Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations
Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg
2007-08-10
In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.
Keeping the edge: an accurate numerical method to solve the stream power law
NASA Astrophysics Data System (ADS)
Campforts, B.; Govers, G.
2015-12-01
Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.
Takahashi, F; Endo, A
2007-01-01
A system utilising radiation transport codes has been developed to derive accurate dose distributions in a human body for radiological accidents. A suitable model is quite essential for a numerical analysis. Therefore, two tools were developed to setup a 'problem-dependent' input file, defining a radiation source and an exposed person to simulate the radiation transport in an accident with the Monte Carlo calculation codes-MCNP and MCNPX. Necessary resources are defined by a dialogue method with a generally used personal computer for both the tools. The tools prepare human body and source models described in the input file format of the employed Monte Carlo codes. The tools were validated for dose assessment in comparison with a past criticality accident and a hypothesized exposure.
A time-accurate adaptive grid method and the numerical simulation of a shock-vortex interaction
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.; Eiseman, Peter R.
1990-01-01
A time accurate, general purpose, adaptive grid method is developed that is suitable for multidimensional steady and unsteady numerical simulations. The grid point movement is performed in a manner that generates smooth grids which resolve the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling of the adaptive grid and the PDE solver is performed with a grid prediction correction method that is simple to implement and ensures the time accuracy of the grid. Time accurate solutions of the 2-D Euler equations for an unsteady shock vortex interaction demonstrate the ability of the adaptive method to accurately adapt the grid to multiple solution features.
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Fast and accurate numerical method for predicting gas chromatography retention time.
Claumann, Carlos Alberto; Wüst Zibetti, André; Bolzan, Ariovaldo; Machado, Ricardo A F; Pinto, Leonel Teixeira
2015-08-07
Predictive modeling for gas chromatography compound retention depends on the retention factor (ki) and on the flow of the mobile phase. Thus, different approaches for determining an analyte ki in column chromatography have been developed. The main one is based on the thermodynamic properties of the component and on the characteristics of the stationary phase. These models can be used to estimate the parameters and to optimize the programming of temperatures, in gas chromatography, for the separation of compounds. Different authors have proposed the use of numerical methods for solving these models, but these methods demand greater computational time. Hence, a new method for solving the predictive modeling of analyte retention time is presented. This algorithm is an alternative to traditional methods because it transforms its attainments into root determination problems within defined intervals. The proposed approach allows for tr calculation, with accuracy determined by the user of the methods, and significant reductions in computational time; it can also be used to evaluate the performance of other prediction methods.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo
2015-11-01
This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.
Practical aspects of spatially high accurate methods
NASA Technical Reports Server (NTRS)
Godfrey, Andrew G.; Mitchell, Curtis R.; Walters, Robert W.
1992-01-01
The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.
NASA Technical Reports Server (NTRS)
Graves, R. A., Jr.
1975-01-01
The previously obtained second-order-accurate partial implicitization numerical technique used in the solution of fluid dynamic problems was modified with little complication to achieve fourth-order accuracy. The Von Neumann stability analysis demonstrated the unconditional linear stability of the technique. The order of the truncation error was deduced from the Taylor series expansions of the linearized difference equations and was verified by numerical solutions to Burger's equation. For comparison, results were also obtained for Burger's equation using a second-order-accurate partial-implicitization scheme, as well as the fourth-order scheme of Kreiss.
Accurate upwind methods for the Euler equations
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1993-01-01
A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.
Accurate, meshless methods for magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.; Raives, Matthias J.
2016-01-01
Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.
Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air
NASA Technical Reports Server (NTRS)
Rupesh, K-A. B.; Ravi, B. R.; Mittal, R.; Raju, R.; Gallas, Q.; Cattafesta, L.
2007-01-01
The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.
Can numerical simulations accurately predict hydrodynamic instabilities in liquid films?
NASA Astrophysics Data System (ADS)
Denner, Fabian; Charogiannis, Alexandros; Pradas, Marc; van Wachem, Berend G. M.; Markides, Christos N.; Kalliadasis, Serafim
2014-11-01
Understanding the dynamics of hydrodynamic instabilities in liquid film flows is an active field of research in fluid dynamics and non-linear science in general. Numerical simulations offer a powerful tool to study hydrodynamic instabilities in film flows and can provide deep insights into the underlying physical phenomena. However, the direct comparison of numerical results and experimental results is often hampered by several reasons. For instance, in numerical simulations the interface representation is problematic and the governing equations and boundary conditions may be oversimplified, whereas in experiments it is often difficult to extract accurate information on the fluid and its behavior, e.g. determine the fluid properties when the liquid contains particles for PIV measurements. In this contribution we present the latest results of our on-going, extensive study on hydrodynamic instabilities in liquid film flows, which includes direct numerical simulations, low-dimensional modelling as well as experiments. The major focus is on wave regimes, wave height and wave celerity as a function of Reynolds number and forcing frequency of a falling liquid film. Specific attention is paid to the differences in numerical and experimental results and the reasons for these differences. The authors are grateful to the EPSRC for their financial support (Grant EP/K008595/1).
Ahmed, Mahmoud; Eslamian, Morteza
2015-12-01
Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.
NASA Astrophysics Data System (ADS)
Ahmed, Mahmoud; Eslamian, Morteza
2015-07-01
Laminar natural convection in differentially heated ( β = 0°, where β is the inclination angle), inclined ( β = 30° and 60°), and bottom-heated ( β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.
Introduction to Numerical Methods
Schoonover, Joseph A.
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
Accurate numerical simulation of short fiber optical parametric amplifiers.
Marhic, M E; Rieznik, A A; Kalogerakis, G; Braimiotis, C; Fragnito, H L; Kazovsky, L G
2008-03-17
We improve the accuracy of numerical simulations for short fiber optical parametric amplifiers (OPAs). Instead of using the usual coarse-step method, we adopt a model for birefringence and dispersion which uses fine-step variations of the parameters. We also improve the split-step Fourier method by exactly treating the nonlinear ellipse rotation terms. We find that results obtained this way for two-pump OPAs can be significantly different from those obtained by using the usual coarse-step fiber model, and/or neglecting ellipse rotation terms.
Accurate methods for large molecular systems.
Gordon, Mark S; Mullin, Jonathan M; Pruitt, Spencer R; Roskop, Luke B; Slipchenko, Lyudmila V; Boatz, Jerry A
2009-07-23
Three exciting new methods that address the accurate prediction of processes and properties of large molecular systems are discussed. The systematic fragmentation method (SFM) and the fragment molecular orbital (FMO) method both decompose a large molecular system (e.g., protein, liquid, zeolite) into small subunits (fragments) in very different ways that are designed to both retain the high accuracy of the chosen quantum mechanical level of theory while greatly reducing the demands on computational time and resources. Each of these methods is inherently scalable and is therefore eminently capable of taking advantage of massively parallel computer hardware while retaining the accuracy of the corresponding electronic structure method from which it is derived. The effective fragment potential (EFP) method is a sophisticated approach for the prediction of nonbonded and intermolecular interactions. Therefore, the EFP method provides a way to further reduce the computational effort while retaining accuracy by treating the far-field interactions in place of the full electronic structure method. The performance of the methods is demonstrated using applications to several systems, including benzene dimer, small organic species, pieces of the alpha helix, water, and ionic liquids.
Accurate method for computing correlated color temperature.
Li, Changjun; Cui, Guihua; Melgosa, Manuel; Ruan, Xiukai; Zhang, Yaoju; Ma, Long; Xiao, Kaida; Luo, M Ronnier
2016-06-27
For the correlated color temperature (CCT) of a light source to be estimated, a nonlinear optimization problem must be solved. In all previous methods available to compute CCT, the objective function has only been approximated, and their predictions have achieved limited accuracy. For example, different unacceptable CCT values have been predicted for light sources located on the same isotemperature line. In this paper, we propose to compute CCT using the Newton method, which requires the first and second derivatives of the objective function. Following the current recommendation by the International Commission on Illumination (CIE) for the computation of tristimulus values (summations at 1 nm steps from 360 nm to 830 nm), the objective function and its first and second derivatives are explicitly given and used in our computations. Comprehensive tests demonstrate that the proposed method, together with an initial estimation of CCT using Robertson's method [J. Opt. Soc. Am. 58, 1528-1535 (1968)], gives highly accurate predictions below 0.0012 K for light sources with CCTs ranging from 500 K to 10^{6} K.
Accurate paleointensities - the multi-method approach
NASA Astrophysics Data System (ADS)
de Groot, Lennart
2016-04-01
The accuracy of models describing rapid changes in the geomagnetic field over the past millennia critically depends on the availability of reliable paleointensity estimates. Over the past decade methods to derive paleointensities from lavas (the only recorder of the geomagnetic field that is available all over the globe and through geologic times) have seen significant improvements and various alternative techniques were proposed. The 'classical' Thellier-style approach was optimized and selection criteria were defined in the 'Standard Paleointensity Definitions' (Paterson et al, 2014). The Multispecimen approach was validated and the importance of additional tests and criteria to assess Multispecimen results must be emphasized. Recently, a non-heating, relative paleointensity technique was proposed -the pseudo-Thellier protocol- which shows great potential in both accuracy and efficiency, but currently lacks a solid theoretical underpinning. Here I present work using all three of the aforementioned paleointensity methods on suites of young lavas taken from the volcanic islands of Hawaii, La Palma, Gran Canaria, Tenerife, and Terceira. Many of the sampled cooling units are <100 years old, the actual field strength at the time of cooling is therefore reasonably well known. Rather intuitively, flows that produce coherent results from two or more different paleointensity methods yield the most accurate estimates of the paleofield. Furthermore, the results for some flows pass the selection criteria for one method, but fail in other techniques. Scrutinizing and combing all acceptable results yielded reliable paleointensity estimates for 60-70% of all sampled cooling units - an exceptionally high success rate. This 'multi-method paleointensity approach' therefore has high potential to provide the much-needed paleointensities to improve geomagnetic field models for the Holocene.
Fast and Accurate Learning When Making Discrete Numerical Estimates
Sanborn, Adam N.; Beierholm, Ulrik R.
2016-01-01
Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155
NASA Astrophysics Data System (ADS)
Mehrmann, Volker; Xu, Hongguo
2000-11-01
We study classical control problems like pole assignment, stabilization, linear quadratic control and H[infinity] control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.
Numerical comparison between DHF and RHF methods
NASA Astrophysics Data System (ADS)
Kobus, J.; Jaskolski, W.
1987-10-01
A detailed numerical comparison of the Dirac-Hartree-Fock method and the relativistic Hartree-Fock (RHF) method of Cowan and Griffith (1976) is presented, considering the total energy, the orbital energies, and the one-electron and two-electron integrals. The RHF method is found to yield accurate values of the relativistic transition energies. Using accurate values of the correlation corrections for p-electron and d-electron systems, the usefulness of the RHF method in obtaining relativistic corrections to the differential term energies is demonstrated. Advantages of the method for positron scattering on heavy systems are also pointed out.
Accurate spectral numerical schemes for kinetic equations with energy diffusion
NASA Astrophysics Data System (ADS)
Wilkening, Jon; Cerfon, Antoine J.; Landreman, Matt
2015-08-01
We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial differential equation describing energy diffusion in velocity space due to Fokker-Planck collisions. This relatively simple case allows us to compare the results of the projected dynamics with an expensive but highly accurate spectral transform approach. It also allows us to integrate in time exactly, and to focus entirely on the effectiveness of the discretization of the speed variable. We show that for a fixed number of modes or grid points, the non-classical polynomials can be many orders of magnitude more accurate than classical Hermite polynomials or finite-difference solvers for kinetic equations in plasma physics. We provide a detailed analysis of the difference in behavior and accuracy of the two families of polynomials. For the non-classical polynomials, if the initial condition is not smooth at the origin when interpreted as a three-dimensional radial function, the exact solution leaves the polynomial subspace for a time, but returns (up to roundoff accuracy) to the same point evolved to by the projected dynamics in that time. By contrast, using classical polynomials, the exact solution differs significantly from the projected dynamics solution when it returns to the subspace. We also explore the connection between eigenfunctions of the projected evolution operator and (non-normalizable) eigenfunctions of the full evolution operator, as well as the effect of truncating the computational domain.
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Schwanghart, Wolfgang; Govers, Gerard
2017-01-01
Landscape evolution models (LEMs) allow the study of earth surface responses to changing climatic and tectonic forcings. While much effort has been devoted to the development of LEMs that simulate a wide range of processes, the numerical accuracy of these models has received less attention. Most LEMs use first-order accurate numerical methods that suffer from substantial numerical diffusion. Numerical diffusion particularly affects the solution of the advection equation and thus the simulation of retreating landforms such as cliffs and river knickpoints. This has potential consequences for the integrated response of the simulated landscape. Here we test a higher-order flux-limiting finite volume method that is total variation diminishing (TVD-FVM) to solve the partial differential equations of river incision and tectonic displacement. We show that using the TVD-FVM to simulate river incision significantly influences the evolution of simulated landscapes and the spatial and temporal variability of catchment-wide erosion rates. Furthermore, a two-dimensional TVD-FVM accurately simulates the evolution of landscapes affected by lateral tectonic displacement, a process whose simulation was hitherto largely limited to LEMs with flexible spatial discretization. We implement the scheme in TTLEM (TopoToolbox Landscape Evolution Model), a spatially explicit, raster-based LEM for the study of fluvially eroding landscapes in TopoToolbox 2.
Accurate numerical solutions for elastic-plastic models. [LMFBR
Schreyer, H. L.; Kulak, R. F.; Kramer, J. M.
1980-03-01
The accuracy of two integration algorithms is studied for the common engineering condition of a von Mises, isotropic hardening model under plane stress. Errors in stress predictions for given total strain increments are expressed with contour plots of two parameters: an angle in the pi plane and the difference between the exact and computed yield-surface radii. The two methods are the tangent-predictor/radial-return approach and the elastic-predictor/radial-corrector algorithm originally developed by Mendelson. The accuracy of a combined tangent-predictor/radial-corrector algorithm is also investigated.
Numerical assessment of accurate measurements of laminar flame speed
NASA Astrophysics Data System (ADS)
Goulier, Joules; Bizon, Katarzyna; Chaumeix, Nabiha; Meynet, Nicolas; Continillo, Gaetano
2016-12-01
In combustion, the laminar flame speed constitutes an important parameter that reflects the chemistry of oxidation for a given fuel, along with its transport and thermal properties. Laminar flame speeds are used (i) in turbulent models used in CFD codes, and (ii) to validate detailed or reduced mechanisms, often derived from studies using ideal reactors and in diluted conditions as in jet stirred reactors and in shock tubes. End-users of such mechanisms need to have an assessment of their capability to predict the correct heat released by combustion in realistic conditions. In this view, the laminar flame speed constitutes a very convenient parameter, and it is then very important to have a good knowledge of the experimental errors involved with its determination. Stationary configurations (Bunsen burners, counter-flow flames, heat flux burners) or moving flames (tubes, spherical vessel, soap bubble) can be used. The spherical expanding flame configuration has recently become popular, since it can be used at high pressures and temperatures. With this method, the flame speed is not measured directly, but derived through the recording of the flame radius. The method used to process the radius history will have an impact on the estimated flame speed. Aim of this work is to propose a way to derive the laminar flame speed from experimental recording of expanding flames, and to assess the error magnitude.
An accurate solution of elastodynamic problems by numerical local Green's functions
NASA Astrophysics Data System (ADS)
Loureiro, F. S.; Silva, J. E. A.; Mansur, W. J.
2015-09-01
Green's function based methodologies for elastodynamics in both time and frequency domains, which can be either numerical or analytical, appear in many branches of physics and engineering. Thus, the development of exact expressions for Green's functions is of great importance. Unfortunately, such expressions are known only for relatively few kinds of geometry, medium and boundary conditions. In this way, due to the difficulty in finding exact Green's functions, specially in the time domain, the present paper presents a solution of the transient elastodynamic equations by a time-stepping technique based on the Explicit Green's Approach method written in terms of the Green's and Step response functions, both being computed numerically by the finite element method. The major feature is the computation of these functions separately by the central difference time integration scheme and locally owing to the principle of causality. More precisely, Green's functions are computed only at t = Δt adopting two time substeps while Step response functions are computed directly without substeps. The proposed time-stepping method shows to be quite accurate with distinct numerical properties not presented in the standard central difference scheme as addressed in the numerical example.
NASA Technical Reports Server (NTRS)
VanZante, Dale E.; Strazisar, Anthony J.; Wood, Jerry R,; Hathaway, Michael D.; Okiishi, Theodore H.
2000-01-01
The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.
Towards numerically accurate many-body perturbation theory: Short-range correlation effects
Gulans, Andris
2014-10-28
The example of the uniform electron gas is used for showing that the short-range electron correlation is difficult to handle numerically, while it noticeably contributes to the self-energy. Nonetheless, in condensed-matter applications studied with advanced methods, such as the GW and random-phase approximations, it is common to neglect contributions due to high-momentum (large q) transfers. Then, the short-range correlation is poorly described, which leads to inaccurate correlation energies and quasiparticle spectra. To circumvent this problem, an accurate extrapolation scheme is proposed. It is based on an analytical derivation for the uniform electron gas presented in this paper, and it provides an explanation why accurate GW quasiparticle spectra are easy to obtain for some compounds and very difficult for others.
A numerical method of regenerator
NASA Astrophysics Data System (ADS)
Zhu, Shaowei; Matsubara, Yoichi
2004-02-01
A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.
An accurate moving boundary formulation in cut-cell methods
NASA Astrophysics Data System (ADS)
Schneiders, Lennart; Hartmann, Daniel; Meinke, Matthias; Schröder, Wolfgang
2013-02-01
A cut-cell method for Cartesian meshes to simulate viscous compressible flows with moving boundaries is presented. We focus on eliminating unphysical oscillations occurring in Cartesian grid methods extended to moving-boundary problems. In these methods, cells either lie completely in the fluid or solid region or are intersected by the boundary. For the latter cells, the time dependent volume fraction lying in the fluid region can be so small that explicit time-integration schemes become unstable and a special treatment of these cells is necessary. When the boundary moves, a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level. This causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme. This temporally discontinuous alteration is shown to act like an unphysical source term, which deteriorates the numerical solution, i.e., it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary. We develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut-cell method which avoids these discontinuities. Results for canonical two- and three-dimensional test cases evidence the accuracy and robustness of the newly developed scheme.
A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation
NASA Astrophysics Data System (ADS)
Parand, Kourosh; Yousefi, Hossein; Delkhosh, Mehdi; Ghaderi, Amin
2016-07-01
In this paper, a new algorithm based on the fractional order of rational Euler functions (FRE) is introduced to study the Thomas-Fermi (TF) model which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This problem, using the quasilinearization method (QLM), converts to the sequence of linear ordinary differential equations to obtain the solution. For the first time, the rational Euler (RE) and the FRE have been made based on Euler polynomials. In addition, the equation will be solved on a semi-infinite domain without truncating it to a finite domain by taking FRE as basic functions for the collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations. We demonstrated that the new proposed algorithm is efficient for obtaining the value of y'(0) , y(x) and y'(x) . Comparison with some numerical and analytical solutions shows that the present solution is highly accurate.
Second Order Accurate Finite Difference Methods
1984-08-20
a study of the idealized material has direct applications to some polymer structures (4, 5). Wave propagation studies in hyperelastic materials have...34Acceleration Wave Propagation in Hyperelastic Rods of Variable Cross- section. Wave Motion, V4, pp. 173-180, 1982. 9. M. Hirao and N. Sugimoto...Waves in Hyperelastic Road," Quart. Appl. Math., V37, pp. 377-399, 1979. 11. G. A. Sod. "A Survey of Several Finite Difference Methods for Systems of
Numerical relativity and spectral methods
NASA Astrophysics Data System (ADS)
Grandclement, P.
2016-12-01
The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.
A numerical method to model excitable cells.
