, which is one direction. In another direction, speech recognizer should be able to restore the missing elements due to deleting low SNR elements before performing the recognition. This is can be done using different spectrogram reconstruction methods. In this paper, the geometrical spectrogram reconstruction methods suggested by some researchers are implemented as a toolbox. In these geometrical reconstruction methods, the linear interpolation along time or frequency methods are used to predict the missing elements between adjacent observed elements in the spectrogram. Moreover, a new linear interpolation method using time and frequency together is presented. The CMU Sphinx III software is used in the experiments to test the performance of the linear interpolation reconstruction method. The experiments are done under different conditions such as different lengths of the window and different lengths of utterances. Speech corpus consists of 20 males and 20 females; each one has two different utterances are used in the experiments. As a result, 80% recognition accuracy is achieved with 25% SNR ratio.

Effect of interpolation on parameters extracted from seating interface pressure arrays.

PubMed

Wininger, Michael; Crane, Barbara

2014-01-01

Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pressure array data and compared against a conventional low-pass filtering operation. Additionally, analysis of the effect of tandem filtering and interpolation, as well as the interpolation degree (interpolating to 2, 4, and 8 times sampling density), was undertaken. The following recommendations are made regarding approaches that minimized distortion of features extracted from the pressure maps: (1) filter prior to interpolate (strong effect); (2) use of cubic interpolation versus linear (slight effect); and (3) nominal difference between interpolation orders of 2, 4, and 8 times (negligible effect). We invite other investigators to perform similar benchmark analyses on their own data in the interest of establishing a community consensus of best practices in pressure array data processing.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Py-SPHViewer: Cosmological simulations using Smoothed Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Benítez-Llambay, Alejandro

2017-12-01

Py-SPHViewer visualizes and explores N-body + Hydrodynamics simulations. The code interpolates the underlying density field (or any other property) traced by a set of particles, using the Smoothed Particle Hydrodynamics (SPH) interpolation scheme, thus producing not only beautiful but also useful scientific images. Py-SPHViewer enables the user to explore simulated volumes using different projections. Py-SPHViewer also provides a natural way to visualize (in a self-consistent fashion) gas dynamical simulations, which use the same technique to compute the interactions between particles.

Registration-based interpolation applied to cardiac MRI

NASA Astrophysics Data System (ADS)

Ólafsdóttir, Hildur; Pedersen, Henrik; Hansen, Michael S.; Lyksborg, Mark; Hansen, Mads Fogtmann; Darkner, Sune; Larsen, Rasmus

2010-03-01

Various approaches have been proposed for segmentation of cardiac MRI. An accurate segmentation of the myocardium and ventricles is essential to determine parameters of interest for the function of the heart, such as the ejection fraction. One problem with MRI is the poor resolution in one dimension. A 3D registration algorithm will typically use a trilinear interpolation of intensities to determine the intensity of a deformed template image. Due to the poor resolution across slices, such linear approximation is highly inaccurate since the assumption of smooth underlying intensities is violated. Registration-based interpolation is based on 2D registrations between adjacent slices and is independent of segmentations. Hence, rather than assuming smoothness in intensity, the assumption is that the anatomy is consistent across slices. The basis for the proposed approach is the set of 2D registrations between each pair of slices, both ways. The intensity of a new slice is then weighted by (i) the deformation functions and (ii) the intensities in the warped images. Unlike the approach by Penney et al. 2004, this approach takes into account deformation both ways, which gives more robustness where correspondence between slices is poor. We demonstrate the approach on a toy example and on a set of cardiac CINE MRI. Qualitative inspection reveals that the proposed approach provides a more convincing transition between slices than images obtained by linear interpolation. A quantitative validation reveals significantly lower reconstruction errors than both linear and registration-based interpolation based on one-way registrations.

Detection and correction of laser induced breakdown spectroscopy spectral background based on spline interpolation method

NASA Astrophysics Data System (ADS)

Tan, Bing; Huang, Min; Zhu, Qibing; Guo, Ya; Qin, Jianwei

2017-12-01

Laser-induced breakdown spectroscopy (LIBS) is an analytical technique that has gained increasing attention because of many applications. The production of continuous background in LIBS is inevitable because of factors associated with laser energy, gate width, time delay, and experimental environment. The continuous background significantly influences the analysis of the spectrum. Researchers have proposed several background correction methods, such as polynomial fitting, Lorenz fitting and model-free methods. However, less of them apply these methods in the field of LIBS Technology, particularly in qualitative and quantitative analyses. This study proposes a method based on spline interpolation for detecting and estimating the continuous background spectrum according to its smooth property characteristic. Experiment on the background correction simulation indicated that, the spline interpolation method acquired the largest signal-to-background ratio (SBR) over polynomial fitting, Lorenz fitting and model-free method after background correction. These background correction methods all acquire larger SBR values than that acquired before background correction (The SBR value before background correction is 10.0992, whereas the SBR values after background correction by spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 26.9576, 24.6828, 18.9770, and 25.6273 respectively). After adding random noise with different kinds of signal-to-noise ratio to the spectrum, spline interpolation method acquires large SBR value, whereas polynomial fitting and model-free method obtain low SBR values. All of the background correction methods exhibit improved quantitative results of Cu than those acquired before background correction (The linear correlation coefficient value before background correction is 0.9776. Moreover, the linear correlation coefficient values after background correction using spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 0.9998, 0.9915, 0.9895, and 0.9940 respectively). The proposed spline interpolation method exhibits better linear correlation and smaller error in the results of the quantitative analysis of Cu compared with polynomial fitting, Lorentz fitting and model-free methods, The simulation and quantitative experimental results show that the spline interpolation method can effectively detect and correct the continuous background.

On the Problem of Deformed Spherical Systems in Modified Newtonian Dynamics

NASA Astrophysics Data System (ADS)

Ko, Chung-Ming

2016-04-01

Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equation, which is difficult to analyze for arbitrary matter distributions. We study the MONDian gravitational field generated by slightly non-spherically symmetric mass distributions based on the fact that both Newtonian and MONDian fields are conservative (which we refer to as the compatibility condition). As the non-relativistic version of MOND has two different formulations (AQUAL and QuMOND) and the compatibility condition can be expressed in two ways, there are four approaches to the problem in total. The method involves solving a suitably defined linear deformation potential, which generally depends on the choice of MOND interpolation function. However, for some specific form of the deformation potential, the solution is independent of the interpolation function.

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

PubMed

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Adaptive image coding based on cubic-spline interpolation

NASA Astrophysics Data System (ADS)

Jiang, Jian-Xing; Hong, Shao-Hua; Lin, Tsung-Ching; Wang, Lin; Truong, Trieu-Kien

2014-09-01

It has been investigated that at low bit rates, downsampling prior to coding and upsampling after decoding can achieve better compression performance than standard coding algorithms, e.g., JPEG and H. 264/AVC. However, at high bit rates, the sampling-based schemes generate more distortion. Additionally, the maximum bit rate for the sampling-based scheme to outperform the standard algorithm is image-dependent. In this paper, a practical adaptive image coding algorithm based on the cubic-spline interpolation (CSI) is proposed. This proposed algorithm adaptively selects the image coding method from CSI-based modified JPEG and standard JPEG under a given target bit rate utilizing the so called ρ-domain analysis. The experimental results indicate that compared with the standard JPEG, the proposed algorithm can show better performance at low bit rates and maintain the same performance at high bit rates.

A practical implementation of wave front construction for 3-D isotropic media

NASA Astrophysics Data System (ADS)

Chambers, K.; Kendall, J.-M.

2008-06-01

Wave front construction (WFC) methods are a useful tool for tracking wave fronts and are a natural extension to standard ray shooting methods. Here we describe and implement a simple WFC method that is used to interpolate wavefield properties throughout a 3-D heterogeneous medium. Our approach differs from previous 3-D WFC procedures primarily in the use of a ray interpolation scheme, based on approximating the wave front as a `locally spherical' surface and a `first arrival mode', which reduces computation times, where only first arrivals are required. Both of these features have previously been included in 2-D WFC algorithms; however, until now they have not been extended to 3-D systems. The wave front interpolation scheme allows for rays to be traced from a nearly arbitrary distribution of take-off angles, and the calculation of derivatives with respect to take-off angles is not required for wave front interpolation. However, in regions of steep velocity gradient, the locally spherical approximation is not valid, and it is necessary to backpropagate rays to a sufficiently homogenous region before interpolation of the new ray. Our WFC technique is illustrated using a realistic velocity model, based on a North Sea oil reservoir. We examine wavefield quantities such as traveltimes, ray angles, source take-off angles and geometrical spreading factors, all of which are interpolated on to a regular grid. We compare geometrical spreading factors calculated using two methods: using the ray Jacobian and by taking the ratio of a triangular area of wave front to the corresponding solid angle at the source. The results show that care must be taken when using ray Jacobians to calculate geometrical spreading factors, as the poles of the source coordinate system produce unreliable values, which can be spread over a large area, as only a few initial rays are traced in WFC. We also show that the use of the first arrival mode can reduce computation time by ~65 per cent, with the accuracy of the interpolated traveltimes, ray angles and source take-off angles largely unchanged. However, the first arrival mode does lead to inaccuracies in interpolated angles near caustic surfaces, as well as small variations in geometrical spreading factors for ray tubes that have passed through caustic surfaces.

On-chip frame memory reduction using a high-compression-ratio codec in the overdrives of liquid-crystal displays

NASA Astrophysics Data System (ADS)

Wang, Jun; Min, Kyeong-Yuk; Chong, Jong-Wha

2010-11-01

Overdrive is commonly used to reduce the liquid-crystal response time and motion blur in liquid-crystal displays (LCDs). However, overdrive requires a large frame memory in order to store the previous frame for reference. In this paper, a high-compression-ratio codec is presented to compress the image data stored in the on-chip frame memory so that only 1 Mbit of on-chip memory is required in the LCD overdrives of mobile devices. The proposed algorithm further compresses the color bitmaps and representative values (RVs) resulting from the block truncation coding (BTC). The color bitmaps are represented by a luminance bitmap, which is further reduced and reconstructed using median filter interpolation in the decoder, while the RVs are compressed using adaptive quantization coding (AQC). Interpolation and AQC can provide three-level compression, which leads to 16 combinations. Using a rate-distortion analysis, we select the three optimal schemes to compress the image data for video graphics array (VGA), wide-VGA LCD, and standard-definitionTV applications. Our simulation results demonstrate that the proposed schemes outperform interpolation BTC both in PSNR (by 1.479 to 2.205 dB) and in subjective visual quality.

Subcellular localization for Gram positive and Gram negative bacterial proteins using linear interpolation smoothing model.

PubMed

Saini, Harsh; Raicar, Gaurav; Dehzangi, Abdollah; Lal, Sunil; Sharma, Alok

2015-12-07

Protein subcellular localization is an important topic in proteomics since it is related to a protein׳s overall function, helps in the understanding of metabolic pathways, and in drug design and discovery. In this paper, a basic approximation technique from natural language processing called the linear interpolation smoothing model is applied for predicting protein subcellular localizations. The proposed approach extracts features from syntactical information in protein sequences to build probabilistic profiles using dependency models, which are used in linear interpolation to determine how likely is a sequence to belong to a particular subcellular location. This technique builds a statistical model based on maximum likelihood. It is able to deal effectively with high dimensionality that hinders other traditional classifiers such as Support Vector Machines or k-Nearest Neighbours without sacrificing performance. This approach has been evaluated by predicting subcellular localizations of Gram positive and Gram negative bacterial proteins. Copyright © 2015 Elsevier Ltd. All rights reserved.

Restoring method for missing data of spatial structural stress monitoring based on correlation

NASA Astrophysics Data System (ADS)

Zhang, Zeyu; Luo, Yaozhi

2017-07-01

Long-term monitoring of spatial structures is of great importance for the full understanding of their performance and safety. The missing part of the monitoring data link will affect the data analysis and safety assessment of the structure. Based on the long-term monitoring data of the steel structure of the Hangzhou Olympic Center Stadium, the correlation between the stress change of the measuring points is studied, and an interpolation method of the missing stress data is proposed. Stress data of correlated measuring points are selected in the 3 months of the season when missing data is required for fitting correlation. Data of daytime and nighttime are fitted separately for interpolation. For a simple linear regression when single point's correlation coefficient is 0.9 or more, the average error of interpolation is about 5%. For multiple linear regression, the interpolation accuracy is not significantly increased after the number of correlated points is more than 6. Stress baseline value of construction step should be calculated before interpolating missing data in the construction stage, and the average error is within 10%. The interpolation error of continuous missing data is slightly larger than that of the discrete missing data. The data missing rate of this method should better not exceed 30%. Finally, a measuring point's missing monitoring data is restored to verify the validity of the method.

Grid adaption using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Grid adaptation using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Enhancement of panoramic image resolution based on swift interpolation of Bezier surface

NASA Astrophysics Data System (ADS)

Xiao, Xiao; Yang, Guo-guang; Bai, Jian

2007-01-01

Panoramic annular lens project the view of the entire 360 degrees around the optical axis onto an annular plane based on the way of flat cylinder perspective. Due to the infinite depth of field and the linear mapping relationship between an object and an image, the panoramic imaging system plays important roles in the applications of robot vision, surveillance and virtual reality. An annular image needs to be unwrapped to conventional rectangular image without distortion, in which interpolation algorithm is necessary. Although cubic splines interpolation can enhance the resolution of unwrapped image, it occupies too much time to be applied in practices. This paper adopts interpolation method based on Bezier surface and proposes a swift interpolation algorithm for panoramic image, considering the characteristic of panoramic image. The result indicates that the resolution of the image is well enhanced compared with the image by cubic splines and bilinear interpolation. Meanwhile the time consumed is shortened up by 78% than the time consumed cubic interpolation.

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

NASA Astrophysics Data System (ADS)

Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

2018-04-01

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual artifact banding phenomenon unlike the proposed method and USRM. In all, the proposed permeability and porosity fields generation coupled with the numerical simulator developed will aid in developing efficient mobility control schemes to improve on poor volumetric sweep efficiency in porous media.

Interpolation algorithm for asynchronous ADC-data

NASA Astrophysics Data System (ADS)

Bramburger, Stefan; Zinke, Benny; Killat, Dirk

2017-09-01

This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT) algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.

Multivariate optimum interpolation of surface pressure and winds over oceans

NASA Technical Reports Server (NTRS)

Bloom, S. C.

1984-01-01

The observations of surface pressure are quite sparse over oceanic areas. An effort to improve the analysis of surface pressure over oceans through the development of a multivariate surface analysis scheme which makes use of surface pressure and wind data is discussed. Although the present research used ship winds, future versions of this analysis scheme could utilize winds from additional sources, such as satellite scatterometer data.

Development of Three-Dimensional DRAGON Grid Technology

NASA Technical Reports Server (NTRS)

Zheng, Yao; Kiou, Meng-Sing; Civinskas, Kestutis C.

1999-01-01

For a typical three dimensional flow in a practical engineering device, the time spent in grid generation can take 70 percent of the total analysis effort, resulting in a serious bottleneck in the design/analysis cycle. The present research attempts to develop a procedure that can considerably reduce the grid generation effort. The DRAGON grid, as a hybrid grid, is created by means of a Direct Replacement of Arbitrary Grid Overlapping by Nonstructured grid. The DRAGON grid scheme is an adaptation to the Chimera thinking. The Chimera grid is a composite structured grid, composing a set of overlapped structured grids, which are independently generated and body-fitted. The grid is of high quality and amenable for efficient solution schemes. However, the interpolation used in the overlapped region between grids introduces error, especially when a sharp-gradient region is encountered. The DRAGON grid scheme is capable of completely eliminating the interpolation and preserving the conservation property. It maximizes the advantages of the Chimera scheme and adapts the strengths of the unstructured and while at the same time keeping its weaknesses minimal. In the present paper, we describe the progress towards extending the DRAGON grid technology into three dimensions. Essential and programming aspects of the extension, and new challenges for the three-dimensional cases, are addressed.

Development of the general interpolants method for the CYBER 200 series of supercomputers

NASA Technical Reports Server (NTRS)

Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.

1988-01-01

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

An Energy Decaying Scheme for Nonlinear Dynamics of Shells

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

a Study of Multiplexing Schemes for Voice and Data.

NASA Astrophysics Data System (ADS)

Sriram, Kotikalapudi

Voice traffic variations are characterized by on/off transitions of voice calls, and talkspurt/silence transitions of speakers in conversations. A speaker is known to be in silence for more than half the time during a telephone conversation. In this dissertation, we study some schemes which exploit speaker silences for an efficient utilization of the transmission capacity in integrated voice/data multiplexing and in digital speech interpolation. We study two voice/data multiplexing schemes. In each scheme, any time slots momentarily unutilized by the voice traffic are made available to data. In the first scheme, the multiplexer does not use speech activity detectors (SAD), and hence the voice traffic variations are due to call on/off only. In the second scheme, the multiplexer detects speaker silences using SAD and transmits voice only during talkspurts. The multiplexer with SAD performs digital speech interpolation (DSI) as well as dynamic channel allocation to voice and data. The performance of the two schemes is evaluated using discrete-time modeling and analysis. The data delay performance for the case of English speech is compared with that for the case of Japanese speech. A closed form expression for the mean data message delay is derived for the single-channel single-talker case. In a DSI system, occasional speech losses occur whenever the number of speakers in simultaneous talkspurt exceeds the number of TDM voice channels. In a buffered DSI system, speech loss is further reduced at the cost of delay. We propose a novel fixed-delay buffered DSI scheme. In this scheme, speech fill-in/hangover is not required because there are no variable delays. Hence, all silences that naturally occur in speech are fully utilized. Consequently, a substantial improvement in the DSI performance is made possible. The scheme is modeled and analyzed in discrete -time. Its performance is evaluated in terms of the probability of speech clipping, packet rejection ratio, DSI advantage, and the delay.

Bi-cubic interpolation for shift-free pan-sharpening

NASA Astrophysics Data System (ADS)

Aiazzi, Bruno; Baronti, Stefano; Selva, Massimo; Alparone, Luciano

2013-12-01

Most of pan-sharpening techniques require the re-sampling of the multi-spectral (MS) image for matching the size of the panchromatic (Pan) image, before the geometric details of Pan are injected into the MS image. This operation is usually performed in a separable fashion by means of symmetric digital low-pass filtering kernels with odd lengths that utilize piecewise local polynomials, typically implementing linear or cubic interpolation functions. Conversely, constant, i.e. nearest-neighbour, and quadratic kernels, implementing zero and two degree polynomials, respectively, introduce shifts in the magnified images, that are sub-pixel in the case of interpolation by an even factor, as it is the most usual case. However, in standard satellite systems, the point spread functions (PSF) of the MS and Pan instruments are centered in the middle of each pixel. Hence, commercial MS and Pan data products, whose scale ratio is an even number, are relatively shifted by an odd number of half pixels. Filters of even lengths may be exploited to compensate the half-pixel shifts between the MS and Pan sampling grids. In this paper, it is shown that separable polynomial interpolations of odd degrees are feasible with linear-phase kernels of even lengths. The major benefit is that bi-cubic interpolation, which is known to represent the best trade-off between performances and computational complexity, can be applied to commercial MS + Pan datasets, without the need of performing a further half-pixel registration after interpolation, to align the expanded MS with the Pan image.

Area under precision-recall curves for weighted and unweighted data.

PubMed

Keilwagen, Jens; Grosse, Ivo; Grau, Jan

2014-01-01

Precision-recall curves are highly informative about the performance of binary classifiers, and the area under these curves is a popular scalar performance measure for comparing different classifiers. However, for many applications class labels are not provided with absolute certainty, but with some degree of confidence, often reflected by weights or soft labels assigned to data points. Computing the area under the precision-recall curve requires interpolating between adjacent supporting points, but previous interpolation schemes are not directly applicable to weighted data. Hence, even in cases where weights were available, they had to be neglected for assessing classifiers using precision-recall curves. Here, we propose an interpolation for precision-recall curves that can also be used for weighted data, and we derive conditions for classification scores yielding the maximum and minimum area under the precision-recall curve. We investigate accordances and differences of the proposed interpolation and previous ones, and we demonstrate that taking into account existing weights of test data is important for the comparison of classifiers.

Area under Precision-Recall Curves for Weighted and Unweighted Data

PubMed Central

Grosse, Ivo

2014-01-01

Precision-recall curves are highly informative about the performance of binary classifiers, and the area under these curves is a popular scalar performance measure for comparing different classifiers. However, for many applications class labels are not provided with absolute certainty, but with some degree of confidence, often reflected by weights or soft labels assigned to data points. Computing the area under the precision-recall curve requires interpolating between adjacent supporting points, but previous interpolation schemes are not directly applicable to weighted data. Hence, even in cases where weights were available, they had to be neglected for assessing classifiers using precision-recall curves. Here, we propose an interpolation for precision-recall curves that can also be used for weighted data, and we derive conditions for classification scores yielding the maximum and minimum area under the precision-recall curve. We investigate accordances and differences of the proposed interpolation and previous ones, and we demonstrate that taking into account existing weights of test data is important for the comparison of classifiers. PMID:24651729

Large time-step stability of explicit one-dimensional advection schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

There is a wide-spread belief that most explicit one-dimensional advection schemes need to satisfy the so-called 'CFL condition' - that the Courant number, c = udelta(t)/delta(x), must be less than or equal to one, for stability in the von Neumann sense. This puts severe limitations on the time-step in high-speed, fine-grid calculations and is an impetus for the development of implicit schemes, which often require less restrictive time-step conditions for stability, but are more expensive per time-step. However, it turns out that, at least in one dimension, if explicit schemes are formulated in a consistent flux-based conservative finite-volume form, von Neumann stability analysis does not place any restriction on the allowable Courant number. Any explicit scheme that is stable for c is less than 1, with a complex amplitude ratio, G(c), can be easily extended to arbitrarily large c. The complex amplitude ratio is then given by exp(- (Iota)(Nu)(Theta)) G(delta(c)), where N is the integer part of c, and delta(c) = c - N (less than 1); this is clearly stable. The CFL condition is, in fact, not a stability condition at all, but, rather, a 'range restriction' on the 'pieces' in a piece-wise polynomial interpolation. When a global view is taken of the interpolation, the need for a CFL condition evaporates. A number of well-known explicit advection schemes are considered and thus extended to large delta(t). The analysis also includes a simple interpretation of (large delta(t)) total-variation-diminishing (TVD) constraints.

S-Boxes Based on Affine Mapping and Orbit of Power Function

NASA Astrophysics Data System (ADS)

Khan, Mubashar; Azam, Naveed Ahmed

2015-06-01

The demand of data security against computational attacks such as algebraic, differential, linear and interpolation attacks has been increased as a result of rapid advancement in the field of computation. It is, therefore, necessary to develop such cryptosystems which can resist current cryptanalysis and more computational attacks in future. In this paper, we present a multiple S-boxes scheme based on affine mapping and orbit of the power function used in Advanced Encryption Standard (AES). The proposed technique results in 256 different S-boxes named as orbital S-boxes. Rigorous tests and comparisons are performed to analyse the cryptographic strength of each of the orbital S-boxes. Furthermore, gray scale images are encrypted by using multiple orbital S-boxes. Results and simulations show that the encryption strength of the orbital S-boxes against computational attacks is better than that of the existing S-boxes.

Numerical simulation of aerothermal loads in hypersonic engine inlets due to shock impingement

NASA Technical Reports Server (NTRS)

Ramakrishnan, R.

1992-01-01

The effect of shock impingement on an axial corner simulating the inlet of a hypersonic vehicle engine is modeled using a finite-difference procedure. A three-dimensional dynamic grid adaptation procedure is utilized to move the grids to regions with strong flow gradients. The adaptation procedure uses a grid relocation stencil that is valid at both the interior and boundary points of the finite-difference grid. A linear combination of spatial derivatives of specific flow variables, calculated with finite-element interpolation functions, are used as adaptation measures. This computational procedure is used to study laminar and turbulent Mach 6 flows in the axial corner. The description of flow physics and qualitative measures of heat transfer distributions on cowl and strut surfaces obtained from the analysis are compared with experimental observations. Conclusions are drawn regarding the capability of the numerical scheme for enhanced modeling of high-speed compressible flows.

Automatic Tortuosity-Based Retinopathy of Prematurity Screening System

NASA Astrophysics Data System (ADS)

Sukkaew, Lassada; Uyyanonvara, Bunyarit; Makhanov, Stanislav S.; Barman, Sarah; Pangputhipong, Pannet

Retinopathy of Prematurity (ROP) is an infant disease characterized by increased dilation and tortuosity of the retinal blood vessels. Automatic tortuosity evaluation from retinal digital images is very useful to facilitate an ophthalmologist in the ROP screening and to prevent childhood blindness. This paper proposes a method to automatically classify the image into tortuous and non-tortuous. The process imitates expert ophthalmologists' screening by searching for clearly tortuous vessel segments. First, a skeleton of the retinal blood vessels is extracted from the original infant retinal image using a series of morphological operators. Next, we propose to partition the blood vessels recursively using an adaptive linear interpolation scheme. Finally, the tortuosity is calculated based on the curvature of the resulting vessel segments. The retinal images are then classified into two classes using segments characterized by the highest tortuosity. For an optimal set of training parameters the prediction is as high as 100%.

High-Speed Digital Scan Converter for High-Frequency Ultrasound Sector Scanners

PubMed Central

Chang, Jin Ho; Yen, Jesse T.; Shung, K. Kirk

2008-01-01

This paper presents a high-speed digital scan converter (DSC) capable of providing more than 400 images per second, which is necessary to examine the activities of the mouse heart whose rate is 5–10 beats per second. To achieve the desired high-speed performance in cost-effective manner, the DSC developed adopts a linear interpolation algorithm in which two nearest samples to each object pixel of a monitor are selected and only angular interpolation is performed. Through computer simulation with the Field II program, its accuracy was investigated by comparing it to that of bilinear interpolation known as the best algorithm in terms of accuracy and processing speed. The simulation results show that the linear interpolation algorithm is capable of providing an acceptable image quality, which means that the difference of the root mean square error (RMSE) values of the linear and bilinear interpolation algorithms is below 1 %, if the sample rate of the envelope samples is at least four times higher than the Nyquist rate for the baseband component of echo signals. The designed DSC was implemented with a single FPGA (Stratix EP1S60F1020C6, Altera Corporation, San Jose, CA) on a DSC board that is a part of a high-speed ultrasound imaging system developed. The temporal and spatial resolutions of the implemented DSC were evaluated by examining its maximum processing time with a time stamp indicating when an image is completely formed and wire phantom testing, respectively. The experimental results show that the implemented DSC is capable of providing images at the rate of 400 images per second with negligible processing error. PMID:18430449

Transmissivity interpolation using Fluid Flow Log data at different depth level in Liwa Aquifer, UAE.

NASA Astrophysics Data System (ADS)

Gülşen, Esra; Kurtulus, Bedri; Necati Yaylim, Tolga; Avsar, Ozgur

2017-04-01

In groundwater studies, quantification and detection of fluid flows in borehole is an important part of assessment aquifer characteristic at different depths. Monitoring wells disturbs the natural flow field and this disturbance creates different flow paths to an aquifer. Vertical flow fluid analyses are one of the important techniques to deal with the detection and quantification of these vertical flows in borehole/monitoring wells. Liwa region is located about 146 km to the south west of Abu Dhabi city and about 36 km southwest of Madinat Zayed. SWSR (Strategic Water Storage & Recovery Project) comprises three Schemes (A, B and C) and each scheme contains an infiltration basin in the center, 105 recovery wells, 10 clusters and each cluster comprises 3 monitoring wells with different depths; shallow ( 50 m), intermediate ( 75 m) and deep ( 100 m). The scope of this study is to calculate the transmissivity values at different depth and evaluate the Fluid Flow Log (FFL) data for Scheme A (105 recovery wells) in order to understand the aquifer characteristic at different depths. The transmissivity values at different depth levels are calculated using Razack and Huntley (1991) equation for vertical flow rates of 30 m3 /h, 60 m3 /h, 90 m3 /h, 120 m3 /h and then Empirical Bayesian Kriging is used for interpolation in Scheme A using ArcGIS 10.2 software. FFL are drawn by GeODin software. Derivative analysis of fluid flow data are done by Microsoft Office: Excel software. All statistical analyses are calculated by IBMSPSS software. The interpolation results show that the transmissivity values are higher at the top of the aquifer. In other word, the aquifer is found more productive at the upper part of the Liwa aquifer. We are very grateful for financial support and providing us the data to ZETAS Dubai Inc.

Model Based Predictive Control of Multivariable Hammerstein Processes with Fuzzy Logic Hypercube Interpolated Models

PubMed Central

Coelho, Antonio Augusto Rodrigues

2016-01-01

This paper introduces the Fuzzy Logic Hypercube Interpolator (FLHI) and demonstrates applications in control of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) processes with Hammerstein nonlinearities. FLHI consists of a Takagi-Sugeno fuzzy inference system where membership functions act as kernel functions of an interpolator. Conjunction of membership functions in an unitary hypercube space enables multivariable interpolation of N-dimensions. Membership functions act as interpolation kernels, such that choice of membership functions determines interpolation characteristics, allowing FLHI to behave as a nearest-neighbor, linear, cubic, spline or Lanczos interpolator, to name a few. The proposed interpolator is presented as a solution to the modeling problem of static nonlinearities since it is capable of modeling both a function and its inverse function. Three study cases from literature are presented, a single-input single-output (SISO) system, a MISO and a MIMO system. Good results are obtained regarding performance metrics such as set-point tracking, control variation and robustness. Results demonstrate applicability of the proposed method in modeling Hammerstein nonlinearities and their inverse functions for implementation of an output compensator with Model Based Predictive Control (MBPC), in particular Dynamic Matrix Control (DMC). PMID:27657723

Application of Design Methodologies for Feedback Compensation Associated with Linear Systems

NASA Technical Reports Server (NTRS)

Smith, Monty J.

1996-01-01

The work that follows is concerned with the application of design methodologies for feedback compensation associated with linear systems. In general, the intent is to provide a well behaved closed loop system in terms of stability and robustness (internal signals remain bounded with a certain amount of uncertainty) and simultaneously achieve an acceptable level of performance. The approach here has been to convert the closed loop system and control synthesis problem into the interpolation setting. The interpolation formulation then serves as our mathematical representation of the design process. Lifting techniques have been used to solve the corresponding interpolation and control synthesis problems. Several applications using this multiobjective design methodology have been included to show the effectiveness of these techniques. In particular, the mixed H 2-H performance criteria with algorithm has been used on several examples including an F-18 HARV (High Angle of Attack Research Vehicle) for sensitivity performance.

Directional sinogram interpolation for sparse angular acquisition in cone-beam computed tomography.

PubMed

Zhang, Hua; Sonke, Jan-Jakob

2013-01-01

Cone-beam (CB) computed tomography (CT) is widely used in the field of medical imaging for guidance. Inspired by Betram's directional interpolation (BDI) methods, directional sinogram interpolation (DSI) was implemented to generate more CB projections by optimized (iterative) double-orientation estimation in sinogram space and directional interpolation. A new CBCT was subsequently reconstructed with the Feldkamp algorithm using both the original and interpolated CB projections. The proposed method was evaluated on both phantom and clinical data, and image quality was assessed by correlation ratio (CR) between the interpolated image and a gold standard obtained from full measured projections. Additionally, streak artifact reduction and image blur were assessed. In a CBCT reconstructed by 40 acquired projections over an arc of 360 degree, streak artifacts dropped 20.7% and 6.7% in a thorax phantom, when our method was compared to linear interpolation (LI) and BDI methods. Meanwhile, image blur was assessed by a head-and-neck phantom, where image blur of DSI was 20.1% and 24.3% less than LI and BDI. When our method was compared to LI and DI methods, CR increased by 4.4% and 3.1%. Streak artifacts of sparsely acquired CBCT were decreased by our method and image blur induced by interpolation was constrained to below other interpolation methods.

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 2. Numerical experiments

NASA Astrophysics Data System (ADS)

Akmaev, R. a.

1999-04-01

In Part 1 of this work ([Akmaev, 1999]), an overview of the theory of optimal interpolation (OI) ([Gandin, 1963]) and related techniques of data assimilation based on linear optimal estimation ([Liebelt, 1967]; [Catlin, 1989]; [Mendel, 1995]) is presented. The approach implies the use in data analysis of additional statistical information in the form of statistical moments, e.g., the mean and covariance (correlation). The a priori statistical characteristics, if available, make it possible to constrain expected errors and obtain optimal in some sense estimates of the true state from a set of observations in a given domain in space and/or time. The primary objective of OI is to provide estimates away from the observations, i.e., to fill in data voids in the domain under consideration. Additionally, OI performs smoothing suppressing the noise, i.e., the spectral components that are presumably not present in the true signal. Usually, the criterion of optimality is minimum variance of the expected errors and the whole approach may be considered constrained least squares or least squares with a priori information. Obviously, data assimilation techniques capable of incorporating any additional information are potentially superior to techniques that have no access to such information as, for example, the conventional least squares (e.g., [Liebelt, 1967]; [Weisberg, 1985]; [Press et al., 1992]; [Mendel, 1995]).

Positivity-preserving High Order Finite Difference WENO Schemes for Compressible Euler Equations

DTIC Science & Technology

2011-07-15

the WENO reconstruction. We assume that there is a polynomial vector qi(x) = (ρi(x), mi(x), Ei(x)) T with degree k which are (k + 1)-th order accurate...i+ 1 2 = qi(xi+ 1 2 ). The existence of such polynomials can be established by interpolation for WENO schemes. For example, for the fifth or- der...WENO scheme, there is a unique vector of polynomials of degree four qi(x) satisfying qi(xi− 1 2 ) = w+ i− 1 2 , qi(xi+ 1 2 ) = w− i+ 1 2 and 1 ∆x ∫ Ij qi

Nonlinear effects in the time measurement device based on surface acoustic wave filter excitation.

PubMed

Prochazka, Ivan; Panek, Petr

2009-07-01

A transversal surface acoustic wave filter has been used as a time interpolator in a time interval measurement device. We are presenting the experiments and results of an analysis of the nonlinear effects in such a time interpolator. The analysis shows that the nonlinear distortion in the time interpolator circuits causes a deterministic measurement error which can be understood as the time interpolation nonlinearity. The dependence of this error on time of the measured events can be expressed as a sparse Fourier series thus it usually oscillates very quickly in comparison to the clock period. The theoretical model is in good agreement with experiments carried out on an experimental two-channel timing system. Using highly linear amplifiers in the time interpolator and adjusting the filter excitation level to the optimum, we have achieved the interpolation nonlinearity below 0.2 ps. The overall single-shot precision of the experimental timing device is 0.9 ps rms in each channel.

Parallel Anisotropic Tetrahedral Adaptation

NASA Technical Reports Server (NTRS)

Park, Michael A.; Darmofal, David L.

2008-01-01

An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

VizieR Online Data Catalog: New atmospheric parameters of MILES cool stars (Sharma+, 2016)

NASA Astrophysics Data System (ADS)

Sharma, K.; Prugniel, P.; Singh, H. P.

2015-11-01

MILES V2 spectral interpolator The FITS file is an improved version of MILES interpolator previously presented in PVK. It contains the coefficients of the interpolator, which allows one to compute an interpolated spectrum, giving an effective temperature, log of surface gravity and metallicity (Teff, logg, and [Fe/H]). The file consists of three extensions containing the three temperature regimes described in the paper. Extension Teff range 0 warm 4000-9000K 1 hot >7000K 2 cold <4550K The three functions are linearly interpolated in the Teff overlapping regions. Each extension contains a 2D image-type array, whose first axis is the wavelength described by a WCS (Air wavelength, starting at 3536Å, step=0.9Å). This FITS file can be used by the ULySS v1.3 or higher. (5 data files).

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

PubMed

Chen, Bor-Sen; Hsu, Chih-Yuan

2012-10-26

Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

PubMed Central

2012-01-01

Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. Conclusion If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks. PMID:23101662

Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

NASA Astrophysics Data System (ADS)

Amsallem, David; Tezaur, Radek; Farhat, Charbel

2016-12-01

A comprehensive approach for real-time computations using a database of parametric, linear, projection-based reduced-order models (ROMs) based on arbitrary underlying meshes is proposed. In the offline phase of this approach, the parameter space is sampled and linear ROMs defined by linear reduced operators are pre-computed at the sampled parameter points and stored. Then, these operators and associated ROMs are transformed into counterparts that satisfy a certain notion of consistency. In the online phase of this approach, a linear ROM is constructed in real-time at a queried but unsampled parameter point by interpolating the pre-computed linear reduced operators on matrix manifolds and therefore computing an interpolated linear ROM. The proposed overall model reduction framework is illustrated with two applications: a parametric inverse acoustic scattering problem associated with a mockup submarine, and a parametric flutter prediction problem associated with a wing-tank system. The second application is implemented on a mobile device, illustrating the capability of the proposed computational framework to operate in real-time.

Embedded WENO: A design strategy to improve existing WENO schemes

NASA Astrophysics Data System (ADS)

van Lith, Bart S.; ten Thije Boonkkamp, Jan H. M.; IJzerman, Wilbert L.

2017-02-01

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

A new interpolation method for gridded extensive variables with application in Lagrangian transport and dispersion models

NASA Astrophysics Data System (ADS)

Hittmeir, Sabine; Philipp, Anne; Seibert, Petra

2017-04-01

In discretised form, an extensive variable usually represents an integral over a 3-dimensional (x,y,z) grid cell. In the case of vertical fluxes, gridded values represent integrals over a horizontal (x,y) grid face. In meteorological models, fluxes (precipitation, turbulent fluxes, etc.) are usually written out as temporally integrated values, thus effectively forming 3D (x,y,t) integrals. Lagrangian transport models require interpolation of all relevant variables towards the location in 4D space of each of the computational particles. Trivial interpolation algorithms usually implicitly assume the integral value to be a point value valid at the grid centre. If the integral value would be reconstructed from the interpolated point values, it would in general not be correct. If nonlinear interpolation methods are used, non-negativity cannot easily be ensured. This problem became obvious with respect to the interpolation of precipitation for the calculation of wet deposition FLEXPART (http://flexpart.eu) which uses ECMWF model output or other gridded input data. The presently implemented method consists of a special preprocessing in the input preparation software and subsequent linear interpolation in the model. The interpolated values are positive but the criterion of cell-wise conservation of the integral property is violated; it is also not very accurate as it smoothes the field. A new interpolation algorithm was developed which introduces additional supporting grid points in each time interval with linear interpolation to be applied in FLEXPART later between them. It preserves the integral precipitation in each time interval, guarantees the continuity of the time series, and maintains non-negativity. The function values of the remapping algorithm at these subgrid points constitute the degrees of freedom which can be prescribed in various ways. Combining the advantages of different approaches leads to a final algorithm respecting all the required conditions. To improve the monotonicity behaviour we additionally derived a filter to restrict over- or undershooting. At the current stage, the algorithm is meant primarily for the temporal dimension. It can also be applied with operator-splitting to include the two horizontal dimensions. An extension to 2D appears feasible, while a fully 3D version would most likely not justify the effort compared to the operator-splitting approach.

A general tool for the evaluation of spiral CT interpolation algorithms: revisiting the effect of pitch in multislice CT.

PubMed

Bricault, Ivan; Ferretti, Gilbert

2005-01-01

While multislice spiral computed tomography (CT) scanners are provided by all major manufacturers, their specific interpolation algorithms have been rarely evaluated. Because the results published so far relate to distinct particular cases and differ significantly, there are contradictory recommendations about the choice of pitch in clinical practice. In this paper, we present a new tool for the evaluation of multislice spiral CT z-interpolation algorithms, and apply it to the four-slice case. Our software is based on the computation of a "Weighted Radiation Profile" (WRP), and compares WRP to an expected ideal profile in terms of widening and heterogeneity. It provides a unique scheme for analyzing a large variety of spiral CT acquisition procedures. Freely chosen parameters include: number of detector rows, detector collimation, nominal slice width, helical pitch, and interpolation algorithm with any filter shape and width. Moreover, it is possible to study any longitudinal and off-isocenter positions. Theoretical and experimental results show that WRP, more than Slice Sensitivity Profile (SSP), provides a comprehensive characterization of interpolation algorithms. WRP analysis demonstrates that commonly "preferred helical pitches" are actually nonoptimal regarding the formerly distinguished z-sampling gap reduction criterion. It is also shown that "narrow filter" interpolation algorithms do not enable a general preferred pitch discussion, since they present poor properties with large longitudinal and off-center variations. In the more stable case of "wide filter" interpolation algorithms, SSP width or WRP widening are shown to be almost constant. Therefore, optimal properties should no longer be sought in terms of these criteria. On the contrary, WRP heterogeneity is related to variable artifact phenomena and can pertinently characterize optimal pitches. In particular, the exemplary interpolation properties of pitch = 1 "wide filter" mode are demonstrated.

Fourier-interpolation superresolution optical fluctuation imaging (fSOFi) (Conference Presentation)

NASA Astrophysics Data System (ADS)

Enderlein, Joerg; Stein, Simon C.; Huss, Anja; Hähnel, Dirk; Gregor, Ingo

2016-02-01

Stochastic Optical Fluctuation Imaging (SOFI) is a superresolution fluorescence microscopy technique which allows to enhance the spatial resolution of an image by evaluating the temporal fluctuations of blinking fluorescent emitters. SOFI is not based on the identification and localization of single molecules such as in the widely used Photoactivation Localization Microsopy (PALM) or Stochastic Optical Reconstruction Microscopy (STORM), but computes a superresolved image via temporal cumulants from a recorded movie. A technical challenge hereby is that, when directly applying the SOFI algorithm to a movie of raw images, the pixel size of the final SOFI image is the same as that of the original images, which becomes problematic when the final SOFI resolution is much smaller than this value. In the past, sophisticated cross-correlation schemes have been used for tackling this problem. Here, we present an alternative, exact, straightforward, and simple solution using an interpolation scheme based on Fourier transforms. We exemplify the method on simulated and experimental data.

Landmark-based elastic registration using approximating thin-plate splines.

PubMed

Rohr, K; Stiehl, H S; Sprengel, R; Buzug, T M; Weese, J; Kuhn, M H

2001-06-01

We consider elastic image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. This approach is an extension of the original interpolating thin-plate spline approach and allows to take into account landmark localization errors. The extension is important for clinical applications since landmark extraction is always prone to error. Our approach is based on a minimizing functional and can cope with isotropic as well as anisotropic landmark errors. In particular, in the latter case it is possible to include different types of landmarks, e.g., unique point landmarks as well as arbitrary edge points. Also, the scheme is general with respect to the image dimension and the order of smoothness of the underlying functional. Optimal affine transformations as well as interpolating thin-plate splines are special cases of this scheme. To localize landmarks we use a semi-automatic approach which is based on three-dimensional (3-D) differential operators. Experimental results are presented for two-dimensional as well as 3-D tomographic images of the human brain.

Evaluation of the sparse coding super-resolution method for improving image quality of up-sampled images in computed tomography

NASA Astrophysics Data System (ADS)

Ota, Junko; Umehara, Kensuke; Ishimaru, Naoki; Ohno, Shunsuke; Okamoto, Kentaro; Suzuki, Takanori; Shirai, Naoki; Ishida, Takayuki

2017-02-01

As the capability of high-resolution displays grows, high-resolution images are often required in Computed Tomography (CT). However, acquiring high-resolution images takes a higher radiation dose and a longer scanning time. In this study, we applied the Sparse-coding-based Super-Resolution (ScSR) method to generate high-resolution images without increasing the radiation dose. We prepared the over-complete dictionary learned the mapping between low- and highresolution patches and seek a sparse representation of each patch of the low-resolution input. These coefficients were used to generate the high-resolution output. For evaluation, 44 CT cases were used as the test dataset. We up-sampled images up to 2 or 4 times and compared the image quality of the ScSR scheme and bilinear and bicubic interpolations, which are the traditional interpolation schemes. We also compared the image quality of three learning datasets. A total of 45 CT images, 91 non-medical images, and 93 chest radiographs were used for dictionary preparation respectively. The image quality was evaluated by measuring peak signal-to-noise ratio (PSNR) and structure similarity (SSIM). The differences of PSNRs and SSIMs between the ScSR method and interpolation methods were statistically significant. Visual assessment confirmed that the ScSR method generated a high-resolution image with sharpness, whereas conventional interpolation methods generated over-smoothed images. To compare three different training datasets, there were no significance between the CT, the CXR and non-medical datasets. These results suggest that the ScSR provides a robust approach for application of up-sampling CT images and yields substantial high image quality of extended images in CT.

An objective isobaric/isentropic technique for upper air analysis

NASA Technical Reports Server (NTRS)

Mancuso, R. L.; Endlich, R. M.; Ehernberger, L. J.

1981-01-01

An objective meteorological analysis technique is presented whereby both horizontal and vertical upper air analyses are performed. The process used to interpolate grid-point values from the upper-air station data is the same as for grid points on both an isobaric surface and a vertical cross-sectional plane. The nearby data surrounding each grid point are used in the interpolation by means of an anisotropic weighting scheme, which is described. The interpolation for a grid-point potential temperature is performed isobarically; whereas wind, mixing-ratio, and pressure height values are interpolated from data that lie on the isentropic surface that passes through the grid point. Two versions (A and B) of the technique are evaluated by qualitatively comparing computer analyses with subjective handdrawn analyses. The objective products of version A generally have fair correspondence with the subjective analyses and with the station data, and depicted the structure of the upper fronts, tropopauses, and jet streams fairly well. The version B objective products correspond more closely to the subjective analyses, and show the same strong gradients across the upper front with only minor smoothing.

A Comparative Study of Three Spatial Interpolation Methodologies for the Analysis of Air Pollution Concentrations in Athens, Greece

NASA Astrophysics Data System (ADS)

Deligiorgi, Despina; Philippopoulos, Kostas; Thanou, Lelouda; Karvounis, Georgios

2010-01-01

Spatial interpolation in air pollution modeling is the procedure for estimating ambient air pollution concentrations at unmonitored locations based on available observations. The selection of the appropriate methodology is based on the nature and the quality of the interpolated data. In this paper, an assessment of three widely used interpolation methodologies is undertaken in order to estimate the errors involved. For this purpose, air quality data from January 2001 to December 2005, from a network of seventeen monitoring stations, operating at the greater area of Athens in Greece, are used. The Nearest Neighbor and the Liner schemes were applied to the mean hourly observations, while the Inverse Distance Weighted (IDW) method to the mean monthly concentrations. The discrepancies of the estimated and measured values are assessed for every station and pollutant, using the correlation coefficient, the scatter diagrams and the statistical residuals. The capability of the methods to estimate air quality data in an area with multiple land-use types and pollution sources, such as Athens, is discussed.

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

NASA Astrophysics Data System (ADS)

Hu, Shou-Cun; Ji, Jiang-Hui

2017-12-01

In asteroid rendezvous missions, the dynamical environment near an asteroid’s surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes, which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped near-Earth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.

Investigation of interpolation techniques for the reconstruction of the first dimension of comprehensive two-dimensional liquid chromatography-diode array detector data.

PubMed

Allen, Robert C; Rutan, Sarah C

2011-10-31

Simulated and experimental data were used to measure the effectiveness of common interpolation techniques during chromatographic alignment of comprehensive two-dimensional liquid chromatography-diode array detector (LC×LC-DAD) data. Interpolation was used to generate a sufficient number of data points in the sampled first chromatographic dimension to allow for alignment of retention times from different injections. Five different interpolation methods, linear interpolation followed by cross correlation, piecewise cubic Hermite interpolating polynomial, cubic spline, Fourier zero-filling, and Gaussian fitting, were investigated. The fully aligned chromatograms, in both the first and second chromatographic dimensions, were analyzed by parallel factor analysis to determine the relative area for each peak in each injection. A calibration curve was generated for the simulated data set. The standard error of prediction and percent relative standard deviation were calculated for the simulated peak for each technique. The Gaussian fitting interpolation technique resulted in the lowest standard error of prediction and average relative standard deviation for the simulated data. However, upon applying the interpolation techniques to the experimental data, most of the interpolation methods were not found to produce statistically different relative peak areas from each other. While most of the techniques were not statistically different, the performance was improved relative to the PARAFAC results obtained when analyzing the unaligned data. Copyright © 2011 Elsevier B.V. All rights reserved.

Reducing numerical diffusion for incompressible flow calculations

NASA Technical Reports Server (NTRS)

Claus, R. W.; Neely, G. M.; Syed, S. A.

1984-01-01

A number of approaches for improving the accuracy of incompressible, steady-state flow calculations are examined. Two improved differencing schemes, Quadratic Upstream Interpolation for Convective Kinematics (QUICK) and Skew-Upwind Differencing (SUD), are applied to the convective terms in the Navier-Stokes equations and compared with results obtained using hybrid differencing. In a number of test calculations, it is illustrated that no single scheme exhibits superior performance for all flow situations. However, both SUD and QUICK are shown to be generally more accurate than hybrid differencing.

THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mignone, A.; Tzeferacos, P.; Zanni, C.

We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory,more » or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.« less

Matched Interface and Boundary Method for Elasticity Interface Problems

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms. PMID:25914439

An Adaptive Prediction-Based Approach to Lossless Compression of Floating-Point Volume Data.

PubMed

Fout, N; Ma, Kwan-Liu

2012-12-01

In this work, we address the problem of lossless compression of scientific and medical floating-point volume data. We propose two prediction-based compression methods that share a common framework, which consists of a switched prediction scheme wherein the best predictor out of a preset group of linear predictors is selected. Such a scheme is able to adapt to different datasets as well as to varying statistics within the data. The first method, called APE (Adaptive Polynomial Encoder), uses a family of structured interpolating polynomials for prediction, while the second method, which we refer to as ACE (Adaptive Combined Encoder), combines predictors from previous work with the polynomial predictors to yield a more flexible, powerful encoder that is able to effectively decorrelate a wide range of data. In addition, in order to facilitate efficient visualization of compressed data, our scheme provides an option to partition floating-point values in such a way as to provide a progressive representation. We compare our two compressors to existing state-of-the-art lossless floating-point compressors for scientific data, with our data suite including both computer simulations and observational measurements. The results demonstrate that our polynomial predictor, APE, is comparable to previous approaches in terms of speed but achieves better compression rates on average. ACE, our combined predictor, while somewhat slower, is able to achieve the best compression rate on all datasets, with significantly better rates on most of the datasets.

Deep learning methods for CT image-domain metal artifact reduction

NASA Astrophysics Data System (ADS)

Gjesteby, Lars; Yang, Qingsong; Xi, Yan; Shan, Hongming; Claus, Bernhard; Jin, Yannan; De Man, Bruno; Wang, Ge

2017-09-01

Artifacts resulting from metal objects have been a persistent problem in CT images over the last four decades. A common approach to overcome their effects is to replace corrupt projection data with values synthesized from an interpolation scheme or by reprojection of a prior image. State-of-the-art correction methods, such as the interpolation- and normalization-based algorithm NMAR, often do not produce clinically satisfactory results. Residual image artifacts remain in challenging cases and even new artifacts can be introduced by the interpolation scheme. Metal artifacts continue to be a major impediment, particularly in radiation and proton therapy planning as well as orthopedic imaging. A new solution to the long-standing metal artifact reduction (MAR) problem is deep learning, which has been successfully applied to medical image processing and analysis tasks. In this study, we combine a convolutional neural network (CNN) with the state-of-the-art NMAR algorithm to reduce metal streaks in critical image regions. Training data was synthesized from CT simulation scans of a phantom derived from real patient images. The CNN is able to map metal-corrupted images to artifact-free monoenergetic images to achieve additional correction on top of NMAR for improved image quality. Our results indicate that deep learning is a novel tool to address CT reconstruction challenges, and may enable more accurate tumor volume estimation for radiation therapy planning.

A multistage motion vector processing method for motion-compensated frame interpolation.

PubMed

Huang, Ai- Mei; Nguyen, Truong Q

2008-05-01

In this paper, a novel, low-complexity motion vector processing algorithm at the decoder is proposed for motion-compensated frame interpolation or frame rate up-conversion. We address the problems of having broken edges and deformed structures in an interpolated frame by hierarchically refining motion vectors on different block sizes. Our method explicitly considers the reliability of each received motion vector and has the capability of preserving the structure information. This is achieved by analyzing the distribution of residual energies and effectively merging blocks that have unreliable motion vectors. The motion vector reliability information is also used as a prior knowledge in motion vector refinement using a constrained vector median filter to avoid choosing identical unreliable one. We also propose using chrominance information in our method. Experimental results show that the proposed scheme has better visual quality and is also robust, even in video sequences with complex scenes and fast motion.

Investigations into the shape-preserving interpolants using symbolic computation

NASA Technical Reports Server (NTRS)

Lam, Maria

1988-01-01

Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines.

A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

NASA Astrophysics Data System (ADS)

Huang, Wen-Feng; Ren, Yu-Xin; Jiang, Xiong

2018-02-01

This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifth-order WENO-JS (WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202-228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable. The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On non-uniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime, the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

NASA Astrophysics Data System (ADS)

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Noack, Bernd R.

2017-04-01

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Selection of a Geostatistical Method to Interpolate Soil Properties of the State Crop Testing Fields using Attributes of a Digital Terrain Model

NASA Astrophysics Data System (ADS)

Sahabiev, I. A.; Ryazanov, S. S.; Kolcova, T. G.; Grigoryan, B. R.

2018-03-01

The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.

A downscaling scheme for atmospheric variables to drive soil-vegetation-atmosphere transfer models

NASA Astrophysics Data System (ADS)

Schomburg, A.; Venema, V.; Lindau, R.; Ament, F.; Simmer, C.

2010-09-01

For driving soil-vegetation-transfer models or hydrological models, high-resolution atmospheric forcing data is needed. For most applications the resolution of atmospheric model output is too coarse. To avoid biases due to the non-linear processes, a downscaling system should predict the unresolved variability of the atmospheric forcing. For this purpose we derived a disaggregation system consisting of three steps: (1) a bi-quadratic spline-interpolation of the low-resolution data, (2) a so-called `deterministic' part, based on statistical rules between high-resolution surface variables and the desired atmospheric near-surface variables and (3) an autoregressive noise-generation step. The disaggregation system has been developed and tested based on high-resolution model output (400m horizontal grid spacing). A novel automatic search-algorithm has been developed for deriving the deterministic downscaling rules of step 2. When applied to the atmospheric variables of the lowest layer of the atmospheric COSMO-model, the disaggregation is able to adequately reconstruct the reference fields. Applying downscaling step 1 and 2, root mean square errors are decreased. Step 3 finally leads to a close match of the subgrid variability and temporal autocorrelation with the reference fields. The scheme can be applied to the output of atmospheric models, both for stand-alone offline simulations, and a fully coupled model system.

Development of a Grid-Based Gyro-Kinetic Simulation Code

NASA Astrophysics Data System (ADS)

Lapillonne, Xavier; Brunetti, Maura; Tran, Trach-Minh; Brunner, Stephan

2006-10-01

A grid-based semi-Lagrangian code using cubic spline interpolation is being developed at CRPP, for solving the electrostatic drift-kinetic equations [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)] in a cylindrical system. This 4-dim code, CYGNE, is part of a project with long term aim of studying microturbulence in toroidal fusion devices, in the more general frame of gyro-kinetic equations. Towards their non-linear phase, the simulations from this code are subject to significant overshoot problems, reflected by the development of negative value regions of the distribution function, which leads to bad energy conservation. This has motivated the study of alternative schemes. On the one hand, new time integration algorithms are considered in the semi-Lagrangian frame. On the other hand, fully Eulerian schemes, which separate time and space discretisation (method of lines), are investigated. In particular, the Essentially Non Oscillatory (ENO) approach, constructed so as to minimize the overshoot problem, has been considered. All these methods have first been tested in the simpler case of the 2-dim guiding-center model for the Kelvin-Helmholtz instability, which enables to address the specific issue of the E xB drift also met in the more complex gyrokinetic-type equations. Based on these preliminary studies, the most promising methods are being implemented and tested in CYGNE.

Weighted statistical parameters for irregularly sampled time series

NASA Astrophysics Data System (ADS)

Rimoldini, Lorenzo

2014-01-01

Unevenly spaced time series are common in astronomy because of the day-night cycle, weather conditions, dependence on the source position in the sky, allocated telescope time and corrupt measurements, for example, or inherent to the scanning law of satellites like Hipparcos and the forthcoming Gaia. Irregular sampling often causes clumps of measurements and gaps with no data which can severely disrupt the values of estimators. This paper aims at improving the accuracy of common statistical parameters when linear interpolation (in time or phase) can be considered an acceptable approximation of a deterministic signal. A pragmatic solution is formulated in terms of a simple weighting scheme, adapting to the sampling density and noise level, applicable to large data volumes at minimal computational cost. Tests on time series from the Hipparcos periodic catalogue led to significant improvements in the overall accuracy and precision of the estimators with respect to the unweighted counterparts and those weighted by inverse-squared uncertainties. Automated classification procedures employing statistical parameters weighted by the suggested scheme confirmed the benefits of the improved input attributes. The classification of eclipsing binaries, Mira, RR Lyrae, Delta Cephei and Alpha2 Canum Venaticorum stars employing exclusively weighted descriptive statistics achieved an overall accuracy of 92 per cent, about 6 per cent higher than with unweighted estimators.

Origin of Lβ20 satellite in higher Z elements

NASA Astrophysics Data System (ADS)

Trivedi, Rajeev K.; Kendurkar, Renuka; Shrivastava, B. D.

2017-05-01

One of the satellite lines accompanied with the intense diagram line Lβ2 (L3-N5) on the higher energy side, is the satellite β20 in the elements from 71Lu to 84Po, 88Ra, 90Th and 92U. Shahlot and Soni have theoretically investigated this satellite and have found all the possible transitions using jj coupling scheme using Hartree-Fock-Slater formulae. A perusal of their results shows that in some cases the agreement between theoretical and experimental values is not so good. Hence, in the present investigation we have tried alternative calculations by using the tables of Parente et al. While these calculations are relativistic ab initio calculations, those of Shahlot and Soni are non-relativistic semi-empirical calculations. Considering the same grouping of transition schemes as assigned by Shahlot and Soni, calculations have been done by us using the tables of Parente et al, which gives the values of transition energies only for the 11 elements. The transition energies for intermediate elements have been calculated by us by linear interpolation method. Our calculations show better agreement with the experimental values than that obtained from the values of Shahlot and Soni. However, in some cases, our calculations also do not yield good results and this has been discussed.

Comparison of the common spatial interpolation methods used to analyze potentially toxic elements surrounding mining regions.

PubMed

Ding, Qian; Wang, Yong; Zhuang, Dafang

2018-04-15

The appropriate spatial interpolation methods must be selected to analyze the spatial distributions of Potentially Toxic Elements (PTEs), which is a precondition for evaluating PTE pollution. The accuracy and effect of different spatial interpolation methods, which include inverse distance weighting interpolation (IDW) (power = 1, 2, 3), radial basis function interpolation (RBF) (basis function: thin-plate spline (TPS), spline with tension (ST), completely regularized spline (CRS), multiquadric (MQ) and inverse multiquadric (IMQ)) and ordinary kriging interpolation (OK) (semivariogram model: spherical, exponential, gaussian and linear), were compared using 166 unevenly distributed soil PTE samples (As, Pb, Cu and Zn) in the Suxian District, Chenzhou City, Hunan Province as the study subject. The reasons for the accuracy differences of the interpolation methods and the uncertainties of the interpolation results are discussed, then several suggestions for improving the interpolation accuracy are proposed, and the direction of pollution control is determined. The results of this study are as follows: (i) RBF-ST and OK (exponential) are the optimal interpolation methods for As and Cu, and the optimal interpolation method for Pb and Zn is RBF-IMQ. (ii) The interpolation uncertainty is positively correlated with the PTE concentration, and higher uncertainties are primarily distributed around mines, which is related to the strong spatial variability of PTE concentrations caused by human interference. (iii) The interpolation accuracy can be improved by increasing the sample size around the mines, introducing auxiliary variables in the case of incomplete sampling and adopting the partition prediction method. (iv) It is necessary to strengthen the prevention and control of As and Pb pollution, particularly in the central and northern areas. The results of this study can provide an effective reference for the optimization of interpolation methods and parameters for unevenly distributed soil PTE data in mining areas. Copyright © 2018 Elsevier Ltd. All rights reserved.

Extrapolation of Functions of Many Variables by Means of Metric Analysis

NASA Astrophysics Data System (ADS)

Kryanev, Alexandr; Ivanov, Victor; Romanova, Anastasiya; Sevastianov, Leonid; Udumyan, David

2018-02-01

The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

A computationally efficient scheme for the non-linear diffusion equation

NASA Astrophysics Data System (ADS)

Termonia, P.; Van de Vyver, H.

2009-04-01

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.

Image registration using stationary velocity fields parameterized by norm-minimizing Wendland kernel

NASA Astrophysics Data System (ADS)

Pai, Akshay; Sommer, Stefan; Sørensen, Lauge; Darkner, Sune; Sporring, Jon; Nielsen, Mads

2015-03-01

Interpolating kernels are crucial to solving a stationary velocity field (SVF) based image registration problem. This is because, velocity fields need to be computed in non-integer locations during integration. The regularity in the solution to the SVF registration problem is controlled by the regularization term. In a variational formulation, this term is traditionally expressed as a squared norm which is a scalar inner product of the interpolating kernels parameterizing the velocity fields. The minimization of this term using the standard spline interpolation kernels (linear or cubic) is only approximative because of the lack of a compatible norm. In this paper, we propose to replace such interpolants with a norm-minimizing interpolant - the Wendland kernel which has the same computational simplicity like B-Splines. An application on the Alzheimer's disease neuroimaging initiative showed that Wendland SVF based measures separate (Alzheimer's disease v/s normal controls) better than both B-Spline SVFs (p<0.05 in amygdala) and B-Spline freeform deformation (p<0.05 in amygdala and cortical gray matter).