Joyner, R W; Westerfield, M; Moore, J W; Stockbridge, N
1978-01-01
We have extended a fast, stable, and accurate method for the numerical solution of cable equations to include changes in geometry and membrane properties in order to model a single excitable cell realistically. In addition, by including the provision that the radius may be a function of distance along an axis, we have achieved a general and powerful method for simulating a cell with any number of branched processes, any or all of which may be nonuniform in diameter, and with no restriction on the branching pattern. PMID:656539
Implicit Numerical Methods in Meteorology
NASA Technical Reports Server (NTRS)
Augenbaum, J.
1984-01-01
The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.
Numerical methods for turbulent flow
NASA Technical Reports Server (NTRS)
Turner, James C., Jr.
1988-01-01
It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.
Numerical methods for multibody systems
NASA Technical Reports Server (NTRS)
Glowinski, Roland; Nasser, Mahmoud G.
1994-01-01
This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.
Numerical methods for problems in computational aeroacoustics
NASA Astrophysics Data System (ADS)
Mead, Jodi Lorraine
1998-12-01
A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev
Linearized Implicit Numerical Method for Burgers' Equation
NASA Astrophysics Data System (ADS)
Mukundan, Vijitha; Awasthi, Ashish
2016-12-01
In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers' equation. The Burgers' equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.
Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows
Johnson, B M; Guan, X; Gammie, F
2008-04-11
In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the timestep is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves {del} {center_dot} B = 0 to machine precision. The main restriction is that B must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.
Spectral Methods for Numerical Relativity.
Grandclément, Philippe; Novak, Jérôme
2009-01-01
Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.
A Simple and Accurate Method for Measuring Enzyme Activity.
ERIC Educational Resources Information Center
Yip, Din-Yan
1997-01-01
Presents methods commonly used for investigating enzyme activity using catalase and presents a new method for measuring catalase activity that is more reliable and accurate. Provides results that are readily reproduced and quantified. Can also be used for investigations of enzyme properties such as the effects of temperature, pH, inhibitors,…
Numerical methods used in fusion science numerical modeling
NASA Astrophysics Data System (ADS)
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
Quantifying Accurate Calorie Estimation Using the "Think Aloud" Method
ERIC Educational Resources Information Center
Holmstrup, Michael E.; Stearns-Bruening, Kay; Rozelle, Jeffrey
2013-01-01
Objective: Clients often have limited time in a nutrition education setting. An improved understanding of the strategies used to accurately estimate calories may help to identify areas of focused instruction to improve nutrition knowledge. Methods: A "Think Aloud" exercise was recorded during the estimation of calories in a standard dinner meal…
Numerical solution methods for viscoelastic orthotropic materials
NASA Technical Reports Server (NTRS)
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1988-01-01
Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
Accurate upwind-monotone (nonoscillatory) methods for conservation laws
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1992-01-01
The well known MUSCL scheme of Van Leer is constructed using a piecewise linear approximation. The MUSCL scheme is second order accurate at the smooth part of the solution except at extrema where the accuracy degenerates to first order due to the monotonicity constraint. To construct accurate schemes which are free from oscillations, the author introduces the concept of upwind monotonicity. Several classes of schemes, which are upwind monotone and of uniform second or third order accuracy are then presented. Results for advection with constant speed are shown. It is also shown that the new scheme compares favorably with state of the art methods.
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.
The chain collocation method: A spectrally accurate calculus of forms
NASA Astrophysics Data System (ADS)
Rufat, Dzhelil; Mason, Gemma; Mullen, Patrick; Desbrun, Mathieu
2014-01-01
Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.
Accurate Method for Determining Adhesion of Cantilever Beams
Michalske, T.A.; de Boer, M.P.
1999-01-08
Using surface micromachined samples, we demonstrate the accurate measurement of cantilever beam adhesion by using test structures which are adhered over long attachment lengths. We show that this configuration has a deep energy well, such that a fracture equilibrium is easily reached. When compared to the commonly used method of determining the shortest attached beam, the present method is much less sensitive to variations in surface topography or to details of capillary drying.
Seth A Veitzer
2008-10-21
Effects of stray electrons are a main factor limiting performance of many accelerators. Because heavy-ion fusion (HIF) accelerators will operate in regimes of higher current and with walls much closer to the beam than accelerators operating today, stray electrons might have a large, detrimental effect on the performance of an HIF accelerator. A primary source of stray electrons is electrons generated when halo ions strike the beam pipe walls. There is some research on these types of secondary electrons for the HIF community to draw upon, but this work is missing one crucial ingredient: the effect of grazing incidence. The overall goal of this project was to develop the numerical tools necessary to accurately model the effect of grazing incidence on the behavior of halo ions in a HIF accelerator, and further, to provide accurate models of heavy ion stopping powers with applications to ICF, WDM, and HEDP experiments.
Accurate compressed look up table method for CGH in 3D holographic display.
Gao, Chuan; Liu, Juan; Li, Xin; Xue, Gaolei; Jia, Jia; Wang, Yongtian
2015-12-28
Computer generated hologram (CGH) should be obtained with high accuracy and high speed in 3D holographic display, and most researches focus on the high speed. In this paper, a simple and effective computation method for CGH is proposed based on Fresnel diffraction theory and look up table. Numerical simulations and optical experiments are performed to demonstrate its feasibility. The proposed method can obtain more accurate reconstructed images with lower memory usage compared with split look up table method and compressed look up table method without sacrificing the computational speed in holograms generation, so it is called accurate compressed look up table method (AC-LUT). It is believed that AC-LUT method is an effective method to calculate the CGH of 3D objects for real-time 3D holographic display where the huge information data is required, and it could provide fast and accurate digital transmission in various dynamic optical fields in the future.
Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods
NASA Technical Reports Server (NTRS)
Atkins, Harold L.; Pampell, Alyssa
2011-01-01
A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies.
Mapping methods for computationally efficient and accurate structural reliability
NASA Technical Reports Server (NTRS)
Shiao, Michael C.; Chamis, Christos C.
1992-01-01
Mapping methods are developed to improve the accuracy and efficiency of probabilistic structural analyses with coarse finite element meshes. The mapping methods consist of: (1) deterministic structural analyses with fine (convergent) finite element meshes, (2) probabilistic structural analyses with coarse finite element meshes, (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes, and (4) a probabilistic mapping. The results show that the scatter of the probabilistic structural responses and structural reliability can be accurately predicted using a coarse finite element model with proper mapping methods. Therefore, large structures can be analyzed probabilistically using finite element methods.
CT Scan Method Accurately Assesses Humeral Head Retroversion
Boileau, P.; Mazzoleni, N.; Walch, G.; Urien, J. P.
2008-01-01
Humeral head retroversion is not well described with the literature controversial regarding accuracy of measurement methods and ranges of normal values. We therefore determined normal humeral head retroversion and assessed the measurement methods. We measured retroversion in 65 cadaveric humeri, including 52 paired specimens, using four methods: radiographic, computed tomography (CT) scan, computer-assisted, and direct methods. We also assessed the distance between the humeral head central axis and the bicipital groove. CT scan methods accurately measure humeral head retroversion, while radiographic methods do not. The retroversion with respect to the transepicondylar axis was 17.9° and 21.5° with respect to the trochlear tangent axis. The difference between the right and left humeri was 8.9°. The distance between the central axis of the humeral head and the bicipital groove was 7.0 mm and was consistent between right and left humeri. Humeral head retroversion may be most accurately obtained using the patient’s own anatomic landmarks or, if not, identifiable retroversion as measured by those landmarks on contralateral side or the bicipital groove. PMID:18264854
AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)
A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...
An Accurate and Efficient Method of Computing Differential Seismograms
NASA Astrophysics Data System (ADS)
Hu, S.; Zhu, L.
2013-12-01
Inversion of seismic waveforms for Earth structure usually requires computing partial derivatives of seismograms with respect to velocity model parameters. We developed an accurate and efficient method to calculate differential seismograms for multi-layered elastic media, based on the Thompson-Haskell propagator matrix technique. We first derived the partial derivatives of the Haskell matrix and its compound matrix respect to the layer parameters (P wave velocity, shear wave velocity and density). We then derived the partial derivatives of surface displacement kernels in the frequency-wavenumber domain. The differential seismograms are obtained by using the frequency-wavenumber double integration method. The implementation is computationally efficient and the total computing time is proportional to the time of computing the seismogram itself, i.e., independent of the number of layers in the model. We verified the correctness of results by comparing with differential seismograms computed using the finite differences method. Our results are more accurate because of the analytical nature of the derived partial derivatives.
Accurate optical CD profiler based on specialized finite element method
NASA Astrophysics Data System (ADS)
Carrero, Jesus; Perçin, Gökhan
2012-03-01
As the semiconductor industry is moving to very low-k1 patterning solutions, the metrology problems facing process engineers are becoming much more complex. Choosing the right optical critical dimension (OCD) metrology technique is essential for bridging the metrology gap and achieving the required manufacturing volume throughput. The critical dimension scanning electron microscope (CD-SEM) measurement is usually distorted by the high aspect ratio of the photoresist and hard mask layers. CD-SEM measurements cease to correlate with complex three-dimensional profiles, such as the cases for double patterning and FinFETs, thus necessitating sophisticated, accurate and fast computational methods to bridge the gap. In this work, a suite of computational methods that complement advanced OCD equipment, and enabling them to operate at higher accuracies, are developed. In this article, a novel method for accurately modeling OCD profiles is presented. A finite element formulation in primal form is used to discretize the equations. The implementation uses specialized finite element spaces to solve Maxwell equations in two dimensions.
Method for Accurate Surface Temperature Measurements During Fast Induction Heating
NASA Astrophysics Data System (ADS)
Larregain, Benjamin; Vanderesse, Nicolas; Bridier, Florent; Bocher, Philippe; Arkinson, Patrick
2013-07-01
A robust method is proposed for the measurement of surface temperature fields during induction heating. It is based on the original coupling of temperature-indicating lacquers and a high-speed camera system. Image analysis tools have been implemented to automatically extract the temporal evolution of isotherms. This method was applied to the fast induction treatment of a 4340 steel spur gear, allowing the full history of surface isotherms to be accurately documented for a sequential heating, i.e., a medium frequency preheating followed by a high frequency final heating. Three isotherms, i.e., 704, 816, and 927°C, were acquired every 0.3 ms with a spatial resolution of 0.04 mm per pixel. The information provided by the method is described and discussed. Finally, the transformation temperature Ac1 is linked to the temperature on specific locations of the gear tooth.
Blackman, Jonathan; Field, Scott E; Galley, Chad R; Szilágyi, Béla; Scheel, Mark A; Tiglio, Manuel; Hemberger, Daniel A
2015-09-18
Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic _{-2}Y_{ℓm} waveform modes resolved by the NR code up to ℓ=8. We compare our surrogate model to effective one body waveforms from 50M_{⊙} to 300M_{⊙} for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).
PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release
NASA Astrophysics Data System (ADS)
Pizzocri, D.; Rabiti, C.; Luzzi, L.; Barani, T.; Van Uffelen, P.; Pastore, G.
2016-09-01
The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this paper, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, combined with polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of PolyPole-1 is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.
Quinci, Federico; Dressler, Matthew; Strickland, Anthony M; Limbert, Georges
2014-04-01
Considerable progress has been made in understanding implant wear and developing numerical models to predict wear for new orthopaedic devices. However any model of wear could be improved through a more accurate representation of the biomaterial mechanics, including time-varying dynamic and inelastic behaviour such as viscosity and plastic deformation. In particular, most computational models of wear of UHMWPE implement a time-invariant version of Archard's law that links the volume of worn material to the contact pressure between the metal implant and the polymeric tibial insert. During in-vivo conditions, however, the contact area is a time-varying quantity and is therefore dependent upon the dynamic deformation response of the material. From this observation one can conclude that creep deformations of UHMWPE may be very important to consider when conducting computational wear analyses, in stark contrast to what can be found in the literature. In this study, different numerical modelling techniques are compared with experimental creep testing on a unicondylar knee replacement system in a physiologically representative context. Linear elastic, plastic and time-varying visco-dynamic models are benchmarked using literature data to predict contact deformations, pressures and areas. The aim of this study is to elucidate the contributions of viscoelastic and plastic effects on these surface quantities. It is concluded that creep deformations have a significant effect on the contact pressure measured (experiment) and calculated (computational models) at the surface of the UHMWPE unicondylar insert. The use of a purely elastoplastic constitutive model for UHMWPE lead to compressive deformations of the insert which are much smaller than those predicted by a creep-capturing viscoelastic model (and those measured experimentally). This shows again the importance of including creep behaviour into a constitutive model in order to predict the right level of surface deformation
Novel dispersion tolerant interferometry method for accurate measurements of displacement
NASA Astrophysics Data System (ADS)
Bradu, Adrian; Maria, Michael; Leick, Lasse; Podoleanu, Adrian G.
2015-05-01
We demonstrate that the recently proposed master-slave interferometry method is able to provide true dispersion free depth profiles in a spectrometer-based set-up that can be used for accurate displacement measurements in sensing and optical coherence tomography. The proposed technique is based on correlating the channelled spectra produced by the linear camera in the spectrometer with previously recorded masks. As such technique is not based on Fourier transformations (FT), it does not require any resampling of data and is immune to any amounts of dispersion left unbalanced in the system. In order to prove the tolerance of technique to dispersion, different lengths of optical fiber are used in the interferometer to introduce dispersion and it is demonstrated that neither the sensitivity profile versus optical path difference (OPD) nor the depth resolution are affected. In opposition, it is shown that the classical FT based methods using calibrated data provide less accurate optical path length measurements and exhibit a quicker decays of sensitivity with OPD.
Accurate finite difference methods for time-harmonic wave propagation
NASA Technical Reports Server (NTRS)
Harari, Isaac; Turkel, Eli
1994-01-01
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
An Accurate Projector Calibration Method Based on Polynomial Distortion Representation
Liu, Miao; Sun, Changku; Huang, Shujun; Zhang, Zonghua
2015-01-01
In structure light measurement systems or 3D printing systems, the errors caused by optical distortion of a digital projector always affect the precision performance and cannot be ignored. Existing methods to calibrate the projection distortion rely on calibration plate and photogrammetry, so the calibration performance is largely affected by the quality of the plate and the imaging system. This paper proposes a new projector calibration approach that makes use of photodiodes to directly detect the light emitted from a digital projector. By analyzing the output sequence of the photoelectric module, the pixel coordinates can be accurately obtained by the curve fitting method. A polynomial distortion representation is employed to reduce the residuals of the traditional distortion representation model. Experimental results and performance evaluation show that the proposed calibration method is able to avoid most of the disadvantages in traditional methods and achieves a higher accuracy. This proposed method is also practically applicable to evaluate the geometric optical performance of other optical projection system. PMID:26492247
Numerical Methods For Chemically Reacting Flows
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1990-01-01
Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.
NASA Technical Reports Server (NTRS)
Ellison, Donald; Conway, Bruce; Englander, Jacob
2015-01-01
A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.
Ad hoc methods for accurate determination of Bader's atomic boundary
NASA Astrophysics Data System (ADS)
Polestshuk, Pavel M.
2013-08-01
In addition to the recently published triangulation method [P. M. Polestshuk, J. Comput. Chem. 34, 206 (2013)], 10.1002/jcc.23121, two new highly accurate approaches, ZFSX and SINTY, for the integration over an atomic region covered by a zero-flux surface (zfs) were developed and efficiently interfaced into the TWOE program. ZFSX method was realized as three independent modules (ZFSX-1, ZFSX-3, and ZFSX-5) handling interatomic surfaces of a different complexity. Details of algorithmic implementation of ZFSX and SINTY are discussed. A special attention to an extended analysis of errors in calculations of atomic properties is paid. It was shown that uncertainties in zfs determination caused by ZFSX and SINTY approaches contribute negligibly (less than 10-6 a.u.) to the total atomic integration errors. Moreover, the new methods are able to evaluate atomic integrals with a reasonable time and can be universally applied for the systems of any complexity. It is suggested, therefore, that ZFSX and SINTY can be regarded as benchmark methods for the computation of any Quantum Theory of Atoms in Molecules atomic property.
Ad hoc methods for accurate determination of Bader's atomic boundary.
Polestshuk, Pavel M
2013-08-07
In addition to the recently published triangulation method [P. M. Polestshuk, J. Comput. Chem. 34, 206 (2013)], two new highly accurate approaches, ZFSX and SINTY, for the integration over an atomic region covered by a zero-flux surface (zfs) were developed and efficiently interfaced into the TWOE program. ZFSX method was realized as three independent modules (ZFSX-1, ZFSX-3, and ZFSX-5) handling interatomic surfaces of a different complexity. Details of algorithmic implementation of ZFSX and SINTY are discussed. A special attention to an extended analysis of errors in calculations of atomic properties is paid. It was shown that uncertainties in zfs determination caused by ZFSX and SINTY approaches contribute negligibly (less than 10(-6) a.u.) to the total atomic integration errors. Moreover, the new methods are able to evaluate atomic integrals with a reasonable time and can be universally applied for the systems of any complexity. It is suggested, therefore, that ZFSX and SINTY can be regarded as benchmark methods for the computation of any Quantum Theory of Atoms in Molecules atomic property.
A numerical method for phase-change problems
NASA Technical Reports Server (NTRS)
Kim, Charn-Jung; Kaviany, Massoud
1990-01-01
A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.
Advanced numerical techniques for accurate unsteady simulations of a wingtip vortex
NASA Astrophysics Data System (ADS)
Ahmad, Shakeel
A numerical technique is developed to simulate the vortices associated with stationary and flapping wings. The Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations are used over an unstructured grid. The present work assesses the locations of the origins of vortex generation, models those locations and develops a systematic mesh refinement strategy to simulate vortices more accurately using the URANS model. The vortex center plays a key role in the analysis of the simulation data. A novel approach to locating a vortex center is also developed referred to as the Max-Max criterion. Experimental validation of the simulated vortex from a stationary NACA0012 wing is achieved. The tangential velocity along the core of the vortex falls within five percent of the experimental data in the case of the stationary NACA0012 simulation. The wing surface pressure coefficient also matches with the experimental data. The refinement techniques are then focused on unsteady simulations of pitching and dual-mode wing flapping. Tip vortex strength, location, and wing surface pressure are analyzed. Links to vortex behavior and wing motion are inferred. Key words: vortex, tangential velocity, Cp, vortical flow, unsteady vortices, URANS, Max-Max, Vortex center
Accurate measurement method for tube's endpoints based on machine vision
NASA Astrophysics Data System (ADS)
Liu, Shaoli; Jin, Peng; Liu, Jianhua; Wang, Xiao; Sun, Peng
2017-01-01
Tubes are used widely in aerospace vehicles, and their accurate assembly can directly affect the assembling reliability and the quality of products. It is important to measure the processed tube's endpoints and then fix any geometric errors correspondingly. However, the traditional tube inspection method is time-consuming and complex operations. Therefore, a new measurement method for a tube's endpoints based on machine vision is proposed. First, reflected light on tube's surface can be removed by using photometric linearization. Then, based on the optimization model for the tube's endpoint measurements and the principle of stereo matching, the global coordinates and the relative distance of the tube's endpoint are obtained. To confirm the feasibility, 11 tubes are processed to remove the reflected light and then the endpoint's positions of tubes are measured. The experiment results show that the measurement repeatability accuracy is 0.167 mm, and the absolute accuracy is 0.328 mm. The measurement takes less than 1 min. The proposed method based on machine vision can measure the tube's endpoints without any surface treatment or any tools and can realize on line measurement.
On an efficient and accurate method to integrate restricted three-body orbits
NASA Technical Reports Server (NTRS)
Murison, Marc A.
1989-01-01
This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.
Perception of numerical methods in rarefied gasdynamics
NASA Technical Reports Server (NTRS)
Bird, G. A.
1989-01-01
The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.