A general method for generating bathymetric data for hydrodynamic computer models

USGS Publications Warehouse

Burau, J.R.; Cheng, R.T.

1989-01-01

To generate water depth data from randomly distributed bathymetric data for numerical hydrodymamic models, raw input data from field surveys, water depth data digitized from nautical charts, or a combination of the two are sorted to given an ordered data set on which a search algorithm is used to isolate data for interpolation. Water depths at locations required by hydrodynamic models are interpolated from the bathymetric data base using linear or cubic shape functions used in the finite-element method. The bathymetric database organization and preprocessing, the search algorithm used in finding the bounding points for interpolation, the mathematics of the interpolation formulae, and the features of the automatic generation of water depths at hydrodynamic model grid points are included in the analysis. This report includes documentation of two computer programs which are used to: (1) organize the input bathymetric data; and (2) to interpolate depths for hydrodynamic models. An example of computer program operation is drawn from a realistic application to the San Francisco Bay estuarine system. (Author 's abstract)

Simple scale interpolator facilitates reading of graphs

NASA Technical Reports Server (NTRS)

Fazio, A.; Henry, B.; Hood, D.

1966-01-01

Set of cards with scale divisions and a scale finder permits accurate reading of the coordinates of points on linear or logarithmic graphs plotted on rectangular grids. The set contains 34 different scales for linear plotting and 28 single cycle scales for log plots.

Context dependent anti-aliasing image reconstruction

NASA Technical Reports Server (NTRS)

Beaudet, Paul R.; Hunt, A.; Arlia, N.

1989-01-01

Image Reconstruction has been mostly confined to context free linear processes; the traditional continuum interpretation of digital array data uses a linear interpolator with or without an enhancement filter. Here, anti-aliasing context dependent interpretation techniques are investigated for image reconstruction. Pattern classification is applied to each neighborhood to assign it a context class; a different interpolation/filter is applied to neighborhoods of differing context. It is shown how the context dependent interpolation is computed through ensemble average statistics using high resolution training imagery from which the lower resolution image array data is obtained (simulation). A quadratic least squares (LS) context-free image quality model is described from which the context dependent interpolation coefficients are derived. It is shown how ensembles of high-resolution images can be used to capture the a priori special character of different context classes. As a consequence, a priori information such as the translational invariance of edges along the edge direction, edge discontinuity, and the character of corners is captured and can be used to interpret image array data with greater spatial resolution than would be expected by the Nyquist limit. A Gibb-like artifact associated with this super-resolution is discussed. More realistic context dependent image quality models are needed and a suggestion is made for using a quality model which now is finding application in data compression.

Apparent Half-Lives of Dioxins, Furans, and Polychlorinated Biphenyls as a Function of Age, Body Fat, Smoking Status, and Breast-Feeding

PubMed Central

Milbrath, Meghan O’Grady; Wenger, Yvan; Chang, Chiung-Wen; Emond, Claude; Garabrant, David; Gillespie, Brenda W.; Jolliet, Olivier

2009-01-01

Objective In this study we reviewed the half-life data in the literature for the 29 dioxin, furan, and polychlorinated biphenyl congeners named in the World Health Organization toxic equivalency factor scheme, with the aim of providing a reference value for the half-life of each congener in the human body and a method of half-life estimation that accounts for an individual’s personal characteristics. Data sources and extraction We compared data from > 30 studies containing congener-specific elimination rates. Half-life data were extracted and compiled into a summary table. We then created a subset of these data based on defined exclusionary criteria. Data synthesis We defined values for each congener that approximate the half-life in an infant and in an adult. A linear interpolation of these values was used to examine the relationship between half-life and age, percent body fat, and absolute body fat. We developed predictive equations based on these relationships and adjustments for individual characteristics. Conclusions The half-life of dioxins in the body can be predicted using a linear relationship with age adjusted for body fat, smoking, and breast-feeding. Data suggest an alternative method based on a linear relationship between half-life and total body fat, but this approach requires further testing and validation with individual measurements. PMID:19337517

A 3D Optimal Interpolation Assimilation Scheme of HF Radar Current Data into a Numerical Ocean Model

NASA Astrophysics Data System (ADS)

Ragnoli, Emanuele; Zhuk, Sergiy; Donncha, Fearghal O.; Suits, Frank; Hartnett, Michael

2013-04-01

In this work a technique for the 3D assimilation of ocean surface current measurements into a numerical ocean model based on data from High Frequency Radar (HFR) systems is presented. The technique is the combination of supplementary forcing on the surface and of and Ekman layer projection of the correction in the depth. Optimal interpolation through BLUE (Best Linear Unbiased Estimator) of the model predicted velocity and HFR observations is computed in order to derive a supplementary forcing applied at the surface boundary. In the depth the assimilation is propagated using an additional Ekman pumping (vertical velocity) based on the correction achieved by BLUE. In this work a HFR data assimilation system for hydrodynamic modelling of Galway Bay in Ireland is developed; it demonstrates the viability of adopting data assimilation techniques to improve the performance of numerical models in regions characterized by significant wind-driven flows. A network of CODAR Seasonde high frequency radars (HFR) deployed within Galway Bay, on the West Coast of Ireland, provides flow measurements adopted for this study. This system provides real-time synoptic measurements of both ocean surface currents and ocean surface waves in regions of the bay where radials from two or more radars intersect. Radar systems have a number of unique advantages in ocean modelling data assimilation schemes, namely, the ability to provide two-dimensional mapping of surface currents at resolutions that capture the complex structure related to coastal topography and the intrinsic instability scales of coastal circulation at a relatively low-cost. The radar system used in this study operates at a frequency of 25MHz which provides a sampling range of 25km at a spatial resolution of 300m.A detailed dataset of HFR observed velocities is collected at 60 minute intervals for a period chosen for comparison due to frequent occurrences of highly-energetic, storm-force events. In conjunction with this, a comprehensive weather station, tide gauge and river monitoring program is conducted. The data are then used to maintain density fields within the model and to force the wind direction and magnitude on flows. The Data Assimilation scheme is then assessed and validated via HFR surface flow measurements.

Dynamic graphs, community detection, and Riemannian geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakker, Craig; Halappanavar, Mahantesh; Visweswara Sathanur, Arun

A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited tomore » dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.« less

A Linearized Prognostic Cloud Scheme in NASAs Goddard Earth Observing System Data Assimilation Tools

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Errico, Ronald M.; Gelaro, Ronald; Kim, Jong G.; Mahajan, Rahul

2015-01-01

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA's Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation

PubMed Central

Li, Mingchu; Guo, Cheng; Choo, Kim-Kwang Raymond; Ren, Yizhi

2016-01-01

After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t′, n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely. PMID:27792784

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows.

PubMed

Sanjeevi, Sathish K P; Zarghami, Ahad; Padding, Johan T

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation.

PubMed

Yuan, Lifeng; Li, Mingchu; Guo, Cheng; Choo, Kim-Kwang Raymond; Ren, Yizhi

2016-01-01

After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t', n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

NASA Astrophysics Data System (ADS)

Sanjeevi, Sathish K. P.; Zarghami, Ahad; Padding, Johan T.

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

A hybrid Lagrangian Voronoi-SPH scheme

NASA Astrophysics Data System (ADS)

Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

2018-07-01

A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

A hybrid Lagrangian Voronoi-SPH scheme

NASA Astrophysics Data System (ADS)

Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

2017-11-01

A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

Simulation of Pellet Ablation

NASA Astrophysics Data System (ADS)

Parks, P. B.; Ishizaki, Ryuichi

2000-10-01

In order to clarify the structure of the ablation flow, 2D simulation is carried out with a fluid code solving temporal evolution of MHD equations. The code includes electrostatic sheath effect at the cloud interface.(P.B. Parks et al.), Plasma Phys. Contr. Fusion 38, 571 (1996). An Eulerian cylindrical coordinate system (r,z) is used with z in a spherical pellet. The code uses the Cubic-Interpolated Psudoparticle (CIP) method(H. Takewaki and T. Yabe, J. Comput. Phys. 70), 355 (1987). that divides the fluid equations into non-advection and advection phases. The most essential element of the CIP method is in calculation of the advection phase. In this phase, a cubic interpolated spatial profile is shifted in space according to the total derivative equations, similarly to a particle scheme. Since the profile is interpolated by using the value and the spatial derivative value at each grid point, there is no numerical oscillation in space, that often appears in conventional spline interpolation. A free boundary condition is used in the code. The possibility of a stationary shock will also be shown in the presentation because the supersonic ablation flow across the magnetic field is impeded.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

A comparative study of upwind and MacCormack schemes for CAA benchmark problems

NASA Technical Reports Server (NTRS)

Viswanathan, K.; Sankar, L. N.

1995-01-01

In this study, upwind schemes and MacCormack schemes are evaluated as to their suitability for aeroacoustic applications. The governing equations are cast in a curvilinear coordinate system and discretized using finite volume concepts. A flux splitting procedure is used for the upwind schemes, where the signals crossing the cell faces are grouped into two categories: signals that bring information from outside into the cell, and signals that leave the cell. These signals may be computed in several ways, with the desired spatial and temporal accuracy achieved by choosing appropriate interpolating polynomials. The classical MacCormack schemes employed here are fourth order accurate in time and space. Results for categories 1, 4, and 6 of the workshop's benchmark problems are presented. Comparisons are also made with the exact solutions, where available. The main conclusions of this study are finally presented.

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1997-01-01

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

Pearson correlation estimation for irregularly sampled time series

NASA Astrophysics Data System (ADS)

Rehfeld, K.; Marwan, N.; Heitzig, J.; Kurths, J.

2012-04-01

Many applications in the geosciences call for the joint and objective analysis of irregular time series. For automated processing, robust measures of linear and nonlinear association are needed. Up to now, the standard approach would have been to reconstruct the time series on a regular grid, using linear or spline interpolation. Interpolation, however, comes with systematic side-effects, as it increases the auto-correlation in the time series. We have searched for the best method to estimate Pearson correlation for irregular time series, i.e. the one with the lowest estimation bias and variance. We adapted a kernel-based approach, using Gaussian weights. Pearson correlation is calculated, in principle, as a mean over products of previously centralized observations. In the regularly sampled case, observations in both time series were observed at the same time and thus the allocation of measurement values into pairs of products is straightforward. In the irregularly sampled case, however, measurements were not necessarily observed at the same time. Now, the key idea of the kernel-based method is to calculate weighted means of products, with the weight depending on the time separation between the observations. If the lagged correlation function is desired, the weights depend on the absolute difference between observation time separation and the estimation lag. To assess the applicability of the approach we used extensive simulations to determine the extent of interpolation side-effects with increasing irregularity of time series. We compared different approaches, based on (linear) interpolation, the Lomb-Scargle Fourier Transform, the sinc kernel and the Gaussian kernel. We investigated the role of kernel bandwidth and signal-to-noise ratio in the simulations. We found that the Gaussian kernel approach offers significant advantages and low Root-Mean Square Errors for regular, slightly irregular and very irregular time series. We therefore conclude that it is a good (linear) similarity measure that is appropriate for irregular time series with skewed inter-sampling time distributions.

Simulations of Turbulent Flow Over Complex Terrain Using an Immersed-Boundary Method

NASA Astrophysics Data System (ADS)

DeLeon, Rey; Sandusky, Micah; Senocak, Inanc

2018-02-01

We present an immersed-boundary method to simulate high-Reynolds-number turbulent flow over the complex terrain of Askervein and Bolund Hills under neutrally-stratified conditions. We reconstruct both the velocity and the eddy-viscosity fields in the terrain-normal direction to produce turbulent stresses as would be expected from the application of a surface-parametrization scheme based on Monin-Obukhov similarity theory. We find that it is essential to be consistent in the underlying assumptions for the velocity reconstruction and the eddy-viscosity relation to produce good results. To this end, we reconstruct the tangential component of the velocity field using a logarithmic velocity profile and adopt the mixing-length model in the near-surface turbulence model. We use a linear interpolation to reconstruct the normal component of the velocity to enforce the impermeability condition. Our approach works well for both the Askervein and Bolund Hills when the flow is attached to the surface, but shows slight disagreement in regions of flow recirculation, despite capturing the flow reversal.

Simulations of Turbulent Flow Over Complex Terrain Using an Immersed-Boundary Method

NASA Astrophysics Data System (ADS)

DeLeon, Rey; Sandusky, Micah; Senocak, Inanc

2018-06-01

We present an immersed-boundary method to simulate high-Reynolds-number turbulent flow over the complex terrain of Askervein and Bolund Hills under neutrally-stratified conditions. We reconstruct both the velocity and the eddy-viscosity fields in the terrain-normal direction to produce turbulent stresses as would be expected from the application of a surface-parametrization scheme based on Monin-Obukhov similarity theory. We find that it is essential to be consistent in the underlying assumptions for the velocity reconstruction and the eddy-viscosity relation to produce good results. To this end, we reconstruct the tangential component of the velocity field using a logarithmic velocity profile and adopt the mixing-length model in the near-surface turbulence model. We use a linear interpolation to reconstruct the normal component of the velocity to enforce the impermeability condition. Our approach works well for both the Askervein and Bolund Hills when the flow is attached to the surface, but shows slight disagreement in regions of flow recirculation, despite capturing the flow reversal.

Directional filtering for block recovery using wavelet features

NASA Astrophysics Data System (ADS)

Hyun, Seung H.; Eom, Il K.; Kim, Yoo S.

2005-07-01

When images compressed with block-based compression techniques are transmitted over a noisy channel, unexpected block losses occur. Conventional methods that do not consider edge directions can cause blocked blurring artifacts. In this paper, we present a post-processing-based block recovery scheme using Haar wavelet features. The adaptive selection of neighboring blocks is performed based on the energy of wavelet subbands (EWS) and difference between DC values (DDC). The lost blocks are recovered by linear interpolation in the spatial domain using selected blocks. The method using only EWS performs well for horizontal and vertical edges, but not as well for diagonal edges. Conversely, only using DDC performs well for diagonal edges with the exception of line- or roof-type edge profiles. Therefore, we combine EWS and DDC for better results. The proposed directional recovery method is effective for the strong edge because exploit the varying neighboring blocks adaptively according to the edges and the directional information in the image. The proposed method outperforms the previous methods that used only fixed blocks.

VOFTools - A software package of calculation tools for volume of fluid methods using general convex grids

NASA Astrophysics Data System (ADS)

López, J.; Hernández, J.; Gómez, P.; Faura, F.

2018-02-01

The VOFTools library includes efficient analytical and geometrical routines for (1) area/volume computation, (2) truncation operations that typically arise in VOF (volume of fluid) methods, (3) area/volume conservation enforcement (VCE) in PLIC (piecewise linear interface calculation) reconstruction and(4) computation of the distance from a given point to the reconstructed interface. The computation of a polyhedron volume uses an efficient formula based on a quadrilateral decomposition and a 2D projection of each polyhedron face. The analytical VCE method is based on coupling an interpolation procedure to bracket the solution with an improved final calculation step based on the above volume computation formula. Although the library was originally created to help develop highly accurate advection and reconstruction schemes in the context of VOF methods, it may have more general applications. To assess the performance of the supplied routines, different tests, which are provided in FORTRAN and C, were implemented for several 2D and 3D geometries.

Ball-morph: definition, implementation, and comparative evaluation.

PubMed

Whited, Brian; Rossignac, Jaroslaw Jarek

2011-06-01

We define b-compatibility for planar curves and propose three ball morphing techniques between pairs of b-compatible curves. Ball-morphs use the automatic ball-map correspondence, proposed by Chazal et al., from which we derive different vertex trajectories (linear, circular, and parabolic). All three morphs are symmetric, meeting both curves with the same angle, which is a right angle for the circular and parabolic. We provide simple constructions for these ball-morphs and compare them to each other and other simple morphs (linear-interpolation, closest-projection, curvature-interpolation, Laplace-blending, and heat-propagation) using six cost measures (travel-distance, distortion, stretch, local acceleration, average squared mean curvature, and maximum squared mean curvature). The results depend heavily on the input curves. Nevertheless, we found that the linear ball-morph has consistently the shortest travel-distance and the circular ball-morph has the least amount of distortion.

On-line estimation of error covariance parameters for atmospheric data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1995-01-01

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

Atmospheric Downscaling using Genetic Programming

NASA Astrophysics Data System (ADS)

Zerenner, Tanja; Venema, Victor; Simmer, Clemens

2013-04-01

Coupling models for the different components of the Soil-Vegetation-Atmosphere-System requires up-and downscaling procedures. Subject of our work is the downscaling scheme used to derive high resolution forcing data for land-surface and subsurface models from coarser atmospheric model output. The current downscaling scheme [Schomburg et. al. 2010, 2012] combines a bi-quadratic spline interpolation, deterministic rules and autoregressive noise. For the development of the scheme, training and validation data sets have been created by carrying out high-resolution runs of the atmospheric model. The deterministic rules in this scheme are partly based on known physical relations and partly determined by an automated search for linear relationships between the high resolution fields of the atmospheric model output and high resolution data on surface characteristics. Up to now deterministic rules are available for downscaling surface pressure and partially, depending on the prevailing weather conditions, for near surface temperature and radiation. Aim of our work is to improve those rules and to find deterministic rules for the remaining variables, which require downscaling, e.g. precipitation or near surface specifc humidity. To accomplish that, we broaden the search by allowing for interdependencies between different atmospheric parameters, non-linear relations, non-local and time-lagged relations. To cope with the vast number of possible solutions, we use genetic programming, a method from machine learning, which is based on the principles of natural evolution. We are currently working with GPLAB, a Genetic Programming toolbox for Matlab. At first we have tested the GP system to retrieve the known physical rule for downscaling surface pressure, i.e. the hydrostatic equation, from our training data. We have found this to be a simple task to the GP system. Furthermore we have improved accuracy and efficiency of the GP solution by implementing constant variation and optimization as genetic operators. Next we have worked on an improvement of the downscaling rule for the two-meter-temperature. We have added an if-function with four input arguments to the function set. Since this has shown to increase bloat we have additionally modified our fitness function by including penalty terms for both the size of the solutions and the number intron nodes, i.e program parts that are never evaluated. Starting from the known downscaling rule for the two-meter temperature, which linearly exploits the orography anomalies allowed or disallowed by a certain temperature gradient, our GP system has been able to find an improvement. The rule produced by the GP clearly shows a better performance concerning the reproduced small-scale variability.

Characterization and Modeling of Indium Gallium Antimonide Avalanche Photodiode and of Indium Gallium Arsenide Two-band Detector

NASA Technical Reports Server (NTRS)

2006-01-01

A model of the optical properties of Al(x)Ga(1-x)As(y)Sb(1-y) and In(x)Ga(1-x)As(y)Sb(1-y) is presented, including the refractive, extinction, absorption and reflection coefficients in terms of the optical dielectric function of the materials. Energy levels and model parameters for each binary compound are interpolated to obtain the needed ternaries and quaternaries for various compositions. Bowing parameters are considered in the interpolation scheme to take into account the deviation of the calculated ternary and quaternary values from experimental data due to lattice disorders. The inclusion of temperature effects is currently being considered.

Hierarchial parallel computer architecture defined by computational multidisciplinary mechanics

NASA Technical Reports Server (NTRS)

Padovan, Joe; Gute, Doug; Johnson, Keith

1989-01-01

The goal is to develop an architecture for parallel processors enabling optimal handling of multi-disciplinary computation of fluid-solid simulations employing finite element and difference schemes. The goals, philosphical and modeling directions, static and dynamic poly trees, example problems, interpolative reduction, the impact on solvers are shown in viewgraph form.

Bayesian calibration of coarse-grained forces: Efficiently addressing transferability

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Rosch, Thomas W.; Phelan, Frederick R.

2016-04-01

Generating and calibrating forces that are transferable across a range of state-points remains a challenging task in coarse-grained (CG) molecular dynamics. In this work, we present a coarse-graining workflow, inspired by ideas from uncertainty quantification and numerical analysis, to address this problem. The key idea behind our approach is to introduce a Bayesian correction algorithm that uses functional derivatives of CG simulations to rapidly and inexpensively recalibrate initial estimates f0 of forces anchored by standard methods such as force-matching. Taking density-temperature relationships as a running example, we demonstrate that this algorithm, in concert with various interpolation schemes, can be used to efficiently compute physically reasonable force curves on a fine grid of state-points. Importantly, we show that our workflow is robust to several choices available to the modeler, including the interpolation schemes and tools used to construct f0. In a related vein, we also demonstrate that our approach can speed up coarse-graining by reducing the number of atomistic simulations needed as inputs to standard methods for generating CG forces.

A Gridded Daily Min/Max Temperature Dataset With 0.1° Resolution for the Yangtze River Valley and its Error Estimation

NASA Astrophysics Data System (ADS)

Xiong, Qiufen; Hu, Jianglin

2013-05-01

The minimum/maximum (Min/Max) temperature in the Yangtze River valley is decomposed into the climatic mean and anomaly component. A spatial interpolation is developed which combines the 3D thin-plate spline scheme for climatological mean and the 2D Barnes scheme for the anomaly component to create a daily Min/Max temperature dataset. The climatic mean field is obtained by the 3D thin-plate spline scheme because the relationship between the decreases in Min/Max temperature with elevation is robust and reliable on a long time-scale. The characteristics of the anomaly field tend to be related to elevation variation weakly, and the anomaly component is adequately analyzed by the 2D Barnes procedure, which is computationally efficient and readily tunable. With this hybridized interpolation method, a daily Min/Max temperature dataset that covers the domain from 99°E to 123°E and from 24°N to 36°N with 0.1° longitudinal and latitudinal resolution is obtained by utilizing daily Min/Max temperature data from three kinds of station observations, which are national reference climatological stations, the basic meteorological observing stations and the ordinary meteorological observing stations in 15 provinces and municipalities in the Yangtze River valley from 1971 to 2005. The error estimation of the gridded dataset is assessed by examining cross-validation statistics. The results show that the statistics of daily Min/Max temperature interpolation not only have high correlation coefficient (0.99) and interpolation efficiency (0.98), but also the mean bias error is 0.00 °C. For the maximum temperature, the root mean square error is 1.1 °C and the mean absolute error is 0.85 °C. For the minimum temperature, the root mean square error is 0.89 °C and the mean absolute error is 0.67 °C. Thus, the new dataset provides the distribution of Min/Max temperature over the Yangtze River valley with realistic, successive gridded data with 0.1° × 0.1° spatial resolution and daily temporal scale. The primary factors influencing the dataset precision are elevation and terrain complexity. In general, the gridded dataset has a relatively high precision in plains and flatlands and a relatively low precision in mountainous areas.

The Interpolation Theory of Radial Basis Functions

NASA Astrophysics Data System (ADS)

Baxter, Brad

2010-06-01

In this dissertation, it is first shown that, when the radial basis function is a p-norm and 1 < p < 2, interpolation is always possible when the points are all different and there are at least two of them. We then show that interpolation is not always possible when p > 2. Specifically, for every p > 2, we construct a set of different points in some Rd for which the interpolation matrix is singular. The greater part of this work investigates the sensitivity of radial basis function interpolants to changes in the function values at the interpolation points. Our early results show that it is possible to recast the work of Ball, Narcowich and Ward in the language of distributional Fourier transforms in an elegant way. We then use this language to study the interpolation matrices generated by subsets of regular grids. In particular, we are able to extend the classical theory of Toeplitz operators to calculate sharp bounds on the spectra of such matrices. Applying our understanding of these spectra, we construct preconditioners for the conjugate gradient solution of the interpolation equations. Our main result is that the number of steps required to achieve solution of the linear system to within a required tolerance can be independent of the number of interpolation points. The Toeplitz structure allows us to use fast Fourier transform techniques, which imp lies that the total number of operations is a multiple of n log n, where n is the number of interpolation points. Finally, we use some of our methods to study the behaviour of the multiquadric when its shape parameter increases to infinity. We find a surprising link with the sinus cardinalis or sinc function of Whittaker. Consequently, it can be highly useful to use a large shape parameter when approximating band-limited functions.

Comparison of sEMG processing methods during whole-body vibration exercise.

PubMed

Lienhard, Karin; Cabasson, Aline; Meste, Olivier; Colson, Serge S

2015-12-01

The objective was to investigate the influence of surface electromyography (sEMG) processing methods on the quantification of muscle activity during whole-body vibration (WBV) exercises. sEMG activity was recorded while the participants performed squats on the platform with and without WBV. The spikes observed in the sEMG spectrum at the vibration frequency and its harmonics were deleted using state-of-the-art methods, i.e. (1) a band-stop filter, (2) a band-pass filter, and (3) spectral linear interpolation. The same filtering methods were applied on the sEMG during the no-vibration trial. The linear interpolation method showed the highest intraclass correlation coefficients (no vibration: 0.999, WBV: 0.757-0.979) with the comparison measure (unfiltered sEMG during the no-vibration trial), followed by the band-stop filter (no vibration: 0.929-0.975, WBV: 0.661-0.938). While both methods introduced a systematic bias (P < 0.001), the error increased with increasing mean values to a higher degree for the band-stop filter. After adjusting the sEMG(RMS) during WBV for the bias, the performance of the interpolation method and the band-stop filter was comparable. The band-pass filter was in poor agreement with the other methods (ICC: 0.207-0.697), unless the sEMG(RMS) was corrected for the bias (ICC ⩾ 0.931, %LOA ⩽ 32.3). In conclusion, spectral linear interpolation or a band-stop filter centered at the vibration frequency and its multiple harmonics should be applied to delete the artifacts in the sEMG signals during WBV. With the use of a band-stop filter it is recommended to correct the sEMG(RMS) for the bias as this procedure improved its performance. Copyright © 2015 Elsevier Ltd. All rights reserved.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

PubMed Central

Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation.

PubMed

Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

A morphing-based scheme for large deformation analysis with stereo-DIC

NASA Astrophysics Data System (ADS)

Genovese, Katia; Sorgente, Donato

2018-05-01

A key step in the DIC-based image registration process is the definition of the initial guess for the non-linear optimization routine aimed at finding the parameters describing the pixel subset transformation. This initialization may result very challenging and possibly fail when dealing with pairs of largely deformed images such those obtained from two angled-views of not-flat objects or from the temporal undersampling of rapidly evolving phenomena. To address this problem, we developed a procedure that generates a sequence of intermediate synthetic images for gradually tracking the pixel subset transformation between the two extreme configurations. To this scope, a proper image warping function is defined over the entire image domain through the adoption of a robust feature-based algorithm followed by a NURBS-based interpolation scheme. This allows a fast and reliable estimation of the initial guess of the deformation parameters for the subsequent refinement stage of the DIC analysis. The proposed method is described step-by-step by illustrating the measurement of the large and heterogeneous deformation of a circular silicone membrane undergoing axisymmetric indentation. A comparative analysis of the results is carried out by taking as a benchmark a standard reference-updating approach. Finally, the morphing scheme is extended to the most general case of the correspondence search between two largely deformed textured 3D geometries. The feasibility of this latter approach is demonstrated on a very challenging case: the full-surface measurement of the severe deformation (> 150% strain) suffered by an aluminum sheet blank subjected to a pneumatic bulge test.

Using Neural Networks to Improve the Performance of Radiative Transfer Modeling Used for Geometry Dependent LER Calculations

NASA Astrophysics Data System (ADS)

Fasnacht, Z.; Qin, W.; Haffner, D. P.; Loyola, D. G.; Joiner, J.; Krotkov, N. A.; Vasilkov, A. P.; Spurr, R. J. D.

2017-12-01

In order to estimate surface reflectance used in trace gas retrieval algorithms, radiative transfer models (RTM) such as the Vector Linearized Discrete Ordinate Radiative Transfer Model (VLIDORT) can be used to simulate the top of the atmosphere (TOA) radiances with advanced models of surface properties. With large volumes of satellite data, these model simulations can become computationally expensive. Look up table interpolation can improve the computational cost of the calculations, but the non-linear nature of the radiances requires a dense node structure if interpolation errors are to be minimized. In order to reduce our computational effort and improve the performance of look-up tables, neural networks can be trained to predict these radiances. We investigate the impact of using look-up table interpolation versus a neural network trained using the smart sampling technique, and show that neural networks can speed up calculations and reduce errors while using significantly less memory and RTM calls. In future work we will implement a neural network in operational processing to meet growing demands for reflectance modeling in support of high spatial resolution satellite missions.

Spatial Interpolation of Rain-field Dynamic Time-Space Evolution in Hong Kong

NASA Astrophysics Data System (ADS)

Liu, P.; Tung, Y. K.

2017-12-01

Accurate and reliable measurement and prediction of spatial and temporal distribution of rain-field over a wide range of scales are important topics in hydrologic investigations. In this study, geostatistical treatment of precipitation field is adopted. To estimate the rainfall intensity over a study domain with the sample values and the spatial structure from the radar data, the cumulative distribution functions (CDFs) at all unsampled locations were estimated. Indicator Kriging (IK) was used to estimate the exceedance probabilities for different pre-selected cutoff levels and a procedure was implemented for interpolating CDF values between the thresholds that were derived from the IK. Different interpolation schemes of the CDF were proposed and their influences on the performance were also investigated. The performance measures and visual comparison between the observed rain-field and the IK-based estimation suggested that the proposed method can provide fine results of estimation of indicator variables and is capable of producing realistic image.

Application of a medium-range global hydrologic probabilistic forecast scheme to the Ohio River Basin

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voisin, Nathalie; Pappenberger, Florian; Lettenmaier, D. P.

2011-08-15

A 10-day globally applicable flood prediction scheme was evaluated using the Ohio River basin as a test site for the period 2003-2007. The Variable Infiltration Capacity (VIC) hydrology model was initialized with the European Centre for Medium Range Weather Forecasts (ECMWF) analysis temperatures and wind, and Tropical Rainfall Monitoring Mission Multi Satellite Precipitation Analysis (TMPA) precipitation up to the day of forecast. In forecast mode, the VIC model was then forced with a calibrated and statistically downscaled ECMWF ensemble prediction system (EPS) 10-day ensemble forecast. A parallel set up was used where ECMWF EPS forecasts were interpolated to the spatialmore » scale of the hydrology model. Each set of forecasts was extended by 5 days using monthly mean climatological variables and zero precipitation in order to account for the effect of initial conditions. The 15-day spatially distributed ensemble runoff forecasts were then routed to four locations in the basin, each with different drainage areas. Surrogates for observed daily runoff and flow were provided by the reference run, specifically VIC simulation forced with ECMWF analysis fields and TMPA precipitation fields. The flood prediction scheme using the calibrated and downscaled ECMWF EPS forecasts was shown to be more accurate and reliable than interpolated forecasts for both daily distributed runoff forecasts and daily flow forecasts. Initial and antecedent conditions dominated the flow forecasts for lead times shorter than the time of concentration depending on the flow forecast amounts and the drainage area sizes. The flood prediction scheme had useful skill for the 10 following days at all sites.« less

Horn’s Curve Estimation Through Multi-Dimensional Interpolation

DTIC Science & Technology

2013-03-01

complex nature of human behavior has not yet been broached. This is not to say analysts play favorites in reaching conclusions, only that varied...Chapter III, Section 3.7. For now, it is sufficient to say underdetermined data presents technical challenges and all such datasets will be excluded from...database lookup table and then use the method of linear interpolation to instantaneously estimate the unknown points on an as-needed basis ( say from a user

Fast image interpolation via random forests.