NASA Astrophysics Data System (ADS)
Stecca, Guglielmo; Siviglia, Annunziato; Blom, Astrid
2016-07-01
We present an accurate numerical approximation to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in one space dimension. Our solution procedure originates from the fully-unsteady matrix-vector formulation developed in [54]. The principal part of the problem is solved by an explicit Finite Volume upwind method of the path-conservative type, by which all the variables are updated simultaneously in a coupled fashion. The solution to the principal part is embedded into a splitting procedure for the treatment of frictional source terms. The numerical scheme is extended to second-order accuracy and includes a bookkeeping procedure for handling the evolution of size stratification in the substrate. We develop a concept of balancedness for the vertical mass flux between the substrate and active layer under bed degradation, which prevents the occurrence of non-physical oscillations in the grainsize distribution of the substrate. We suitably modify the numerical scheme to respect this principle. We finally verify the accuracy in our solution to the equations, and its ability to reproduce one-dimensional morphodynamics due to streamwise and vertical sorting, using three test cases. In detail, (i) we empirically assess the balancedness of vertical mass fluxes under degradation; (ii) we study the convergence to the analytical linearised solution for the propagation of infinitesimal-amplitude waves [54], which is here employed for the first time to assess a mixed-sediment model; (iii) we reproduce Ribberink's E8-E9 flume experiment [46].
NASA Astrophysics Data System (ADS)
Sudhakar, Y.; Moitinho de Almeida, J. P.; Wall, Wolfgang A.
2014-09-01
We present an accurate method for the numerical integration of polynomials over arbitrary polyhedra. Using the divergence theorem, the method transforms the domain integral into integrals evaluated over the facets of the polyhedra. The necessity of performing symbolic computation during such transformation is eliminated by using one dimensional Gauss quadrature rule. The facet integrals are computed with the help of quadratures available for triangles and quadrilaterals. Numerical examples, in which the proposed method is used to integrate the weak form of the Navier-Stokes equations in an embedded interface method (EIM), are presented. The results show that our method is as accurate and generalized as the most widely used volume decomposition based methods. Moreover, since the method involves neither volume decomposition nor symbolic computations, it is much easier for computer implementation. Also, the present method is more efficient than other available integration methods based on the divergence theorem. Efficiency of the method is also compared with the volume decomposition based methods and moment fitting methods. To our knowledge, this is the first article that compares both accuracy and computational efficiency of methods relying on volume decomposition and those based on the divergence theorem.
IRIS: Towards an Accurate and Fast Stage Weight Prediction Method
NASA Astrophysics Data System (ADS)
Taponier, V.; Balu, A.
2002-01-01
The knowledge of the structural mass fraction (or the mass ratio) of a given stage, which affects the performance of a rocket, is essential for the analysis of new or upgraded launchers or stages, whose need is increased by the quick evolution of the space programs and by the necessity of their adaptation to the market needs. The availability of this highly scattered variable, ranging between 0.05 and 0.15, is of primary importance at the early steps of the preliminary design studies. At the start of the staging and performance studies, the lack of frozen weight data (to be obtained later on from propulsion, trajectory and sizing studies) leads to rely on rough estimates, generally derived from printed sources and adapted. When needed, a consolidation can be acquired trough a specific analysis activity involving several techniques and implying additional effort and time. The present empirical approach allows thus to get approximated values (i.e. not necessarily accurate or consistent), inducing some result inaccuracy as well as, consequently, difficulties of performance ranking for a multiple option analysis, and an increase of the processing duration. This forms a classical harsh fact of the preliminary design system studies, insufficiently discussed to date. It appears therefore highly desirable to have, for all the evaluation activities, a reliable, fast and easy-to-use weight or mass fraction prediction method. Additionally, the latter should allow for a pre selection of the alternative preliminary configurations, making possible a global system approach. For that purpose, an attempt at modeling has been undertaken, whose objective was the determination of a parametric formulation of the mass fraction, to be expressed from a limited number of parameters available at the early steps of the project. It is based on the innovative use of a statistical method applicable to a variable as a function of several independent parameters. A specific polynomial generator
A high-order accurate embedded boundary method for first order hyperbolic equations
NASA Astrophysics Data System (ADS)
Mattsson, Ken; Almquist, Martin
2017-04-01
A stable and high-order accurate embedded boundary method for first order hyperbolic equations is derived. Where the grid-boundaries and the physical boundaries do not coincide, high order interpolation is used. The boundary stencils are based on a summation-by-parts framework, and the boundary conditions are imposed by the SAT penalty method, which guarantees linear stability for one-dimensional problems. Second-, fourth-, and sixth-order finite difference schemes are considered. The resulting schemes are fully explicit. Accuracy and numerical stability of the proposed schemes are demonstrated for both linear and nonlinear hyperbolic systems in one and two spatial dimensions.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
Quantifying Methane Fluxes Simply and Accurately: The Tracer Dilution Method
NASA Astrophysics Data System (ADS)
Rella, Christopher; Crosson, Eric; Green, Roger; Hater, Gary; Dayton, Dave; Lafleur, Rick; Merrill, Ray; Tan, Sze; Thoma, Eben
2010-05-01
Methane is an important atmospheric constituent with a wide variety of sources, both natural and anthropogenic, including wetlands and other water bodies, permafrost, farms, landfills, and areas with significant petrochemical exploration, drilling, transport, or processing, or refining occurs. Despite its importance to the carbon cycle, its significant impact as a greenhouse gas, and its ubiquity in modern life as a source of energy, its sources and sinks in marine and terrestrial ecosystems are only poorly understood. This is largely because high quality, quantitative measurements of methane fluxes in these different environments have not been available, due both to the lack of robust field-deployable instrumentation as well as to the fact that most significant sources of methane extend over large areas (from 10's to 1,000,000's of square meters) and are heterogeneous emitters - i.e., the methane is not emitted evenly over the area in question. Quantifying the total methane emissions from such sources becomes a tremendous challenge, compounded by the fact that atmospheric transport from emission point to detection point can be highly variable. In this presentation we describe a robust, accurate, and easy-to-deploy technique called the tracer dilution method, in which a known gas (such as acetylene, nitrous oxide, or sulfur hexafluoride) is released in the same vicinity of the methane emissions. Measurements of methane and the tracer gas are then made downwind of the release point, in the so-called far-field, where the area of methane emissions cannot be distinguished from a point source (i.e., the two gas plumes are well-mixed). In this regime, the methane emissions are given by the ratio of the two measured concentrations, multiplied by the known tracer emission rate. The challenges associated with atmospheric variability and heterogeneous methane emissions are handled automatically by the transport and dispersion of the tracer. We present detailed methane flux
Numerical Methods for Nonlinear Hillslope Transport Laws
NASA Astrophysics Data System (ADS)
Perron, J. T.
2008-12-01
The numerical methods used to solve nonlinear sediment transport equations often set restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Standard explicit finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. Methods that rely on cell-to-cell sediment routing schemes can introduce significant errors that may not be obvious unless the numerical solution is compared with a known solution. I present a new, implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport but avoids the use of a cell-to-cell sediment routing scheme. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the new method retains the accuracy of the explicit method while allowing timesteps several orders of magnitude longer than the maximum timesteps permitted by the explicit method. The method can be adapted to any transport law in which the expression for sediment flux is differentiable, including coupled systems in which sediment flux is a function of quantities such as soil depth.
Numerical Methods for Initial Value Problems.
1980-07-01
of general multistep methods for ordinary differential equations a4 to implement an efficient algorithm for the solution of stiff equations . Still...integral equations II. Roundoff error for variants of Gaussian elimination III. Multistep methods for ordinary differential equations IV. Multi-grid...62 -! Paige III. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS ....... 63 1. Equivalent Forms of Multistep
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
The numerical mirage method for photothermal characterization of materials.
Demko, Michael T; Hostler, Stephen R; Abramson, Alexis R
2008-04-01
Noncontact thermal measurement techniques offer rapid thermal characterization without modification or destruction of the sample being studied. A simple and versatile method has been developed, termed the "numerical mirage method," that utilizes the transient photothermal deflection of a laser beam traversing a modulated temperature gradient. This method expands the range and simplifies the experimental procedure of traditional mirage methods. A numerical solver is used to create accurate deflection profile models and a linear curve fitting routine is developed, from which the thermal diffusivity of a material may be determined. This method allows for rapid modification of sample and heating configurations. Verification of the method is performed on bismuth and fused quartz reference samples, and good agreement with literature is obtained.
Accurate numerical forward model for optimal retracking of SIRAL2 SAR echoes over open ocean
NASA Astrophysics Data System (ADS)
Phalippou, L.; Demeestere, F.
2011-12-01
The SAR mode of SIRAL-2 on board Cryosat-2 has been designed to measure primarily sea-ice and continental ice (Wingham et al. 2005). In 2005, K. Raney (KR, 2005) pointed out the improvements brought by SAR altimeter for open ocean. KR results were mostly based on 'rule of thumb' considerations on speckle noise reduction due to the higher PRF and to speckle decorrelation after SAR processing. In 2007, Phalippou and Enjolras (PE,2007) provided the theoretical background for optimal retracking of SAR echoes over ocean with a focus on the forward modelling of the power-waveforms. The accuracies of geophysical parameters (range, significant wave heights, and backscattering coefficient) retrieved from SAR altimeter data were derived accounting for SAR echo shape and speckle noise accurate modelling. The step forward to optimal retracking using numerical forward model (NFM) was also pointed out. NFM of the power waveform avoids analytical approximation, a warranty to minimise the geophysical dependent biases in the retrieval. NFM have been used for many years, in operational meteorology in particular, for retrieving temperature and humidity profiles from IR and microwave radiometers as the radiative transfer function is complex (Eyre, 1989). So far this technique was not used in the field of ocean conventional altimetry as analytical models (e.g. Brown's model for instance) were found to give sufficient accuracy. However, although NFM seems desirable even for conventional nadir altimetry, it becomes inevitable if one wish to process SAR altimeter data as the transfer function is too complex to be approximated by a simple analytical function. This was clearly demonstrated in PE 2007. The paper describes the background to SAR data retracking over open ocean. Since PE 2007 improvements have been brought to the forward model and it is shown that the altimeter on-ground and in flight characterisation (e.g antenna pattern range impulse response, azimuth impulse response
NASA Astrophysics Data System (ADS)
Wosnik, M.; Bachant, P.
2014-12-01
Cross-flow turbines, often referred to as vertical-axis turbines, show potential for success in marine hydrokinetic (MHK) and wind energy applications, ranging from small- to utility-scale installations in tidal/ocean currents and offshore wind. As turbine designs mature, the research focus is shifting from individual devices to the optimization of turbine arrays. It would be expensive and time-consuming to conduct physical model studies of large arrays at large model scales (to achieve sufficiently high Reynolds numbers), and hence numerical techniques are generally better suited to explore the array design parameter space. However, since the computing power available today is not sufficient to conduct simulations of the flow in and around large arrays of turbines with fully resolved turbine geometries (e.g., grid resolution into the viscous sublayer on turbine blades), the turbines' interaction with the energy resource (water current or wind) needs to be parameterized, or modeled. Models used today--a common model is the actuator disk concept--are not able to predict the unique wake structure generated by cross-flow turbines. This wake structure has been shown to create "constructive" interference in some cases, improving turbine performance in array configurations, in contrast with axial-flow, or horizontal axis devices. Towards a more accurate parameterization of cross-flow turbines, an extensive experimental study was carried out using a high-resolution turbine test bed with wake measurement capability in a large cross-section tow tank. The experimental results were then "interpolated" using high-fidelity Navier--Stokes simulations, to gain insight into the turbine's near-wake. The study was designed to achieve sufficiently high Reynolds numbers for the results to be Reynolds number independent with respect to turbine performance and wake statistics, such that they can be reliably extrapolated to full scale and used for model validation. The end product of
A time-accurate finite volume method valid at all flow velocities
NASA Astrophysics Data System (ADS)
Kim, S.-W.
1993-07-01
A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil
Numerical methods for nonlinear hillslope transport laws
NASA Astrophysics Data System (ADS)
Perron, J. Taylor
2011-06-01
The numerical methods used to solve nonlinear sediment transport equations often set very restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Explicit-time finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. I present an implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport and improves stability and accuracy by avoiding the direct calculation of sediment flux. This method can be adapted to any transport law in which the expression for sediment flux is differentiable. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the implicit method retains the accuracy of a standard explicit method while permitting time steps several orders of magnitude longer than the maximum stable time step for the explicit method. The ability to take long time steps affords a substantial savings in overall computation time, despite the implicit method's higher per-iteration computational cost. Implicit models for hillslope evolution also offer a distinct advantage when modeling the response of hillslopes to incising channels.
Stable and accurate difference methods for seismic wave propagation on locally refined meshes
NASA Astrophysics Data System (ADS)
Petersson, A.; Rodgers, A.; Nilsson, S.; Sjogreen, B.; McCandless, K.
2006-12-01
To overcome some of the shortcomings of previous numerical methods for the elastic wave equation subject to stress-free boundary conditions, we are incorporating recent results from numerical analysis to develop a new finite difference method which discretizes the governing equations in second order displacement formulation. The most challenging aspect of finite difference methods for time dependent hyperbolic problems is clearly stability and some previous methods are known to be unstable when the material has a compressional velocity which exceeds about three times the shear velocity. Since the material properties in seismic applications often vary rapidly on the computational grid, the most straight forward approach for guaranteeing stability is through an energy estimate. For a hyperbolic system in second order formulation, the key to an energy estimate is a spatial discretization which is self-adjoint, i.e. corresponds to a symmetric or symmetrizable matrix. At the same time we want the scheme to be efficient and fully explicit, so only local operations are necessary to evolve the solution in the interior of the domain as well as on the free-surface boundary. Furthermore, we want the solution to be accurate when the data is smooth. Using these specifications, we developed an explicit second order accurate discretization where stability is guaranteed through an energy estimate for all ratios Cp/Cs. An implementation of our finite difference method was used to simulate ground motions during the 1906 San Francisco earthquake on a uniform grid with grid sizes down to 100 meters corresponding to over 4 Billion grid points. These simulations were run on 1024 processors on one of the supercomputers at Lawrence Livermore National Lab. To reduce the computational requirements for these simulations, we are currently extending the numerical method to use a locally refined mesh where the mesh size approximately follows the velocity structure in the domain. Some
Numerical Methods through Open-Ended Projects
ERIC Educational Resources Information Center
Cline, Kelly S.
2005-01-01
We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…
A numerical method of detecting singularity
NASA Technical Reports Server (NTRS)
Laporte, M.; Vignes, J.
1978-01-01
A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.
Numerical methods for aerothermodynamic design of hypersonic space transport vehicles
NASA Astrophysics Data System (ADS)
Wanie, K. M.; Brenneis, A.; Eberle, A.; Heiss, S.
1993-04-01
The requirement of the design process of hypersonic vehicles to predict flow past entire configurations with wings, fins, flaps, and propulsion system represents one of the major challenges for aerothermodynamics. In this context computational fluid dynamics has come up as a powerful tool to support the experimental work. A couple of numerical methods developed at MBB designed to fulfill the needs of the design process are described. The governing equations and fundamental details of the solution methods are shortly reviewed. Results are given for both geometrically simple test cases and realistic hypersonic configurations. Since there is still a considerable lack of experience for hypersonic flow calculations an extensive testing and verification is essential. This verification is done by comparison of results with experimental data and other numerical methods. The results presented prove that the methods used are robust, flexible, and accurate enough to fulfill the strong needs of the design process.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
Method and apparatus for accurately manipulating an object during microelectrophoresis
Parvin, Bahram A.; Maestre, Marcos F.; Fish, Richard H.; Johnston, William E.
1997-01-01
An apparatus using electrophoresis provides accurate manipulation of an object on a microscope stage for further manipulations add reactions. The present invention also provides an inexpensive and easily accessible means to move an object without damage to the object. A plurality of electrodes are coupled to the stage in an array whereby the electrode array allows for distinct manipulations of the electric field for accurate manipulations of the object. There is an electrode array control coupled to the plurality of electrodes for manipulating the electric field. In an alternative embodiment, a chamber is provided on the stage to hold the object. The plurality of electrodes are positioned in the chamber, and the chamber is filled with fluid. The system can be automated using visual servoing, which manipulates the control parameters, i.e., x, y stage, applying the field, etc., after extracting the significant features directly from image data. Visual servoing includes an imaging device and computer system to determine the location of the object. A second stage having a plurality of tubes positioned on top of the second stage, can be accurately positioned by visual servoing so that one end of one of the plurality of tubes surrounds at least part of the object on the first stage.
Method and apparatus for accurately manipulating an object during microelectrophoresis
Parvin, B.A.; Maestre, M.F.; Fish, R.H.; Johnston, W.E.
1997-09-23
An apparatus using electrophoresis provides accurate manipulation of an object on a microscope stage for further manipulations and reactions. The present invention also provides an inexpensive and easily accessible means to move an object without damage to the object. A plurality of electrodes are coupled to the stage in an array whereby the electrode array allows for distinct manipulations of the electric field for accurate manipulations of the object. There is an electrode array control coupled to the plurality of electrodes for manipulating the electric field. In an alternative embodiment, a chamber is provided on the stage to hold the object. The plurality of electrodes are positioned in the chamber, and the chamber is filled with fluid. The system can be automated using visual servoing, which manipulates the control parameters, i.e., x, y stage, applying the field, etc., after extracting the significant features directly from image data. Visual servoing includes an imaging device and computer system to determine the location of the object. A second stage having a plurality of tubes positioned on top of the second stage, can be accurately positioned by visual servoing so that one end of one of the plurality of tubes surrounds at least part of the object on the first stage. 11 figs.
A new class of accurate, mesh-free hydrodynamic simulation methods
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.
2015-06-01
We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.
Fast and stable numerical method for neuronal modelling
NASA Astrophysics Data System (ADS)
Hashemi, Soheil; Abdolali, Ali
2016-11-01
Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.
New numerical method to study phase transitions and its applications
Lee, Jooyoung; Kosterlitz, J.M.
1991-11-01
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/{xi} < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.
An explicit mixed numerical method for mesoscale model
NASA Technical Reports Server (NTRS)
Hsu, H.-M.
1981-01-01
A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.
Hyperbolic conservation laws and numerical methods
NASA Technical Reports Server (NTRS)
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems
Cai, Wei
2014-05-15
Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.
Mapping methods for computationally efficient and accurate structural reliability
NASA Technical Reports Server (NTRS)
Shiao, Michael C.; Chamis, Christos C.
1992-01-01
Mapping methods are developed to improve the accuracy and efficiency of probabilistic structural analyses with coarse finite element meshes. The mapping methods consist of the following: (1) deterministic structural analyses with fine (convergent) finite element meshes; (2) probabilistic structural analyses with coarse finite element meshes; (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes; and (4) a probabilistic mapping. The results show that the scatter in the probabilistic structural responses and structural reliability can be efficiently predicted using a coarse finite element model and proper mapping methods with good accuracy. Therefore, large structures can be efficiently analyzed probabilistically using finite element methods.
Numerical methods for hypersonic boundary layer stability
NASA Technical Reports Server (NTRS)
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Method accurately measures mean particle diameters of monodisperse polystyrene latexes
NASA Technical Reports Server (NTRS)
Kubitschek, H. E.
1967-01-01
Photomicrographic method determines mean particle diameters of monodisperse polystyrene latexes. Many diameters are measured simultaneously by measuring row lengths of particles in a triangular array at a glass-oil interface. The method provides size standards for electronic particle counters and prevents distortions, softening, and flattening.
Express method of construction of accurate inverse pole figures
NASA Astrophysics Data System (ADS)
Perlovich, Yu; Isaenkova, M.; Fesenko, V.
2016-04-01
With regard to metallic materials with the FCC and BCC crystal lattice a new method for constructing the X-ray texture inverse pole figures (IPF) by using tilt curves of spinning sample, characterized by high accuracy and rapidity (express), was proposed. In contrast to the currently widespread method to construct IPF using orientation distribution function (ODF), synthesized in several partial direct pole figures, the proposed method is based on a simple geometrical interpretation of a measurement procedure, requires a minimal operating time of the X-ray diffractometer.
NASA Technical Reports Server (NTRS)
Yungster, Shaye; Radhakrishnan, Krishnan
1994-01-01
A new fully implicit, time accurate algorithm suitable for chemically reacting, viscous flows in the transonic-to-hypersonic regime is described. The method is based on a class of Total Variation Diminishing (TVD) schemes and uses successive Gauss-Siedel relaxation sweeps. The inversion of large matrices is avoided by partitioning the system into reacting and nonreacting parts, but still maintaining a fully coupled interaction. As a result, the matrices that have to be inverted are of the same size as those obtained with the commonly used point implicit methods. In this paper we illustrate the applicability of the new algorithm to hypervelocity unsteady combustion applications. We present a series of numerical simulations of the periodic combustion instabilities observed in ballistic-range experiments of blunt projectiles flying at subdetonative speeds through hydrogen-air mixtures. The computed frequencies of oscillation are in excellent agreement with experimental data.
RELAP-7 Numerical Stabilization: Entropy Viscosity Method
R. A. Berry; M. O. Delchini; J. Ragusa
2014-06-01
The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.
NASA Astrophysics Data System (ADS)
Huerta, Eliu; Agarwal, Bhanu; Chua, Alvin; George, Daniel; Haas, Roland; Hinder, Ian; Kumar, Prayush; Moore, Christopher; Pfeiffer, Harald
2017-01-01
We recently constructed an inspiral-merger-ringdown (IMR) waveform model to describe the dynamical evolution of compact binaries on eccentric orbits, and used this model to constrain the eccentricity with which the gravitational wave transients currently detected by LIGO could be effectively recovered with banks of quasi-circular templates. We now present the second generation of this model, which is calibrated using a large catalog of eccentric numerical relativity simulations. We discuss the new features of this model, and show that its enhance accuracy makes it a powerful tool to detect eccentric signals with LIGO.
NASA Technical Reports Server (NTRS)
Constantinescu, G.S.; Lele, S. K.
2000-01-01
The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions
NASA Astrophysics Data System (ADS)
Simmons, Daniel; Cools, Kristof; Sewell, Phillip
2016-11-01
Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications.
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Athavale, M. M.; Hendricks, R. C.; Steinetz, B. M.
2006-01-01
Detailed information of the flow-fields in the secondary flowpaths and their interaction with the primary flows in gas turbine engines is necessary for successful designs with optimized secondary flow streams. Present work is focused on the development of a simulation methodology for coupled time-accurate solutions of the two flowpaths. The secondary flowstream is treated using SCISEAL, an unstructured adaptive Cartesian grid code developed for secondary flows and seals, while the mainpath flow is solved using TURBO, a density based code with capability of resolving rotor-stator interaction in multi-stage machines. An interface is being tested that links the two codes at the rim seal to allow data exchange between the two codes for parallel, coupled execution. A description of the coupling methodology and the current status of the interface development is presented. Representative steady-state solutions of the secondary flow in the UTRC HP Rig disc cavity are also presented.
Efficient numerical methods for nonlinear Schrodinger equations
NASA Astrophysics Data System (ADS)
Liang, Xiao
The nonlinear Schrodinger equations are widely used to model a number of important physical phenomena, including solitary wave propagations in optical fibers, deep water turbulence, laser beam transmissions, and the Bose-Einstein condensation, just to mention a few. In the field of optics and photonics, the systems of nonlinear Schrodinger equations can be used to model multi-component solitons and the interaction of self-focusing laser beams. In three spatial dimensions, the nonlinear Schrodinger equation is known as the Gross-Pitaevskii equation, which models the soliton in a low-cost graded-index fiber. Recently, research on nonlinear space fractional Schrodinger equations, which capture the self-similarity in the fractional environment, has become prevalent. Our study includes the systems of multi-dimensional nonlinear space fractional Schrodinger equations. To solve the systems of multi-dimensional nonlinear Schrodinger equations efficiently, several novel numerical methods are presented. The central difference and quartic spline approximation based exponential time differencing Crank-Nicolson method is introduced for solving systems of one- and two-dimensional nonlinear Schrodinger equations. A local extrapolation is employed to achieve fourth-order accuracy in time. The numerical examples include the transmission of a self-focusing laser beam. The local discontinuous Galerkin methods combined with the fourth-order exponential time differencing Runge-Kutta time discretization are studied for solving the systems of nonlinear Schrodinger equations with hyperbolic terms, which are critical in modeling optical solitons in the birefringent fibers. The local discontinuous Galerkin method is able to achieve any order of accuracy in space, thanks to the usage of piecewise polynomial spaces. The exponential time differencing methods are employed to deal with the coupled nonlinearities for the reason that there is no need to solve nonlinear systems at every time step
Joint iris boundary detection and fit: a real-time method for accurate pupil tracking.
Barbosa, Marconi; James, Andrew C
2014-08-01
A range of applications in visual science rely on accurate tracking of the human pupil's movement and contraction in response to light. While the literature for independent contour detection and fitting of the iris-pupil boundary is vast, a joint approach, in which it is assumed that the pupil has a given geometric shape has been largely overlooked. We present here a global method for simultaneously finding and fitting of an elliptic or circular contour against a dark interior, which produces consistently accurate results even under non-ideal recording conditions, such as reflections near and over the boundary, droopy eye lids, or the sudden formation of tears. The specific form of the proposed optimization problem allows us to write down closed analytic formulae for the gradient and the Hessian of the objective function. Moreover, both the objective function and its derivatives can be cast into vectorized form, making the proposed algorithm significantly faster than its closest relative in the literature. We compare methods in multiple ways, both analytically and numerically, using real iris images as well as idealizations of the iris for which the ground truth boundary is precisely known. The method proposed here is illustrated under challenging recording conditions and it is shown to be robust.
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
Joint iris boundary detection and fit: a real-time method for accurate pupil tracking
Barbosa, Marconi; James, Andrew C.
2014-01-01
A range of applications in visual science rely on accurate tracking of the human pupil’s movement and contraction in response to light. While the literature for independent contour detection and fitting of the iris-pupil boundary is vast, a joint approach, in which it is assumed that the pupil has a given geometric shape has been largely overlooked. We present here a global method for simultaneously finding and fitting of an elliptic or circular contour against a dark interior, which produces consistently accurate results even under non-ideal recording conditions, such as reflections near and over the boundary, droopy eye lids, or the sudden formation of tears. The specific form of the proposed optimization problem allows us to write down closed analytic formulae for the gradient and the Hessian of the objective function. Moreover, both the objective function and its derivatives can be cast into vectorized form, making the proposed algorithm significantly faster than its closest relative in the literature. We compare methods in multiple ways, both analytically and numerically, using real iris images as well as idealizations of the iris for which the ground truth boundary is precisely known. The method proposed here is illustrated under challenging recording conditions and it is shown to be robust. PMID:25136477
Numerical analysis method for linear induction machines.
NASA Technical Reports Server (NTRS)
Elliott, D. G.
1972-01-01
A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.
An accurate fuzzy edge detection method using wavelet details subimages
NASA Astrophysics Data System (ADS)
Sedaghat, Nafiseh; Pourreza, Hamidreza
2010-02-01
Edge detection is a basic and important subject in computer vision and image processing. An edge detector is defined as a mathematical operator of small spatial extent that responds in some way to these discontinuities, usually classifying every image pixel as either belonging to an edge or not. Many researchers have been spent attempting to develop effective edge detection algorithms. Despite this extensive research, the task of finding the edges that correspond to true physical boundaries remains a difficult problem.Edge detection algorithms based on the application of human knowledge show their flexibility and suggest that the use of human knowledge is a reasonable alternative. In this paper we propose a fuzzy inference system with two inputs: gradient and wavelet details. First input is calculated by Sobel operator and the second is calculated by wavelet transform of input image and then reconstruction of image only with details subimages by inverse wavelet transform. There are many fuzzy edge detection methods, but none of them utilize wavelet transform as it is used in this paper. For evaluating our method, we detect edges of images with different brightness characteristics and compare results with canny edge detector. The results show the high performance of our method in finding true edges.
Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method
NASA Technical Reports Server (NTRS)
Spalart, P. R.
1986-01-01
A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.
Mapping methods for computationally efficient and accurate structural reliability
NASA Technical Reports Server (NTRS)
Shiao, Michael C.; Chamis, Christos C.
1991-01-01
The influence of mesh coarseness in the structural reliability is evaluated. The objectives are to describe the alternatives and to demonstrate their effectiveness. The results show that special mapping methods can be developed by using: (1) deterministic structural responses from a fine (convergent) finite element mesh; (2) probabilistic distributions of structural responses from a coarse finite element mesh; (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes; and (4) probabilistic mapping. The structural responses from different finite element meshes are highly correlated.
Pendant bubble method for an accurate characterization of superhydrophobic surfaces.
Ling, William Yeong Liang; Ng, Tuck Wah; Neild, Adrian
2011-12-06
The commonly used sessile drop method for measuring contact angles and surface tension suffers from errors on superhydrophobic surfaces. This occurs from unavoidable experimental error in determining the vertical location of the liquid-solid-vapor interface due to a camera's finite pixel resolution, thereby necessitating the development and application of subpixel algorithms. We demonstrate here the advantage of a pendant bubble in decreasing the resulting error prior to the application of additional algorithms. For sessile drops to attain an equivalent accuracy, the pixel count would have to be increased by 2 orders of magnitude.
An adaptive, formally second order accurate version of the immersed boundary method
NASA Astrophysics Data System (ADS)
Griffith, Boyce E.; Hornung, Richard D.; McQueen, David M.; Peskin, Charles S.
2007-04-01
Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-)elastic structure (the muscular walls and the valves of the heart). The immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves, and extensions of this work have yielded a three-dimensional model of the heart and great vessels. In the present work, we introduce a new adaptive version of the immersed boundary method. This adaptive scheme employs the same hierarchical structured grid approach (but a different numerical scheme) as the two-dimensional adaptive immersed boundary method of Roma et al. [A multilevel self adaptive version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1996; An adaptive version of the immersed boundary method, J. Comput. Phys. 153 (2) (1999) 509-534] and is based on a formally second order accurate (i.e., second order accurate for problems with sufficiently smooth solutions) version of the immersed boundary method that we have recently described [B.E. Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput. Phys. 208 (1) (2005) 75-105]. Actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell. We also present initial results from the application of this methodology to the three-dimensional simulation of blood flow in the heart and great vessels. The results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves
Mathematica with a Numerical Methods Course
NASA Astrophysics Data System (ADS)
Varley, Rodney
2003-04-01
An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.
Individualizing amikacin regimens: accurate method to achieve therapeutic concentrations.
Zaske, D E; Cipolle, R J; Rotschafer, J C; Kohls, P R; Strate, R G
1991-11-01
Amikacin's pharmacokinetics and dosage requirements were studied in 98 patients receiving treatment for gram-negative infections. A wide interpatient variation in the kinetic parameters of the drug occurred in all patients and in patients who had normal serum creatinine levels or normal creatinine clearance. The half-life ranged from 0.7 to 14.4 h in 74 patients who had normal serum creatinine levels and from 0.7 to 7.2 h in 37 patients who had normal creatinine clearance. The necessary daily dose to obtain therapeutic serum concentrations ranged from 1.25 to 57 mg/kg in patients with normal serum creatinine levels and from 10 to 57 mg/kg in patients with normal creatinine clearance. In four patients (4%), a significant change in baseline serum creatinine level (greater than 0.5 mg/dl) occurred during or after treatment, which may have been amikacin-associated toxicity. Overt ototoxicity occurred in one patient. The method of individualizing dosage regimens provided a clinically useful means of rapidly attaining therapeutic peak and trough serum concentrations.
The use of experimental bending tests to more accurate numerical description of TBC damage process
NASA Astrophysics Data System (ADS)
Sadowski, T.; Golewski, P.
2016-04-01
Thermal barrier coatings (TBCs) have been extensively used in aircraft engines to protect critical engine parts such as blades and combustion chambers, which are exposed to high temperatures and corrosive environment. The blades of turbine engines are additionally exposed to high mechanical loads. These loads are created by the high rotational speed of the rotor (30 000 rot/min), causing the tensile and bending stresses. Therefore, experimental testing of coated samples is necessary in order to determine strength properties of TBCs. Beam samples with dimensions 50×10×2 mm were used in those studies. The TBC system consisted of 150 μm thick bond coat (NiCoCrAlY) and 300 μm thick top coat (YSZ) made by APS (air plasma spray) process. Samples were tested by three-point bending test with various loads. After bending tests, the samples were subjected to microscopic observation to determine the quantity of cracks and their depth. The above mentioned results were used to build numerical model and calibrate material data in Abaqus program. Brittle cracking damage model was applied for the TBC layer, which allows to remove elements after reaching criterion. Surface based cohesive behavior was used to model the delamination which may occur at the boundary between bond coat and top coat.
Homogenization and Numerical Methods for Hyperbolic Equations
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo
1990-01-01
This dissertation studies three aspects of analysis and numerical methods for partial differential equations with oscillatory solutions. 1. Homogenization theory for certain linear hyperbolic equations is developed. We derive the homogenized convection equations for linear convection problems with rapidly varying velocity in space and time. We find that the oscillatory solutions are very sensitive to the arithmetic properties of certain parameters, such as the corresponding rotation number and the ratio between the components of the mean velocity field in linear convection. We also show that the oscillatory velocity field in two dimensional incompressible flow behaves like shear flows. 2. The homogenization of scalar nonlinear conservation laws in several space variables with oscillatory initial data is also discussed. We prove that the initial oscillations will be eliminated for any positive time when the equations are non-degenerate. This is also true for degenerate equations if there is enough mixing among the initial oscillations in the degenerate direction. Otherwise, the initial oscillation, for which the homogenized equation is obtained, will survive and be propagated. The large-time behavior of conservation laws with several space variables is studied. We show that, under a new nondegenerate condition (the second derivatives of the flux functions are linearly independent in any interval), a piecewise smooth periodic solution with converge strongly to the mean value of initial data. This generalizes Glimm and Lax's result for the one dimensional problem (3). 3. Numerical simulations of the oscillatory solutions are also carried out. We give some error estimate for varepsilon-h resonance ( varepsilon: oscillation wave length, h: numerical step) and prove essential convergence (24) of order alpha < 1 for some numerical schemes. These include upwind schemes and particle methods for linear hyperbolic equations with oscillatory coefficients. A stochastic analysis
Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan
2006-01-01
Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.
Ida, Masato; Taniguchi, Nobuyuki
2003-09-01
This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.
A numerical method for solving the Vlasov equation
NASA Technical Reports Server (NTRS)
Satofuka, N.
1982-01-01
A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.
Conservative high-order-accurate finite-difference methods for curvilinear grids
NASA Technical Reports Server (NTRS)
Rai, Man M.; Chakrvarthy, Sukumar
1993-01-01
Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.
Extracting accurate strain measurements in bone mechanics: A critical review of current methods.
Grassi, Lorenzo; Isaksson, Hanna
2015-10-01
Osteoporosis related fractures are a social burden that advocates for more accurate fracture prediction methods. Mechanistic methods, e.g. finite element models, have been proposed as a tool to better predict bone mechanical behaviour and strength. However, there is little consensus about the optimal constitutive law to describe bone as a material. Extracting reliable and relevant strain data from experimental tests is of fundamental importance to better understand bone mechanical properties, and to validate numerical models. Several techniques have been used to measure strain in experimental mechanics, with substantial differences in terms of accuracy, precision, time- and length-scale. Each technique presents upsides and downsides that must be carefully evaluated when designing the experiment. Moreover, additional complexities are often encountered when applying such strain measurement techniques to bone, due to its complex composite structure. This review of literature examined the four most commonly adopted methods for strain measurements (strain gauges, fibre Bragg grating sensors, digital image correlation, and digital volume correlation), with a focus on studies with bone as a substrate material, at the organ and tissue level. For each of them the working principles, a summary of the main applications to bone mechanics at the organ- and tissue-level, and a list of pros and cons are provided.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
NASA Astrophysics Data System (ADS)
Sagui, Celeste
2006-03-01
An accurate and numerically efficient treatment of electrostatics is essential for biomolecular simulations, as this stabilizes much of the delicate 3-d structure associated with biomolecules. Currently, force fields such as AMBER and CHARMM assign ``partial charges'' to every atom in a simulation in order to model the interatomic electrostatic forces, so that the calculation of the electrostatics rapidly becomes the computational bottleneck in large-scale simulations. There are two main issues associated with the current treatment of classical electrostatics: (i) how does one eliminate the artifacts associated with the point-charges (e.g., the underdetermined nature of the current RESP fitting procedure for large, flexible molecules) used in the force fields in a physically meaningful way? (ii) how does one efficiently simulate the very costly long-range electrostatic interactions? Recently, we have dealt with both of these challenges as follows. In order to improve the description of the molecular electrostatic potentials (MEPs), a new distributed multipole analysis based on localized functions -- Wannier, Boys, and Edminston-Ruedenberg -- was introduced, which allows for a first principles calculation of the partial charges and multipoles. Through a suitable generalization of the particle mesh Ewald (PME) and multigrid method, one can treat electrostatic multipoles all the way to hexadecapoles all without prohibitive extra costs. The importance of these methods for large-scale simulations will be discussed, and examplified by simulations from polarizable DNA models.
Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces
NASA Technical Reports Server (NTRS)
Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John
2011-01-01
Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
D. S. Lucas
2004-10-01
A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
A Monte Carlo Method for Making the SDSS u-Band Magnitude More Accurate
NASA Astrophysics Data System (ADS)
Gu, Jiayin; Du, Cuihua; Zuo, Wenbo; Jing, Yingjie; Wu, Zhenyu; Ma, Jun; Zhou, Xu
2016-10-01
We develop a new Monte Carlo-based method to convert the Sloan Digital Sky Survey (SDSS) u-band magnitude to the south Galactic Cap of the u-band Sky Survey (SCUSS) u-band magnitude. Due to the increased accuracy of SCUSS u-band measurements, the converted u-band magnitude becomes more accurate compared with the original SDSS u-band magnitude, in particular at the faint end. The average u-magnitude error (for both SDSS and SCUSS) of numerous main-sequence stars with 0.2\\lt g-r\\lt 0.8 increases as the g-band magnitude becomes fainter. When g = 19.5, the average magnitude error of the SDSS u is 0.11. When g = 20.5, the average SDSS u error rises to 0.22. However, at this magnitude, the average magnitude error of the SCUSS u is just half as much as that of the SDSS u. The SDSS u-band magnitudes of main-sequence stars with 0.2\\lt g-r\\lt 0.8 and 18.5\\lt g\\lt 20.5 are converted, therefore the maximum average error of the converted u-band magnitudes is 0.11. The potential application of this conversion is to derive a more accurate photometric metallicity calibration from SDSS observations, especially for the more distant stars. Thus, we can explore stellar metallicity distributions either in the Galactic halo or some stream stars.
Bozkaya, Uğur
2013-10-21
The extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials (IPs) from any level of theory, in principle. However, for non-variational methods, such as Møller-Plesset perturbation and coupled-cluster theories, the EKT computations can only be performed as by-products of analytic gradients as the relaxed generalized Fock matrix (GFM) and one- and two-particle density matrices (OPDM and TPDM, respectively) are required [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys. 107, 6804 (1997)]. However, for the orbital-optimized methods both the GFM and OPDM are readily available and symmetric, as opposed to the standard post Hartree-Fock (HF) methods. Further, the orbital optimized methods solve the N-representability problem, which may arise when the relaxed particle density matrices are employed for the standard methods, by disregarding the orbital Z-vector contributions for the OPDM. Moreover, for challenging chemical systems, where spin or spatial symmetry-breaking problems are observed, the abnormal orbital response contributions arising from the numerical instabilities in the HF molecular orbital Hessian can be avoided by the orbital-optimization. Hence, it appears that the orbital-optimized methods are the most natural choice for the study of the EKT. In this research, the EKT for the orbital-optimized methods, such as orbital-optimized second- and third-order Møller-Plesset perturbation [U. Bozkaya, J. Chem. Phys. 135, 224103 (2011)] and coupled-electron pair theories [OCEPA(0)] [U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 139, 054104 (2013)], are presented. The presented methods are applied to IPs of the second- and third-row atoms, and closed- and open-shell molecules. Performances of the orbital-optimized methods are compared with those of the counterpart standard methods. Especially, results of the OCEPA(0) method (with the aug-cc-pVTZ basis set) for the lowest IPs of the considered atoms and closed
Shu, Yu-Chen; Chern, I-Liang; Chang, Chien C.
2014-10-15
Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms.
Numerical methods for large eddy simulation of acoustic combustion instabilities
NASA Astrophysics Data System (ADS)
Wall, Clifton T.