PubMed

Huang, Jun-Jie; Siu, Wan-Chi; Liu, Tian-Rui

2015-10-01

This paper proposes a two-stage framework for fast image interpolation via random forests (FIRF). The proposed FIRF method gives high accuracy, as well as requires low computation. The underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low-resolution image patch to high-resolution image patch. The FIRF framework consists of two stages. Stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image, while Stage 2 further refines the Stage 1 interpolated image. By varying the number of decision trees in the random forests and the number of stages applied, the proposed FIRF method can realize computationally scalable image interpolation. Extensive experimental results show that the proposed FIRF(3, 2) method achieves more than 0.3 dB improvement in peak signal-to-noise ratio over the state-of-the-art nonlocal autoregressive modeling (NARM) method. Moreover, the proposed FIRF(1, 1) obtains similar or better results as NARM while only takes its 0.3% computational time.

Lognormal Assimilation of Water Vapor in a WRF-GSI Cycled System

NASA Astrophysics Data System (ADS)

Fletcher, S. J.; Kliewer, A.; Jones, A. S.; Forsythe, J. M.

2015-12-01

Recent publications have shown the viability of both detecting a lognormally-distributed signal for water vapor mixing ratio and the improved quality of satellite retrievals in a 1DVAR mixed lognormal-Gaussian assimilation scheme over a Gaussian-only system. This mixed scheme is incorporated into the Gridpoint Statistical Interpolation (GSI) assimilation scheme with the goal of improving forecasts from the Weather Research and Forecasting (WRF) Model in a cycled system. Results are presented of the impact of treating water vapor as a lognormal random variable. Included in the analysis are: 1) the evolution of Tropical Storm Chris from 2006, and 2) an analysis of a "Pineapple Express" water vapor event from 2005 where a lognormal signal has been previously detected.

Newly-Developed 3D GRMHD Code and its Application to Jet Formation

NASA Technical Reports Server (NTRS)

Mizuno, Y.; Nishikawa, K.-I.; Koide, S.; Hardee, P.; Fishman, G. J.

2006-01-01

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous model. The . preliminary results show the jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field strength.

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

NASA Technical Reports Server (NTRS)

Armstrong, Jeffrey B.; Simon, Donald L.

2012-01-01

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns.

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry.

PubMed

Mathieu, Kelsey B; Kappadath, S Cheenu; White, R Allen; Atkinson, E Neely; Cody, Dianna D

2011-08-01

The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49-33.03 mm Al on a computed tomography (CT) scanner, 0.09-1.93 mm Al on two mammography systems, and 0.1-0.45 mm Cu and 0.49-14.87 mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semi-logarithmic (exponential) and linear interpolation]. The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R2 > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and/or QVL than the traditional methods of semilogarithmic and linear interpolation. The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry).

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry

PubMed Central

Mathieu, Kelsey B.; Kappadath, S. Cheenu; White, R. Allen; Atkinson, E. Neely; Cody, Dianna D.

2011-01-01

Purpose: The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. Methods: An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49–33.03 mm Al on a computed tomography (CT) scanner, 0.09–1.93 mm Al on two mammography systems, and 0.1–0.45 mm Cu and 0.49–14.87 mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semilogarithmic (exponential) and linear interpolation]. Results: The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R2 > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and∕or QVL than the traditional methods of semilogarithmic and linear interpolation. Conclusions: The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry). PMID:21928626

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mathieu, Kelsey B.; Kappadath, S. Cheenu; White, R. Allen

2011-08-15

Purpose: The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. Methods: An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49-33.03 mm Al on a computed tomography (CT) scanner, 0.09-1.93 mm Al on two mammography systems, and 0.1-0.45 mm Cu and 0.49-14.87more » mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semilogarithmic (exponential) and linear interpolation]. Results: The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R{sup 2} > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and/or QVL than the traditional methods of semilogarithmic and linear interpolation. Conclusions: The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry).« less

Daily air temperature interpolated at high spatial resolution over a large mountainous region

USGS Publications Warehouse

Dodson, R.; Marks, D.

1997-01-01

Two methods are investigated for interpolating daily minimum and maximum air temperatures (Tmin and Tmax) at a 1 km spatial resolution over a large mountainous region (830 000 km2) in the U.S. Pacific Northwest. The methods were selected because of their ability to (1) account for the effect of elevation on temperature and (2) efficiently handle large volumes of data. The first method, the neutral stability algorithm (NSA), used the hydrostatic and potential temperature equations to convert measured temperatures and elevations to sea-level potential temperatures. The potential temperatures were spatially interpolated using an inverse-squared-distance algorithm and then mapped to the elevation surface of a digital elevation model (DEM). The second method, linear lapse rate adjustment (LLRA), involved the same basic procedure as the NSA, but used a constant linear lapse rate instead of the potential temperature equation. Cross-validation analyses were performed using the NSA and LLRA methods to interpolate Tmin and Tmax each day for the 1990 water year, and the methods were evaluated based on mean annual interpolation error (IE). The NSA method showed considerable bias for sites associated with vertical extrapolation. A correction based on climate station/grid cell elevation differences was developed and found to successfully remove the bias. The LLRA method was tested using 3 lapse rates, none of which produced a serious extrapolation bias. The bias-adjusted NSA and the 3 LLRA methods produced almost identical levels of accuracy (mean absolute errors between 1.2 and 1.3??C), and produced very similar temperature surfaces based on image difference statistics. In terms of accuracy, speed, and ease of implementation, LLRA was chosen as the best of the methods tested.

SU-G-IeP2-08: Investigation On Signal Detectability in Volumetric Cone Beam CT Images with Anatomical Background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, M; Baek, J

2016-06-15

Purpose: To investigate the slice direction dependent detectability in cone beam CT images with anatomical background. Methods: We generated 3D anatomical background images using breast anatomy model. To generate 3D breast anatomy, we filtered 3D Gaussian noise with a square root of 1/f{sup 3}, and then assigned the attenuation coefficient of glandular (0.8cm{sup −1}) and adipose (0.46 cm{sup −1}) tissues based on voxel values. Projections were acquired by forward projection, and quantum noise was added to the projection data. The projection data were reconstructed by FDK algorithm. We compared the detectability of a 3 mm spherical signal in the imagemore » reconstructed from four different backprojection Methods: Hanning weighted ramp filter with linear interpolation (RECON1), Hanning weighted ramp filter with Fourier interpolation (RECON2), ramp filter with linear interpolation (RECON3), and ramp filter with Fourier interpolation (RECON4), respectively. We computed task SNR of the spherical signal in transverse and longitudinal planes using channelized Hotelling observer with Laguerre-Gauss channels. Results: Transverse plane has similar task SNR values for different backprojection methods, while longitudinal plane has a maximum task SNR value in RECON1. For all backprojection methods, longitudinal plane has higher task SNR than transverse plane. Conclusion: In this work, we investigated detectability for different slice direction in cone beam CT images with anatomical background. Longitudinal plane has a higher task SNR than transverse plane, and backprojection with hanning weighted ramp filter with linear interpolation method (i.e., RECON1) produced the highest task SNR among four different backprojection methods. This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the IT Consilience Creative Programs(IITP-2015-R0346-15-1008) supervised by the IITP (Institute for Information & Communications Technology Promotion), Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the MSIP (2015R1C1A1A01052268) and framework of international cooperation program managed by NRF (NRF-2015K2A1A2067635).« less

Compact cell-centered discretization stencils at fine-coarse block structured grid interfaces

NASA Astrophysics Data System (ADS)

Pletzer, Alexander; Jamroz, Ben; Crockett, Robert; Sides, Scott

2014-03-01

Different strategies for coupling fine-coarse grid patches are explored in the context of the adaptive mesh refinement (AMR) method. We show that applying linear interpolation to fill in the fine grid ghost values can produce a finite volume stencil of comparable accuracy to quadratic interpolation provided the cell volumes are adjusted. The volume of fine cells expands whereas the volume of neighboring coarse cells contracts. The amount by which the cells contract/expand depends on whether the interface is a face, an edge, or a corner. It is shown that quadratic or better interpolation is required when the conductivity is spatially varying, anisotropic, the refinement ratio is other than two, or when the fine-coarse interface is concave.

Chirp Scaling Algorithms for SAR Processing

NASA Technical Reports Server (NTRS)

Jin, M.; Cheng, T.; Chen, M.

1993-01-01

The chirp scaling SAR processing algorithm is both accurate and efficient. Successful implementation requires proper selection of the interval of output samples, which is a function of the chirp interval, signal sampling rate, and signal bandwidth. Analysis indicates that for both airborne and spaceborne SAR applications in the slant range domain a linear chirp scaling is sufficient. To perform nonlinear interpolation process such as to output ground range SAR images, one can use a nonlinear chirp scaling interpolator presented in this paper.

Iteration with Spreadsheets.

ERIC Educational Resources Information Center

Smith, Michael

1990-01-01

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

Rtop - an R package for interpolation along the stream network

NASA Astrophysics Data System (ADS)

Skøien, J. O.

2009-04-01

Rtop - an R package for interpolation along the stream network Geostatistical methods have been used to a limited extent for estimation along stream networks, with a few exceptions(Gottschalk, 1993; Gottschalk, et al., 2006; Sauquet, et al., 2000; Skøien, et al., 2006). Interpolation of runoff characteristics are more complicated than the traditional random variables estimated by geostatistical methods, as the measurements have a more complicated support, and many catchments are nested. Skøien et al. (2006) presented the model Top-kriging which takes these effects into account for interpolation of stream flow characteristics (exemplified by the 100 year flood). The method has here been implemented as a package in the statistical environment R (R Development Core Team, 2004). Taking advantage of the existing methods in R for working with spatial objects, and the extensive possibilities for visualizing the result, this makes it considerably easier to apply the method on new data sets, in comparison to earlier implementation of the method. Gottschalk, L. 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., I. Krasovskaia, E. Leblois, and E. Sauquet. 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Development Core Team. 2004. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Sauquet, E., L. Gottschalk, and E. Leblois. 2000. Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J. O., R. Merz, and G. Blöschl. 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

NASA Astrophysics Data System (ADS)

Bao, Yuanxun; Donev, Aleksandar; Griffith, Boyce E.; McQueen, David M.; Peskin, Charles S.

2017-10-01

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

An improved adaptive interpolation clock recovery loop based on phase splitting algorithm for coherent optical communication system

NASA Astrophysics Data System (ADS)

Liu, Xuan; Liu, Bo; Zhang, Li-jia; Xin, Xiang-jun; Zhang, Qi; Wang, Yong-jun; Tian, Qing-hua; Tian, Feng; Mao, Ya-ya

2018-01-01

Traditional clock recovery scheme achieves timing adjustment by digital interpolation, thus recovering the sampling sequence. Based on this, an improved clock recovery architecture joint channel equalization for coherent optical communication system is presented in this paper. The loop is different from the traditional clock recovery. In order to reduce the interpolation error caused by the distortion in the frequency domain of the interpolator and to suppress the spectral mirroring generated by the sampling rate change, the proposed algorithm joint equalization, improves the original interpolator in the loop, along with adaptive filtering, and makes error compensation for the original signals according to the balanced pre-filtering signals. Then the signals are adaptive interpolated through the feedback loop. Furthermore, the phase splitting timing recovery algorithm is adopted in this paper. The time error is calculated according to the improved algorithm when there is no transition between the adjacent symbols, making calculated timing error more accurate. Meanwhile, Carrier coarse synchronization module is placed before the beginning of timing recovery to eliminate the larger frequency offset interference, which effectively adjust the sampling clock phase. In this paper, the simulation results show that the timing error is greatly reduced after the loop is changed. Based on the phase splitting algorithm, the BER and MSE are better than those in the unvaried architecture. In the fiber channel, using MQAM modulation format, after 100 km-transmission of single-mode fiber, especially when ROF(roll-off factor) values tends to 0, the algorithm shows a better clock performance under different ROFs. When SNR values are less than 8, the BER could achieve 10-2 to 10-1 magnitude. Furthermore, the proposed timing recovery is more suitable for the situation with low SNR values.

Robust sampling-sourced numerical retrieval algorithm for optical energy loss function based on log-log mesh optimization and local monotonicity preserving Steffen spline

NASA Astrophysics Data System (ADS)

Maglevanny, I. I.; Smolar, V. A.

2016-01-01

We introduce a new technique of interpolation of the energy-loss function (ELF) in solids sampled by empirical optical spectra. Finding appropriate interpolation methods for ELFs poses several challenges. The sampled ELFs are usually very heterogeneous, can originate from various sources thus so called "data gaps" can appear, and significant discontinuities and multiple high outliers can be present. As a result an interpolation based on those data may not perform well at predicting reasonable physical results. Reliable interpolation tools, suitable for ELF applications, should therefore satisfy several important demands: accuracy and predictive power, robustness and computational efficiency, and ease of use. We examined the effect on the fitting quality due to different interpolation schemes with emphasis on ELF mesh optimization procedures and we argue that the optimal fitting should be based on preliminary log-log scaling data transforms by which the non-uniformity of sampled data distribution may be considerably reduced. The transformed data are then interpolated by local monotonicity preserving Steffen spline. The result is a piece-wise smooth fitting curve with continuous first-order derivatives that passes through all data points without spurious oscillations. Local extrema can occur only at grid points where they are given by the data, but not in between two adjacent grid points. It is found that proposed technique gives the most accurate results and also that its computational time is short. Thus, it is feasible using this simple method to address practical problems associated with interaction between a bulk material and a moving electron. A compact C++ implementation of our algorithm is also presented.

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barajas-Solano, David A.; Tartakovsky, A. M.

2016-10-13

We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \\emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomainmore » $$\\Omega^{hs}$$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $$\\Omega^{hs}$$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $$\\Omega^{hs}$$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.« less

Theoretical oscillation frequencies for solar-type dwarfs from stellar models with 〈3D〉-atmospheres

NASA Astrophysics Data System (ADS)

Jørgensen, Andreas Christ Sølvsten; Weiss, Achim; Mosumgaard, Jakob Rørsted; Silva Aguirre, Victor; Sahlholdt, Christian Lundsgaard

2017-12-01

We present a new method for replacing the outermost layers of stellar models with interpolated atmospheres based on results from 3D simulations, in order to correct for structural inadequacies of these layers. This replacement is known as patching. Tests, based on 3D atmospheres from three different codes and interior models with different input physics, are performed. Using solar models, we investigate how different patching criteria affect the eigenfrequencies. These criteria include the depth, at which the replacement is performed, the quantity, on which the replacement is based, and the mismatch in Teff and log g between the un-patched model and patched 3D atmosphere. We find the eigenfrequencies to be unaltered by the patching depth deep within the adiabatic region, while changing the patching quantity or the employed atmosphere grid leads to frequency shifts that may exceed 1 μHz. Likewise, the eigenfrequencies are sensitive to mismatches in Teff or log g. A thorough investigation of the accuracy of a new scheme, for interpolating mean 3D stratifications within the atmosphere grids, is furthermore performed. Throughout large parts of the atmosphere grids, our interpolation scheme yields sufficiently accurate results for the purpose of asteroseismology. We apply our procedure in asteroseismic analyses of four Kepler stars and draw the same conclusions as in the solar case: Correcting for structural deficiencies lowers the eigenfrequencies, this correction is slightly sensitive to the patching criteria, and the remaining frequency discrepancy between models and observations is less frequency dependent. Our work shows the applicability and relevance of patching in asteroseismology.

Minimizing Interpolation Bias and Precision Error in In Vivo μCT-based Measurements of Bone Structure and Dynamics

PubMed Central

de Bakker, Chantal M. J.; Altman, Allison R.; Li, Connie; Tribble, Mary Beth; Lott, Carina; Tseng, Wei-Ju; Liu, X. Sherry

2016-01-01

In vivo μCT imaging allows for high-resolution, longitudinal evaluation of bone properties. Based on this technology, several recent studies have developed in vivo dynamic bone histomorphometry techniques that utilize registered μCT images to identify regions of bone formation and resorption, allowing for longitudinal assessment of bone remodeling. However, this analysis requires a direct voxel-by-voxel subtraction between image pairs, necessitating rotation of the images into the same coordinate system, which introduces interpolation errors. We developed a novel image transformation scheme, matched-angle transformation (MAT), whereby the interpolation errors are minimized by equally rotating both the follow-up and baseline images instead of the standard of rotating one image while the other remains fixed. This new method greatly reduced interpolation biases caused by the standard transformation. Additionally, our study evaluated the reproducibility and precision of bone remodeling measurements made via in vivo dynamic bone histomorphometry. Although bone remodeling measurements showed moderate baseline noise, precision was adequate to measure physiologically relevant changes in bone remodeling, and measurements had relatively good reproducibility, with intra-class correlation coefficients of 0.75-0.95. This indicates that, when used in conjunction with MAT, in vivo dynamic histomorphometry provides a reliable assessment of bone remodeling. PMID:26786342

Minimizing Interpolation Bias and Precision Error in In Vivo µCT-Based Measurements of Bone Structure and Dynamics.

PubMed

de Bakker, Chantal M J; Altman, Allison R; Li, Connie; Tribble, Mary Beth; Lott, Carina; Tseng, Wei-Ju; Liu, X Sherry

2016-08-01

In vivo µCT imaging allows for high-resolution, longitudinal evaluation of bone properties. Based on this technology, several recent studies have developed in vivo dynamic bone histomorphometry techniques that utilize registered µCT images to identify regions of bone formation and resorption, allowing for longitudinal assessment of bone remodeling. However, this analysis requires a direct voxel-by-voxel subtraction between image pairs, necessitating rotation of the images into the same coordinate system, which introduces interpolation errors. We developed a novel image transformation scheme, matched-angle transformation (MAT), whereby the interpolation errors are minimized by equally rotating both the follow-up and baseline images instead of the standard of rotating one image while the other remains fixed. This new method greatly reduced interpolation biases caused by the standard transformation. Additionally, our study evaluated the reproducibility and precision of bone remodeling measurements made via in vivo dynamic bone histomorphometry. Although bone remodeling measurements showed moderate baseline noise, precision was adequate to measure physiologically relevant changes in bone remodeling, and measurements had relatively good reproducibility, with intra-class correlation coefficients of 0.75-0.95. This indicates that, when used in conjunction with MAT, in vivo dynamic histomorphometry provides a reliable assessment of bone remodeling.

Sensitivity Analysis of the Static Aeroelastic Response of a Wing

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.

1993-01-01

A technique to obtain the sensitivity of the static aeroelastic response of a three dimensional wing model is designed and implemented. The formulation is quite general and accepts any aerodynamic and structural analysis capability. A program to combine the discipline level, or local, sensitivities into global sensitivity derivatives is developed. A variety of representations of the wing pressure field are developed and tested to determine the most accurate and efficient scheme for representing the field outside of the aerodynamic code. Chebyshev polynomials are used to globally fit the pressure field. This approach had some difficulties in representing local variations in the field, so a variety of local interpolation polynomial pressure representations are also implemented. These panel based representations use a constant pressure value, a bilinearly interpolated value. or a biquadraticallv interpolated value. The interpolation polynomial approaches do an excellent job of reducing the numerical problems of the global approach for comparable computational effort. Regardless of the pressure representation used. sensitivity and response results with excellent accuracy have been produced for large integrated quantities such as wing tip deflection and trim angle of attack. The sensitivities of such things as individual generalized displacements have been found with fair accuracy. In general, accuracy is found to be proportional to the relative size of the derivatives to the quantity itself.

Note: Increasing dynamic range of digital-to-analog converter using a superconducting quantum interference device

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakanishi, Masakazu, E-mail: m.nakanishi@aist.go.jp

Responses of a superconducting quantum interference device (SQUID) are periodically dependent on magnetic flux coupling to its superconducting ring and the period is a flux quantum (Φ{sub o} = h/2e, where h and e, respectively, express Planck's constant and elementary charge). Using this periodicity, we had proposed a digital to analog converter using a SQUID (SQUID DAC) of first generation with linear current output, interval of which corresponded to Φ{sub o}. Modification for increasing dynamic range by interpolating within each interval is reported. Linearity of the interpolation was also based on the quantum periodicity. A SQUID DAC with dynamic rangemore » of about 1.4 × 10{sup 7} was created as a demonstration.« less

Complete Tri-Axis Magnetometer Calibration with a Gyro Auxiliary

PubMed Central

Yang, Deng; You, Zheng; Li, Bin; Duan, Wenrui; Yuan, Binwen

2017-01-01

Magnetometers combined with inertial sensors are widely used for orientation estimation, and calibrations are necessary to achieve high accuracy. This paper presents a complete tri-axis magnetometer calibration algorithm with a gyro auxiliary. The magnetic distortions and sensor errors, including the misalignment error between the magnetometer and assembled platform, are compensated after calibration. With the gyro auxiliary, the magnetometer linear interpolation outputs are calculated, and the error parameters are evaluated under linear operations of magnetometer interpolation outputs. The simulation and experiment are performed to illustrate the efficiency of the algorithm. After calibration, the heading errors calculated by magnetometers are reduced to 0.5° (1σ). This calibration algorithm can also be applied to tri-axis accelerometers whose error model is similar to tri-axis magnetometers. PMID:28587115

Charge-based MOSFET model based on the Hermite interpolation polynomial

NASA Astrophysics Data System (ADS)

Colalongo, Luigi; Richelli, Anna; Kovacs, Zsolt

2017-04-01

An accurate charge-based compact MOSFET model is developed using the third order Hermite interpolation polynomial to approximate the relation between surface potential and inversion charge in the channel. This new formulation of the drain current retains the same simplicity of the most advanced charge-based compact MOSFET models such as BSIM, ACM and EKV, but it is developed without requiring the crude linearization of the inversion charge. Hence, the asymmetry and the non-linearity in the channel are accurately accounted for. Nevertheless, the expression of the drain current can be worked out to be analytically equivalent to BSIM, ACM and EKV. Furthermore, thanks to this new mathematical approach the slope factor is rigorously defined in all regions of operation and no empirical assumption is required.

Efficient Kriging Algorithms

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess

2011-01-01

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Positivity-preserving numerical schemes for multidimensional advection

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Macvean, M. K.; Lock, A. P.

1993-01-01

This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.

Methodology for Image-Based Reconstruction of Ventricular Geometry for Patient-Specific Modeling of Cardiac Electrophysiology

PubMed Central

Prakosa, A.; Malamas, P.; Zhang, S.; Pashakhanloo, F.; Arevalo, H.; Herzka, D. A.; Lardo, A.; Halperin, H.; McVeigh, E.; Trayanova, N.; Vadakkumpadan, F.

2014-01-01

Patient-specific modeling of ventricular electrophysiology requires an interpolated reconstruction of the 3-dimensional (3D) geometry of the patient ventricles from the low-resolution (Lo-res) clinical images. The goal of this study was to implement a processing pipeline for obtaining the interpolated reconstruction, and thoroughly evaluate the efficacy of this pipeline in comparison with alternative methods. The pipeline implemented here involves contouring the epi- and endocardial boundaries in Lo-res images, interpolating the contours using the variational implicit functions method, and merging the interpolation results to obtain the ventricular reconstruction. Five alternative interpolation methods, namely linear, cubic spline, spherical harmonics, cylindrical harmonics, and shape-based interpolation were implemented for comparison. In the thorough evaluation of the processing pipeline, Hi-res magnetic resonance (MR), computed tomography (CT), and diffusion tensor (DT) MR images from numerous hearts were used. Reconstructions obtained from the Hi-res images were compared with the reconstructions computed by each of the interpolation methods from a sparse sample of the Hi-res contours, which mimicked Lo-res clinical images. Qualitative and quantitative comparison of these ventricular geometry reconstructions showed that the variational implicit functions approach performed better than others. Additionally, the outcomes of electrophysiological simulations (sinus rhythm activation maps and pseudo-ECGs) conducted using models based on the various reconstructions were compared. These electrophysiological simulations demonstrated that our implementation of the variational implicit functions-based method had the best accuracy. PMID:25148771

Moving template analysis of crack growth. 1: Procedure development

NASA Astrophysics Data System (ADS)

Padovan, Joe; Guo, Y. H.

1994-06-01

Based on a moving template procedure, this two part series will develop a method to follow the crack tip physics in a self-adaptive manner which provides a uniformly accurate prediction of crack growth. For multiple crack environments, this is achieved by attaching a moving template to each crack tip. The templates are each individually oriented to follow the associated growth orientation and rate. In this part, the essentials of the procedure are derived for application to fatigue crack environments. Overall the scheme derived possesses several hierarchical levels, i.e. the global model, the interpolatively tied moving template, and a multilevel element death option to simulate the crack wake. To speed up computation, the hierarchical polytree scheme is used to reorganize the global stiffness inversion process. In addition to developing the various features of the scheme, the accuracy of predictions for various crack lengths is also benchmarked. Part 2 extends the scheme to multiple crack problems. Extensive benchmarking is also presented to verify the scheme.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

NASA Technical Reports Server (NTRS)

Kent, James; Holdaway, Daniel

2015-01-01

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.

Error Estimation in an Optimal Interpolation Scheme for High Spatial and Temporal Resolution SST Analyses

NASA Technical Reports Server (NTRS)

Rigney, Matt; Jedlovec, Gary; LaFontaine, Frank; Shafer, Jaclyn

2010-01-01

Heat and moisture exchange between ocean surface and atmosphere plays an integral role in short-term, regional NWP. Current SST products lack both spatial and temporal resolution to accurately capture small-scale features that affect heat and moisture flux. NASA satellite is used to produce high spatial and temporal resolution SST analysis using an OI technique.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.

PubMed

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-08-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks

PubMed Central

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-01-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is “non-intrusive” and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design. PMID:26317784

Improved computer-aided detection of small polyps in CT colonography using interpolation for curvature estimationa

PubMed Central

Liu, Jiamin; Kabadi, Suraj; Van Uitert, Robert; Petrick, Nicholas; Deriche, Rachid; Summers, Ronald M.

2011-01-01

Purpose: Surface curvatures are important geometric features for the computer-aided analysis and detection of polyps in CT colonography (CTC). However, the general kernel approach for curvature computation can yield erroneous results for small polyps and for polyps that lie on haustral folds. Those erroneous curvatures will reduce the performance of polyp detection. This paper presents an analysis of interpolation’s effect on curvature estimation for thin structures and its application on computer-aided detection of small polyps in CTC. Methods: The authors demonstrated that a simple technique, image interpolation, can improve the accuracy of curvature estimation for thin structures and thus significantly improve the sensitivity of small polyp detection in CTC. Results: Our experiments showed that the merits of interpolating included more accurate curvature values for simulated data, and isolation of polyps near folds for clinical data. After testing on a large clinical data set, it was observed that sensitivities with linear, quadratic B-spline and cubic B-spline interpolations significantly improved the sensitivity for small polyp detection. Conclusions: The image interpolation can improve the accuracy of curvature estimation for thin structures and thus improve the computer-aided detection of small polyps in CTC. PMID:21859029

Real-time image-based B-mode ultrasound image simulation of needles using tensor-product interpolation.

PubMed

Zhu, Mengchen; Salcudean, Septimiu E

2011-07-01

In this paper, we propose an interpolation-based method for simulating rigid needles in B-mode ultrasound images in real time. We parameterize the needle B-mode image as a function of needle position and orientation. We collect needle images under various spatial configurations in a water-tank using a needle guidance robot. Then we use multidimensional tensor-product interpolation to simulate images of needles with arbitrary poses and positions using collected images. After further processing, the interpolated needle and seed images are superimposed on top of phantom or tissue image backgrounds. The similarity between the simulated and the real images is measured using a correlation metric. A comparison is also performed with in vivo images obtained during prostate brachytherapy. Our results, carried out for both the convex (transverse plane) and linear (sagittal/para-sagittal plane) arrays of a trans-rectal transducer indicate that our interpolation method produces good results while requiring modest computing resources. The needle simulation method we present can be extended to the simulation of ultrasound images of other wire-like objects. In particular, we have shown that the proposed approach can be used to simulate brachytherapy seeds.

Task Assignment and Path Planning for Multiple Autonomous Underwater Vehicles Using 3D Dubins Curves †

PubMed Central

Zhang, Meiyan; Zheng, Yahong Rosa

2017-01-01

This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used to solve the MTSP problem with Euclidean distance as the cost function and the Tour Hop Balance (THB) or Tour Length Balance (TLB) constraints as the stop criterion. The resulting tour sequences are mapped to 2D Dubins curves in the X−Y plane, and then interpolated linearly to obtain the Z coordinates. We demonstrate that the linear interpolation fails to achieve G1 continuity in the 3D Dubins path for multiple targets. Therefore, the interpolated 3D Dubins curves are checked against the AUV dynamics constraint and the ones satisfying the constraint are accepted to finalize the 3D Dubins curve selection. Simulation results demonstrate that the integration of the 3D Dubins curve with the MTSP model is successful and effective for solving the 3D target assignment and path planning problem. PMID:28696377

Task Assignment and Path Planning for Multiple Autonomous Underwater Vehicles Using 3D Dubins Curves †.

PubMed

Cai, Wenyu; Zhang, Meiyan; Zheng, Yahong Rosa

2017-07-11

This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used to solve the MTSP problem with Euclidean distance as the cost function and the Tour Hop Balance (THB) or Tour Length Balance (TLB) constraints as the stop criterion. The resulting tour sequences are mapped to 2D Dubins curves in the X - Y plane, and then interpolated linearly to obtain the Z coordinates. We demonstrate that the linear interpolation fails to achieve G 1 continuity in the 3D Dubins path for multiple targets. Therefore, the interpolated 3D Dubins curves are checked against the AUV dynamics constraint and the ones satisfying the constraint are accepted to finalize the 3D Dubins curve selection. Simulation results demonstrate that the integration of the 3D Dubins curve with the MTSP model is successful and effective for solving the 3D target assignment and path planning problem.

Sub-pixel localisation of passive micro-coil fiducial markers in interventional MRI.