Acoustic combustion instabilities occur when interaction between the combustion process and acoustic modes in a combustor results in periodic oscillations in pressure, velocity, and heat release. If sufficiently large in amplitude, these instabilities can cause operational difficulties or the failure of combustor hardware. In many situations, the dominant instability is the result of the interaction between a low frequency acoustic mode of the combustor and the large scale hydrodynamics. Large eddy simulation (LES), therefore, is a promising tool for the prediction of these instabilities, since both the low frequency acoustic modes and the large scale hydrodynamics are well resolved in LES. Problems with the tractability of such simulations arise, however, due to the difficulty of solving the compressible Navier-Stokes equations efficiently at low Mach number and due to the large number of acoustic periods that are often required for such instabilities to reach limit cycles. An implicit numerical method for the solution of the compressible Navier-Stokes equations has been developed which avoids the acoustic CFL restriction, allowing for significant efficiency gains at low Mach number, while still resolving the low frequency acoustic modes of interest. In the limit of a uniform grid the numerical method causes no artificial damping of acoustic waves. New, non-reflecting boundary conditions have also been developed for use with the characteristic-based approach of Poinsot and Lele (1992). The new boundary conditions are implemented in a manner which allows for significant reduction of the computational domain of an LES by eliminating the need to perform LES in regions where one-dimensional acoustics significantly affect the instability but details of the hydrodynamics do not. These new numerical techniques have been demonstrated in an LES of an experimental combustor. The new techniques are shown to be an efficient means of performing LES of acoustic combustion
NASA Astrophysics Data System (ADS)
Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng
2016-01-01
An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.
NASA Astrophysics Data System (ADS)
Moore, Christopher; Hopkins, Matthew; Moore, Stan; Boerner, Jeremiah; Cartwright, Keith
2015-09-01
Simulation of breakdown is important for understanding and designing a variety of applications such as mitigating undesirable discharge events. Such simulations need to be accurate through early time arc initiation to late time stable arc behavior. Here we examine constraints on the timestep and mesh size required for arc simulations using the particle-in-cell (PIC) method with direct simulation Monte Carlo (DMSC) collisions. Accurate simulation of electron avalanche across a fixed voltage drop and constant neutral density (reduced field of 1000 Td) was found to require a timestep ~ 1/100 of the mean time between collisions and a mesh size ~ 1/25 the mean free path. These constraints are much smaller than the typical PIC-DSMC requirements for timestep and mesh size. Both constraints are related to the fact that charged particles are accelerated by the external field. Thus gradients in the electron energy distribution function can exist at scales smaller than the mean free path and these must be resolved by the mesh size for accurate collision rates. Additionally, the timestep must be small enough that the particle energy change due to the fields be small in order to capture gradients in the cross sections versus energy. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
Ye, Jingfei; Wang, Wei; Gao, Zhishan; Liu, Zhiying; Wang, Shuai; Benítez, Pablo; Miñano, Juan C; Yuan, Qun
2015-10-05
Wavefront estimation from the slope-based sensing metrologies zis important in modern optical testing. A numerical orthogonal transformation method is proposed for deriving the numerical orthogonal gradient polynomials as numerical orthogonal basis functions for directly fitting the measured slope data and then converting to the wavefront in a straightforward way in the modal approach. The presented method can be employed in the wavefront estimation from its slopes over the general shaped aperture. Moreover, the numerical orthogonal transformation method could be applied to the wavefront estimation from its slope measurements over the dynamic varying aperture. The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified by the examples. They indicate that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.
NASA Astrophysics Data System (ADS)
Boerstoel, J. W.
1983-10-01
Numerical methods for the calculation of inviscid Euler flows are reviewed. For aerodynamic applications, the existing methods are accurate and cheap enough. However, shocks and vortex sheets may have to be better modeled to achieve higher numerical accuracy. Computation times can be reduced by applying multigrid methods.
Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry.
Yatabe, Kohei; Ishikawa, Kenji; Oikawa, Yasuhiro
2017-01-01
This paper presents a non-iterative phase retrieval method from randomly phase-shifted fringe images. By combining the hyperaccurate least squares ellipse fitting method with the subspace method (usually called the principal component analysis), a fast and accurate phase retrieval algorithm is realized. The proposed method is simple, flexible, and accurate. It can be easily coded without iteration, initial guess, or tuning parameter. Its flexibility comes from the fact that totally random phase-shifting steps and any number of fringe images greater than two are acceptable without any specific treatment. Finally, it is accurate because the hyperaccurate least squares method and the modified subspace method enable phase retrieval with a small error as shown by the simulations. A MATLAB code, which is used in the experimental section, is provided within the paper to demonstrate its simplicity and easiness.
NASA Technical Reports Server (NTRS)
Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.
1992-01-01
The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.
Fast, accurate and easy-to-pipeline methods for amplicon sequence processing
NASA Astrophysics Data System (ADS)
Antonielli, Livio; Sessitsch, Angela
2016-04-01
Next generation sequencing (NGS) technologies established since years as an essential resource in microbiology. While on the one hand metagenomic studies can benefit from the continuously increasing throughput of the Illumina (Solexa) technology, on the other hand the spreading of third generation sequencing technologies (PacBio, Oxford Nanopore) are getting whole genome sequencing beyond the assembly of fragmented draft genomes, making it now possible to finish bacterial genomes even without short read correction. Besides (meta)genomic analysis next-gen amplicon sequencing is still fundamental for microbial studies. Amplicon sequencing of the 16S rRNA gene and ITS (Internal Transcribed Spacer) remains a well-established widespread method for a multitude of different purposes concerning the identification and comparison of archaeal/bacterial (16S rRNA gene) and fungal (ITS) communities occurring in diverse environments. Numerous different pipelines have been developed in order to process NGS-derived amplicon sequences, among which Mothur, QIIME and USEARCH are the most well-known and cited ones. The entire process from initial raw sequence data through read error correction, paired-end read assembly, primer stripping, quality filtering, clustering, OTU taxonomic classification and BIOM table rarefaction as well as alternative "normalization" methods will be addressed. An effective and accurate strategy will be presented using the state-of-the-art bioinformatic tools and the example of a straightforward one-script pipeline for 16S rRNA gene or ITS MiSeq amplicon sequencing will be provided. Finally, instructions on how to automatically retrieve nucleotide sequences from NCBI and therefore apply the pipeline to targets other than 16S rRNA gene (Greengenes, SILVA) and ITS (UNITE) will be discussed.
Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J
2017-01-01
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
uncertainty quantification. In the last decade much progress has been made in the construction of numerical algorithms to efficiently solve SPDES with...applicable SPDES with efficient numerical methods. This project is intended to address the numerical analysis as well as algorithm aspects of SPDES. Three...differential equations. Our work contains algorithm constructions, rigorous error analysis, and extensive numerical experiments to demonstrate our algorithm
Method for accurate growth of vertical-cavity surface-emitting lasers
Chalmers, S.A.; Killeen, K.P.; Lear, K.L.
1995-03-14
The authors report a method for accurate growth of vertical-cavity surface-emitting lasers (VCSELs). The method uses a single reflectivity spectrum measurement to determine the structure of the partially completed VCSEL at a critical point of growth. This information, along with the extracted growth rates, allows imprecisions in growth parameters to be compensated for during growth of the remaining structure, which can then be completed with very accurate critical dimensions. Using this method, they can now routinely grow lasing VCSELs with Fabry-Perot cavity resonance wavelengths controlled to within 0.5%. 4 figs.
Method for accurate growth of vertical-cavity surface-emitting lasers
Chalmers, Scott A.; Killeen, Kevin P.; Lear, Kevin L.
1995-01-01
We report a method for accurate growth of vertical-cavity surface-emitting lasers (VCSELs). The method uses a single reflectivity spectrum measurement to determine the structure of the partially completed VCSEL at a critical point of growth. This information, along with the extracted growth rates, allows imprecisions in growth parameters to be compensated for during growth of the remaining structure, which can then be completed with very accurate critical dimensions. Using this method, we can now routinely grow lasing VCSELs with Fabry-Perot cavity resonance wavelengths controlled to within 0.5%.
Numerical methods in Markov chain modeling
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
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.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1978-01-01
The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.
A numerical solution method for acoustic radiation from axisymmetric bodies
NASA Technical Reports Server (NTRS)
Caruthers, John E.; Raviprakash, G. K.
1995-01-01
A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.
NASA Astrophysics Data System (ADS)
Liu, Qianlong
2011-09-01
Prosperetti's seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present
Numerical analysis of the orthogonal descent method
Shokov, V.A.; Shchepakin, M.B.
1994-11-01
The author of the orthogonal descent method has been testing it since 1977. The results of these tests have only strengthened the need for further analysis and development of orthogonal descent algorithms for various classes of convex programming problems. Systematic testing of orthogonal descent algorithms and comparison of test results with other nondifferentiable optimization methods was conducted at TsEMI RAN in 1991-1992 using the results.
Fast Monte Carlo Electron-Photon Transport Method and Application in Accurate Radiotherapy
NASA Astrophysics Data System (ADS)
Hao, Lijuan; Sun, Guangyao; Zheng, Huaqing; Song, Jing; Chen, Zhenping; Li, Gui
2014-06-01
Monte Carlo (MC) method is the most accurate computational method for dose calculation, but its wide application on clinical accurate radiotherapy is hindered due to its poor speed of converging and long computation time. In the MC dose calculation research, the main task is to speed up computation while high precision is maintained. The purpose of this paper is to enhance the calculation speed of MC method for electron-photon transport with high precision and ultimately to reduce the accurate radiotherapy dose calculation time based on normal computer to the level of several hours, which meets the requirement of clinical dose verification. Based on the existing Super Monte Carlo Simulation Program (SuperMC), developed by FDS Team, a fast MC method for electron-photon coupled transport was presented with focus on two aspects: firstly, through simplifying and optimizing the physical model of the electron-photon transport, the calculation speed was increased with slightly reduction of calculation accuracy; secondly, using a variety of MC calculation acceleration methods, for example, taking use of obtained information in previous calculations to avoid repeat simulation of particles with identical history; applying proper variance reduction techniques to accelerate MC method convergence rate, etc. The fast MC method was tested by a lot of simple physical models and clinical cases included nasopharyngeal carcinoma, peripheral lung tumor, cervical carcinoma, etc. The result shows that the fast MC method for electron-photon transport was fast enough to meet the requirement of clinical accurate radiotherapy dose verification. Later, the method will be applied to the Accurate/Advanced Radiation Therapy System ARTS as a MC dose verification module.
Numerical methods for reduction of topside ionograms
NASA Technical Reports Server (NTRS)
Mcculley, L.
1972-01-01
Several alternative methods for solving the group height equation are presented. Three of these are now in operation at Ames Research Center and use data contained in a single ionogram trace. From the data an electron density profile N(h) is computed. If the ionogram also exhibits other traces, reverse ionogram traces are computed, using the N(h) profile, for comparison with the redundant data. When agreement is poor, the initial data trace is reinterpreted, another N(h) profile computed, and the reverse traces generated once again. This process is repeated until a desired degree of consistency is achieved. To reduce the necessity for human intervention and eliminate decision making required in conjunction with the preceding methods, a method is proposed that accepts as input, all data from a single ionogram. In general, no electron density function will satisfy these data exactly, but a best N(h) profile can be computed. Finally, a method is described that eliminates the need to assume that the ionosphere is spherically stratified. Horizontal gradients in electron density are detected and accounted for by processing several ionograms from the same satellite pass simultaneously. This idea is derived as an extension of one of the basic methods.
A new method to synthesize competitor RNAs for accurate analyses by competitive RT-PCR.
Ishibashi, O
1997-12-03
A method to synthesize competitor RNAs as internal standards for competitive RT-PCR is improved by using the long accurate PCR (LA-PCR) technique. Competitor templates synthesized by the new method are almost the same in length, and possibly in secondary structure, as target mRNAs to be quantified except that they include the short deletion within the segments to be amplified. This allows the reverse transcription to be achieved with almost the same efficiency from both target mRNAs and competitor RNAs. Therefore, more accurate quantification can be accomplished by using such competitor RNAs.
NASA Technical Reports Server (NTRS)
Loh, Ching Y.; Jorgenson, Philip C. E.
2007-01-01
A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.
An accurate method of extracting fat droplets in liver images for quantitative evaluation
NASA Astrophysics Data System (ADS)
Ishikawa, Masahiro; Kobayashi, Naoki; Komagata, Hideki; Shinoda, Kazuma; Yamaguchi, Masahiro; Abe, Tokiya; Hashiguchi, Akinori; Sakamoto, Michiie
2015-03-01
The steatosis in liver pathological tissue images is a promising indicator of nonalcoholic fatty liver disease (NAFLD) and the possible risk of hepatocellular carcinoma (HCC). The resulting values are also important for ensuring the automatic and accurate classification of HCC images, because the existence of many fat droplets is likely to create errors in quantifying the morphological features used in the process. In this study we propose a method that can automatically detect, and exclude regions with many fat droplets by using the feature values of colors, shapes and the arrangement of cell nuclei. We implement the method and confirm that it can accurately detect fat droplets and quantify the fat droplet ratio of actual images. This investigation also clarifies the effective characteristics that contribute to accurate detection.
Numerical Methods Using B-Splines
NASA Technical Reports Server (NTRS)
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Modelling asteroid brightness variations. I - Numerical methods
NASA Technical Reports Server (NTRS)
Karttunen, H.
1989-01-01
A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.
Numerical methods for determining interstitial oxygen in silicon
Stevenson, J.O.; Medernach, J.W.
1995-01-01
The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1988-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.
Efficient Numerical Methods for Stable Distributions
2007-11-02
0 and cutoffs c1 = −128 and c2 = +127 are used, corresponding to the common values used in digital signal processing. Five new functions for discrete...variables using the Chambers- Mallows - Stuck method, rounding them to the nearest integer, and then cutting off if the value is too high or too low...within the common matlab environment they use. We comment briefly on the commercialization of this in the last section. 3 -100 -50 0 50 100 0. 0 0. 01 0
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Turan, A.
1985-01-01
The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.
The U.S. Department of Agriculture Automated Multiple-Pass Method accurately assesses sodium intakes
Technology Transfer Automated Retrieval System (TEKTRAN)
Accurate and practical methods to monitor sodium intake of the U.S. population are critical given current sodium reduction strategies. While the gold standard for estimating sodium intake is the 24 hour urine collection, few studies have used this biomarker to evaluate the accuracy of a dietary ins...
LSimpute: accurate estimation of missing values in microarray data with least squares methods.
Bø, Trond Hellem; Dysvik, Bjarte; Jonassen, Inge
2004-02-20
Microarray experiments generate data sets with information on the expression levels of thousands of genes in a set of biological samples. Unfortunately, such experiments often produce multiple missing expression values, normally due to various experimental problems. As many algorithms for gene expression analysis require a complete data matrix as input, the missing values have to be estimated in order to analyze the available data. Alternatively, genes and arrays can be removed until no missing values remain. However, for genes or arrays with only a small number of missing values, it is desirable to impute those values. For the subsequent analysis to be as informative as possible, it is essential that the estimates for the missing gene expression values are accurate. A small amount of badly estimated missing values in the data might be enough for clustering methods, such as hierachical clustering or K-means clustering, to produce misleading results. Thus, accurate methods for missing value estimation are needed. We present novel methods for estimation of missing values in microarray data sets that are based on the least squares principle, and that utilize correlations between both genes and arrays. For this set of methods, we use the common reference name LSimpute. We compare the estimation accuracy of our methods with the widely used KNNimpute on three complete data matrices from public data sets by randomly knocking out data (labeling as missing). From these tests, we conclude that our LSimpute methods produce estimates that consistently are more accurate than those obtained using KNNimpute. Additionally, we examine a more classic approach to missing value estimation based on expectation maximization (EM). We refer to our EM implementations as EMimpute, and the estimate errors using the EMimpute methods are compared with those our novel methods produce. The results indicate that on average, the estimates from our best performing LSimpute method are at least as
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.
NASA Astrophysics Data System (ADS)
Lin, Xue-lei; Lu, Xin; Ng, Micheal K.; Sun, Hai-Wei
2016-10-01
A fast accurate approximation method with multigrid solver is proposed to solve a two-dimensional fractional sub-diffusion equation. Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator. Our idea is to make use of the block ɛ-circulant approximation via fast Fourier transforms, so that the resulting task is to solve a block diagonal system, where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a Laplacian matrix. We show that the accuracy of the approximation scheme is of O (ɛ). Because of the special diagonal block structure, we employ the multigrid method to solve the resulting linear systems. The convergence of the multigrid method is studied. Numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver.
An Effective Method to Accurately Calculate the Phase Space Factors for β - β - Decay
Neacsu, Andrei; Horoi, Mihai
2016-01-01
Accurate calculations of the electron phase space factors are necessary for reliable predictions of double-beta decay rates and for the analysis of the associated electron angular and energy distributions. We present an effective method to calculate these phase space factors that takes into account the distorted Coulomb field of the daughter nucleus, yet it allows one to easily calculate the phase space factors with good accuracy relative to the most exact methods available in the recent literature.
Accurate determination of specific heat at high temperatures using the flash diffusivity method
NASA Technical Reports Server (NTRS)
Vandersande, J. W.; Zoltan, A.; Wood, C.
1989-01-01
The flash diffusivity method of Parker et al. (1961) was used to measure accurately the specific heat of test samples simultaneously with thermal diffusivity, thus obtaining the thermal conductivity of these materials directly. The accuracy of data obtained on two types of materials (n-type silicon-germanium alloys and niobium), was + or - 3 percent. It is shown that the method is applicable up to at least 1300 K.
A numerical method for vortex sheet roll-up
NASA Technical Reports Server (NTRS)
Krasny, R.
1986-01-01
The problem of computing vortex sheet roll-up from periodic analytic initial data is studied. Previous theoretical and numerical work is reviewed. Computational difficulties arising from ill posedness and singularity formation are discussed. A desingularization method is proposed to diminish these difficulties. Computations indicate that this approach converges past the time at which previous numerical investigations have failed to converge.
A second-order accurate kinetic-theory-based method for inviscid compressible flows
NASA Technical Reports Server (NTRS)
Deshpande, Suresh M.
1986-01-01
An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.
An effective method for accurate prediction of the first hyperpolarizability of alkalides.
Wang, Jia-Nan; Xu, Hong-Liang; Sun, Shi-Ling; Gao, Ting; Li, Hong-Zhi; Li, Hui; Su, Zhong-Min
2012-01-15
The proper theoretical calculation method for nonlinear optical (NLO) properties is a key factor to design the excellent NLO materials. Yet it is a difficult task to obatin the accurate NLO property of large scale molecule. In present work, an effective intelligent computing method, as called extreme learning machine-neural network (ELM-NN), is proposed to predict accurately the first hyperpolarizability (β(0)) of alkalides from low-accuracy first hyperpolarizability. Compared with neural network (NN) and genetic algorithm neural network (GANN), the root-mean-square deviations of the predicted values obtained by ELM-NN, GANN, and NN with their MP2 counterpart are 0.02, 0.08, and 0.17 a.u., respectively. It suggests that the predicted values obtained by ELM-NN are more accurate than those calculated by NN and GANN methods. Another excellent point of ELM-NN is the ability to obtain the high accuracy level calculated values with less computing cost. Experimental results show that the computing time of MP2 is 2.4-4 times of the computing time of ELM-NN. Thus, the proposed method is a potentially powerful tool in computational chemistry, and it may predict β(0) of the large scale molecules, which is difficult to obtain by high-accuracy theoretical method due to dramatic increasing computational cost.