PubMed

Rea, Marc; McRobbie, Donald; Elhawary, Haytham; Tse, Zion T H; Lamperth, Michael; Young, Ian

2009-04-01

Electromechanical devices enable increased accuracy in surgical procedures, and the recent development of MRI-compatible mechatronics permits the use of MRI for real-time image guidance. Integrated imaging of resonant micro-coil fiducials provides an accurate method of tracking devices in a scanner with increased flexibility compared to gradient tracking. Here we report on the ability of ten different image-processing algorithms to track micro-coil fiducials with sub-pixel accuracy. Five algorithms: maximum pixel, barycentric weighting, linear interpolation, quadratic fitting and Gaussian fitting were applied both directly to the pixel intensity matrix and to the cross-correlation matrix obtained by 2D convolution with a reference image. Using images of a 3 mm fiducial marker and a pixel size of 1.1 mm, intensity linear interpolation, which calculates the position of the fiducial centre by interpolating the pixel data to find the fiducial edges, was found to give the best performance for minimal computing power; a maximum error of 0.22 mm was observed in fiducial localisation for displacements up to 40 mm. The inherent standard deviation of fiducial localisation was 0.04 mm. This work enables greater accuracy to be achieved in passive fiducial tracking.

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Meade, Andrew James, Jr.

1989-01-01

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Non-oscillatory central differencing for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1988-01-01

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Efficacy of Distortion Correction on Diffusion Imaging: Comparison of FSL Eddy and Eddy_Correct Using 30 and 60 Directions Diffusion Encoding

PubMed Central

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, “eddy_correct” and the combination of “eddy” and “topup” in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non–diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non–diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme. PMID:25405472

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

NASA Astrophysics Data System (ADS)

Hill, Peter; Shanahan, Brendan; Dudson, Ben

2017-04-01

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n-axisymmetric configurations for a simple diffusion model in a "straight stellarator" magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Efficacy of distortion correction on diffusion imaging: comparison of FSL eddy and eddy_correct using 30 and 60 directions diffusion encoding.

PubMed

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, "eddy_correct" and the combination of "eddy" and "topup" in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non-diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non-diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme.

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

Cubic spline interpolation with overlapped window and data reuse for on-line Hilbert Huang transform biomedical microprocessor.

PubMed

Chang, Nai-Fu; Chiang, Cheng-Yi; Chen, Tung-Chien; Chen, Liang-Gee

2011-01-01

On-chip implementation of Hilbert-Huang transform (HHT) has great impact to analyze the non-linear and non-stationary biomedical signals on wearable or implantable sensors for the real-time applications. Cubic spline interpolation (CSI) consumes the most computation in HHT, and is the key component for the HHT processor. In tradition, CSI in HHT is usually performed after the collection of a large window of signals, and the long latency violates the realtime requirement of the applications. In this work, we propose to keep processing the incoming signals on-line with small and overlapped data windows without sacrificing the interpolation accuracy. 58% multiplication and 73% division of CSI are saved after the data reuse between the data windows.

Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model

NASA Technical Reports Server (NTRS)

Shen, Samuel S. P.; Lau, William K. M.; Kim, Kyu-Myong; Li, Gui-Long

2001-01-01

This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.

Modelling the Velocity Field in a Regular Grid in the Area of Poland on the Basis of the Velocities of European Permanent Stations

NASA Astrophysics Data System (ADS)

Bogusz, Janusz; Kłos, Anna; Grzempowski, Piotr; Kontny, Bernard

2014-06-01

The paper presents the results of testing the various methods of permanent stations' velocity residua interpolation in a regular grid, which constitutes a continuous model of the velocity field in the territory of Poland. Three packages of software were used in the research from the point of view of interpolation: GMT ( The Generic Mapping Tools), Surfer and ArcGIS. The following methods were tested in the softwares: the Nearest Neighbor, Triangulation (TIN), Spline Interpolation, Surface, Inverse Distance to a Power, Minimum Curvature and Kriging. The presented research used the absolute velocities' values expressed in the ITRF2005 reference frame and the intraplate velocities related to the NUVEL model of over 300 permanent reference stations of the EPN and ASG-EUPOS networks covering the area of Europe. Interpolation for the area of Poland was done using data from the whole area of Europe to make the results at the borders of the interpolation area reliable. As a result of this research, an optimum method of such data interpolation was developed. All the mentioned methods were tested for being local or global, for the possibility to compute errors of the interpolated values, for explicitness and fidelity of the interpolation functions or the smoothing mode. In the authors' opinion, the best data interpolation method is Kriging with the linear semivariogram model run in the Surfer programme because it allows for the computation of errors in the interpolated values and it is a global method (it distorts the results in the least way). Alternately, it is acceptable to use the Minimum Curvature method. Empirical analysis of the interpolation results obtained by means of the two methods showed that the results are identical. The tests were conducted using the intraplate velocities of the European sites. Statistics in the form of computing the minimum, maximum and mean values of the interpolated North and East components of the velocity residuum were prepared for all the tested methods, and each of the resulting continuous velocity fields was visualized by means of the GMT programme. The interpolated components of the velocities and their residua are presented in the form of tables and bar diagrams.

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

2017-02-01

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

An integral conservative gridding--algorithm using Hermitian curve interpolation.

PubMed

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-11-07

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Higher-dimensional Wannier Interpolation for the Modern Theory of the Dzyaloshinskii-Moriya Interaction: Application to Co-based Trilayers

NASA Astrophysics Data System (ADS)

Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy

2018-04-01

We present an advanced first-principles formalism to evaluate the Dzyaloshinskii-Moriya interaction (DMI) in its modern theory as well as Berry curvatures in complex spaces based on a higher-dimensional Wannier interpolation. Our method is applied to the Co-based trilayer systems IrδPt1-δ/Co/Pt and AuγPt1-γ/Co/Pt, where we gain insights into the correlations between the electronic structure and the DMI, and we uncover prominent sign changes of the chiral interaction with the overlayer composition. Beyond the discussed phenomena, the scope of applications of our Wannier-based scheme is particularly broad as it is ideally suited to study efficiently the Hamiltonian evolution under the slow variation of very general parameters.

Automatic elastic image registration by interpolation of 3D rotations and translations from discrete rigid-body transformations.

PubMed

Walimbe, Vivek; Shekhar, Raj

2006-12-01

We present an algorithm for automatic elastic registration of three-dimensional (3D) medical images. Our algorithm initially recovers the global spatial mismatch between the reference and floating images, followed by hierarchical octree-based subdivision of the reference image and independent registration of the floating image with the individual subvolumes of the reference image at each hierarchical level. Global as well as local registrations use the six-parameter full rigid-body transformation model and are based on maximization of normalized mutual information (NMI). To ensure robustness of the subvolume registration with low voxel counts, we calculate NMI using a combination of current and prior mutual histograms. To generate a smooth deformation field, we perform direct interpolation of six-parameter rigid-body subvolume transformations obtained at the last subdivision level. Our interpolation scheme involves scalar interpolation of the 3D translations and quaternion interpolation of the 3D rotational pose. We analyzed the performance of our algorithm through experiments involving registration of synthetically deformed computed tomography (CT) images. Our algorithm is general and can be applied to image pairs of any two modalities of most organs. We have demonstrated successful registration of clinical whole-body CT and positron emission tomography (PET) images using this algorithm. The registration accuracy for this application was evaluated, based on validation using expert-identified anatomical landmarks in 15 CT-PET image pairs. The algorithm's performance was comparable to the average accuracy observed for three expert-determined registrations in the same 15 image pairs.

Cosmic velocity-gravity relation in redshift space

NASA Astrophysics Data System (ADS)

Colombi, Stéphane; Chodorowski, Michał J.; Teyssier, Romain

2007-02-01

We propose a simple way to estimate the parameter β ~= Ω0.6/b from 3D galaxy surveys, where Ω is the non-relativistic matter-density parameter of the Universe and b is the bias between the galaxy distribution and the total matter distribution. Our method consists in measuring the relation between the cosmological velocity and gravity fields, and thus requires peculiar velocity measurements. The relation is measured directly in redshift space, so there is no need to reconstruct the density field in real space. In linear theory, the radial components of the gravity and velocity fields in redshift space are expected to be tightly correlated, with a slope given, in the distant observer approximation, by We test extensively this relation using controlled numerical experiments based on a cosmological N-body simulation. To perform the measurements, we propose a new and rather simple adaptive interpolation scheme to estimate the velocity and the gravity field on a grid. One of the most striking results is that non-linear effects, including `fingers of God', affect mainly the tails of the joint probability distribution function (PDF) of the velocity and gravity field: the 1-1.5 σ region around the maximum of the PDF is dominated by the linear theory regime, both in real and redshift space. This is understood explicitly by using the spherical collapse model as a proxy of non-linear dynamics. Applications of the method to real galaxy catalogues are discussed, including a preliminary investigation on homogeneous (volume-limited) `galaxy' samples extracted from the simulation with simple prescriptions based on halo and substructure identification, to quantify the effects of the bias between the galaxy distribution and the total matter distribution, as well as the effects of shot noise.

DRACO development for 3D simulations

NASA Astrophysics Data System (ADS)

Fatenejad, Milad; Moses, Gregory

2006-10-01

The DRACO (r-z) lagrangian radiation-hydrodynamics laser fusion simulation code is being extended to model 3D hydrodynamics in (x-y-z) coordinates with hexahedral cells on a structured grid. The equation of motion is solved with a lagrangian update with optional rezoning. The fluid equations are solved using an explicit scheme based on (Schulz, 1964) while the SALE-3D algorithm (Amsden, 1981) is used as a template for computing cell volumes and other quantities. A second order rezoner has been added which uses linear interpolation of the underlying continuous functions to preserve accuracy (Van Leer, 1976). Artificial restoring force terms and smoothing algorithms are used to avoid grid distortion in high aspect ratio cells. These include alternate node couplers along with a rotational restoring force based on the Tensor Code (Maenchen, 1964). Electron and ion thermal conduction is modeled using an extension of Kershaw's method (Kershaw, 1981) to 3D geometry. Test problem simulations will be presented to demonstrate the applicability of this new version of DRACO to the study of fluid instabilities in three dimensions.

Directional kriging implementation for gridded data interpolation and comparative study with common methods

NASA Astrophysics Data System (ADS)

Mahmoudabadi, H.; Briggs, G.

2016-12-01

Gridded data sets, such as geoid models or datum shift grids, are commonly used in coordinate transformation algorithms. Grid files typically contain known or measured values at regular fixed intervals. The process of computing a value at an unknown location from the values in the grid data set is called "interpolation". Generally, interpolation methods predict a value at a given point by computing a weighted average of the known values in the neighborhood of the point. Geostatistical Kriging is a widely used interpolation method for irregular networks. Kriging interpolation first analyzes the spatial structure of the input data, then generates a general model to describe spatial dependencies. This model is used to calculate values at unsampled locations by finding direction, shape, size, and weight of neighborhood points. Because it is based on a linear formulation for the best estimation, Kriging it the optimal interpolation method in statistical terms. The Kriging interpolation algorithm produces an unbiased prediction, as well as the ability to calculate the spatial distribution of uncertainty, allowing you to estimate the errors in an interpolation for any particular point. Kriging is not widely used in geospatial applications today, especially applications that run on low power devices or deal with large data files. This is due to the computational power and memory requirements of standard Kriging techniques. In this paper, improvements are introduced in directional kriging implementation by taking advantage of the structure of the grid files. The regular spacing of points simplifies finding the neighborhood points and computing their pairwise distances, reducing the the complexity and improving the execution time of the Kriging algorithm. Also, the proposed method iteratively loads small portion of interest areas in different directions to reduce the amount of required memory. This makes the technique feasible on almost any computer processor. Comparison between kriging and other standard interpolation methods demonstrated more accurate estimations in less denser data files.

Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions.

PubMed

DeGregorio, Nicole; Iyengar, Srinivasan S

2018-01-09

We present two sampling measures to gauge critical regions of potential energy surfaces. These sampling measures employ (a) the instantaneous quantum wavepacket density, an approximation to the (b) potential surface, its (c) gradients, and (d) a Shannon information theory based expression that estimates the local entropy associated with the quantum wavepacket. These four criteria together enable a directed sampling of potential surfaces that appears to correctly describe the local oscillation frequencies, or the local Nyquist frequency, of a potential surface. The sampling functions are then utilized to derive a tessellation scheme that discretizes the multidimensional space to enable efficient sampling of potential surfaces. The sampled potential surface is then combined with four different interpolation procedures, namely, (a) local Hermite curve interpolation, (b) low-pass filtered Lagrange interpolation, (c) the monomial symmetrization approximation (MSA) developed by Bowman and co-workers, and (d) a modified Shepard algorithm. The sampling procedure and the fitting schemes are used to compute (a) potential surfaces in highly anharmonic hydrogen-bonded systems and (b) study hydrogen-transfer reactions in biogenic volatile organic compounds (isoprene) where the transferring hydrogen atom is found to demonstrate critical quantum nuclear effects. In the case of isoprene, the algorithm discussed here is used to derive multidimensional potential surfaces along a hydrogen-transfer reaction path to gauge the effect of quantum-nuclear degrees of freedom on the hydrogen-transfer process. Based on the decreased computational effort, facilitated by the optimal sampling of the potential surfaces through the use of sampling functions discussed here, and the accuracy of the associated potential surfaces, we believe the method will find great utility in the study of quantum nuclear dynamics problems, of which application to hydrogen-transfer reactions and hydrogen-bonded systems is demonstrated here.

A novel forward projection-based metal artifact reduction method for flat-detector computed tomography.

PubMed

Prell, Daniel; Kyriakou, Yiannis; Beister, Marcel; Kalender, Willi A

2009-11-07

Metallic implants generate streak-like artifacts in flat-detector computed tomography (FD-CT) reconstructed volumetric images. This study presents a novel method for reducing these disturbing artifacts by inserting discarded information into the original rawdata using a three-step correction procedure and working directly with each detector element. Computation times are minimized by completely implementing the correction process on graphics processing units (GPUs). First, the original volume is corrected using a three-dimensional interpolation scheme in the rawdata domain, followed by a second reconstruction. This metal artifact-reduced volume is then segmented into three materials, i.e. air, soft-tissue and bone, using a threshold-based algorithm. Subsequently, a forward projection of the obtained tissue-class model substitutes the missing or corrupted attenuation values directly for each flat detector element that contains attenuation values corresponding to metal parts, followed by a final reconstruction. Experiments using tissue-equivalent phantoms showed a significant reduction of metal artifacts (deviations of CT values after correction compared to measurements without metallic inserts reduced typically to below 20 HU, differences in image noise to below 5 HU) caused by the implants and no significant resolution losses even in areas close to the inserts. To cover a variety of different cases, cadaver measurements and clinical images in the knee, head and spine region were used to investigate the effectiveness and applicability of our method. A comparison to a three-dimensional interpolation correction showed that the new approach outperformed interpolation schemes. Correction times are minimized, and initial and corrected images are made available at almost the same time (12.7 s for the initial reconstruction, 46.2 s for the final corrected image compared to 114.1 s and 355.1 s on central processing units (CPUs)).

Influence of survey strategy and interpolation model on DEM quality

NASA Astrophysics Data System (ADS)

Heritage, George L.; Milan, David J.; Large, Andrew R. G.; Fuller, Ian C.

2009-11-01

Accurate characterisation of morphology is critical to many studies in the field of geomorphology, particularly those dealing with changes over time. Digital elevation models (DEMs) are commonly used to represent morphology in three dimensions. The quality of the DEM is largely a function of the accuracy of individual survey points, field survey strategy, and the method of interpolation. Recommendations concerning field survey strategy and appropriate methods of interpolation are currently lacking. Furthermore, the majority of studies to date consider error to be uniform across a surface. This study quantifies survey strategy and interpolation error for a gravel bar on the River Nent, Blagill, Cumbria, UK. Five sampling strategies were compared: (i) cross section; (ii) bar outline only; (iii) bar and chute outline; (iv) bar and chute outline with spot heights; and (v) aerial LiDAR equivalent, derived from degraded terrestrial laser scan (TLS) data. Digital Elevation Models were then produced using five different common interpolation algorithms. Each resultant DEM was differentiated from a terrestrial laser scan of the gravel bar surface in order to define the spatial distribution of vertical and volumetric error. Overall triangulation with linear interpolation (TIN) or point kriging appeared to provide the best interpolators for the bar surface. Lowest error on average was found for the simulated aerial LiDAR survey strategy, regardless of interpolation technique. However, comparably low errors were also found for the bar-chute-spot sampling strategy when TINs or point kriging was used as the interpolator. The magnitude of the errors between survey strategy exceeded those found between interpolation technique for a specific survey strategy. Strong relationships between local surface topographic variation (as defined by the standard deviation of vertical elevations in a 0.2-m diameter moving window), and DEM errors were also found, with much greater errors found at slope breaks such as bank edges. A series of curves are presented that demonstrate these relationships for each interpolation and survey strategy. The simulated aerial LiDAR data set displayed the lowest errors across the flatter surfaces; however, sharp slope breaks are better modelled by the morphologically based survey strategy. The curves presented have general application to spatially distributed data of river beds and may be applied to standard deviation grids to predict spatial error within a surface, depending upon sampling strategy and interpolation algorithm.

Interpolation by new B-splines on a four directional mesh of the plane

NASA Astrophysics Data System (ADS)

Nouisser, O.; Sbibih, D.

2004-01-01

In this paper we construct new simple and composed B-splines on the uniform four directional mesh of the plane, in order to improve the approximation order of B-splines studied in Sablonniere (in: Program on Spline Functions and the Theory of Wavelets, Proceedings and Lecture Notes, Vol. 17, University of Montreal, 1998, pp. 67-78). If φ is such a simple B-spline, we first determine the space of polynomials with maximal total degree included in , and we prove some results concerning the linear independence of the family . Next, we show that the cardinal interpolation with φ is correct and we study in S(φ) a Lagrange interpolation problem. Finally, we define composed B-splines by repeated convolution of φ with the characteristic functions of a square or a lozenge, and we give some of their properties.

A Data Assimilation System For Operational Weather Forecast In Galicia Region (nw Spain)

NASA Astrophysics Data System (ADS)

Balseiro, C. F.; Souto, M. J.; Pérez-Muñuzuri, V.; Brewster, K.; Xue, M.

Regional weather forecast models, such as the Advanced Regional Prediction System (ARPS), over complex environments with varying local influences require an accurate meteorological analysis that should include all local meteorological measurements available. In this work, the ARPS Data Analysis System (ADAS) (Xue et al. 2001) is applied as a three-dimensional weather analysis tool to include surface station and rawinsonde data with the NCEP AVN forecasts as the analysis background. Currently in ADAS, a set of five meteorological variables are considered during the analysis: horizontal grid-relative wind components, pressure, potential temperature and spe- cific humidity. The analysis is used for high resolution numerical weather prediction for the Galicia region. The analysis method used in ADAS is based on the successive corrective scheme of Bratseth (1986), which asymptotically approaches the result of a statistical (optimal) interpolation, but at lower computational cost. As in the optimal interpolation scheme, the Bratseth interpolation method can take into account the rel- ative error between background and observational data, therefore they are relatively insensitive to large variations in data density and can integrate data of mixed accuracy. This method can be applied economically in an operational setting, providing signifi- cant improvement over the background model forecast as well as any analysis without high-resolution local observations. A one-way nesting is applied for weather forecast in Galicia region, and the use of this assimilation system in both domains shows better results not only in initial conditions but also in all forecast periods. Bratseth, A.M. (1986): "Statistical interpolation by means of successive corrections." Tellus, 38A, 439-447. Souto, M. J., Balseiro, C. F., Pérez-Muñuzuri, V., Xue, M. Brewster, K., (2001): "Im- pact of cloud analysis on numerical weather prediction in the galician region of Spain". Submitted to Journal of Applied Meteorology. Xue, M., Wang. D., Gao, J., Brewster, K, Droegemeier, K. K., (2001): "The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation". Meteor. Atmos Physics. Accepted

Parallel Semi-Implicit Spectral Element Atmospheric Model

NASA Astrophysics Data System (ADS)

Fournier, A.; Thomas, S.; Loft, R.

2001-05-01

The shallow-water equations (SWE) have long been used to test atmospheric-modeling numerical methods. The SWE contain essential wave-propagation and nonlinear effects of more complete models. We present a semi-implicit (SI) improvement of the Spectral Element Atmospheric Model to solve the SWE (SEAM, Taylor et al. 1997, Fournier et al. 2000, Thomas & Loft 2000). SE methods are h-p finite element methods combining the geometric flexibility of size-h finite elements with the accuracy of degree-p spectral methods. Our work suggests that exceptional parallel-computation performance is achievable by a General-Circulation-Model (GCM) dynamical core, even at modest climate-simulation resolutions (>1o). The code derivation involves weak variational formulation of the SWE, Gauss(-Lobatto) quadrature over the collocation points, and Legendre cardinal interpolators. Appropriate weak variation yields a symmetric positive-definite Helmholtz operator. To meet the Ladyzhenskaya-Babuska-Brezzi inf-sup condition and avoid spurious modes, we use a staggered grid. The SI scheme combines leapfrog and Crank-Nicholson schemes for the nonlinear and linear terms respectively. The localization of operations to elements ideally fits the method to cache-based microprocessor computer architectures --derivatives are computed as collections of small (8x8), naturally cache-blocked matrix-vector products. SEAM also has desirable boundary-exchange communication, like finite-difference models. Timings on on the IBM SP and Compaq ES40 supercomputers indicate that the SI code (20-min timestep) requires 1/3 the CPU time of the explicit code (2-min timestep) for T42 resolutions. Both codes scale nearly linearly out to 400 processors. We achieved single-processor performance up to 30% of peak for both codes on the 375-MHz IBM Power-3 processors. Fast computation and linear scaling lead to a useful climate-simulation dycore only if enough model time is computed per unit wall-clock time. An efficient SI solver is essential to substantially increase this rate. Parallel preconditioning for an iterative conjugate-gradient elliptic solver is described. We are building a GCM dycore capable of 200 GF% lOPS sustained performance on clustered RISC/cache architectures using hybrid MPI/OpenMP programming.

Transfer of uncertainty of space-borne high resolution rainfall products at ungauged regions

NASA Astrophysics Data System (ADS)

Tang, Ling

Hydrologically relevant characteristics of high resolution (˜ 0.25 degree, 3 hourly) satellite rainfall uncertainty were derived as a function of season and location using a six year (2002-2007) archive of National Aeronautics and Space Administration (NASA)'s Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) precipitation data. The Next Generation Radar (NEXRAD) Stage IV rainfall data over the continental United States was used as ground validation (GV) data. A geostatistical mapping scheme was developed and tested for transfer (i.e., spatial interpolation) of uncertainty information from GV regions to the vast non-GV regions by leveraging the error characterization work carried out in the earlier step. The open question explored here was, "If 'error' is defined on the basis of independent ground validation (GV) data, how are error metrics estimated for a satellite rainfall data product without the need for much extensive GV data?" After a quantitative analysis of the spatial and temporal structure of the satellite rainfall uncertainty, a proof-of-concept geostatistical mapping scheme (based on the kriging method) was evaluated. The idea was to understand how realistic the idea of 'transfer' is for the GPM era. It was found that it was indeed technically possible to transfer error metrics from a gauged to an ungauged location for certain error metrics and that a regionalized error metric scheme for GPM may be possible. The uncertainty transfer scheme based on a commonly used kriging method (ordinary kriging) was then assessed further at various timescales (climatologic, seasonal, monthly and weekly), and as a function of the density of GV coverage. The results indicated that if a transfer scheme for estimating uncertainty metrics was finer than seasonal scale (ranging from 3-6 hourly to weekly-monthly), the effectiveness for uncertainty transfer worsened significantly. Next, a comprehensive assessment of different kriging methods for spatial transfer (interpolation) of error metrics was performed. Three kriging methods for spatial interpolation are compared, which are: ordinary kriging (OK), indicator kriging (IK) and disjunctive kriging (DK). Additional comparison with the simple inverse distance weighting (IDW) method was also performed to quantify the added benefit (if any) of using geostatistical methods. The overall performance ranking of the kriging methods was found to be as follows: OK=DK > IDW > IK. Lastly, various metrics of satellite rainfall uncertainty were identified for two large continental landmasses that share many similar Koppen climate zones, United States and Australia. The dependence of uncertainty as a function of gauge density was then investigated. The investigation revealed that only the first and second ordered moments of error are most amenable to a Koppen-type climate type classification in different continental landmasses.

A rapid boundary integral equation technique for protein electrostatics

NASA Astrophysics Data System (ADS)

Grandison, Scott; Penfold, Robert; Vanden-Broeck, Jean-Marc

2007-06-01

A new boundary integral formulation is proposed for the solution of electrostatic field problems involving piecewise uniform dielectric continua. Direct Coulomb contributions to the total potential are treated exactly and Green's theorem is applied only to the residual reaction field generated by surface polarisation charge induced at dielectric boundaries. The implementation shows significantly improved numerical stability over alternative schemes involving the total field or its surface normal derivatives. Although strictly respecting the electrostatic boundary conditions, the partitioned scheme does introduce a jump artefact at the interface. Comparison against analytic results in canonical geometries, however, demonstrates that simple interpolation near the boundary is a cheap and effective way to circumvent this characteristic in typical applications. The new scheme is tested in a naive model to successfully predict the ground state orientation of biomolecular aggregates comprising the soybean storage protein, glycinin.

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

On Fast Post-Processing of Global Positioning System Simulator Truth Data and Receiver Measurements and Solutions Data

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Day, John H. (Technical Monitor)

2000-01-01

Post-Processing of data related to a Global Positioning System (GPS) simulation is an important activity in qualification of a GPS receiver for space flight. Because a GPS simulator is a critical resource it is desirable to move off the pertinent simulation data from the simulator as soon as a test is completed. The simulator data files are usually moved to a Personal Computer (PC), where the post-processing of the receiver logged measurements and solutions data and simulated data is performed. Typically post-processing is accomplished using PC-based commercial software languages and tools. Because of commercial software systems generality their general-purpose functions are notoriously slow and more than often are the bottleneck problem even for short duration experiments. For example, it may take 8 hours to post-process data from a 6-hour simulation. There is a need to do post-processing faster, especially in order to use the previous test results as feedback for a next simulation setup. This paper demonstrates that a fast software linear interpolation algorithm is applicable to a large class of engineering problems, like GPS simulation data post-processing, where computational time is a critical resource and is one of the most important considerations. An approach is developed that allows to speed-up post-processing by an order of magnitude. It is based on improving the post-processing bottleneck interpolation algorithm using apriori information that is specific to the GPS simulation application. The presented post-processing scheme was used in support of a few successful space flight missions carrying GPS receivers. A future approach to solving the post-processing performance problem using Field Programmable Gate Array (FPGA) technology is described.

New, simplified, interpolation method for estimation of microscopic nuclear masses based on the p-factor, P = N/sub P/N/sub N//(N/sub p/+N/sub n/)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haustein, P.E.; Brenner, D.S.; Casten, R.F.

1987-12-10

A new semi-empirical method, based on the use of the P-factor (P = N/sub p/N/sub n//(N/sub p/+N/sub n/)), is shown to simplify significantly the systematics of atomic masses. Its uses is illustrated for actinide nuclei where complicated patterns of mass systematics seen in traditional plots versus Z, N, or isospin are consolidated and transformed into linear ones extending over long isotopic and isotonic sequences. The linearization of the systematics by this procedure provides a simple basis for mass prediction. For many unmeasured nuclei beyond the known mass surface, the P-factor method operates by interpolation among data for known nuclei rathermore » than by extrapolation, as is common in other mass models.« less

International Geomagnetic Reference Field: the third generation.

USGS Publications Warehouse

Peddie, N.W.

1982-01-01

In August 1981 the International Association of Geomagnetism and Aeronomy revised the International Geomagnetic Reference Field (IGRF). It is the second revision since the inception of the IGRF in 1968. The revision extends the earlier series of IGRF models from 1980 to 1985, introduces a new series of definitive models for 1965-1976, and defines a provisional reference field for 1975- 1980. The revision consists of: 1) a model of the main geomagnetic field at 1980.0, not continuous with the earlier series of IGRF models together with a forecast model of the secular variation of the main field during 1980-1985; 2) definitive models of the main field at 1965.0, 1970.0, and 1975.0, with linear interpolation of the model coefficients specified for intervening dates; and 3) a provisional reference field for 1975-1980, defined as the linear interpolation of the 1975 and 1980 main-field models.-from Author

Modeling of particle interactions in magnetorheological elastomers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biller, A. M., E-mail: kam@icmm.ru; Stolbov, O. V., E-mail: oleg100@gmail.com; Raikher, Yu. L., E-mail: raikher@icmm.ru

2014-09-21

The interaction between two particles made of an isotropic linearly polarizable magnetic material and embedded in an elastomer matrix is studied. In this case, when an external field is imposed, the magnetic attraction of the particles, contrary to point dipoles, is almost wraparound. The exact solution of the magnetic problem in the linear polarization case, although existing, is not practical; to circumvent its use, an interpolation formula is proposed. One more interpolation expression is developed for the resistance of the elastic matrix to the field-induced particle displacements. Minimization of the total energy of the pair reveals its configurational bistability inmore » a certain field range. One of the possible equilibrium states corresponds to the particles dwelling at a distance, the other—to their collapse in a tight dimer. This mesoscopic bistability causes magnetomechanical hysteresis which has important implications for the macroscopic behavior of magnetorheological elastomers.« less

Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

NASA Astrophysics Data System (ADS)

Zhao, Liang; Healy, John J.; Muniraj, Inbarasan; Cui, Xiao-Guang; Malallah, Ra'ed; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

Study of Interpolated Timing Recovery Phase-Locked Loop with Linearly Constrained Adaptive Prefilter for Higher-Density Optical Disc

NASA Astrophysics Data System (ADS)

Kajiwara, Yoshiyuki; Shiraishi, Junya; Kobayashi, Shoei; Yamagami, Tamotsu

2009-03-01

A digital phase-locked loop (PLL) with a linearly constrained adaptive filter (LCAF) has been studied for higher-linear-density optical discs. LCAF has been implemented before an interpolated timing recovery (ITR) PLL unit in order to improve the quality of phase error calculation by using an adaptively equalized partial response (PR) signal. Coefficient update of an asynchronous sampled adaptive FIR filter with a least-mean-square (LMS) algorithm has been constrained by a projection matrix in order to suppress the phase shift of the tap coefficients of the adaptive filter. We have developed projection matrices that are suitable for Blu-ray disc (BD) drive systems by numerical simulation. Results have shown the properties of the projection matrices. Then, we have designed the read channel system of the ITR PLL with an LCAF model on the FPGA board for experiments. Results have shown that the LCAF improves the tilt margins of 30 gigabytes (GB) recordable BD (BD-R) and 33 GB BD read-only memory (BD-ROM) with a sufficient LMS adaptation stability.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.

2003-01-01

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

A Search for Mountain Waves in MLS Stratospheric Limb Radiances from the Winter Northern Hemisphere: Data Analysis and Global Mountain Wave Modeling

DTIC Science & Technology

2004-02-11

the general circulation of the middle atmosphere, Philos. Trans. R. Soc. London, Ser. A, 323, 693–705. Anton , H. (2000), Elementary Linear Algebra ...Because the saturated radiances may depend slightly on tangent height as the limb path length decreases, a linear trend (described by parameters a and b...track days and interpolated onto the same limb-track orbits. The color bar scale for radiance variance is linear . (b) Digital elevations of northern

A linear and non-linear polynomial neural network modeling of dissolved oxygen content in surface water: Inter- and extrapolation performance with inputs' significance analysis.

PubMed

Šiljić Tomić, Aleksandra; Antanasijević, Davor; Ristić, Mirjana; Perić-Grujić, Aleksandra; Pocajt, Viktor

2018-01-01

Accurate prediction of water quality parameters (WQPs) is an important task in the management of water resources. Artificial neural networks (ANNs) are frequently applied for dissolved oxygen (DO) prediction, but often only their interpolation performance is checked. The aims of this research, beside interpolation, were the determination of extrapolation performance of ANN model, which was developed for the prediction of DO content in the Danube River, and the assessment of relationship between the significance of inputs and prediction error in the presence of values which were of out of the range of training. The applied ANN is a polynomial neural network (PNN) which performs embedded selection of most important inputs during learning, and provides a model in the form of linear and non-linear polynomial functions, which can then be used for a detailed analysis of the significance of inputs. Available dataset that contained 1912 monitoring records for 17 water quality parameters was split into a "regular" subset that contains normally distributed and low variability data, and an "extreme" subset that contains monitoring records with outlier values. The results revealed that the non-linear PNN model has good interpolation performance (R 2 =0.82), but it was not robust in extrapolation (R 2 =0.63). The analysis of extrapolation results has shown that the prediction errors are correlated with the significance of inputs. Namely, the out-of-training range values of the inputs with low importance do not affect significantly the PNN model performance, but their influence can be biased by the presence of multi-outlier monitoring records. Subsequently, linear PNN models were successfully applied to study the effect of water quality parameters on DO content. It was observed that DO level is mostly affected by temperature, pH, biological oxygen demand (BOD) and phosphorus concentration, while in extreme conditions the importance of alkalinity and bicarbonates rises over pH and BOD. Copyright © 2017 Elsevier B.V. All rights reserved.

Near-Space TOPSAR Large-Scene Full-Aperture Imaging Scheme Based on Two-Step Processing

PubMed Central

Zhang, Qianghui; Wu, Junjie; Li, Wenchao; Huang, Yulin; Yang, Jianyu; Yang, Haiguang

2016-01-01

Free of the constraints of orbit mechanisms, weather conditions and minimum antenna area, synthetic aperture radar (SAR) equipped on near-space platform is more suitable for sustained large-scene imaging compared with the spaceborne and airborne counterparts. Terrain observation by progressive scans (TOPS), which is a novel wide-swath imaging mode and allows the beam of SAR to scan along the azimuth, can reduce the time of echo acquisition for large scene. Thus, near-space TOPS-mode SAR (NS-TOPSAR) provides a new opportunity for sustained large-scene imaging. An efficient full-aperture imaging scheme for NS-TOPSAR is proposed in this paper. In this scheme, firstly, two-step processing (TSP) is adopted to eliminate the Doppler aliasing of the echo. Then, the data is focused in two-dimensional frequency domain (FD) based on Stolt interpolation. Finally, a modified TSP (MTSP) is performed to remove the azimuth aliasing. Simulations are presented to demonstrate the validity of the proposed imaging scheme for near-space large-scene imaging application. PMID:27472341

A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots

NASA Technical Reports Server (NTRS)

Yang, S. L.; Cline, M. C.; Chen, R.; Chang, Y. L.

1993-01-01

A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots.

Analysis/forecast experiments with a flow-dependent correlation function using FGGE data

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Carus, H.; Nestler, M. S.

1986-01-01

The use of a flow-dependent correlation function to improve the accuracy of an optimum interpolation (OI) scheme is examined. The development of the correlation function for the OI analysis scheme used for numerical weather prediction is described. The scheme uses a multivariate surface analysis over the oceans to model the pressure-wind error cross-correlation and it has the ability to use an error correlation function that is flow- and geographically-dependent. A series of four-day data assimilation experiments, conducted from January 5-9, 1979, were used to investigate the effect of the different features of the OI scheme (error correlation) on forecast skill for the barotropic lows and highs. The skill of the OI was compared with that of a successive correlation method (SCM) of analysis. It is observed that the largest difference in the correlation statistics occurred in barotropic and baroclinic lows and highs. The comparison reveals that the OI forecasts were more accurate than the SCM forecasts.

Development and validation of segmentation and interpolation techniques in sinograms for metal artifact suppression in CT.

PubMed

Veldkamp, Wouter J H; Joemai, Raoul M S; van der Molen, Aart J; Geleijns, Jacob

2010-02-01

Metal prostheses cause artifacts in computed tomography (CT) images. The purpose of this work was to design an efficient and accurate metal segmentation in raw data to achieve artifact suppression and to improve CT image quality for patients with metal hip or shoulder prostheses. The artifact suppression technique incorporates two steps: metal object segmentation in raw data and replacement of the segmented region by new values using an interpolation scheme, followed by addition of the scaled metal signal intensity. Segmentation of metal is performed directly in sinograms, making it efficient and different from current methods that perform segmentation in reconstructed images in combination with Radon transformations. Metal signal segmentation is achieved by using a Markov random field model (MRF). Three interpolation methods are applied and investigated. To provide a proof of concept, CT data of five patients with metal implants were included in the study, as well as CT data of a PMMA phantom with Teflon, PVC, and titanium inserts. Accuracy was determined quantitatively by comparing mean Hounsfield (HU) values and standard deviation (SD) as a measure of distortion in phantom images with titanium (original and suppressed) and without titanium insert. Qualitative improvement was assessed by comparing uncorrected clinical images with artifact suppressed images. Artifacts in CT data of a phantom and five patients were automatically suppressed. The general visibility of structures clearly improved. In phantom images, the technique showed reduced SD close to the SD for the case where titanium was not inserted, indicating improved image quality. HU values in corrected images were different from expected values for all interpolation methods. Subtle differences between interpolation methods were found. The new artifact suppression design is efficient, for instance, in terms of preserving spatial resolution, as it is applied directly to original raw data. It successfully reduced artifacts in CT images of five patients and in phantom images. Sophisticated interpolation methods are needed to obtain reliable HU values close to the prosthesis.

A rapid parallelization of cone-beam projection and back-projection operator based on texture fetching interpolation

NASA Astrophysics Data System (ADS)

Xie, Lizhe; Hu, Yining; Chen, Yang; Shi, Luyao

2015-03-01

Projection and back-projection are the most computational consuming parts in Computed Tomography (CT) reconstruction. Parallelization strategies using GPU computing techniques have been introduced. We in this paper present a new parallelization scheme for both projection and back-projection. The proposed method is based on CUDA technology carried out by NVIDIA Corporation. Instead of build complex model, we aimed on optimizing the existing algorithm and make it suitable for CUDA implementation so as to gain fast computation speed. Besides making use of texture fetching operation which helps gain faster interpolation speed, we fixed sampling numbers in the computation of projection, to ensure the synchronization of blocks and threads, thus prevents the latency caused by inconsistent computation complexity. Experiment results have proven the computational efficiency and imaging quality of the proposed method.

The Mars Climate Database (MCD version 5.2)

NASA Astrophysics Data System (ADS)

Millour, E.; Forget, F.; Spiga, A.; Navarro, T.; Madeleine, J.-B.; Montabone, L.; Pottier, A.; Lefevre, F.; Montmessin, F.; Chaufray, J.-Y.; Lopez-Valverde, M. A.; Gonzalez-Galindo, F.; Lewis, S. R.; Read, P. L.; Huot, J.-P.; Desjean, M.-C.; MCD/GCM development Team

2015-10-01

The Mars Climate Database (MCD) is a database of meteorological fields derived from General Circulation Model (GCM) numerical simulations of the Martian atmosphere and validated using available observational data. The MCD includes complementary post-processing schemes such as high spatial resolution interpolation of environmental data and means of reconstructing the variability thereof. We have just completed (March 2015) the generation of a new version of the MCD, MCD version 5.2

Experimental comparison of landmark-based methods for 3D elastic registration of pre- and postoperative liver CT data

NASA Astrophysics Data System (ADS)

Lange, Thomas; Wörz, Stefan; Rohr, Karl; Schlag, Peter M.

2009-02-01

The qualitative and quantitative comparison of pre- and postoperative image data is an important possibility to validate surgical procedures, in particular, if computer assisted planning and/or navigation is performed. Due to deformations after surgery, partially caused by the removal of tissue, a non-rigid registration scheme is a prerequisite for a precise comparison. Interactive landmark-based schemes are a suitable approach, if high accuracy and reliability is difficult to achieve by automatic registration approaches. Incorporation of a priori knowledge about the anatomical structures to be registered may help to reduce interaction time and improve accuracy. Concerning pre- and postoperative CT data of oncological liver resections the intrahepatic vessels are suitable anatomical structures. In addition to using branching landmarks for registration, we here introduce quasi landmarks at vessel segments with high localization precision perpendicular to the vessels and low precision along the vessels. A comparison of interpolating thin-plate splines (TPS), interpolating Gaussian elastic body splines (GEBS) and approximating GEBS on landmarks at vessel branchings as well as approximating GEBS on the introduced vessel segment landmarks is performed. It turns out that the segment landmarks provide registration accuracies as good as branching landmarks and can improve accuracy if combined with branching landmarks. For a low number of landmarks segment landmarks are even superior.

GNSS Clock Error Impacts on Radio Occultation Retrievals

NASA Astrophysics Data System (ADS)

Weiss, Jan; Sokolovskiy, Sergey; Schreiner, Bill; Yoon, Yoke

2017-04-01

We assess the impacts of GPS and GLONASS clock errors on radio occultation retrieval of bending angle, refractivity, and temperature from low Earth orbit. The major contributing factor is the interpretation of GNSS clock offsets sampled at 30 sec or longer intervals. Using 1 Hz GNSS clock estimates as truth we apply several interpolation and fitting schemes to evaluate how they affect the accuracy of atmospheric retrieval products. The results are organized by GPS and GLONASS space vehicle and the GNSS clock interpolation/fitting scheme. We find that bending angle error is roughly similar for all current GPS transmitters (about 0.7 mcrad) but note some differences related to the type of atomic oscillator onboard the transmitter satellite. GLONASS bending angle errors show more variation over the constellation and are approximately two times larger than GPS. An investigation of the transmitter clock spectra reveals this is due to more power in periods between 2-10 sec. Retrieved refractivity and temperature products show clear differences between GNSS satellite generations, and indicate that GNSS clocks sampled at intervals smaller than 5 sec significantly improve accuracy, particularly for GLONASS. We conclude by summarizing the tested GNSS clock estimation and application strategies in the context of current and future radio occultation missions.

High-quality slab-based intermixing method for fusion rendering of multiple medical objects.

PubMed

Kim, Dong-Joon; Kim, Bohyoung; Lee, Jeongjin; Shin, Juneseuk; Kim, Kyoung Won; Shin, Yeong-Gil

2016-01-01

The visualization of multiple 3D objects has been increasingly required for recent applications in medical fields. Due to the heterogeneity in data representation or data configuration, it is difficult to efficiently render multiple medical objects in high quality. In this paper, we present a novel intermixing scheme for fusion rendering of multiple medical objects while preserving the real-time performance. First, we present an in-slab visibility interpolation method for the representation of subdivided slabs. Second, we introduce virtual zSlab, which extends an infinitely thin boundary (such as polygonal objects) into a slab with a finite thickness. Finally, based on virtual zSlab and in-slab visibility interpolation, we propose a slab-based visibility intermixing method with the newly proposed rendering pipeline. Experimental results demonstrate that the proposed method delivers more effective multiple-object renderings in terms of rendering quality, compared to conventional approaches. And proposed intermixing scheme provides high-quality intermixing results for the visualization of intersecting and overlapping surfaces by resolving aliasing and z-fighting problems. Moreover, two case studies are presented that apply the proposed method to the real clinical applications. These case studies manifest that the proposed method has the outstanding advantages of the rendering independency and reusability. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Tensor scale: An analytic approach with efficient computation and applications☆

PubMed Central

Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

2015-01-01

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

Improving spatial resolution in skin-contact thermography: comparison between a spline based and linear interpolation.

PubMed

Giansanti, Daniele

2008-07-01

A wearable device for skin-contact thermography [Giansanti D, Maccioni G. Development and testing of a wearable integrated thermometer sensor for skin contact thermography. Med Eng Phys 2006 [ahead of print

MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.

2013-01-01

A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton-Raphson formulation, respectively.

A comparison of washout filters using a human dynamic orientation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Riedel, S. A.

1977-01-01

The Ormsby model of human dynamic orientation, a discrete time computer program, was used to provide a vestibular explanation for observed differences between two washout schemes. These washout schemes, a linear washout and a nonlinear washout, were subjectively evaluated. It was found that the linear washout presented false rate cues, causing pilots to rate the simulation fidelity of the linear scheme much lower than the nonlinear scheme. By inputting these motion histories into the Ormsby model, it was shown that the linear filter causes discontinuities in the pilot's perceived angular velocity, resulting in the sensation of an anomalous rate cue. This phenomenon does not occur with the use of the nonlinear filter.

Evaluation of gridding procedures for air temperature over Southern Africa

NASA Astrophysics Data System (ADS)

Eiselt, Kai-Uwe; Kaspar, Frank; Mölg, Thomas; Krähenmann, Stefan; Posada, Rafael; Riede, Jens O.

2017-06-01

Africa is considered to be highly vulnerable to climate change, yet the availability of observational data and derived products is limited. As one element of the SASSCAL initiative (Southern African Science Service Centre for Climate Change and Adaptive Land Management), a cooperation of Angola, Botswana, Namibia, Zambia, South Africa and Germany, networks of automatic weather stations have been installed or improved (http://www.sasscalweathernet.org). The increased availability of meteorological observations improves the quality of gridded products for the region. Here we compare interpolation methods for monthly minimum and maximum temperatures which were calculated from hourly measurements. Due to a lack of longterm records we focused on data ranging from September 2014 to August 2016. The best interpolation results have been achieved combining multiple linear regression (elevation, a continentality index and latitude as predictors) with three dimensional inverse distance weighted interpolation.

Randomized interpolative decomposition of separated representations

NASA Astrophysics Data System (ADS)

Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory

2015-01-01

We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.

Tomography for two-dimensional gas temperature distribution based on TDLAS

NASA Astrophysics Data System (ADS)

Luo, Can; Wang, Yunchu; Xing, Fei

2018-03-01

Based on tunable diode laser absorption spectroscopy (TDLAS), the tomography is used to reconstruct the combustion gas temperature distribution. The effects of number of rays, number of grids, and spacing of rays on the temperature reconstruction results for parallel ray are researched. The reconstruction quality is proportional to the ray number. The quality tends to be smoother when the ray number exceeds a certain value. The best quality is achieved when η is between 0.5 and 1. A virtual ray method combined with the reconstruction algorithms is tested. It is found that virtual ray method is effective to improve the accuracy of reconstruction results, compared with the original method. The linear interpolation method and cubic spline interpolation method, are used to improve the calculation accuracy of virtual ray absorption value. According to the calculation results, cubic spline interpolation is better. Moreover, the temperature distribution of a TBCC combustion chamber is used to validate those conclusions.

Analysis/forecast experiments with a multivariate statistical analysis scheme using FGGE data

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1985-01-01

A three-dimensional, multivariate, statistical analysis method, optimal interpolation (OI) is described for modeling meteorological data from widely dispersed sites. The model was developed to analyze FGGE data at the NASA-Goddard Laboratory of Atmospherics. The model features a multivariate surface analysis over the oceans, including maintenance of the Ekman balance and a geographically dependent correlation function. Preliminary comparisons are made between the OI model and similar schemes employed at the European Center for Medium Range Weather Forecasts and the National Meteorological Center. The OI scheme is used to provide input to a GCM, and model error correlations are calculated for forecasts of 500 mb vertical water mixing ratios and the wind profiles. Comparisons are made between the predictions and measured data. The model is shown to be as accurate as a successive corrections model out to 4.5 days.

Development of a new metal artifact reduction algorithm by using an edge preserving method for CBCT imaging

NASA Astrophysics Data System (ADS)

Kim, Juhye; Nam, Haewon; Lee, Rena

2015-07-01

CT (computed tomography) images, metal materials such as tooth supplements or surgical clips can cause metal artifact and degrade image quality. In severe cases, this may lead to misdiagnosis. In this research, we developed a new MAR (metal artifact reduction) algorithm by using an edge preserving filter and the MATLAB program (Mathworks, version R2012a). The proposed algorithm consists of 6 steps: image reconstruction from projection data, metal segmentation, forward projection, interpolation, applied edge preserving smoothing filter, and new image reconstruction. For an evaluation of the proposed algorithm, we obtained both numerical simulation data and data for a Rando phantom. In the numerical simulation data, four metal regions were added into the Shepp Logan phantom for metal artifacts. The projection data of the metal-inserted Rando phantom were obtained by using a prototype CBCT scanner manufactured by medical engineering and medical physics (MEMP) laboratory research group in medical science at Ewha Womans University. After these had been adopted the proposed algorithm was performed, and the result were compared with the original image (with metal artifact without correction) and with a corrected image based on linear interpolation. Both visual and quantitative evaluations were done. Compared with the original image with metal artifacts and with the image corrected by using linear interpolation, both the numerical and the experimental phantom data demonstrated that the proposed algorithm reduced the metal artifact. In conclusion, the evaluation in this research showed that the proposed algorithm outperformed the interpolation based MAR algorithm. If an optimization and a stability evaluation of the proposed algorithm can be performed, the developed algorithm is expected to be an effective tool for eliminating metal artifacts even in commercial CT systems.

Deterministic implementations of single-photon multi-qubit Deutsch-Jozsa algorithms with linear optics

NASA Astrophysics Data System (ADS)

Wei, Hai-Rui; Liu, Ji-Zhen

2017-02-01

It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch-Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.

Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn; Liu, Ji-Zhen

2017-02-15

It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch–Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.

A Technique of Treating Negative Weights in WENO Schemes

NASA Technical Reports Server (NTRS)

Shi, Jing; Hu, Changqing; Shu, Chi-Wang

2000-01-01

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

Elastic-wave-mode separation in TTI media with inverse-distance weighted interpolation involving position shading

NASA Astrophysics Data System (ADS)

Wang, Jian; Meng, Xiaohong; Zheng, Wanqiu

2017-10-01

The elastic-wave reverse-time migration of inhomogeneous anisotropic media is becoming the hotspot of research today. In order to ensure the accuracy of the migration, it is necessary to separate the wave mode into P-wave and S-wave before migration. For inhomogeneous media, the Kelvin-Christoffel equation can be solved in the wave-number domain by using the anisotropic parameters of the mesh nodes, and the polarization vector of the P-wave and S-wave at each node can be calculated and transformed into the space domain to obtain the quasi-differential operators. However, this method is computationally expensive, especially for the process of quasi-differential operators. In order to reduce the computational complexity, the wave-mode separation of mixed domain can be realized on the basis of a reference model in the wave-number domain. But conventional interpolation methods and reference model selection methods reduce the separation accuracy. In order to further improve the separation effect, this paper introduces an inverse-distance interpolation method involving position shading and uses the reference model selection method of random points scheme. This method adds the spatial weight coefficient K, which reflects the orientation of the reference point on the conventional IDW algorithm, and the interpolation process takes into account the combined effects of the distance and azimuth of the reference points. Numerical simulation shows that the proposed method can separate the wave mode more accurately using fewer reference models and has better practical value.

Progress in Grid Generation: From Chimera to DRAGON Grids

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Kao, Kai-Hsiung

1994-01-01

Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are discretized using the newly proposed flux scheme, AUSM+, which will be briefly described herein. Numerical tests on representative 2D inviscid flows are given for demonstration. Finally, extension to 3D is underway, only paced by the availability of the 3D unstructured grid generator.

Improved Visualization of Gastrointestinal Slow Wave Propagation Using a Novel Wavefront-Orientation Interpolation Technique.

PubMed

Mayne, Terence P; Paskaranandavadivel, Niranchan; Erickson, Jonathan C; OGrady, Gregory; Cheng, Leo K; Angeli, Timothy R

2018-02-01

High-resolution mapping of gastrointestinal (GI) slow waves is a valuable technique for research and clinical applications. Interpretation of high-resolution GI mapping data relies on animations of slow wave propagation, but current methods remain as rudimentary, pixelated electrode activation animations. This study aimed to develop improved methods of visualizing high-resolution slow wave recordings that increases ease of interpretation. The novel method of "wavefront-orientation" interpolation was created to account for the planar movement of the slow wave wavefront, negate any need for distance calculations, remain robust in atypical wavefronts (i.e., dysrhythmias), and produce an appropriate interpolation boundary. The wavefront-orientation method determines the orthogonal wavefront direction and calculates interpolated values as the mean slow wave activation-time (AT) of the pair of linearly adjacent electrodes along that direction. Stairstep upsampling increased smoothness and clarity. Animation accuracy of 17 human high-resolution slow wave recordings (64-256 electrodes) was verified by visual comparison to the prior method showing a clear improvement in wave smoothness that enabled more accurate interpretation of propagation, as confirmed by an assessment of clinical applicability performed by eight GI clinicians. Quantitatively, the new method produced accurate interpolation values compared to experimental data (mean difference 0.02 ± 0.05 s) and was accurate when applied solely to dysrhythmic data (0.02 ± 0.06 s), both within the error in manual AT marking (mean 0.2 s). Mean interpolation processing time was 6.0 s per wave. These novel methods provide a validated visualization platform that will improve analysis of high-resolution GI mapping in research and clinical translation.

Accuracy of stream habitat interpolations across spatial scales

USGS Publications Warehouse

Sheehan, Kenneth R.; Welsh, Stuart A.

2013-01-01

Stream habitat data are often collected across spatial scales because relationships among habitat, species occurrence, and management plans are linked at multiple spatial scales. Unfortunately, scale is often a factor limiting insight gained from spatial analysis of stream habitat data. Considerable cost is often expended to collect data at several spatial scales to provide accurate evaluation of spatial relationships in streams. To address utility of single scale set of stream habitat data used at varying scales, we examined the influence that data scaling had on accuracy of natural neighbor predictions of depth, flow, and benthic substrate. To achieve this goal, we measured two streams at gridded resolution of 0.33 × 0.33 meter cell size over a combined area of 934 m2 to create a baseline for natural neighbor interpolated maps at 12 incremental scales ranging from a raster cell size of 0.11 m2 to 16 m2 . Analysis of predictive maps showed a logarithmic linear decay pattern in RMSE values in interpolation accuracy for variables as resolution of data used to interpolate study areas became coarser. Proportional accuracy of interpolated models (r2 ) decreased, but it was maintained up to 78% as interpolation scale moved from 0.11 m2 to 16 m2 . Results indicated that accuracy retention was suitable for assessment and management purposes at various scales different from the data collection scale. Our study is relevant to spatial modeling, fish habitat assessment, and stream habitat management because it highlights the potential of using a single dataset to fulfill analysis needs rather than investing considerable cost to develop several scaled datasets.

Some results on numerical methods for hyperbolic conservation laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang Huanan.

1989-01-01

This dissertation contains some results on the numerical solutions of hyperbolic conservation laws. (1) The author introduced an artificial compression method as a correction to the basic ENO schemes. The method successfully prevents contact discontinuities from being smeared. This is achieved by increasing the slopes of the ENO reconstructions in such a way that the essentially non-oscillatory property of the schemes is kept. He analyzes the non-oscillatory property of the new artificial compression method by applying it to the UNO scheme which is a second order accurate ENO scheme, and proves that the resulting scheme is indeed non-oscillatory. Extensive 1-Dmore » numerical results and some preliminary 2-D ones are provided to show the strong performance of the method. (2) He combines the ENO schemes and the centered difference schemes into self-adjusting hybrid schemes which will be called the localized ENO schemes. At or near the jumps, he uses the ENO schemes with the field by field decompositions, otherwise he simply uses the centered difference schemes without the field by field decompositions. The method involves a new interpolation analysis. In the numerical experiments on several standard test problems, the quality of the numerical results of this method is close to that of the pure ENO results. The localized ENO schemes can be equipped with the above artificial compression method. In this way, he dramatically improves the resolutions of the contact discontinuities at very little additional costs. (3) He introduces a space-time mesh refinement method for time dependent problems.« less

An improved local radial point interpolation method for transient heat conduction analysis

NASA Astrophysics Data System (ADS)

Wang, Feng; Lin, Gao; Zheng, Bao-Jing; Hu, Zhi-Qiang

2013-06-01

The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.

Numerical analysis of a high-order unstructured overset grid method for compressible LES of turbomachinery

NASA Astrophysics Data System (ADS)

de Laborderie, J.; Duchaine, F.; Gicquel, L.; Vermorel, O.; Wang, G.; Moreau, S.

2018-06-01

Large-Eddy Simulation (LES) is recognized as a promising method for high-fidelity flow predictions in turbomachinery applications. The presented approach consists of the coupling of several instances of the same LES unstructured solver through an overset grid method. A high-order interpolation, implemented within this coupling method, is introduced and evaluated on several test cases. It is shown to be third order accurate, to preserve the accuracy of various second and third order convective schemes and to ensure the continuity of diffusive fluxes and subgrid scale tensors even in detrimental interface configurations. In this analysis, three types of spurious waves generated at the interface are identified. They are significantly reduced by the high-order interpolation at the interface. The latter having the same cost as the original lower order method, the high-order overset grid method appears as a promising alternative to be used in all the applications.

A fast simulation method for radiation maps using interpolation in a virtual environment.

PubMed

Li, Meng-Kun; Liu, Yong-Kuo; Peng, Min-Jun; Xie, Chun-Li; Yang, Li-Qun

2018-05-10

In nuclear decommissioning, virtual simulation technology is a useful tool to achieve an effective work process by using virtual environments to represent the physical and logical scheme of a real decommissioning project. This technology is cost-saving and time-saving, with the capacity to develop various decommissioning scenarios and reduce the risk of retrofitting. The method utilises a radiation map in a virtual simulation as the basis for the assessment of exposure to a virtual human. In this paper, we propose a fast simulation method using a known radiation source. The method has a unique advantage over point kernel and Monte Carlo methods because it generates the radiation map using interpolation in a virtual environment. The simulation of the radiation map including the calculation and the visualisation were realised using UNITY and MATLAB. The feasibility of the proposed method was tested on a hypothetical case and the results obtained are discussed in this paper.

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

NASA Technical Reports Server (NTRS)

Kenwright, David; Lane, David

1995-01-01

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

A comparison of high-frequency cross-correlation measures

NASA Astrophysics Data System (ADS)

Precup, Ovidiu V.; Iori, Giulia

2004-12-01

On a high-frequency scale the time series are not homogeneous, therefore standard correlation measures cannot be directly applied to the raw data. There are two ways to deal with this problem. The time series can be homogenised through an interpolation method (An Introduction to High-Frequency Finance, Academic Press, NY, 2001) (linear or previous tick) and then the Pearson correlation statistic computed. Recently, methods that can handle raw non-synchronous time series have been developed (Int. J. Theor. Appl. Finance 6(1) (2003) 87; J. Empirical Finance 4 (1997) 259). This paper compares two traditional methods that use interpolation with an alternative method applied directly to the actual time series.

Performance of Statistical Temporal Downscaling Techniques of Wind Speed Data Over Aegean Sea

NASA Astrophysics Data System (ADS)

Gokhan Guler, Hasan; Baykal, Cuneyt; Ozyurt, Gulizar; Kisacik, Dogan

2016-04-01

Wind speed data is a key input for many meteorological and engineering applications. Many institutions provide wind speed data with temporal resolutions ranging from one hour to twenty four hours. Higher temporal resolution is generally required for some applications such as reliable wave hindcasting studies. One solution to generate wind data at high sampling frequencies is to use statistical downscaling techniques to interpolate values of the finer sampling intervals from the available data. In this study, the major aim is to assess temporal downscaling performance of nine statistical interpolation techniques by quantifying the inherent uncertainty due to selection of different techniques. For this purpose, hourly 10-m wind speed data taken from 227 data points over Aegean Sea between 1979 and 2010 having a spatial resolution of approximately 0.3 degrees are analyzed from the National Centers for Environmental Prediction (NCEP) The Climate Forecast System Reanalysis database. Additionally, hourly 10-m wind speed data of two in-situ measurement stations between June, 2014 and June, 2015 are considered to understand effect of dataset properties on the uncertainty generated by interpolation technique. In this study, nine statistical interpolation techniques are selected as w0 (left constant) interpolation, w6 (right constant) interpolation, averaging step function interpolation, linear interpolation, 1D Fast Fourier Transform interpolation, 2nd and 3rd degree Lagrange polynomial interpolation, cubic spline interpolation, piecewise cubic Hermite interpolating polynomials. Original data is down sampled to 6 hours (i.e. wind speeds at 0th, 6th, 12th and 18th hours of each day are selected), then 6 hourly data is temporally downscaled to hourly data (i.e. the wind speeds at each hour between the intervals are computed) using nine interpolation technique, and finally original data is compared with the temporally downscaled data. A penalty point system based on coefficient of variation root mean square error, normalized mean absolute error, and prediction skill is selected to rank nine interpolation techniques according to their performance. Thus, error originated from the temporal downscaling technique is quantified which is an important output to determine wind and wave modelling uncertainties, and the performance of these techniques are demonstrated over Aegean Sea indicating spatial trends and discussing relevance to data type (i.e. reanalysis data or in-situ measurements). Furthermore, bias introduced by the best temporal downscaling technique is discussed. Preliminary results show that overall piecewise cubic Hermite interpolating polynomials have the highest performance to temporally downscale wind speed data for both reanalysis data and in-situ measurements over Aegean Sea. However, it is observed that cubic spline interpolation performs much better along Aegean coastline where the data points are close to the land. Acknowledgement: This research was partly supported by TUBITAK Grant number 213M534 according to Turkish Russian Joint research grant with RFBR and the CoCoNET (Towards Coast to Coast Network of Marine Protected Areas Coupled by Wİnd Energy Potential) project funded by European Union FP7/2007-2013 program.

A Practical and Secure Coercion-Resistant Scheme for Internet Voting

NASA Astrophysics Data System (ADS)

Araújo, Roberto; Foulle, Sébastien; Traoré, Jacques

Juels, Catalano, and Jakobsson (JCJ) proposed at WPES 2005 the first voting scheme that considers real-world threats and that is more realistic for Internet elections. Their scheme, though, has a quadratic work factor and thereby is not efficient for large scale elections. Based on the work of JCJ, Smith proposed an efficient scheme that has a linear work factor. In this paper we first show that Smith's scheme is insecure. Then we present a new coercion-resistant election scheme with a linear work factor that overcomes the flaw of Smith's proposal. Our solution is based on the group signature scheme of Camenisch and Lysyanskaya (Crypto 2004).