NASA Astrophysics Data System (ADS)
Ban, Yunyun; Chen, Tianqin; Yan, Jun; Lei, Tingwu
2017-04-01
The measurement of sediment concentration in water is of great importance in soil erosion research and soil and water loss monitoring systems. The traditional weighing method has long been the foundation of all the other measuring methods and instrument calibration. The development of a new method to replace the traditional oven-drying method is of interest in research and practice for the quick and efficient measurement of sediment concentration, especially field measurements. A new method is advanced in this study for accurately measuring the sediment concentration based on the accurate measurement of the mass of the sediment-water mixture in the confined constant volume container (CVC). A sediment-laden water sample is put into the CVC to determine its mass before the CVC is filled with water and weighed again for the total mass of the water and sediments in the container. The known volume of the CVC, the mass of sediment-laden water, and sediment particle density are used to calculate the mass of water, which is replaced by sediments, therefore sediment concentration of the sample is calculated. The influence of water temperature was corrected by measuring water density to determine the temperature of water before measurements were conducted. The CVC was used to eliminate the surface tension effect so as to obtain the accurate volume of water and sediment mixture. Experimental results showed that the method was capable of measuring the sediment concentration from 0.5 up to 1200 kg m‑3. A good liner relationship existed between the designed and measured sediment concentrations with all the coefficients of determination greater than 0.999 and the averaged relative error less than 0.2%. All of these seem to indicate that the new method is capable of measuring a full range of sediment concentration above 0.5 kg m‑3 to replace the traditional oven-drying method as a standard method for evaluating and calibrating other methods.
Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method
NASA Technical Reports Server (NTRS)
Smith, James P.
1996-01-01
A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.
Kearns, F L; Hudson, P S; Boresch, S; Woodcock, H L
2016-01-01
Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.
Numerical Simulation of Turbulent Flames using Vortex Methods.
1987-10-05
layer," Phys. Fluids , 30, pp. 706-721, 1987. (11) Ghoniem, A.F., and Knio, O.M., "Numerical Simulation of Flame Propagation in Constant Volume Chambers...1985. 4. "Numerical solution of a confined shear layer using vortex methods," The International Symposium on Computational Fluid Dynamics, Tokyo...Symposium on Computational Fluid Dynamics, Tokyo, Japan, September 1985. 8. "Application of Computational Methods in Turbulent Reacting Flow
A safe and accurate method to perform esthetic mandibular contouring surgery for Far Eastern Asians.
Hsieh, A M-C; Huon, L-K; Jiang, H-R; Liu, S Y-C
2017-05-01
A tapered mandibular contour is popular with Far Eastern Asians. This study describes a safe and accurate method of using preoperative virtual surgical planning (VSP) and an intraoperative ostectomy guide to maximize the esthetic outcomes of mandibular symmetry and tapering while mitigating injury to the inferior alveolar nerve (IAN). Twelve subjects with chief complaints of a wide and square lower face underwent this protocol from January to June 2015. VSP was used to confirm symmetry and preserve the IAN while maximizing the surgeon's ability to taper the lower face via mandibular inferior border ostectomy. The accuracy of this method was confirmed by superimposition of the perioperative computed tomography scans in all subjects. No subjects complained of prolonged paresthesia after 3 months. A safe and accurate protocol for achieving an esthetic lower face in indicated Far Eastern individuals is described.
A fast and accurate method to predict 2D and 3D aerodynamic boundary layer flows
NASA Astrophysics Data System (ADS)
Bijleveld, H. A.; Veldman, A. E. P.
2014-12-01
A quasi-simultaneous interaction method is applied to predict 2D and 3D aerodynamic flows. This method is suitable for offshore wind turbine design software as it is a very accurate and computationally reasonably cheap method. This study shows the results for a NACA 0012 airfoil. The two applied solvers converge to the experimental values when the grid is refined. We also show that in separation the eigenvalues remain positive thus avoiding the Goldstein singularity at separation. In 3D we show a flow over a dent in which separation occurs. A rotating flat plat is used to show the applicability of the method for rotating flows. The shown capabilities of the method indicate that the quasi-simultaneous interaction method is suitable for design methods for offshore wind turbine blades.
Fazio, Massimo A; Bruno, Luigi; Reynaud, Juan F; Poggialini, Andrea; Downs, J Crawford
2012-03-01
We proposed and validated a compensation method that accounts for the optical distortion inherent in measuring displacements on specimens immersed in aqueous solution. A spherically-shaped rubber specimen was mounted and pressurized on a custom apparatus, with the resulting surface displacements recorded using electronic speckle pattern interferometry (ESPI). Point-to-point light direction computation is achieved by a ray-tracing strategy coupled with customized B-spline-based analytical representation of the specimen shape. The compensation method reduced the mean magnitude of the displacement error induced by the optical distortion from 35% to 3%, and ESPI displacement measurement repeatability showed a mean variance of 16 nm at the 95% confidence level for immersed specimens. The ESPI interferometer and numerical data analysis procedure presented herein provide reliable, accurate, and repeatable measurement of sub-micrometer deformations obtained from pressurization tests of spherically-shaped specimens immersed in aqueous salt solution. This method can be used to quantify small deformations in biological tissue samples under load, while maintaining the hydration necessary to ensure accurate material property assessment.
NASA Technical Reports Server (NTRS)
Myhill, Elizabeth A.; Boss, Alan P.
1993-01-01
In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.
Hassouna, M Sabry; Farag, A A
2007-09-01
A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.
An accurate and practical method for inference of weak gravitational lensing from galaxy images
NASA Astrophysics Data System (ADS)
Bernstein, Gary M.; Armstrong, Robert; Krawiec, Christina; March, Marisa C.
2016-07-01
We demonstrate highly accurate recovery of weak gravitational lensing shear using an implementation of the Bayesian Fourier Domain (BFD) method proposed by Bernstein & Armstrong, extended to correct for selection biases. The BFD formalism is rigorously correct for Nyquist-sampled, background-limited, uncrowded images of background galaxies. BFD does not assign shapes to galaxies, instead compressing the pixel data D into a vector of moments M, such that we have an analytic expression for the probability P(M|g) of obtaining the observations with gravitational lensing distortion g along the line of sight. We implement an algorithm for conducting BFD's integrations over the population of unlensed source galaxies which measures ≈10 galaxies s-1 core-1 with good scaling properties. Initial tests of this code on ≈109 simulated lensed galaxy images recover the simulated shear to a fractional accuracy of m = (2.1 ± 0.4) × 10-3, substantially more accurate than has been demonstrated previously for any generally applicable method. Deep sky exposures generate a sufficiently accurate approximation to the noiseless, unlensed galaxy population distribution assumed as input to BFD. Potential extensions of the method include simultaneous measurement of magnification and shear; multiple-exposure, multiband observations; and joint inference of photometric redshifts and lensing tomography.
Asymptotic-induced numerical methods for conservation laws
NASA Technical Reports Server (NTRS)
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
Numerical methods for solving ODEs on the infinity computer
NASA Astrophysics Data System (ADS)
Mazzia, F.; Sergeyev, Ya. D.; Iavernaro, F.; Amodio, P.; Mukhametzhanov, M. S.
2016-10-01
New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial conditions are proposed. They are designed for working on a new kind of a supercomputer - the Infinity Computer - that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods are able to work with the exact values of the derivatives, instead of their approximations. Within this context, variants of one-step multi-point methods closely related to the classical Taylor formulae and to the Obrechkoff methods are considered. To get numerical evidence of the theoretical results, test problems are solved by means of the new methods and the results compared with the performance of classical methods.
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I.; Caruge, D.
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
NASA Astrophysics Data System (ADS)
Godin, T. J.; Haydock, Roger
1991-04-01
The Block Recursion Library, a collection of FORTRAN subroutines, calculates submatrices of the resolvent of a linear operator. The resolvent, in matrix theory, is a powerful tool for extracting information about solutions of linear systems. The routines use the block recursion method and achieve high accuracy for very large systems of coupled equations. This technique is a generalization of the scalar recursion method, an accurate technique for finding the local density of states. A sample program uses these routines to find the quantum mechanical transmittance of a randomly disordered two-dimensional cluster of atoms.
NASA Astrophysics Data System (ADS)
Ho, Kung-Chu; Su, Vin-Cent; Huang, Da-Yo; Lee, Ming-Lun; Chou, Nai-Kuan; Kuan, Chieh-Hsiung
2017-01-01
This paper reports the investigation of strong electrolytic solutions operated in low frequency regime through an accurate electrical impedance method realized with a specific microfluidic device and high resolution instruments. Experimental results show the better repeatability and accuracy of the proposed impedance method. Moreover, all electrolytic solutions appear the so-called relaxation frequency at each peak value of dielectric loss due to relaxing total polarization inside the device. The relaxation frequency of concentrated electrolytes becomes higher owing to the stronger total polarization behavior coming from the higher conductivity as well as the lower resistance in the electrolytic solutions.
Wang, Xue-Yong; Liao, Cai-Li; Liu, Si-Qi; Liu, Chun-Sheng; Shao, Ai-Juan; Huang, Lu-Qi
2013-05-01
This paper put forward a more accurate identification method for identification of Chinese materia medica (CMM), the systematic identification of Chinese materia medica (SICMM) , which might solve difficulties in CMM identification used the ordinary traditional ways. Concepts, mechanisms and methods of SICMM were systematically introduced and possibility was proved by experiments. The establishment of SICMM will solve problems in identification of Chinese materia medica not only in phenotypic characters like the mnorphous, microstructure, chemical constituents, but also further discovery evolution and classification of species, subspecies and population in medical plants. The establishment of SICMM will improve the development of identification of CMM and create a more extensive study space.
Hwang, Beomsoo; Jeon, Doyoung
2015-04-09
In exoskeletal robots, the quantification of the user's muscular effort is important to recognize the user's motion intentions and evaluate motor abilities. In this paper, we attempt to estimate users' muscular efforts accurately using joint torque sensor which contains the measurements of dynamic effect of human body such as the inertial, Coriolis, and gravitational torques as well as torque by active muscular effort. It is important to extract the dynamic effects of the user's limb accurately from the measured torque. The user's limb dynamics are formulated and a convenient method of identifying user-specific parameters is suggested for estimating the user's muscular torque in robotic exoskeletons. Experiments were carried out on a wheelchair-integrated lower limb exoskeleton, EXOwheel, which was equipped with torque sensors in the hip and knee joints. The proposed methods were evaluated by 10 healthy participants during body weight-supported gait training. The experimental results show that the torque sensors are to estimate the muscular torque accurately in cases of relaxed and activated muscle conditions.
Deng, Yan; Zhou, Bin; Xing, Chao; Zhang, Rong
2014-10-17
A novel multifrequency excitation (MFE) method is proposed to realize rapid and accurate dynamic testing of micromachined gyroscope chips. Compared with the traditional sweep-frequency excitation (SFE) method, the computational time for testing one chip under four modes at a 1-Hz frequency resolution and 600-Hz bandwidth was dramatically reduced from 10 min to 6 s. A multifrequency signal with an equal amplitude and initial linear-phase-difference distribution was generated to ensure test repeatability and accuracy. The current test system based on LabVIEW using the SFE method was modified to use the MFE method without any hardware changes. The experimental results verified that the MFE method can be an ideal solution for large-scale dynamic testing of gyroscope chips and gyroscopes.
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
FRANCOIS, MARIANNE M.; DENDY, EDWARD D.; LOWRIE, ROBERT B.; LIVESCU, DANIEL; STEINKAMP, MICHAEL J.
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
NASA Astrophysics Data System (ADS)
Chiumenti, M.; Cervera, M.; Agelet de Saracibar, C.; Dialami, N.
2013-05-01
In this work a novel finite element technology based on a three-field mixed formulation is presented. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear piece-wise interpolations for displacement, stress and pressure fields, respectively. The result is an enhanced stress field approximation which enables for stress-accurate results in nonlinear computational mechanics. The use of an independent nodal variable for the pressure field allows for an adhoc treatment of the incompressibility constraint. This is a mandatory requirement due to the isochoric nature of the plastic strain in metal forming processes. The highly non-linear stress field typically encountered in the Friction Stir Welding (FSW) process is used as an example to show the performance of this new FE technology. The numerical simulation of the FSW process is tackled by means of an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The computational domain is split into three different zones: the work.piece (defined by a rigid visco-plastic behaviour in the Eulerian framework), the pin (within the Lagrangian framework) and finally the stirzone (ALE formulation). A fully coupled thermo-mechanical analysis is introduced showing the heat fluxes generated by the plastic dissipation in the stir-zone (Sheppard rigid-viscoplastic constitutive model) as well as the frictional dissipation at the contact interface (Norton frictional contact model). Finally, tracers have been implemented to show the material flow around the pin allowing a better understanding of the welding mechanism. Numerical results are compared with experimental evidence.
A Novel Method for Accurate Operon Predictions in All SequencedProkaryotes
Price, Morgan N.; Huang, Katherine H.; Alm, Eric J.; Arkin, Adam P.
2004-12-01
We combine comparative genomic measures and the distance separating adjacent genes to predict operons in 124 completely sequenced prokaryotic genomes. Our method automatically tailors itself to each genome using sequence information alone, and thus can be applied to any prokaryote. For Escherichia coli K12 and Bacillus subtilis, our method is 85 and 83% accurate, respectively, which is similar to the accuracy of methods that use the same features but are trained on experimentally characterized transcripts. In Halobacterium NRC-1 and in Helicobacterpylori, our method correctly infers that genes in operons are separated by shorter distances than they are in E.coli, and its predictions using distance alone are more accurate than distance-only predictions trained on a database of E.coli transcripts. We use microarray data from sixphylogenetically diverse prokaryotes to show that combining intergenic distance with comparative genomic measures further improves accuracy and that our method is broadly effective. Finally, we survey operon structure across 124 genomes, and find several surprises: H.pylori has many operons, contrary to previous reports; Bacillus anthracis has an unusual number of pseudogenes within conserved operons; and Synechocystis PCC6803 has many operons even though it has unusually wide spacings between conserved adjacent genes.
Accurate Time/Frequency Transfer Method Using Bi-Directional WDM Transmission
NASA Technical Reports Server (NTRS)
Imaoka, Atsushi; Kihara, Masami
1996-01-01
An accurate time transfer method is proposed using b-directional wavelength division multiplexing (WDM) signal transmission along a single optical fiber. This method will be used in digital telecommunication networks and yield a time synchronization accuracy of better than 1 ns for long transmission lines over several tens of kilometers. The method can accurately measure the difference in delay between two wavelength signals caused by the chromatic dispersion of the fiber in conventional simple bi-directional dual-wavelength frequency transfer methods. We describe the characteristics of this difference in delay and then show that the accuracy of the delay measurements can be obtained below 0.1 ns by transmitting 156 Mb/s times reference signals of 1.31 micrometer and 1.55 micrometers along a 50 km fiber using the proposed method. The sub-nanosecond delay measurement using the simple bi-directional dual-wavelength transmission along a 100 km fiber with a wavelength spacing of 1 nm in the 1.55 micrometer range is also shown.
Celeste, Ricardo; Maringolo, Milena P; Comar, Moacyr; Viana, Rommel B; Guimarães, Amanda R; Haiduke, Roberto L A; da Silva, Albérico B F
2015-10-01
Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations.
Numeric Modified Adomian Decomposition Method for Power System Simulations
Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth
2016-01-01
This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.
A numerical method for solving singular De`s
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2013-01-01
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
Accurate method for including solid-fluid boundary interactions in mesoscopic model fluids
Berkenbos, A. Lowe, C.P.
2008-04-20
Particle models are attractive methods for simulating the dynamics of complex mesoscopic fluids. Many practical applications of this methodology involve flow through a solid geometry. As the system is modeled using particles whose positions move continuously in space, one might expect that implementing the correct stick boundary condition exactly at the solid-fluid interface is straightforward. After all, unlike discrete methods there is no mapping onto a grid to contend with. In this article we describe a method that, for axisymmetric flows, imposes both the no-slip condition and continuity of stress at the interface. We show that the new method then accurately reproduces correct hydrodynamic behavior right up to the location of the interface. As such, computed flow profiles are correct even using a relatively small number of particles to model the fluid.
Accurate force fields and methods for modelling organic molecular crystals at finite temperatures.
Nyman, Jonas; Pundyke, Orla Sheehan; Day, Graeme M
2016-06-21
We present an assessment of the performance of several force fields for modelling intermolecular interactions in organic molecular crystals using the X23 benchmark set. The performance of the force fields is compared to several popular dispersion corrected density functional methods. In addition, we present our implementation of lattice vibrational free energy calculations in the quasi-harmonic approximation, using several methods to account for phonon dispersion. This allows us to also benchmark the force fields' reproduction of finite temperature crystal structures. The results demonstrate that anisotropic atom-atom multipole-based force fields can be as accurate as several popular DFT-D methods, but have errors 2-3 times larger than the current best DFT-D methods. The largest error in the examined force fields is a systematic underestimation of the (absolute) lattice energy.
Accurate Wind Characterization in Complex Terrain Using the Immersed Boundary Method
Lundquist, K A; Chow, F K; Lundquist, J K; Kosovic, B
2009-09-30
This paper describes an immersed boundary method (IBM) that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Two different interpolation methods, trilinear and inverse distance weighting, are used at the core of the IBM algorithm. Functional aspects of the algorithm's implementation and the accuracy of results are considered. Simulations of flow over a three-dimensional hill with shallow terrain slopes are preformed with both WRF's native terrain-following coordinate and with both IB methods. Comparisons of flow fields from the three simulations show excellent agreement, indicating that both IB methods produce accurate results. However, when ease of implementation is considered, inverse distance weighting is superior. Furthermore, inverse distance weighting is shown to be more adept at handling highly complex urban terrain, where the trilinear interpolation algorithm breaks down. This capability is demonstrated by using the inverse distance weighting core of the IBM to model atmospheric flow in downtown Oklahoma City.
NASA Astrophysics Data System (ADS)
Tang, Xiaojun
2016-04-01
The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.
25 Years of Self-organized Criticality: Numerical Detection Methods
NASA Astrophysics Data System (ADS)
McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna
2016-01-01
The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.
Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Soh, Woo Y.
1992-01-01
A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.
A Simple yet Accurate Method for the Estimation of the Biovolume of Planktonic Microorganisms
2016-01-01
Determining the biomass of microbial plankton is central to the study of fluxes of energy and materials in aquatic ecosystems. This is typically accomplished by applying proper volume-to-carbon conversion factors to group-specific abundances and biovolumes. A critical step in this approach is the accurate estimation of biovolume from two-dimensional (2D) data such as those available through conventional microscopy techniques or flow-through imaging systems. This paper describes a simple yet accurate method for the assessment of the biovolume of planktonic microorganisms, which works with any image analysis system allowing for the measurement of linear distances and the estimation of the cross sectional area of an object from a 2D digital image. The proposed method is based on Archimedes’ principle about the relationship between the volume of a sphere and that of a cylinder in which the sphere is inscribed, plus a coefficient of ‘unellipticity’ introduced here. Validation and careful evaluation of the method are provided using a variety of approaches. The new method proved to be highly precise with all convex shapes characterised by approximate rotational symmetry, and combining it with an existing method specific for highly concave or branched shapes allows covering the great majority of cases with good reliability. Thanks to its accuracy, consistency, and low resources demand, the new method can conveniently be used in substitution of any extant method designed for convex shapes, and can readily be coupled with automated cell imaging technologies, including state-of-the-art flow-through imaging devices. PMID:27195667
Method for accurate optical alignment using diffraction rings from lenses with spherical aberration.
Gwynn, R B; Christensen, D A
1993-03-01
A useful alignment method is presented that exploits the closely spaced concentric fringes that form in the longitudinal spherical aberration region of positive spherical lenses imaging a point source. To align one or more elements to a common axis, spherical lenses are attached precisely to the elements and the resulting diffraction rings are made to coincide. We modeled the spherical aberration of the lenses by calculating the diffraction patterns of converging plane waves passing through concentric narrow annular apertures. The validity of the model is supported by experimental data and is determined to be accurate for a prototype penumbral imaging alignment system developed at Lawrence Livermore National Laboratory.
Vincent, Mark A; Hillier, Ian H
2014-08-25
The accurate prediction of the adsorption energies of unsaturated molecules on graphene in the presence of water is essential for the design of molecules that can modify its properties and that can aid its processability. We here show that a semiempirical MO method corrected for dispersive interactions (PM6-DH2) can predict the adsorption energies of unsaturated hydrocarbons and the effect of substitution on these values to an accuracy comparable to DFT values and in good agreement with the experiment. The adsorption energies of TCNE, TCNQ, and a number of sulfonated pyrenes are also predicted, along with the effect of hydration using the COSMO model.
A simple and accurate resist parameter extraction method for sub-80-nm DRAM patterns
NASA Astrophysics Data System (ADS)
Lee, Sook; Hwang, Chan; Park, Dong-Woon; Kim, In-Sung; Kim, Ho-Chul; Woo, Sang-Gyun; Cho, Han-Ku; Moon, Joo-Tae
2004-05-01
Due to the polarization effect of high NA lithography, the consideration of resist effect in lithography simulation becomes increasingly important. In spite of the importance of resist simulation, many process engineers are reluctant to consider resist effect in lithography simulation due to time-consuming procedure to extract required resist parameters and the uncertainty of measurement of some parameters. Weiss suggested simplified development model, and this model does not require the complex kinetic parameters. For the device fabrication engineers, there is a simple and accurate parameter extraction and optimizing method using Weiss model. This method needs refractive index, Dill"s parameters and development rate monitoring (DRM) data in parameter extraction. The parameters extracted using referred sequence is not accurate, so that we have to optimize the parameters to fit the critical dimension scanning electron microscopy (CD SEM) data of line and space patterns. Hence, the FiRM of Sigma-C is utilized as a resist parameter-optimizing program. According to our study, the illumination shape, the aberration and the pupil mesh point have a large effect on the accuracy of resist parameter in optimization. To obtain the optimum parameters, we need to find the saturated mesh points in terms of normalized intensity log slope (NILS) prior to an optimization. The simulation results using the optimized parameters by this method shows good agreement with experiments for iso-dense bias, Focus-Exposure Matrix data and sub 80nm device pattern simulation.
NASA Astrophysics Data System (ADS)
Emmrich, Etienne; Thalhammer, Mechthild
2010-04-01
Stiffly accurate implicit Runge-Kutta methods are studied for the time discretisation of nonlinear first-order evolution equations. The equation is supposed to be governed by a time-dependent hemicontinuous operator that is (up to a shift) monotone and coercive, and fulfills a certain growth condition. It is proven that the piecewise constant as well as the piecewise linear interpolant of the time-discrete solution converges towards the exact weak solution, provided the Runge-Kutta method is consistent and satisfies a stability criterion that implies algebraic stability; examples are the Radau IIA and Lobatto IIIC methods. The convergence analysis is also extended to problems involving a strongly continuous perturbation of the monotone main part.
A numerical method for acoustic oscillations in tubes
NASA Technical Reports Server (NTRS)
Gary, John M.
1988-01-01
A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium-filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second-order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.
Numerical results for extended field method applications. [thin plates
NASA Technical Reports Server (NTRS)
Donaldson, B. K.; Chander, S.
1973-01-01
This paper presents the numerical results obtained when a new method of analysis, called the extended field method, was applied to several thin plate problems including one with non-rectangular geometry, and one problem involving both beams and a plate. The numerical results show that the quality of the single plate solutions was satisfactory for all cases except those involving a freely deflecting plate corner. The results for the beam and plate structure were satisfactory even though the structure had a freely deflecting corner.
Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis
Abbasi, Mahdi
2014-01-01
Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N2log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR. PMID:24696808
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
NASA Technical Reports Server (NTRS)
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
NASA Technical Reports Server (NTRS)
Cook, C. H.
1977-01-01
The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.
NASA Astrophysics Data System (ADS)
Tirupathi, S.; Schiemenz, A. R.; Liang, Y.; Parmentier, E.; Hesthaven, J.
2013-12-01
The style and mode of melt migration in the mantle are important to the interpretation of basalts erupted on the surface. Both grain-scale diffuse porous flow and channelized melt migration have been proposed. To better understand the mechanisms and consequences of melt migration in a heterogeneous mantle, we have undertaken a numerical study of reactive dissolution in an upwelling and viscously deformable mantle where solubility of pyroxene increases upwards. Our setup is similar to that described in [1], except we use a larger domain size in 2D and 3D and a new numerical method. To enable efficient simulations in 3D through parallel computing, we developed a high-order accurate numerical method for the magma dynamics problem using discontinuous Galerkin methods and constructed the problem using the numerical library deal.II [2]. Linear stability analyses of the reactive dissolution problem reveal three dynamically distinct regimes [3] and the simulations reported in this study were run in the stable regime and the unstable wave regime where small perturbations in porosity grows periodically. The wave regime is more relevant to melt migration beneath the mid-ocean ridges but computationally more challenging. Extending the 2D simulations in the stable regime in [1] to 3D using various combinations of sustained perturbations in porosity at the base of the upwelling column (which may result from a viened mantle), we show the geometry and distribution of dunite channel and high-porosity melt channels are highly correlated with inflow perturbation through superposition. Strong nonlinear interactions among compaction, dissolution, and upwelling give rise to porosity waves and high-porosity melt channels in the wave regime. These compaction-dissolution waves have well organized but time-dependent structures in the lower part of the simulation domain. High-porosity melt channels nucleate along nodal lines of the porosity waves, growing downwards. The wavelength scales
Hoo, Zhe Hui; Curley, Rachael; Campbell, Michael J; Walters, Stephen J; Hind, Daniel; Wildman, Martin J
2016-01-01
Background Preventative inhaled treatments in cystic fibrosis will only be effective in maintaining lung health if used appropriately. An accurate adherence index should therefore reflect treatment effectiveness, but the standard method of reporting adherence, that is, as a percentage of the agreed regimen between clinicians and people with cystic fibrosis, does not account for the appropriateness of the treatment regimen. We describe two different indices of inhaled therapy adherence for adults with cystic fibrosis which take into account effectiveness, that is, “simple” and “sophisticated” normative adherence. Methods to calculate normative adherence Denominator adjustment involves fixing a minimum appropriate value based on the recommended therapy given a person’s characteristics. For simple normative adherence, the denominator is determined by the person’s Pseudomonas status. For sophisticated normative adherence, the denominator is determined by the person’s Pseudomonas status and history of pulmonary exacerbations over the previous year. Numerator adjustment involves capping the daily maximum inhaled therapy use at 100% so that medication overuse does not artificially inflate the adherence level. Three illustrative cases Case A is an example of inhaled therapy under prescription based on Pseudomonas status resulting in lower simple normative adherence compared to unadjusted adherence. Case B is an example of inhaled therapy under-prescription based on previous exacerbation history resulting in lower sophisticated normative adherence compared to unadjusted adherence and simple normative adherence. Case C is an example of nebulizer overuse exaggerating the magnitude of unadjusted adherence. Conclusion Different methods of reporting adherence can result in different magnitudes of adherence. We have proposed two methods of standardizing the calculation of adherence which should better reflect treatment effectiveness. The value of these indices can
Numerical method for the stochastic projected Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Rooney, S. J.; Blakie, P. B.; Bradley, A. S.
2014-01-01
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
Novel method for accurate g measurements in electron-spin resonance
NASA Astrophysics Data System (ADS)
Stesmans, A.; Van Gorp, G.
1989-09-01
In high-accuracy work, electron-spin-resonance (ESR) g values are generally determined by calibrating against the accurately known proton nuclear magnetic resonance (NMR). For that method—based on leakage of microwave energy out of the ESR cavity—a convenient technique is presented to obtain accurate g values without needing conscientious precalibration procedures or cumbersome constructions. As main advantages, the method allows the easy monitoring of the positioning of the ESR and NMR samples while they are mounted as close as physically realizable at all time during their simultaneous resonances. Relative accuracies on g of ≊2×10-6 are easily achieved for ESR signals of peak-to-peak width ΔBpp≲0.3 G. The method has been applied to calibrate the g value of conduction electrons of small Li particles embedded in LiF—a frequently used g marker—resulting in gLiF: Li=2.002 293±0.000 002.
Vent-Schmidt, Jens; Waltz, Xavier; Pichon, Aurélien; Hardy-Dessources, Marie-Dominique; Romana, Marc; Connes, Philippe
2015-01-01
The aim of this study was to test the accuracy of viscosimetric method to estimate the red blood cell (RBC) deformability properties. Thirty-three subjects were enrolled in this study: 6 healthy subjects (AA), 11 patients with sickle cell-hemoglobin C disease (SC) and 16 patients with sickle cell anemia (SS). Two methods were used to assess RBC deformability: 1) indirect viscosimetric method and 2) ektacytometry. The indirect viscosimetric method was based on the Dintenfass equation where blood viscosity, plasma viscosity and hematocrit are measured and used to calculate an index of RBC rigidity (Tk index). The RBC deformability/rigidity of the three groups was compared using the two methods. Tk index was not different between SS and SC patients and the two groups had higher values than AA group. When ektacytometry was used, RBC deformability was lower in SS and SC groups compared to the AA group and SS and SC patients were different. Although the two measures of RBC deformability were correlated, the association was not very high. Bland and Altman analysis demonstrated a 3.25 bias suggesting a slight difference between the two methods. In addition, the limit of agreement represented 28% (>15%) of the mean values of RBC deformability, showing no interchangeability between the two methods. In conclusion, measuring RBC deformability by indirect viscosimetry is less accurate than by ektacytometry, which is considered the gold standard.
An unconditionally stable method for numerically solving solar sail spacecraft equations of motion
NASA Astrophysics Data System (ADS)
Karwas, Alex
Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach
Gupta, Divya; Kagemann, Larry; Schuman, Joel S.; SundarRaj, Nirmala
2012-01-01
Purpose. This study explored the efficacy of optical coherence tomography (OCT) as a high-resolution, noncontact method for imaging the palisades of Vogt by correlating OCT and confocal microscopy images. Methods. Human limbal rims were acquired and imaged with OCT and confocal microscopy. The area of the epithelial basement membrane in each of these sets was digitally reconstructed, and the models were compared. Results. OCT identified the palisades within the limbus and exhibited excellent structural correlation with immunostained tissue imaged by confocal microscopy. Conclusions. OCT successfully identified the limbal palisades of Vogt that constitute the corneal epithelial stem cell niche. These findings offer the exciting potential to characterize the architecture of the palisades in vivo, to harvest stem cells for transplantation more accurately, to track palisade structure for better diagnosis, follow-up and staging of treatment, and to assess and intervene in the progression of stem cell depletion by monitoring changes in the structure of the palisades. PMID:22266521
Troeltzsch, Matthias; Liedtke, Jan; Troeltzsch, Volker; Frankenberger, Roland; Steiner, Timm; Troeltzsch, Markus
2012-10-01
Odontomas account for the largest fraction of odontogenic tumors and are frequent causes of tooth impaction. A case of a 13-year-old female patient with an odontoma-associated impaction of a mandibular molar is presented with a review of the literature. Preoperative planning involved simple and convenient methods such as clinical examination and panoramic radiography, which led to a diagnosis of complex odontoma and warranted surgical removal. The clinical diagnosis was confirmed histologically. Multidisciplinary consultation may enable the clinician to find the accurate diagnosis and appropriate therapy based on the clinical and radiographic appearance. Modern radiologic methods such as cone-beam computed tomography or computed tomography should be applied only for special cases, to decrease radiation.
Numerical methods for solving terminal optimal control problems
NASA Astrophysics Data System (ADS)
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Numerical methods and calculations for droplet flow, heating and ignition
NASA Technical Reports Server (NTRS)
Dwyer, H. A.; Sanders, B. R.; Dandy, D.
1982-01-01
A numerical method was devised and employed to solve a variety of problems related to liquid droplet combustion. The basic transport equations of mass, momentum and energy were formulated in terms of generalized nonorthogonal coordinates, which allows for adaptive griding and arbitrary particle shape. Example problems are solved for internal droplet heating, droplet ignition and high Reynolds number flow over a droplet.
A numerical method for unsteady aerodynamics via acoustics
NASA Technical Reports Server (NTRS)
Hodge, Steve
1991-01-01
Formal solutions to the wave equation may be conveniently described within the framework of generalized function theory. A generalized function theory is used to yield a formulation and formal solution of a wave equation describing oscillation of a flat plate from which a numerical method may be derived.
COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE
Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov
2011-08-10
Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the
Johnsen, Eric Larsson, Johan Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.
2010-02-20
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
NASA Astrophysics Data System (ADS)
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.
NASA Astrophysics Data System (ADS)
Wang, Benfeng; Jakobsen, Morten; Wu, Ru-Shan; Lu, Wenkai; Chen, Xiaohong
2017-03-01
Full waveform inversion (FWI) has been regarded as an effective tool to build the velocity model for the following pre-stack depth migration. Traditional inversion methods are built on Born approximation and are initial model dependent, while this problem can be avoided by introducing Transmission matrix (T-matrix), because the T-matrix includes all orders of scattering effects. The T-matrix can be estimated from the spatial aperture and frequency bandwidth limited seismic data using linear optimization methods. However the full T-matrix inversion method (FTIM) is always required in order to estimate velocity perturbations, which is very time consuming. The efficiency can be improved using the previously proposed inverse thin-slab propagator (ITSP) method, especially for large scale models. However, the ITSP method is currently designed for smooth media, therefore the estimation results are unsatisfactory when the velocity perturbation is relatively large. In this paper, we propose a domain decomposition method (DDM) to improve the efficiency of the velocity estimation for models with large perturbations, as well as guarantee the estimation accuracy. Numerical examples for smooth Gaussian ball models and a reservoir model with sharp boundaries are performed using the ITSP method, the proposed DDM and the FTIM. The estimated velocity distributions, the relative errors and the elapsed time all demonstrate the validity of the proposed DDM.
Efficient numerical methods for entropy-linear programming problems
NASA Astrophysics Data System (ADS)
Gasnikov, A. V.; Gasnikova, E. B.; Nesterov, Yu. E.; Chernov, A. V.
2016-04-01
Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.
A novel gas-droplet numerical method for spray combustion
NASA Technical Reports Server (NTRS)
Chen, C. P.; Shang, H. M.; Jiang, Y.
1991-01-01
This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.
A highly accurate method for the determination of mass and center of mass of a spacecraft
NASA Technical Reports Server (NTRS)
Chow, E. Y.; Trubert, M. R.; Egwuatu, A.
1978-01-01
An extremely accurate method for the measurement of mass and the lateral center of mass of a spacecraft has been developed. The method was needed for the Voyager spacecraft mission requirement which limited the uncertainty in the knowledge of lateral center of mass of the spacecraft system weighing 750 kg to be less than 1.0 mm (0.04 in.). The method consists of using three load cells symmetrically located at 120 deg apart on a turntable with respect to the vertical axis of the spacecraft and making six measurements for each load cell. These six measurements are taken by cyclic rotations of the load cell turntable and of the spacecraft, about the vertical axis of the measurement fixture. This method eliminates all alignment, leveling, and load cell calibration errors for the lateral center of mass determination, and permits a statistical best fit of the measurement data. An associated data reduction computer program called MASCM has been written to implement this method and has been used for the Voyager spacecraft.
An accurate and efficient bayesian method for automatic segmentation of brain MRI.
Marroquin, J L; Vemuri, B C; Botello, S; Calderon, F; Fernandez-Bouzas, A
2002-08-01
Automatic three-dimensional (3-D) segmentation of the brain from magnetic resonance (MR) scans is a challenging problem that has received an enormous amount of attention lately. Of the techniques reported in the literature, very few are fully automatic. In this paper, we present an efficient and accurate, fully automatic 3-D segmentation procedure for brain MR scans. It has several salient features; namely, the following. 1) Instead of a single multiplicative bias field that affects all tissue intensities, separate parametric smooth models are used for the intensity of each class. 2) A brain atlas is used in conjunction with a robust registration procedure to find a nonrigid transformation that maps the standard brain to the specimen to be segmented. This transformation is then used to: segment the brain from nonbrain tissue; compute prior probabilities for each class at each voxel location and find an appropriate automatic initialization. 3) Finally, a novel algorithm is presented which is a variant of the expectation-maximization procedure, that incorporates a fast and accurate way to find optimal segmentations, given the intensity models along with the spatial coherence assumption. Experimental results with both synthetic and real data are included, as well as comparisons of the performance of our algorithm with that of other published methods.
NASA Astrophysics Data System (ADS)
He, Wantao; Li, Zhongwei; Zhong, Kai; Shi, Yusheng; Zhao, Can; Cheng, Xu
2014-11-01
Fast and precise 3D inspection system is in great demand in modern manufacturing processes. At present, the available sensors have their own pros and cons, and hardly exist an omnipotent sensor to handle the complex inspection task in an accurate and effective way. The prevailing solution is integrating multiple sensors and taking advantages of their strengths. For obtaining a holistic 3D profile, the data from different sensors should be registrated into a coherent coordinate system. However, some complex shape objects own thin wall feather such as blades, the ICP registration method would become unstable. Therefore, it is very important to calibrate the extrinsic parameters of each sensor in the integrated measurement system. This paper proposed an accurate and automatic extrinsic parameter calibration method for blade measurement system integrated by different optical sensors. In this system, fringe projection sensor (FPS) and conoscopic holography sensor (CHS) is integrated into a multi-axis motion platform, and the sensors can be optimally move to any desired position at the object's surface. In order to simple the calibration process, a special calibration artifact is designed according to the characteristics of the two sensors. An automatic registration procedure based on correlation and segmentation is used to realize the artifact datasets obtaining by FPS and CHS rough alignment without any manual operation and data pro-processing, and then the Generalized Gauss-Markoff model is used to estimate the optimization transformation parameters. The experiments show the measurement result of a blade, where several sampled patches are merged into one point cloud, and it verifies the performance of the proposed method.
Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin
2015-06-05
The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.
Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...
2015-06-05
The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less
Singularity Preserving Numerical Methods for Boundary Integral Equations
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Vonlavante, Ernst; Nelson, N. Duane
1986-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.
A numerical method for interface problems in elastodynamics
NASA Technical Reports Server (NTRS)
Mcghee, D. S.
1984-01-01
The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.
Pavanello, Michele; Van Voorhis, Troy; Visscher, Lucas; Neugebauer, Johannes
2013-02-07
Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Angstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.
Wang, Fei; Dong, Hang; Chen, Yanan; Zheng, Nanning
2016-01-01
Strong demands for accurate non-cooperative target measurement have been arising recently for the tasks of assembling and capturing. Spherical objects are one of the most common targets in these applications. However, the performance of the traditional vision-based reconstruction method was limited for practical use when handling poorly-textured targets. In this paper, we propose a novel multi-sensor fusion system for measuring and reconstructing textureless non-cooperative spherical targets. Our system consists of four simple lasers and a visual camera. This paper presents a complete framework of estimating the geometric parameters of textureless spherical targets: (1) an approach to calibrate the extrinsic parameters between a camera and simple lasers; and (2) a method to reconstruct the 3D position of the laser spots on the target surface and achieve the refined results via an optimized scheme. The experiment results show that our proposed calibration method can obtain a fine calibration result, which is comparable to the state-of-the-art LRF-based methods, and our calibrated system can estimate the geometric parameters with high accuracy in real time. PMID:27941705
Kliment, Corrine R; Englert, Judson M; Crum, Lauren P; Oury, Tim D
2011-01-01
Aim: The purpose of this study was to develop an improved method for collagen and protein assessment of fibrotic lungs while decreasing animal use. methods: 8-10 week old, male C57BL/6 mice were given a single intratracheal instillation of crocidolite asbestos or control titanium dioxide. Lungs were collected on day 14 and dried as whole lung, or homogenized in CHAPS buffer, for hydroxyproline analysis. Insoluble and salt-soluble collagen content was also determined in lung homogenates using a modified Sirius red colorimetric 96-well plate assay. results: The hydroxyproline assay showed significant increases in collagen content in the lungs of asbestos-treated mice. Identical results were present between collagen content determined on dried whole lung or whole lung homogenates. The Sirius red plate assay showed a significant increase in collagen content in lung homogenates however, this assay grossly over-estimated the total amount of collagen and underestimated changes between control and fibrotic lungs, conclusions: The proposed method provides accurate quantification of collagen content in whole lungs and additional homogenate samples for biochemical analysis from a single animal. The Sirius-red colorimetric plate assay provides a complementary method for determination of the relative changes in lung collagen but the values tend to overestimate absolute values obtained by the gold standard hydroxyproline assay and underestimate the overall fibrotic injury. PMID:21577320
Wang, Fei; Dong, Hang; Chen, Yanan; Zheng, Nanning
2016-12-09
Strong demands for accurate non-cooperative target measurement have been arising recently for the tasks of assembling and capturing. Spherical objects are one of the most common targets in these applications. However, the performance of the traditional vision-based reconstruction method was limited for practical use when handling poorly-textured targets. In this paper, we propose a novel multi-sensor fusion system for measuring and reconstructing textureless non-cooperative spherical targets. Our system consists of four simple lasers and a visual camera. This paper presents a complete framework of estimating the geometric parameters of textureless spherical targets: (1) an approach to calibrate the extrinsic parameters between a camera and simple lasers; and (2) a method to reconstruct the 3D position of the laser spots on the target surface and achieve the refined results via an optimized scheme. The experiment results show that our proposed calibration method can obtain a fine calibration result, which is comparable to the state-of-the-art LRF-based methods, and our calibrated system can estimate the geometric parameters with high accuracy in real time.