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Murman, S. M.; Berger, M. J.

2003-01-01

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Flow-covariate prediction of stream pesticide concentrations.

PubMed

Mosquin, Paul L; Aldworth, Jeremy; Chen, Wenlin

2018-01-01

Potential peak functions (e.g., maximum rolling averages over a given duration) of annual pesticide concentrations in the aquatic environment are important exposure parameters (or target quantities) for ecological risk assessments. These target quantities require accurate concentration estimates on nonsampled days in a monitoring program. We examined stream flow as a covariate via universal kriging to improve predictions of maximum m-day (m = 1, 7, 14, 30, 60) rolling averages and the 95th percentiles of atrazine concentration in streams where data were collected every 7 or 14 d. The universal kriging predictions were evaluated against the target quantities calculated directly from the daily (or near daily) measured atrazine concentration at 32 sites (89 site-yr) as part of the Atrazine Ecological Monitoring Program in the US corn belt region (2008-2013) and 4 sites (62 site-yr) in Ohio by the National Center for Water Quality Research (1993-2008). Because stream flow data are strongly skewed to the right, 3 transformations of the flow covariate were considered: log transformation, short-term flow anomaly, and normalized Box-Cox transformation. The normalized Box-Cox transformation resulted in predictions of the target quantities that were comparable to those obtained from log-linear interpolation (i.e., linear interpolation on the log scale) for 7-d sampling. However, the predictions appeared to be negatively affected by variability in regression coefficient estimates across different sample realizations of the concentration time series. Therefore, revised models incorporating seasonal covariates and partially or fully constrained regression parameters were investigated, and they were found to provide much improved predictions in comparison with those from log-linear interpolation for all rolling average measures. Environ Toxicol Chem 2018;37:260-273. © 2017 SETAC. © 2017 SETAC.

Numerical simulation of large-scale ocean-atmosphere coupling and the ocean's role in climate

NASA Technical Reports Server (NTRS)

Gates, W. L.

1983-01-01

The problem of reducing model generated sigma coordinate data to pressure levels is considered. A mass consistent scheme for performing budget analyses is proposed, wherein variables interpolated to a given pressure level are weighted according to the mass between a nominal pressure level above and either a nominal pressure level below or the Earth's surface, whichever is closer. The method is applied to the atmospheric energy cycle as simulated by the OSU two level atmospheric general circulation model. The results are more realistic than sigma coordinate analyses with respect to eddy decomposition, and are in agreement with the sigma coordinate evaluation of the numerical energy sink. Comparison with less sophisticated budget schemes indicates superiority locally, but not globally.

Flow solution on a dual-block grid around an airplane

NASA Technical Reports Server (NTRS)

Eriksson, Lars-Erik

1987-01-01

The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shalaby, Mohamad; Broderick, Avery E.; Chang, Philip

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to the fifth order). We validate our algorithm against several test problems—thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutionsmore » of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.« less

Performance of signal-to-noise ratio estimation for scanning electron microscope using autocorrelation Levinson-Durbin recursion model.

PubMed

Sim, K S; Lim, M S; Yeap, Z X

2016-07-01

A new technique to quantify signal-to-noise ratio (SNR) value of the scanning electron microscope (SEM) images is proposed. This technique is known as autocorrelation Levinson-Durbin recursion (ACLDR) model. To test the performance of this technique, the SEM image is corrupted with noise. The autocorrelation function of the original image and the noisy image are formed. The signal spectrum based on the autocorrelation function of image is formed. ACLDR is then used as an SNR estimator to quantify the signal spectrum of noisy image. The SNR values of the original image and the quantified image are calculated. The ACLDR is then compared with the three existing techniques, which are nearest neighbourhood, first-order linear interpolation and nearest neighbourhood combined with first-order linear interpolation. It is shown that ACLDR model is able to achieve higher accuracy in SNR estimation. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

Multiple-degree-of-freedom vehicle

DOEpatents

Borenstein, Johann

1995-01-01

A multi-degree-of-freedom vehicle employs a compliant linkage to accommodate the need for a variation in the distance between drive wheels or drive systems which are independently steerable and drivable. The subject vehicle is provided with rotary encodes to provide signals representative of the orientation of the steering pivot associated with each such drive wheel or system, and a linear encoder which issues a signal representative of the fluctuations in the distance between the drive elements. The wheels of the vehicle are steered and driven in response to the linear encoder signal, there being provided a controller system for minimizing the fluctuations in the distance. The controller system is a software implementation of a plurality of controllers, operating at the chassis level and at the vehicle level. A trajectory interpolator receives x-displacement, y-displacement, and .theta.-displacement signals and produces to the vehicle level controller trajectory signals corresponding to interpolated control signals. The x-displacement, y-displacement, and .theta.-displacement signals are received from a human operator, via a manipulable joy stick.

AN ADVANCED LEAKAGE SCHEME FOR NEUTRINO TREATMENT IN ASTROPHYSICAL SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perego, A.; Cabezón, R. M.; Käppeli, R., E-mail: albino.perego@physik.tu-darmstadt.de

We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae (CCSNe) and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively) separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmannmore » transport in the context of Newtonian spherically symmetric models of CCSNe. ASL shows a very good qualitative and a partial quantitative agreement for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme, coupling it to an axisymmetric Eulerian and to a three-dimensional smoothed particle hydrodynamics code to simulate core collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or are currently computationally too expensive.« less

A fast iterative scheme for the linearized Boltzmann equation

NASA Astrophysics Data System (ADS)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed.

Large Eddy Simulation (LES) of Particle-Laden Temporal Mixing Layers

NASA Technical Reports Server (NTRS)

Bellan, Josette; Radhakrishnan, Senthilkumaran

2012-01-01

High-fidelity models of plume-regolith interaction are difficult to develop because of the widely disparate flow conditions that exist in this process. The gas in the core of a rocket plume can often be modeled as a time-dependent, high-temperature, turbulent, reacting continuum flow. However, due to the vacuum conditions on the lunar surface, the mean molecular path in the outer parts of the plume is too long for the continuum assumption to remain valid. Molecular methods are better suited to model this region of the flow. Finally, granular and multiphase flow models must be employed to describe the dust and debris that are displaced from the surface, as well as how a crater is formed in the regolith. At present, standard commercial CFD (computational fluid dynamics) software is not capable of coupling each of these flow regimes to provide an accurate representation of this flow process, necessitating the development of custom software. This software solves the fluid-flow-governing equations in an Eulerian framework, coupled with the particle transport equations that are solved in a Lagrangian framework. It uses a fourth-order explicit Runge-Kutta scheme for temporal integration, an eighth-order central finite differencing scheme for spatial discretization. The non-linear terms in the governing equations are recast in cubic skew symmetric form to reduce aliasing error. The second derivative viscous terms are computed using eighth-order narrow stencils that provide better diffusion for the highest resolved wave numbers. A fourth-order Lagrange interpolation procedure is used to obtain gas-phase variable values at the particle locations.

Experimental verification of a GPC-LPV method with RLS and P1-TS fuzzy-based estimation for limiting the transient and residual vibration of a crane system

NASA Astrophysics Data System (ADS)

Smoczek, Jaroslaw

2015-10-01

The paper deals with the problem of reducing the residual vibration and limiting the transient oscillations of a flexible and underactuated system with respect to the variation of operating conditions. The comparative study of generalized predictive control (GPC) and fuzzy scheduling scheme developed based on the P1-TS fuzzy theory, local pole placement method and interval analysis of closed-loop system polynomial coefficients is addressed to the problem of flexible crane control. The two alternatives of a GPC-based method are proposed that enable to realize this technique either with or without a sensor of payload deflection. The first control technique is based on the recursive least squares (RLS) method applied to on-line estimate the parameters of a linear parameter varying (LPV) model of a crane dynamic system. The second GPC-based approach is based on a payload deflection feedback estimated using a pendulum model with the parameters interpolated using the P1-TS fuzzy system. Feasibility and applicability of the developed methods were confirmed through experimental verification performed on a laboratory scaled overhead crane.

A Lagrangian dynamic subgrid-scale model turbulence

NASA Technical Reports Server (NTRS)

Meneveau, C.; Lund, T. S.; Cabot, W.

1994-01-01

A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

Maximum likelihood convolutional decoding (MCD) performance due to system losses

NASA Technical Reports Server (NTRS)

Webster, L.

1976-01-01

A model for predicting the computational performance of a maximum likelihood convolutional decoder (MCD) operating in a noisy carrier reference environment is described. This model is used to develop a subroutine that will be utilized by the Telemetry Analysis Program to compute the MCD bit error rate. When this computational model is averaged over noisy reference phase errors using a high-rate interpolation scheme, the results are found to agree quite favorably with experimental measurements.

Computation of Acoustic Waves Through Sliding-Zone Interfaces Using an Euler/Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.

1996-01-01

The effect of a patched sliding-zone interface on the transmission of acoustic waves is examined for two- and three-dimensional model problems. A simple but general interpolation scheme at the patched boundary passes acoustic waves without distortion, provided that a sufficiently small time step is taken. A guideline is provided for the maximum permissible time step or zone speed that gives an acceptable error introduced by the sliding-zone interface.

Three-Dimensional Unsteady Separation at Low Reynolds Numbers

DTIC Science & Technology

1990-07-01

novel, robust adaptive- grid technique for incompressible flow (Shen & Reed 1990a "Shepard’s Interpolation for Solution-Adaptive Methods" submitted to...3-D adaptive- grid schemes developed for flat plate for full, unsteady, incompressible Navier Stokes. 4. 2-D and 3-D unsteady, vortex-lattice code...perforated to tailor suction through wall. Honeycomb and contractiong uide flow uniformly crons "a dn muwet a m Fiur32 c ic R n R ev lving -disc seals

Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

NASA Astrophysics Data System (ADS)

García-Senz, Domingo; Cabezón, Rubén M.; Escartín, José A.; Ebinger, Kevin

2014-10-01

Context. The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. Aims: We propose and check a method to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the sinc function). Methods: The proposed method was checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities, and the collapse of a Sun-like polytrope. Results: The analysis of the hydrodynamical simulations suggests that the scheme devised to equalize the accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Assimilation of remote sensing observations into a sediment transport model of China's largest freshwater lake: spatial and temporal effects.

PubMed

Zhang, Peng; Chen, Xiaoling; Lu, Jianzhong; Zhang, Wei

2015-12-01

Numerical models are important tools that are used in studies of sediment dynamics in inland and coastal waters, and these models can now benefit from the use of integrated remote sensing observations. This study explores a scheme for assimilating remotely sensed suspended sediment (from charge-coupled device (CCD) images obtained from the Huanjing (HJ) satellite) into a two-dimensional sediment transport model of Poyang Lake, the largest freshwater lake in China. Optimal interpolation is used as the assimilation method, and model predictions are obtained by combining four remote sensing images. The parameters for optimal interpolation are determined through a series of assimilation experiments evaluating the sediment predictions based on field measurements. The model with assimilation of remotely sensed sediment reduces the root-mean-square error of the predicted sediment concentrations by 39.4% relative to the model without assimilation, demonstrating the effectiveness of the assimilation scheme. The spatial effect of assimilation is explored by comparing model predictions with remotely sensed sediment, revealing that the model with assimilation generates reasonable spatial distribution patterns of suspended sediment. The temporal effect of assimilation on the model's predictive capabilities varies spatially, with an average temporal effect of approximately 10.8 days. The current velocities which dominate the rate and direction of sediment transport most likely result in spatial differences in the temporal effect of assimilation on model predictions.

How to improve breeding value prediction for feed conversion ratio in the case of incomplete longitudinal body weights.

PubMed

Tran, V H Huynh; Gilbert, H; David, I

2017-01-01

With the development of automatic self-feeders, repeated measurements of feed intake are becoming easier in an increasing number of species. However, the corresponding BW are not always recorded, and these missing values complicate the longitudinal analysis of the feed conversion ratio (FCR). Our aim was to evaluate the impact of missing BW data on estimations of the genetic parameters of FCR and ways to improve the estimations. On the basis of the missing BW profile in French Large White pigs (male pigs weighed weekly, females and castrated males weighed monthly), we compared 2 different ways of predicting missing BW, 1 using a Gompertz model and 1 using a linear interpolation. For the first part of the study, we used 17,398 weekly records of BW and feed intake recorded over 16 consecutive weeks in 1,222 growing male pigs. We performed a simulation study on this data set to mimic missing BW values according to the pattern of weekly proportions of incomplete BW data in females and castrated males. The FCR was then computed for each week using observed data (obser_FCR), data with missing BW (miss_FCR), data with BW predicted using a Gompertz model (Gomp_FCR), and data with BW predicted by linear interpolation (interp_FCR). Heritability (h) was estimated, and the EBV was predicted for each repeated FCR using a random regression model. In the second part of the study, the full data set (males with their complete BW records, castrated males and females with missing BW) was analyzed using the same methods (miss_FCR, Gomp_FCR, and interp_FCR). Results of the simulation study showed that h were overestimated in the case of missing BW and that predicting BW using a linear interpolation provided a more accurate estimation of h and of EBV than a Gompertz model. Over 100 simulations, the correlation between obser_EBV and interp_EBV, Gomp_EBV, and miss_EBV was 0.93 ± 0.02, 0.91 ± 0.01, and 0.79 ± 0.04, respectively. The heritabilities obtained with the full data set were quite similar for miss_FCR, Gomp_FCR, and interp_FCR. In conclusion, when the proportion of missing BW is high, genetic parameters of FCR are not well estimated. In French Large White pigs, in the growing period extending from d 65 to 168, prediction of missing BW using a Gompertz growth model slightly improved the estimations, but the linear interpolation improved the estimation to a greater extent. This result is due to the linear rather than sigmoidal increase in BW over the study period.

Topology optimization for design of segmented permanent magnet arrays with ferromagnetic materials

NASA Astrophysics Data System (ADS)

Lee, Jaewook; Yoon, Minho; Nomura, Tsuyoshi; Dede, Ercan M.

2018-03-01

This paper presents multi-material topology optimization for the co-design of permanent magnet segments and iron material. Specifically, a co-design methodology is proposed to find an optimal border of permanent magnet segments, a pattern of magnetization directions, and an iron shape. A material interpolation scheme is proposed for material property representation among air, permanent magnet, and iron materials. In this scheme, the permanent magnet strength and permeability are controlled by density design variables, and permanent magnet magnetization directions are controlled by angle design variables. In addition, a scheme to penalize intermediate magnetization direction is proposed to achieve segmented permanent magnet arrays with discrete magnetization directions. In this scheme, permanent magnet strength is controlled depending on magnetization direction, and consequently the final permanent magnet design converges into permanent magnet segments having target discrete directions. To validate the effectiveness of the proposed approach, three design examples are provided. The examples include the design of a dipole Halbach cylinder, magnetic system with arbitrarily-shaped cavity, and multi-objective problem resembling a magnetic refrigeration device.

Rtop - an R package for interpolation of data with a variable spatial support - examples from river networks

NASA Astrophysics Data System (ADS)

Olav Skøien, Jon; Laaha, Gregor; Koffler, Daniel; Blöschl, Günter; Pebesma, Edzer; Parajka, Juraj; Viglione, Alberto

2013-04-01

Geostatistical methods have been applied only to a limited extent for spatial interpolation in applications where the observations have an irregular support, such as runoff characteristics or population health data. Several studies have shown the potential of such methods (Gottschalk 1993, Sauquet et al. 2000, Gottschalk et al. 2006, Skøien et al. 2006, Goovaerts 2008), but these developments have so far not led to easily accessible, versatile, easy to apply and open source software. Based on the top-kriging approach suggested by Skøien et al. (2006), we will here present the package rtop, which has been implemented in the statistical environment R (R Core Team 2012). Taking advantage of the existing methods in R for analysis of spatial objects (Bivand et al. 2008), and the extensive possibilities for visualizing the results, rtop makes it easy to apply geostatistical interpolation methods when observations have a non-point spatial support. Although the package is flexible regarding data input, the main application so far has been for interpolation along river networks. We will present some examples showing how the package can easily be used for such interpolation. The model will soon be uploaded to CRAN, but is in the meantime also available from R-forge and can be installed by: > install.packages("rtop", repos="http://R-Forge.R-project.org") Bivand, R.S., Pebesma, E.J. & Gómez-Rubio, V., 2008. Applied spatial data analysis with r: Springer. Goovaerts, P., 2008. Kriging and semivariogram deconvolution in the presence of irregular geographical units. Mathematical Geosciences, 40 (1), 101-128. Gottschalk, L., 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., Krasovskaia, I., Leblois, E. & Sauquet, E., 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Core Team, 2012. R: A language and environment for statistical computing. Vienna, Austria, ISBN 3-900051-07-0. Sauquet, E., Gottschalk, L. & Leblois, E., 2000. Mapping average annual runoff: A hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J.O., Merz, R. & Blöschl, G., 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

The Canadian Precipitation Analysis (CaPA): Evaluation of the statistical interpolation scheme

NASA Astrophysics Data System (ADS)

Evans, Andrea; Rasmussen, Peter; Fortin, Vincent

2013-04-01

CaPA (Canadian Precipitation Analysis) is a data assimilation system which employs statistical interpolation to combine observed precipitation with gridded precipitation fields produced by Environment Canada's Global Environmental Multiscale (GEM) climate model into a final gridded precipitation analysis. Precipitation is important in many fields and applications, including agricultural water management projects, flood control programs, and hydroelectric power generation planning. Precipitation is a key input to hydrological models, and there is a desire to have access to the best available information about precipitation in time and space. The principal goal of CaPA is to produce this type of information. In order to perform the necessary statistical interpolation, CaPA requires the estimation of a semi-variogram. This semi-variogram is used to describe the spatial correlations between precipitation innovations, defined as the observed precipitation amounts minus the GEM forecasted amounts predicted at the observation locations. Currently, CaPA uses a single isotropic variogram across the entire analysis domain. The present project investigates the implications of this choice by first conducting a basic variographic analysis of precipitation innovation data across the Canadian prairies, with specific interest in identifying and quantifying potential anisotropy within the domain. This focus is further expanded by identifying the effect of storm type on the variogram. The ultimate goal of the variographic analysis is to develop improved semi-variograms for CaPA that better capture the spatial complexities of precipitation over the Canadian prairies. CaPA presently applies a Box-Cox data transformation to both the observations and the GEM data, prior to the calculation of the innovations. The data transformation is necessary to satisfy the normal distribution assumption, but introduces a significant bias. The second part of the investigation aims at devising a bias correction scheme based on a moving-window averaging technique. For both the variogram and bias correction components of this investigation, a series of trial runs are conducted to evaluate the impact of these changes on the resulting CaPA precipitation analyses.

Comparison of spatiotemporal interpolators for 4D image reconstruction from 2D transesophageal ultrasound

NASA Astrophysics Data System (ADS)

Haak, Alexander; van Stralen, Marijn; van Burken, Gerard; Klein, Stefan; Pluim, Josien P. W.; de Jong, Nico; van der Steen, Antonius F. W.; Bosch, Johan G.

2012-03-01

°For electrophysiology intervention monitoring, we intend to reconstruct 4D ultrasound (US) of structures in the beating heart from 2D transesophageal US by scanplane rotation. The image acquisition is continuous but unsynchronized to the heart rate, which results in a sparsely and irregularly sampled dataset and a spatiotemporal interpolation method is desired. Previously, we showed the potential of normalized convolution (NC) for interpolating such datasets. We explored 4D interpolation by 3 different methods: NC, nearest neighbor (NN), and temporal binning followed by linear interpolation (LTB). The test datasets were derived by slicing three 4D echocardiography datasets at random rotation angles (θ, range: 0-180) and random normalized cardiac phase (τ, range: 0-1). Four different distributions of rotated 2D images with 600, 900, 1350, and 1800 2D input images were created from all TEE sets. A 2D Gaussian kernel was used for NC and optimal kernel sizes (σθ and στ) were found by performing an exhaustive search. The RMS gray value error (RMSE) of the reconstructed images was computed for all interpolation methods. The estimated optimal kernels were in the range of σθ = 3.24 - 3.69°/ στ = 0.045 - 0.048, σθ = 2.79°/ στ = 0.031 - 0.038, σθ = 2.34°/ στ = 0.023 - 0.026, and σθ = 1.89°/ στ = 0.021 - 0.023 for 600, 900, 1350, and 1800 input images respectively. We showed that NC outperforms NN and LTB. For a small number of input images the advantage of NC is more pronounced.

Stream Kriging: Incremental and recursive ordinary Kriging over spatiotemporal data streams

NASA Astrophysics Data System (ADS)

Zhong, Xu; Kealy, Allison; Duckham, Matt

2016-05-01

Ordinary Kriging is widely used for geospatial interpolation and estimation. Due to the O (n3) time complexity of solving the system of linear equations, ordinary Kriging for a large set of source points is computationally intensive. Conducting real-time Kriging interpolation over continuously varying spatiotemporal data streams can therefore be especially challenging. This paper develops and tests two new strategies for improving the performance of an ordinary Kriging interpolator adapted to a stream-processing environment. These strategies rely on the expectation that, over time, source data points will frequently refer to the same spatial locations (for example, where static sensor nodes are generating repeated observations of a dynamic field). First, an incremental strategy improves efficiency in cases where a relatively small proportion of previously processed spatial locations are absent from the source points at any given iteration. Second, a recursive strategy improves efficiency in cases where there is substantial set overlap between the sets of spatial locations of source points at the current and previous iterations. These two strategies are evaluated in terms of their computational efficiency in comparison to ordinary Kriging algorithm. The results show that these two strategies can reduce the time taken to perform the interpolation by up to 90%, and approach average-case time complexity of O (n2) when most but not all source points refer to the same locations over time. By combining the approaches developed in this paper with existing heuristic ordinary Kriging algorithms, the conclusions indicate how further efficiency gains could potentially be accrued. The work ultimately contributes to the development of online ordinary Kriging interpolation algorithms, capable of real-time spatial interpolation with large streaming data sets.

A comparison of spatial analysis methods for the construction of topographic maps of retinal cell density.

PubMed

Garza-Gisholt, Eduardo; Hemmi, Jan M; Hart, Nathan S; Collin, Shaun P

2014-01-01

Topographic maps that illustrate variations in the density of different neuronal sub-types across the retina are valuable tools for understanding the adaptive significance of retinal specialisations in different species of vertebrates. To date, such maps have been created from raw count data that have been subjected to only limited analysis (linear interpolation) and, in many cases, have been presented as iso-density contour maps with contour lines that have been smoothed 'by eye'. With the use of stereological approach to count neuronal distribution, a more rigorous approach to analysing the count data is warranted and potentially provides a more accurate representation of the neuron distribution pattern. Moreover, a formal spatial analysis of retinal topography permits a more robust comparison of topographic maps within and between species. In this paper, we present a new R-script for analysing the topography of retinal neurons and compare methods of interpolating and smoothing count data for the construction of topographic maps. We compare four methods for spatial analysis of cell count data: Akima interpolation, thin plate spline interpolation, thin plate spline smoothing and Gaussian kernel smoothing. The use of interpolation 'respects' the observed data and simply calculates the intermediate values required to create iso-density contour maps. Interpolation preserves more of the data but, consequently includes outliers, sampling errors and/or other experimental artefacts. In contrast, smoothing the data reduces the 'noise' caused by artefacts and permits a clearer representation of the dominant, 'real' distribution. This is particularly useful where cell density gradients are shallow and small variations in local density may dramatically influence the perceived spatial pattern of neuronal topography. The thin plate spline and the Gaussian kernel methods both produce similar retinal topography maps but the smoothing parameters used may affect the outcome.

Single Image Super-Resolution Using Global Regression Based on Multiple Local Linear Mappings.

PubMed

Choi, Jae-Seok; Kim, Munchurl

2017-03-01

Super-resolution (SR) has become more vital, because of its capability to generate high-quality ultra-high definition (UHD) high-resolution (HR) images from low-resolution (LR) input images. Conventional SR methods entail high computational complexity, which makes them difficult to be implemented for up-scaling of full-high-definition input images into UHD-resolution images. Nevertheless, our previous super-interpolation (SI) method showed a good compromise between Peak-Signal-to-Noise Ratio (PSNR) performances and computational complexity. However, since SI only utilizes simple linear mappings, it may fail to precisely reconstruct HR patches with complex texture. In this paper, we present a novel SR method, which inherits the large-to-small patch conversion scheme from SI but uses global regression based on local linear mappings (GLM). Thus, our new SR method is called GLM-SI. In GLM-SI, each LR input patch is divided into 25 overlapped subpatches. Next, based on the local properties of these subpatches, 25 different local linear mappings are applied to the current LR input patch to generate 25 HR patch candidates, which are then regressed into one final HR patch using a global regressor. The local linear mappings are learned cluster-wise in our off-line training phase. The main contribution of this paper is as follows: Previously, linear-mapping-based conventional SR methods, including SI only used one simple yet coarse linear mapping to each patch to reconstruct its HR version. On the contrary, for each LR input patch, our GLM-SI is the first to apply a combination of multiple local linear mappings, where each local linear mapping is found according to local properties of the current LR patch. Therefore, it can better approximate nonlinear LR-to-HR mappings for HR patches with complex texture. Experiment results show that the proposed GLM-SI method outperforms most of the state-of-the-art methods, and shows comparable PSNR performance with much lower computational complexity when compared with a super-resolution method based on convolutional neural nets (SRCNN15). Compared with the previous SI method that is limited with a scale factor of 2, GLM-SI shows superior performance with average 0.79 dB higher in PSNR, and can be used for scale factors of 3 or higher.

Interpolation Approaches for Characterizing Spatial Variability of Soil Properties in Tuz Lake Basin of Turkey

NASA Astrophysics Data System (ADS)

Gorji, Taha; Sertel, Elif; Tanik, Aysegul

2017-12-01

Soil management is an essential concern in protecting soil properties, in enhancing appropriate soil quality for plant growth and agricultural productivity, and in preventing soil erosion. Soil scientists and decision makers require accurate and well-distributed spatially continuous soil data across a region for risk assessment and for effectively monitoring and managing soils. Recently, spatial interpolation approaches have been utilized in various disciplines including soil sciences for analysing, predicting and mapping distribution and surface modelling of environmental factors such as soil properties. The study area selected in this research is Tuz Lake Basin in Turkey bearing ecological and economic importance. Fertile soil plays a significant role in agricultural activities, which is one of the main industries having great impact on economy of the region. Loss of trees and bushes due to intense agricultural activities in some parts of the basin lead to soil erosion. Besides, soil salinization due to both human-induced activities and natural factors has exacerbated its condition regarding agricultural land development. This study aims to compare capability of Local Polynomial Interpolation (LPI) and Radial Basis Functions (RBF) as two interpolation methods for mapping spatial pattern of soil properties including organic matter, phosphorus, lime and boron. Both LPI and RBF methods demonstrated promising results for predicting lime, organic matter, phosphorous and boron. Soil samples collected in the field were used for interpolation analysis in which approximately 80% of data was used for interpolation modelling whereas the remaining for validation of the predicted results. Relationship between validation points and their corresponding estimated values in the same location is examined by conducting linear regression analysis. Eight prediction maps generated from two different interpolation methods for soil organic matter, phosphorus, lime and boron parameters were examined based on R2 and RMSE values. The outcomes indicate that RBF performance in predicting lime, organic matter and boron put forth better results than LPI. However, LPI shows better results for predicting phosphorus.

An algorithm for treating flat areas and depressions in digital elevation models using linear interpolation

EPA Science Inventory

Digital elevation model (DEM) data are essential to hydrological applications and have been widely used to calculate a variety of useful topographic characteristics, e.g., slope, flow direction, flow accumulation area, stream channel network, topographic index, and others. Excep...

General MoM Solutions for Large Arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fasenfest, B; Capolino, F; Wilton, D R

2003-07-22

This paper focuses on a numerical procedure that addresses the difficulties of dealing with large, finite arrays while preserving the generality and robustness of full-wave methods. We present a fast method based on approximating interactions between sufficiently separated array elements via a relatively coarse interpolation of the Green's function on a uniform grid commensurate with the array's periodicity. The interaction between the basis and testing functions is reduced to a three-stage process. The first stage is a projection of standard (e.g., RWG) subdomain bases onto a set of interpolation functions that interpolate the Green's function on the array face. Thismore » projection, which is used in a matrix/vector product for each array cell in an iterative solution process, need only be carried out once for a single cell and results in a low-rank matrix. An intermediate stage matrix/vector product computation involving the uniformly sampled Green's function is of convolutional form in the lateral (transverse) directions so that a 2D FFT may be used. The final stage is a third matrix/vector product computation involving a matrix resulting from projecting testing functions onto the Green's function interpolation functions; the low-rank matrix is either identical to (using Galerkin's method) or similar to that for the bases projection. An effective MoM solution scheme is developed for large arrays using a modification of the AIM (Adaptive Integral Method) method. The method permits the analysis of arrays with arbitrary contours and nonplanar elements. Both fill and solve times within the MoM method are improved with respect to more standard MoM solvers.« less

A Meshless Method for Magnetohydrodynamics and Applications to Protoplanetary Disks

NASA Astrophysics Data System (ADS)

McNally, Colin P.

2012-08-01

This thesis presents an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. The code has been parallelized by adapting the framework provided by Gadget-2. A set of standard test problems, including one part in a million amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities are presented. Finally we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. We provide a rigorous methodology for verifying a numerical method on two dimensional Kelvin-Helmholtz instability. The test problem was run in the Pencil Code, Athena, Enzo, NDSPHMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, although this work provides the mathematical framewor! k needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of Smoothed Particle Hydrodynamics. We then comment on the connection between this behavior and the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics interpolation. In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations, numerically enforcing the divergence free constraint on the magnetic field has been difficult. We observe that for point-based discretization, as used in finite-difference type and pseudo-spectral methods, the divergence free constraint can be satisfied entirely by a choice of interpolation used to define the derivatives of the magnetic field. As an example we demonstrate a new class of finite-difference type derivative operators on a regular grid which has the divergence free property. This principle clarifies the nature of magnetic monopole errors. The principles and techniques demonstrated in this chapter are particularly useful for the magnetic field, but can be applied to any vector field. Finally, we examine global zoom-in simulations of turbulent magnetorotationally unstable flow. We extract and analyze the high-current regions produced in the turbulent flow. Basic parameters of these regions are abstracted, and we build one dimensional models including non-ideal MHD, and radiative transfer. For sufficiently high temperatures, an instability resulting from the temperature dependence of the Ohmic resistivity is found. This instability concentrates current sheets, resulting in the possibility of rapid heating from temperatures on the order of 600 Kelvin to 2000 Kelvin in magnetorotationally turbulent regions of protoplanetary disks. This is a possible local mechanism for the melting of chondrules and the formation of other high-temperature materials in protoplanetary disks.

An adaptive multi-moment FVM approach for incompressible flows

NASA Astrophysics Data System (ADS)

Liu, Cheng; Hu, Changhong

2018-04-01

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder (Re = 3000 , 9500), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers (Re = 10000 , 45000), the predicted drag coefficient (CD) and lift coefficient (CL) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions (Re = 5000 , 40000), the predicted CD, CL and CM (moment coefficient) are in good agreement with those obtained by other numerical methods.

Numerical shockwave anomalies in presence of hydraulic jumps in the SWE with variable bed elevation.

NASA Astrophysics Data System (ADS)

Navas-Montilla, Adrian; Murillo, Javier

2017-04-01

When solving the shallow water equations appropriate numerical solvers must allow energy-dissipative solutions in presence of steady and unsteady hydraulic jumps. Hydraulic jumps are present in surface flows and may produce significant morphological changes. Unfortunately, it has been documented that some numerical anomalies may appear. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump produced by a non-linearity of the Hugoniot locus connecting the states at both sides of the jump. Therefore, this problem remains unresolved in the context of Godunov's schemes applied to shallow flows. This issue is usually ignored as it does not affect to the solution in steady cases. However, it produces undesirable spurious oscillations in transient cases that can lead to misleading conclusions when moving to realistic scenarios. Using spike-reducing techniques based on the construction of interpolated fluxes, it is possible to define numerical methods including discontinuous topography that reduce the presence of the aforementioned numerical anomalies. References: T. W. Roberts, The behavior of flux difference splitting schemes near slowly moving shock waves, J. Comput. Phys., 90 (1990) 141-160. Y. Stiriba, R. Donat, A numerical study of postshock oscillations in slowly moving shock waves, Comput. Math. with Appl., 46 (2003) 719-739. E. Johnsen, S. K. Lele, Numerical errors generated in simulations of slowly moving shocks, Center for Turbulence Research, Annual Research Briefs, (2008) 1-12. D. W. Zaide, P. L. Roe, Flux functions for reducing numerical shockwave anomalies. ICCFD7, Big Island, Hawaii, (2012) 9-13. D. W. Zaide, Numerical Shockwave Anomalies, PhD thesis, Aerospace Engineering and Scientific Computing, University of Michigan, 2012. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms, J. Comput. Phys. 317 (2016) 108-147. J. Murillo and A. Navas-Montilla, A comprehensive explanation and exercise of the source terms in hyperbolic systems using Roe type solutions. Application to the 1D-2D shallow water equations, Advances in Water Resources {98} (2016) 70-96.

A comparison of two multi-variable integrator windup protection schemes

NASA Technical Reports Server (NTRS)

Mattern, Duane

1993-01-01

Two methods are examined for limit and integrator wind-up protection for multi-input, multi-output linear controllers subject to actuator constraints. The methods begin with an existing linear controller that satisfies the specifications for the nominal, small perturbation, linear model of the plant. The controllers are formulated to include an additional contribution to the state derivative calculations. The first method to be examined is the multi-variable version of the single-input, single-output, high gain, Conventional Anti-Windup (CAW) scheme. Except for the actuator limits, the CAW scheme is linear. The second scheme to be examined, denoted the Modified Anti-Windup (MAW) scheme, uses a scalar to modify the magnitude of the controller output vector while maintaining the vector direction. The calculation of the scalar modifier is a nonlinear function of the controller outputs and the actuator limits. In both cases the constrained actuator is tracked. These two integrator windup protection methods are demonstrated on a turbofan engine control system with five measurements, four control variables, and four actuators. The closed-loop responses of the two schemes are compared and contrasted during limit operation. The issue of maintaining the direction of the controller output vector using the Modified Anti-Windup scheme is discussed and the advantages and disadvantages of both of the IWP methods are presented.

Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.

PubMed

Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi

2017-10-11

We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.

Impact of rain gauge quality control and interpolation on streamflow simulation: an application to the Warwick catchment, Australia

NASA Astrophysics Data System (ADS)

Liu, Shulun; Li, Yuan; Pauwels, Valentijn R. N.; Walker, Jeffrey P.

2017-12-01

Rain gauges are widely used to obtain temporally continuous point rainfall records, which are then interpolated into spatially continuous data to force hydrological models. However, rainfall measurements and interpolation procedure are subject to various uncertainties, which can be reduced by applying quality control and selecting appropriate spatial interpolation approaches. Consequently, the integrated impact of rainfall quality control and interpolation on streamflow simulation has attracted increased attention but not been fully addressed. This study applies a quality control procedure to the hourly rainfall measurements obtained in the Warwick catchment in eastern Australia. The grid-based daily precipitation from the Australian Water Availability Project was used as a reference. The Pearson correlation coefficient between the daily accumulation of gauged rainfall and the reference data was used to eliminate gauges with significant quality issues. The unrealistic outliers were censored based on a comparison between gauged rainfall and the reference. Four interpolation methods, including the inverse distance weighting (IDW), nearest neighbors (NN), linear spline (LN), and ordinary Kriging (OK), were implemented. The four methods were firstly assessed through a cross-validation using the quality-controlled rainfall data. The impacts of the quality control and interpolation on streamflow simulation were then evaluated through a semi-distributed hydrological model. The results showed that the Nash–Sutcliffe model efficiency coefficient (NSE) and Bias of the streamflow simulations were significantly improved after quality control. In the cross-validation, the IDW and OK methods resulted in good interpolation rainfall, while the NN led to the worst result. In term of the impact on hydrological prediction, the IDW led to the most consistent streamflow predictions with the observations, according to the validation at five streamflow-gauged locations. The OK method performed second best according to streamflow predictions at the five gauges in the calibration period (01/01/2007–31/12/2011) and four gauges during the validation period (01/01/2012–30/06/2014). However, NN produced the worst prediction at the outlet of the catchment in the validation period, indicating a low robustness. While the IDW exhibited the best performance in the study catchment in terms of accuracy, robustness and efficiency, more general recommendations on the selection of rainfall interpolation methods need to be further explored.

Impact of rain gauge quality control and interpolation on streamflow simulation: an application to the Warwick catchment, Australia

NASA Astrophysics Data System (ADS)

Liu, Shulun; Li, Yuan; Pauwels, Valentijn R. N.; Walker, Jeffrey P.

2018-01-01

Rain gauges are widely used to obtain temporally continuous point rainfall records, which are then interpolated into spatially continuous data to force hydrological models. However, rainfall measurements and interpolation procedure are subject to various uncertainties, which can be reduced by applying quality control and selecting appropriate spatial interpolation approaches. Consequently, the integrated impact of rainfall quality control and interpolation on streamflow simulation has attracted increased attention but not been fully addressed. This study applies a quality control procedure to the hourly rainfall measurements obtained in the Warwick catchment in eastern Australia. The grid-based daily precipitation from the Australian Water Availability Project was used as a reference. The Pearson correlation coefficient between the daily accumulation of gauged rainfall and the reference data was used to eliminate gauges with significant quality issues. The unrealistic outliers were censored based on a comparison between gauged rainfall and the reference. Four interpolation methods, including the inverse distance weighting (IDW), nearest neighbors (NN), linear spline (LN), and ordinary Kriging (OK), were implemented. The four methods were firstly assessed through a cross-validation using the quality-controlled rainfall data. The impacts of the quality control and interpolation on streamflow simulation were then evaluated through a semi-distributed hydrological model. The results showed that the Nash–Sutcliffe model efficiency coefficient (NSE) and Bias of the streamflow simulations were significantly improved after quality control. In the cross-validation, the IDW and OK methods resulted in good interpolation rainfall, while the NN led to the worst result. In term of the impact on hydrological prediction, the IDW led to the most consistent streamflow predictions with the observations, according to the validation at five streamflow-gauged locations. The OK method performed second best according to streamflow predictions at the five gauges in the calibration period (01/01/2007–31/12/2011) and four gauges during the validation period (01/01/2012–30/06/2014). However, NN produced the worst prediction at the outlet of the catchment in the validation period, indicating a low robustness. While the IDW exhibited the best performance in the study catchment in terms of accuracy, robustness and efficiency, more general recommendations on the selection of rainfall interpolation methods need to be further explored.

On the Treatment of Electric and Magnetic Loss in the Linear Bicharacteristic Scheme for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.

2000-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been extended to treat lossy dielectric and magnetic materials. This paper examines different methodologies for treatment of the electric loss term in the Linear Bicharacteristic Scheme for computational electromagnetics. Several different treatments of the electric loss term using the LBS are explored and compared on one-dimensional model problems involving reflection from lossy dielectric materials on both uniform and nonuniform grids. Results using these LBS implementations are also compared with the FDTD method for convenience.

Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence

NASA Astrophysics Data System (ADS)

Belli, Emily Ann

Advanced numerical algorithms for gyrokinetic simulations are explored for more effective studies of plasma turbulent transport. The gyrokinetic equations describe the dynamics of particles in 5-dimensional phase space, averaging over the fast gyromotion, and provide a foundation for studying plasma microturbulence in fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/continuum gyrokinetic solvers are compared. An iterative implicit scheme based on numerical approximations of the plasma response is developed. This method reduces the long time needed to set-up implicit arrays, yet still has larger time step advantages similar to a fully implicit method. Various model preconditioners and iteration schemes, including Krylov-based solvers, are explored. An Alternating Direction Implicit algorithm is also studied and is surprisingly found to yield a severe stability restriction on the time step. Overall, an iterative Krylov algorithm might be the best approach for extensions of core tokamak gyrokinetic simulations to edge kinetic formulations and may be particularly useful for studies of large-scale ExB shear effects. The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic equilibria based on interpolations of representative JET-like shapes. High shaping is found to be a stabilizing influence on both the linear ITG instability and nonlinear ITG turbulence. A scaling of the heat flux with elongation of chi ˜ kappa-1.5 or kappa-2 (depending on the triangularity) is observed, which is consistent with previous gyrofluid simulations. Thus, the GS2 turbulence simulations are explaining a significant fraction, but not all, of the empirical elongation scaling. The remainder of the scaling may come from (1) the edge boundary conditions for core turbulence, and (2) the larger Dimits nonlinear critical temperature gradient shift due to the enhancement of zonal flows with shaping, which is observed with the GS2 simulations. Finally, a local linear trial function-based gyrokinetic code is developed to aid in fast scoping studies of gyrokinetic linear stability. This code is successfully benchmarked with the full GS2 code in the collisionless, electrostatic limit, as well as in the more general electromagnetic description with higher-order Hermite basis functions.

Satellite radiothermovision of atmospheric mesoscale processes: case study of tropical cyclones

NASA Astrophysics Data System (ADS)

Ermakov, D. M.; Sharkov, E. A.; Chernushich, A. P.

2015-04-01

Satellite radiothermovision is a set of processing techniques applicable for multisource data of radiothermal monitoring of oceanatmosphere system, which allows creating dynamic description of mesoscale and synoptic atmospheric processes and estimating physically meaningful integral characteristics of the observed processes (like avdective flow of the latent heat through a given border). The approach is based on spatiotemporal interpolation of the satellite measurements which allows reconstructing the radiothermal fields (as well as the fields of geophysical parameters) of the ocean-atmosphere system at global scale with spatial resolution of about 0.125° and temporal resolution of 1.5 hour. The accuracy of spatiotemporal interpolation was estimated by direct comparison of interpolated data with the data of independent asynchronous measurements and was shown to correspond to the best achievable as reported in literature (for total precipitable water fields the accuracy is about 0.8 mm). The advantages of the implemented interpolation scheme are: closure under input radiothermal data, homogeneity in time scale (all data are interpolated through the same time intervals), automatic estimation of both the intermediate states of scalar field of the studied geophysical parameter and of vector field of effective velocity of advection (horizontal movements). Using this pair of fields one can calculate the flow of a given geophysical quantity though any given border. For example, in case of total precipitable water field, this flow (under proper calibration) has the meaning of latent heat advective flux. This opportunity was used to evaluate the latent heat flux though a set of circular contours, enclosing a tropical cyclone and drifting with it during its evolution. A remarkable interrelation was observed between the calculated magnitude and sign of advective latent flux and the intensity of a tropical cyclone. This interrelation is demonstrated in several examples of hurricanes and tropical cyclones of August, 2000, and typhoons of November, 2013, including super typhoon Haiyan.

40 CFR 86.094-16 - Prohibition of defeat devices.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Provisions for Emission Regulations for 1977 and Later Model Year New Light-Duty Vehicles, Light-Duty Trucks and Heavy-Duty Engines, and for 1985 and Later Model Year New Gasoline Fueled, Natural Gas-Fueled... congruity across the intermediate temperature range is the linear interpolation between the CO standard...

Ambient Ozone Exposure in Czech Forests: A GIS-Based Approach to Spatial Distribution Assessment

PubMed Central

Hůnová, I.; Horálek, J.; Schreiberová, M.; Zapletal, M.

2012-01-01

Ambient ozone (O3) is an important phytotoxic pollutant, and detailed knowledge of its spatial distribution is becoming increasingly important. The aim of the paper is to compare different spatial interpolation techniques and to recommend the best approach for producing a reliable map for O3 with respect to its phytotoxic potential. For evaluation we used real-time ambient O3 concentrations measured by UV absorbance from 24 Czech rural sites in the 2007 and 2008 vegetation seasons. We considered eleven approaches for spatial interpolation used for the development of maps for mean vegetation season O3 concentrations and the AOT40F exposure index for forests. The uncertainty of maps was assessed by cross-validation analysis. The root mean square error (RMSE) of the map was used as a criterion. Our results indicate that the optimal interpolation approach is linear regression of O3 data and altitude with subsequent interpolation of its residuals by ordinary kriging. The relative uncertainty of the map of O3 mean for the vegetation season is less than 10%, using the optimal method as for both explored years, and this is a very acceptable value. In the case of AOT40F, however, the relative uncertainty of the map is notably worse, reaching nearly 20% in both examined years. PMID:22566757

Linear and nonlinear schemes applied to pitch control of wind turbines.

PubMed

Geng, Hua; Yang, Geng

2014-01-01

Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.

A new solution-adaptive grid generation method for transonic airfoil flow calculations

NASA Technical Reports Server (NTRS)

Nakamura, S.; Holst, T. L.

1981-01-01

The clustering algorithm is controlled by a second-order, ordinary differential equation which uses the airfoil surface density gradient as a forcing function. The solution to this differential equation produces a surface grid distribution which is automatically clustered in regions with large gradients. The interior grid points are established from this surface distribution by using an interpolation scheme which is fast and retains the desirable properties of the original grid generated from the standard elliptic equation approach.

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

A data base and analysis program for shuttle main engine dynamic pressure measurements. Appendix F: Data base plots for SSME tests 750-120 through 750-200

NASA Technical Reports Server (NTRS)

Coffin, T.

1986-01-01

A dynamic pressure data base and data base management system developed to characterize the Space Shuttle Main Engine (SSME) dynamic pressure environment is presented. The data base represents dynamic pressure measurements obtained during single engine hot firing tests of the SSME. Software is provided to permit statistical evaluation of selected measurements under specified operating conditions. An interpolation scheme is also included to estimate spectral trends with SSME power level.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Current Saturation Avoidance with Real-Time Control using DPCS

NASA Astrophysics Data System (ADS)

Ferrara, M.; Hutchinson, I.; Wolfe, S.; Stillerman, J.; Fredian, T.

2008-11-01

Tokamak ohmic-transformer and equilibrium-field coils need to be able to operate near their maximum current capabilities. However if they reach their upper limit during high-performance discharges or in the presence of a strong off-normal event, shape control is compromised, and instability, even plasma disruptions can result. On Alcator C-Mod we designed and tested an anti-saturation routine which detects the impending saturation of OH and EF currents and interpolates to a neighboring safe equilibrium in real-time. The routine was implemented with a multi-processor, multi-time-scale control scheme, which is based on a master process and multiple asynchronous slave processes. The scheme is general and can be used for any computationally-intensive algorithm. USDoE award DE- FC02-99ER545512.

Cost-effective accurate coarse-grid method for highly convective multidimensional unsteady flows

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Niknafs, H. S.

1991-01-01

A fundamentally multidimensional convection scheme is described based on vector transient interpolation modeling rewritten in conservative control-volume form. Vector third-order upwinding is used as the basis of the algorithm; this automatically introduces important cross-difference terms that are absent from schemes using component-wise one-dimensional formulas. Third-order phase accuracy is good; this is important for coarse-grid large-eddy or full simulation. Potential overshoots or undershoots are avoided by using a recently developed universal limiter. Higher order accuracy is obtained locally, where needed, by the cost-effective strategy of adaptive stencil expansion in a direction normal to each control-volume face; this is controlled by monitoring the absolute normal gradient and curvature across the face. Higher (than third) order cross-terms do not appear to be needed. Since the wider stencil is used only in isolated narrow regions (near discontinuities), extremely high (in this case, seventh) order accuracy can be achieved for little more than the cost of a globally third-order scheme.

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 3: Advanced Fan Section Grid Generator Final Report and Computer Program User's Manual

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1991-01-01

A procedure is studied for generating three-dimensional grids for advanced turbofan engine fan section geometries. The procedure constructs a discrete mesh about engine sections containing the fan stage, an arbitrary number of axisymmetric radial flow splitters, a booster stage, and a bifurcated core/bypass flow duct with guide vanes. The mesh is an h-type grid system, the points being distributed with a transfinite interpolation scheme with axial and radial spacing being user specified. Elliptic smoothing of the grid in the meridional plane is a post-process option. The grid generation scheme is consistent with aerodynamic analyses utilizing the average-passage equation system developed by Dr. John Adamczyk of NASA Lewis. This flow solution scheme requires a series of blade specific grids each having a common axisymmetric mesh, but varying in the circumferential direction according to the geometry of the specific blade row.

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

NASA Technical Reports Server (NTRS)

Chuang, C.-H.; Goodson, Troy D.; Ledsinger, Laura A.

1995-01-01

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Enhanced Night Vision Via a Combination of Poisson Interpolation and Machine Learning

DTIC Science & Technology

2006-02-01

of 0-255, they are mostly similar. The right plot shows a family of m(x, ψ) curves of ψ=2 (the most linear) through ψ=1024 (the most curved ...complicating low-light imaging. Nayar and Branzoi [04] later suggested a second variant using a DLP micromirror array to modulate the exposure, via time...255, they are mostly similar. The right plot shows a family of m(x, ψ) curves of ψ=2 (the most linear) through ψ=1024 (the most curved

Local projection stabilization for linearized Brinkman-Forchheimer-Darcy equation

NASA Astrophysics Data System (ADS)

Skrzypacz, Piotr

2017-09-01

The Local Projection Stabilization (LPS) is presented for the linearized Brinkman-Forchheimer-Darcy equation with high Reynolds numbers. The considered equation can be used to model porous medium flows in chemical reactors of packed bed type. The detailed finite element analysis is presented for the case of nonconstant porosity. The enriched variant of LPS is based on the equal order interpolation for the velocity and pressure. The optimal error bounds for the velocity and pressure errors are justified numerically.

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

Output Consensus of Heterogeneous Linear Multi-Agent Systems by Distributed Event-Triggered/Self-Triggered Strategy.

PubMed

Hu, Wenfeng; Liu, Lu; Feng, Gang

2016-09-02

This paper addresses the output consensus problem of heterogeneous linear multi-agent systems. We first propose a novel distributed event-triggered control scheme. It is shown that, with the proposed control scheme, the output consensus problem can be solved if two matrix equations are satisfied. Then, we further propose a novel self-triggered control scheme, with which continuous monitoring is avoided. By introducing a fixed timer into both event- and self-triggered control schemes, Zeno behavior can be ruled out for each agent. The effectiveness of the event- and self-triggered control schemes is illustrated by an example.

Benefits of incorporating the adaptive dynamic range optimization amplification scheme into an assistive listening device for people with mild or moderate hearing loss.

PubMed

Chang, Hung-Yue; Luo, Ching-Hsing; Lo, Tun-Shin; Chen, Hsiao-Chuan; Huang, Kuo-You; Liao, Wen-Huei; Su, Mao-Chang; Liu, Shu-Yu; Wang, Nan-Mai

2017-08-28

This study investigated whether a self-designed assistive listening device (ALD) that incorporates an adaptive dynamic range optimization (ADRO) amplification strategy can surpass a commercially available monaurally worn linear ALD, SM100. Both subjective and objective measurements were implemented. Mandarin Hearing-In-Noise Test (MHINT) scores were the objective measurement, whereas participant satisfaction was the subjective measurement. The comparison was performed in a mixed design (i.e., subjects' hearing status being mild or moderate, quiet versus noisy, and linear versus ADRO scheme). The participants were two groups of hearing-impaired subjects, nine mild and eight moderate, respectively. The results of the ADRO system revealed a significant difference in the MHINT sentence reception threshold (SRT) in noisy environments between monaurally aided and unaided conditions, whereas the linear system did not. The benchmark results showed that the ADRO scheme is effectively beneficial to people who experience mild or moderate hearing loss in noisy environments. The satisfaction rating regarding overall speech quality indicated that the participants were satisfied with the speech quality of both ADRO and linear schemes in quiet environments, and they were more satisfied with ADRO than they with the linear scheme in noisy environments.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Concurrent topological design of composite structures and materials containing multiple phases of distinct Poisson's ratios

NASA Astrophysics Data System (ADS)

Long, Kai; Yuan, Philip F.; Xu, Shanqing; Xie, Yi Min

2018-04-01

Most studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson's ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson's ratios. The proposed method aims to minimize the mean compliance of the macrostructure with a given mass of base materials. In contrast to the traditional interpolation of the stiffness matrix through numerical results, an interpolation scheme of the Young's modulus and Poisson's ratio using different parameters is adopted. The numerical results demonstrate that the Poisson effect plays a key role in reducing the mean compliance of the final design. An important contribution of the present study is that the proposed concurrent optimization method can automatically distribute base materials with distinct Poisson's ratios between the macrostructural and microstructural levels under a single constraint of the total mass.

A stabilized element-based finite volume method for poroelastic problems

NASA Astrophysics Data System (ADS)

Honório, Hermínio T.; Maliska, Clovis R.; Ferronato, Massimiliano; Janna, Carlo

2018-07-01

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier-Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

A refined characterization of the alluvial geology of yucca flat and its effect on bulk hydraulic conductivity

USGS Publications Warehouse

Phelps, G.A.; Halford, K.J.

2011-01-01

In Yucca Flat, on the Nevada National Security Site in southern Nevada, the migration of radionuclides from tests located in the alluvial deposits into the Paleozoic carbonate aquifer involves passage through a thick, heterogeneous section of late Tertiary and Quaternary alluvial sediments. An understanding of the lateral and vertical changes in the material properties of the alluvial sediments will aid in the further development of the hydrogeologic framework and the delineation of hydrostratigraphic units and hydraulic properties required for simulating groundwater flow in the Yucca Flat area. Previously published geologic models for the alluvial sediments within Yucca Flat are based on extensive examination and categorization of drill-hole data, combined with a simple, data-driven interpolation scheme. The U.S. Geological Survey, in collaboration with Stanford University, is researching improvements to the modeling of the alluvial section, incorporating prior knowledge of geologic structure into the interpolation method and estimating the uncertainty of the modeled hydrogeologic units.

The concentration dependence of the galaxy–halo connection: Modeling assembly bias with abundance matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehmann, Benjamin V.; Mao, Yao -Yuan; Becker, Matthew R.

Empirical methods for connecting galaxies to their dark matter halos have become essential for interpreting measurements of the spatial statistics of galaxies. In this work, we present a novel approach for parameterizing the degree of concentration dependence in the abundance matching method. Furthermore, this new parameterization provides a smooth interpolation between two commonly used matching proxies: the peak halo mass and the peak halo maximal circular velocity. This parameterization controls the amount of dependence of galaxy luminosity on halo concentration at a fixed halo mass. Effectively this interpolation scheme enables abundance matching models to have adjustable assembly bias in the resulting galaxy catalogs. With the newmore » $$400\\,\\mathrm{Mpc}\\,{h}^{-1}$$ DarkSky Simulation, whose larger volume provides lower sample variance, we further show that low-redshift two-point clustering and satellite fraction measurements from SDSS can already provide a joint constraint on this concentration dependence and the scatter within the abundance matching framework.« less

The concentration dependence of the galaxy–halo connection: Modeling assembly bias with abundance matching

DOE PAGES

Lehmann, Benjamin V.; Mao, Yao -Yuan; Becker, Matthew R.; ...

2016-12-28

Empirical methods for connecting galaxies to their dark matter halos have become essential for interpreting measurements of the spatial statistics of galaxies. In this work, we present a novel approach for parameterizing the degree of concentration dependence in the abundance matching method. Furthermore, this new parameterization provides a smooth interpolation between two commonly used matching proxies: the peak halo mass and the peak halo maximal circular velocity. This parameterization controls the amount of dependence of galaxy luminosity on halo concentration at a fixed halo mass. Effectively this interpolation scheme enables abundance matching models to have adjustable assembly bias in the resulting galaxy catalogs. With the newmore » $$400\\,\\mathrm{Mpc}\\,{h}^{-1}$$ DarkSky Simulation, whose larger volume provides lower sample variance, we further show that low-redshift two-point clustering and satellite fraction measurements from SDSS can already provide a joint constraint on this concentration dependence and the scatter within the abundance matching framework.« less

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE PAGES

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.; ...

2016-11-07

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

14 CFR Appendix B to Part 33 - Certification Standard Atmospheric Concentrations of Rain and Hail

Code of Federal Regulations, 2011 CFR

2011-01-01

... interpolation. Note: Source of data—Results of the Aerospace Industries Association (AIA) Propulsion Committee... above 29,000 feet is based on linearly extrapolated data. Note: Source of data—Results of the Aerospace... the Aerospace Industries Association (AIA Propulsion Committee (PC) Study, Project PC 338-1, June 1990...

14 CFR Appendix B to Part 33 - Certification Standard Atmospheric Concentrations of Rain and Hail

Code of Federal Regulations, 2012 CFR

2012-01-01

... interpolation. Note: Source of data—Results of the Aerospace Industries Association (AIA) Propulsion Committee... above 29,000 feet is based on linearly extrapolated data. Note: Source of data—Results of the Aerospace... the Aerospace Industries Association (AIA Propulsion Committee (PC) Study, Project PC 338-1, June 1990...

14 CFR Appendix B to Part 33 - Certification Standard Atmospheric Concentrations of Rain and Hail

Code of Federal Regulations, 2013 CFR

2013-01-01

... interpolation. Note: Source of data—Results of the Aerospace Industries Association (AIA) Propulsion Committee... above 29,000 feet is based on linearly extrapolated data. Note: Source of data—Results of the Aerospace... the Aerospace Industries Association (AIA Propulsion Committee (PC) Study, Project PC 338-1, June 1990...

14 CFR Appendix B to Part 33 - Certification Standard Atmospheric Concentrations of Rain and Hail

Code of Federal Regulations, 2014 CFR

2014-01-01

... interpolation. Note: Source of data—Results of the Aerospace Industries Association (AIA) Propulsion Committee... above 29,000 feet is based on linearly extrapolated data. Note: Source of data—Results of the Aerospace... the Aerospace Industries Association (AIA Propulsion Committee (PC) Study, Project PC 338-1, June 1990...

Stochastic Quantitative Reasoning for Autonomous Mission Planning

DTIC Science & Technology

2014-04-09

points. Figure 4: Linear interpolation Table 1: Wind speed prediction information (ID:0-2 for Albany, ID:3-5 for Pittston, and ID:6-8 for JFK Airport ID...Pittston, and JFK Airport in Table 1, how can we estimate a reasonable wind speed for the current location at the current time? Figure 5: Example

Autoregressive linear least square single scanning electron microscope image signal-to-noise ratio estimation.

PubMed

Sim, Kok Swee; NorHisham, Syafiq

2016-11-01

A technique based on linear Least Squares Regression (LSR) model is applied to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. In order to test the accuracy of this technique on SNR estimation, a number of SEM images are initially corrupted with white noise. The autocorrelation function (ACF) of the original and the corrupted SEM images are formed to serve as the reference point to estimate the SNR value of the corrupted image. The LSR technique is then compared with the previous three existing techniques known as nearest neighbourhood, first-order interpolation, and the combination of both nearest neighborhood and first-order interpolation. The actual and the estimated SNR values of all these techniques are then calculated for comparison purpose. It is shown that the LSR technique is able to attain the highest accuracy compared to the other three existing techniques as the absolute difference between the actual and the estimated SNR value is relatively small. SCANNING 38:771-782, 2016. © 2016 Wiley Periodicals, Inc. © Wiley Periodicals, Inc.

Targeted ENO schemes with tailored resolution property for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-11-01

In this paper, we extend the range of targeted ENO (TENO) schemes (Fu et al. (2016) [18]) by proposing an eighth-order TENO8 scheme. A general formulation to construct the high-order undivided difference τK within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for τK in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes.

General-Purpose Software For Computer Graphics

NASA Technical Reports Server (NTRS)

Rogers, Joseph E.

1992-01-01

NASA Device Independent Graphics Library (NASADIG) is general-purpose computer-graphics package for computer-based engineering and management applications which gives opportunity to translate data into effective graphical displays for presentation. Features include two- and three-dimensional plotting, spline and polynomial interpolation, control of blanking of areas, multiple log and/or linear axes, control of legends and text, control of thicknesses of curves, and multiple text fonts. Included are subroutines for definition of areas and axes of plots; setup and display of text; blanking of areas; setup of style, interpolation, and plotting of lines; control of patterns and of shading of colors; control of legends, blocks of text, and characters; initialization of devices; and setting of mixed alphabets. Written in FORTRAN 77.

Use B-spline interpolation fitting baseline for low concentration 2, 6-di-tertbutyl p-cresol determination in jet fuels by differential pulse voltammetry

NASA Astrophysics Data System (ADS)

Wen, D. S.; Wen, H.; Shi, Y. G.; Su, B.; Li, Z. C.; Fan, G. Z.

2018-01-01

The B-spline interpolation fitting baseline in electrochemical analysis by differential pulse voltammetry was established for determining the lower concentration 2,6-di-tert-butyl p-cresol(BHT) in Jet Fuel that was less than 5.0 mg/L in the condition of the presence of the 6-tert-butyl-2,4-xylenol.The experimental results has shown that the relative errors are less than 2.22%, the sum of standard deviations less than 0.134mg/L, the correlation coefficient more than 0.9851. If the 2,6-ditert-butyl p-cresol concentration is higher than 5.0mg/L, linear fitting baseline method would be more applicable and simpler.

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

NASA Technical Reports Server (NTRS)

Kim, Hyoungin; Liou, Meng-Sing

2011-01-01

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Eulerian and Lagrangian approaches to multidimensional condensation and collection

NASA Astrophysics Data System (ADS)

Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.

2017-06-01

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.