Accurate description of the electronic structure of organic semiconductors by GW methods
NASA Astrophysics Data System (ADS)
Marom, Noa
2017-03-01
Electronic properties associated with charged excitations, such as the ionization potential (IP), the electron affinity (EA), and the energy level alignment at interfaces, are critical parameters for the performance of organic electronic devices. To computationally design organic semiconductors and functional interfaces with tailored properties for target applications it is necessary to accurately predict these properties from first principles. Many-body perturbation theory is often used for this purpose within the GW approximation, where G is the one particle Green’s function and W is the dynamically screened Coulomb interaction. Here, the formalism of GW methods at different levels of self-consistency is briefly introduced and some recent applications to organic semiconductors and interfaces are reviewed.
NASA Astrophysics Data System (ADS)
Zacharias, Panagiotis P.; Chatzineofytou, Elpida G.; Spantideas, Sotirios T.; Capsalis, Christos N.
2016-07-01
In the present work, the determination of the magnetic behavior of localized magnetic sources from near-field measurements is examined. The distance power law of the magnetic field fall-off is used in various cases to accurately predict the magnetic signature of an equipment under test (EUT) consisting of multiple alternating current (AC) magnetic sources. Therefore, parameters concerning the location of the observation points (magnetometers) are studied towards this scope. The results clearly show that these parameters are independent of the EUT's size and layout. Additionally, the techniques developed in the present study enable the placing of the magnetometers close to the EUT, thus achieving high signal-to-noise ratio (SNR). Finally, the proposed method is verified by real measurements, using a mobile phone as an EUT.
Methods to achieve accurate projection of regional and global raster databases
Usery, E. Lynn; Seong, Jeong Chang; Steinwand, Dan
2002-01-01
Modeling regional and global activities of climatic and human-induced change requires accurate geographic data from which we can develop mathematical and statistical tabulations of attributes and properties of the environment. Many of these models depend on data formatted as raster cells or matrices of pixel values. Recently, it has been demonstrated that regional and global raster datasets are subject to significant error from mathematical projection and that these errors are of such magnitude that model results may be jeopardized (Steinwand, et al., 1995; Yang, et al., 1996; Usery and Seong, 2001; Seong and Usery, 2001). There is a need to develop methods of projection that maintain the accuracy of these datasets to support regional and global analyses and modeling
Methods for accurate analysis of galaxy clustering on non-linear scales
NASA Astrophysics Data System (ADS)
Vakili, Mohammadjavad
2017-01-01
Measurements of galaxy clustering with the low-redshift galaxy surveys provide sensitive probe of cosmology and growth of structure. Parameter inference with galaxy clustering relies on computation of likelihood functions which requires estimation of the covariance matrix of the observables used in our analyses. Therefore, accurate estimation of the covariance matrices serves as one of the key ingredients in precise cosmological parameter inference. This requires generation of a large number of independent galaxy mock catalogs that accurately describe the statistical distribution of galaxies in a wide range of physical scales. We present a fast method based on low-resolution N-body simulations and approximate galaxy biasing technique for generating mock catalogs. Using a reference catalog that was created using the high resolution Big-MultiDark N-body simulation, we show that our method is able to produce catalogs that describe galaxy clustering at a percentage-level accuracy down to highly non-linear scales in both real-space and redshift-space.In most large-scale structure analyses, modeling of galaxy bias on non-linear scales is performed assuming a halo model. Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as assembly bias. Standard large-scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. However, modeling of galaxy bias can face systematic effects if the number of galaxies are correlated with other halo properties. Using the Small MultiDark-Planck high resolution N-body simulation and the clustering measurements of Sloan Digital Sky Survey DR7 main galaxy sample, we investigate the extent to which the dependence of galaxy bias on halo concentration can improve our modeling of galaxy clustering.
Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions
NASA Astrophysics Data System (ADS)
Cappellari, Michele
2017-04-01
I start by providing an updated summary of the penalized pixel-fitting (PPXF) method that is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies, via full spectrum fitting. I then focus on the problem of extracting the kinematics when the velocity dispersion σ is smaller than the velocity sampling ΔV that is generally, by design, close to the instrumental dispersion σinst. The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when σ ≲ ΔV/2, due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids the evaluation of the undersampled kernel and instead directly computes its well-sampled analytic Fourier transform, for use with the convolution theorem. A simple analytic transform exists when the kernel is described by the popular Gauss-Hermite parametrization (which includes the Gaussian as special case) for the line-of-sight velocity distribution. I describe how this idea was implemented in a significant upgrade to the publicly available PPXF software. The key advantage of the new approach is that it provides accurate velocities regardless of σ. This is important e.g. for spectroscopic surveys targeting galaxies with σ ≪ σinst, for galaxy redshift determinations or for measuring line-of-sight velocities of individual stars. The proposed method could also be used to fix Gaussian convolution algorithms used in today's popular software packages.
An Inexpensive, Accurate, and Precise Wet-Mount Method for Enumerating Aquatic Viruses
Cunningham, Brady R.; Brum, Jennifer R.; Schwenck, Sarah M.; Sullivan, Matthew B.
2015-01-01
Viruses affect biogeochemical cycling, microbial mortality, gene flow, and metabolic functions in diverse environments through infection and lysis of microorganisms. Fundamental to quantitatively investigating these roles is the determination of viral abundance in both field and laboratory samples. One current, widely used method to accomplish this with aquatic samples is the “filter mount” method, in which samples are filtered onto costly 0.02-μm-pore-size ceramic filters for enumeration of viruses by epifluorescence microscopy. Here we describe a cost-effective (ca. 500-fold-lower materials cost) alternative virus enumeration method in which fluorescently stained samples are wet mounted directly onto slides, after optional chemical flocculation of viruses in samples with viral concentrations of <5 × 107 viruses ml−1. The concentration of viruses in the sample is then determined from the ratio of viruses to a known concentration of added microsphere beads via epifluorescence microscopy. Virus concentrations obtained by using this wet-mount method, with and without chemical flocculation, were significantly correlated with, and had precision equivalent to, those obtained by the filter mount method across concentrations ranging from 2.17 × 106 to 1.37 × 108 viruses ml−1 when tested by using cultivated viral isolates and natural samples from marine and freshwater environments. In summary, the wet-mount method is significantly less expensive than the filter mount method and is appropriate for rapid, precise, and accurate enumeration of aquatic viruses over a wide range of viral concentrations (≥1 × 106 viruses ml−1) encountered in field and laboratory samples. PMID:25710369
An inexpensive, accurate, and precise wet-mount method for enumerating aquatic viruses.
Cunningham, Brady R; Brum, Jennifer R; Schwenck, Sarah M; Sullivan, Matthew B; John, Seth G
2015-05-01
Viruses affect biogeochemical cycling, microbial mortality, gene flow, and metabolic functions in diverse environments through infection and lysis of microorganisms. Fundamental to quantitatively investigating these roles is the determination of viral abundance in both field and laboratory samples. One current, widely used method to accomplish this with aquatic samples is the "filter mount" method, in which samples are filtered onto costly 0.02-μm-pore-size ceramic filters for enumeration of viruses by epifluorescence microscopy. Here we describe a cost-effective (ca. 500-fold-lower materials cost) alternative virus enumeration method in which fluorescently stained samples are wet mounted directly onto slides, after optional chemical flocculation of viruses in samples with viral concentrations of <5×10(7) viruses ml(-1). The concentration of viruses in the sample is then determined from the ratio of viruses to a known concentration of added microsphere beads via epifluorescence microscopy. Virus concentrations obtained by using this wet-mount method, with and without chemical flocculation, were significantly correlated with, and had precision equivalent to, those obtained by the filter mount method across concentrations ranging from 2.17×10(6) to 1.37×10(8) viruses ml(-1) when tested by using cultivated viral isolates and natural samples from marine and freshwater environments. In summary, the wet-mount method is significantly less expensive than the filter mount method and is appropriate for rapid, precise, and accurate enumeration of aquatic viruses over a wide range of viral concentrations (≥1×10(6) viruses ml(-1)) encountered in field and laboratory samples.
The ray projection method: a numerical approach for determining ideal camera placement.
Manal, Kurt; Gardinier, Joseph
2007-02-01
Data piloting is important to ensure accurate marker coordinate data and to minimize camera dropout. Camera dropout results when a camera fails to image a marker, which often occurs when markers merge or become occluded. In this article, we present the conceptual framework for a numerical method of determining where video cameras, if placed, would have an occluded or a merged view of the tracking markers. Experimental data are presented to demonstrate the efficacy of the method as a tool to complement existing data piloting procedures.
Lim, Fong Yin; Bao, Weizhu
2008-12-01
We propose efficient and accurate numerical methods for computing the ground-state solution of spin-1 Bose-Einstein condensates subjected to a uniform magnetic field. The key idea in designing the numerical method is based on the normalized gradient flow with the introduction of a third normalization condition, together with two physical constraints on the conservation of total mass and conservation of total magnetization. Different treatments of the Zeeman energy terms are found to yield different numerical accuracies and stabilities. Numerical comparison between different numerical schemes is made, and the best scheme is identified. The numerical scheme is then applied to compute the condensate ground state in a harmonic plus optical lattice potential, and the effect of the periodic potential, in particular to the relative population of each hyperfine component, is investigated through comparison to the condensate ground state in a pure harmonic trap.
Numerical Polynomial Homotopy Continuation Method and String Vacua
Mehta, Dhagash
2011-01-01
Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Simple numerical method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible inviscid flows is developed. The method is based on the concept of flux vector splitting in its implicit form and is tested on several demanding configurations. Time marching to steady state is accelerated by the implementation of the multigrid procedure which very effectively increases the rate of convergence. Steady-state results are obtained for various test cases. Only short computational times are required due to the relative efficiency of the basic method.
A Numerical Method for Incompressible Flow with Heat Transfer
NASA Technical Reports Server (NTRS)
Sa, Jong-Youb; Kwak, Dochan
1997-01-01
A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.
Computational methods for aerodynamic design using numerical optimization
NASA Technical Reports Server (NTRS)
Peeters, M. F.
1983-01-01
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
Numerical Method and Analysis of Consistency for Electrodiffusion Problem
NASA Astrophysics Data System (ADS)
Filipek, R.; Szyszkiewicz, K.; Danielewski, M.; Lewenstam, A.
2007-12-01
Numerical procedure based on method of lines for time-dependent electrodiffusion transport is developed. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analyzed and compared. The resulting stiff system of ODEs is effectively solved using the Radau IIa integrator. The applications to selected electrochemical systems: liquid junction, bi-ionic case and fused salts have been tested. Results for ion-selective electrodes are demonstrated.
A Method for Accurate Reconstructions of the Upper Airway Using Magnetic Resonance Images
Xiong, Huahui; Huang, Xiaoqing; Li, Yong; Li, Jianhong; Xian, Junfang; Huang, Yaqi
2015-01-01
Objective The purpose of this study is to provide an optimized method to reconstruct the structure of the upper airway (UA) based on magnetic resonance imaging (MRI) that can faithfully show the anatomical structure with a smooth surface without artificial modifications. Methods MRI was performed on the head and neck of a healthy young male participant in the axial, coronal and sagittal planes to acquire images of the UA. The level set method was used to segment the boundary of the UA. The boundaries in the three scanning planes were registered according to the positions of crossing points and anatomical characteristics using a Matlab program. Finally, the three-dimensional (3D) NURBS (Non-Uniform Rational B-Splines) surface of the UA was constructed using the registered boundaries in all three different planes. Results A smooth 3D structure of the UA was constructed, which captured the anatomical features from the three anatomical planes, particularly the location of the anterior wall of the nasopharynx. The volume and area of every cross section of the UA can be calculated from the constructed 3D model of UA. Conclusions A complete scheme of reconstruction of the UA was proposed, which can be used to measure and evaluate the 3D upper airway accurately. PMID:26066461
Simons, Craig J; Cobb, Loren; Davidson, Bradley S
2014-04-01
In vivo measurement of lumbar spine configuration is useful for constructing quantitative biomechanical models. Positional magnetic resonance imaging (MRI) accommodates a larger range of movement in most joints than conventional MRI and does not require a supine position. However, this is achieved at the expense of image resolution and contrast. As a result, quantitative research using positional MRI has required long reconstruction times and is sensitive to incorrectly identifying the vertebral boundary due to low contrast between bone and surrounding tissue in the images. We present a semi-automated method used to obtain digitized reconstructions of lumbar vertebrae in any posture of interest. This method combines a high-resolution reference scan with a low-resolution postural scan to provide a detailed and accurate representation of the vertebrae in the posture of interest. Compared to a criterion standard, translational reconstruction error ranged from 0.7 to 1.6 mm and rotational reconstruction error ranged from 0.3 to 2.6°. Intraclass correlation coefficients indicated high interrater reliability for measurements within the imaging plane (ICC 0.97-0.99). Computational efficiency indicates that this method may be used to compile data sets large enough to account for population variance, and potentially expand the use of positional MRI as a quantitative biomechanics research tool.
NASA Astrophysics Data System (ADS)
Lee, Jeongjin; Kim, Namkug; Lee, Ho; Seo, Joon Beom; Won, Hyung Jin; Shin, Yong Moon; Shin, Yeong Gil
2007-03-01
Automatic liver segmentation is still a challenging task due to the ambiguity of liver boundary and the complex context of nearby organs. In this paper, we propose a faster and more accurate way of liver segmentation in CT images with an enhanced level set method. The speed image for level-set propagation is smoothly generated by increasing number of iterations in anisotropic diffusion filtering. This prevents the level-set propagation from stopping in front of local minima, which prevails in liver CT images due to irregular intensity distributions of the interior liver region. The curvature term of shape modeling level-set method captures well the shape variations of the liver along the slice. Finally, rolling ball algorithm is applied for including enhanced vessels near the liver boundary. Our approach are tested and compared to manual segmentation results of eight CT scans with 5mm slice distance using the average distance and volume error. The average distance error between corresponding liver boundaries is 1.58 mm and the average volume error is 2.2%. The average processing time for the segmentation of each slice is 5.2 seconds, which is much faster than the conventional ones. Accurate and fast result of our method will expedite the next stage of liver volume quantification for liver transplantations.
Mezei, Pál D; Csonka, Gábor I; Ruzsinszky, Adrienn; Sun, Jianwei
2015-01-13
A correct description of the anion-π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion-π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π-anion-π' sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values. We give a detailed explanation of the origin of anion-π interactions, using the permanent quadrupole moments, static dipole polarizabilities, and electrostatic potential maps. We use symmetry-adapted perturbation theory (SAPT) to calculate the components of the anion-π interaction energies. We examine the performance of the direct random phase approximation (dRPA), the second-order screened exchange (SOSEX), local-pair natural-orbital (LPNO) coupled electron pair approximation (CEPA), and several dispersion-corrected density functionals (including generalized gradient approximation (GGA), meta-GGA, and double hybrid density functional). The LPNO-CEPA/1 results show the best agreement with the reference results. The dRPA method is only slightly less accurate and precise than the LPNO-CEPA/1, but it is considerably more efficient (6-17 times faster) for the binary complexes studied in this paper. For 30 ternary π-anion-π' sandwich complexes, we give dRPA interaction energies as reference values. The double hybrid functionals are much more efficient but less accurate and precise than dRPA. The dispersion-corrected double hybrid PWPB95-D3(BJ) and B2PLYP-D3(BJ) functionals perform better than the GGA and meta
Automatic numerical integration methods for Feynman integrals through 3-loop
NASA Astrophysics Data System (ADS)
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.
NASA Astrophysics Data System (ADS)
An, Zhe; Rey, Daniel; Ye, Jingxin; Abarbanel, Henry D. I.
2017-01-01
The problem of forecasting the behavior of a complex dynamical system through analysis of observational time-series data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a β plane, standard nudging techniques require observing approximately 70 % of the full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. We show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and high-quality predictions. In particular, we find that this estimate of 70 % can be reduced to about 33 % using time delays, and even further if Lagrangian drifter locations are also used as measurements.
NASA Astrophysics Data System (ADS)
Deguchi, Daiki; Sato, Kazunori; Kino, Hiori; Kotani, Takao
2016-05-01
We have recently implemented a new version of the quasiparticle self-consistent GW (QSGW) method in the ecalj package released at http://github.com/tkotani/ecalj. Since the new version of the ecalj package is numerically stable and more accurate than the previous versions, we can perform calculations easily without being bothered with tuning input parameters. Here we examine its ability to describe energy band properties, e.g., band-gap energy, eigenvalues at special points, and effective mass, for a variety of semiconductors and insulators. We treat C, Si, Ge, Sn, SiC (in 2H, 3C, and 4H structures), (Al, Ga, In) × (N, P, As, Sb), (Zn, Cd, Mg) × (O, S, Se, Te), SiO2, HfO2, ZrO2, SrTiO3, PbS, PbTe, MnO, NiO, and HgO. We propose that a hybrid QSGW method, where we mix 80% of QSGW and 20% of LDA, gives universally good agreement with experiments for these materials.
NASA Technical Reports Server (NTRS)
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
Accurate Evaluation of Quantum Integrals
NASA Technical Reports Server (NTRS)
Galant, D. C.; Goorvitch, D.; Witteborn, Fred C. (Technical Monitor)
1995-01-01
Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Jiwari, Ram
2011-01-01
In this paper, a rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical study of a two-dimensional reaction-diffusion Brusselator system. In the Brusselator system the reaction terms arise from the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. By employing DQM, accurate results can be obtained using fewer grid points in spatial domain for a large value of T = 50. We also found that Chebyshev-Gauss-Lobatto grid points give excellent results in comparison to other grid points such as uniform grid points. Three examples are solved to illustrate the accuracy and efficiency of the DQM. Convergence and stability of the method is also examined.
Applying multi-resolution numerical methods to geodynamics
NASA Astrophysics Data System (ADS)
Davies, David Rhodri
Computational models yield inaccurate results if the underlying numerical grid fails to provide the necessary resolution to capture a simulation's important features. For the large-scale problems regularly encountered in geodynamics, inadequate grid resolution is a major concern. The majority of models involve multi-scale dynamics, being characterized by fine-scale upwelling and downwelling activity in a more passive, large-scale background flow. Such configurations, when coupled to the complex geometries involved, present a serious challenge for computational methods. Current techniques are unable to resolve localized features and, hence, such models cannot be solved efficiently. This thesis demonstrates, through a series of papers and closely-coupled appendices, how multi-resolution finite-element methods from the forefront of computational engineering can provide a means to address these issues. The problems examined achieve multi-resolution through one of two methods. In two-dimensions (2-D), automatic, unstructured mesh refinement procedures are utilized. Such methods improve the solution quality of convection dominated problems by adapting the grid automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. Thermal and thermo-chemical validation tests illustrate that the technique is robust and highly successful, improving solution accuracy whilst increasing computational efficiency. These points are reinforced when the technique is applied to geophysical simulations of mid-ocean ridge and subduction zone magmatism. To date, successful goal-orientated/error-guided grid adaptation techniques have not been utilized within the field of geodynamics. The work included herein is therefore the first geodynamical application of such methods. In view of the existing three-dimensional (3-D) spherical mantle dynamics codes, which are built upon a quasi-uniform discretization of the sphere and closely coupled
Numerical methods for control optimization in linear systems
NASA Astrophysics Data System (ADS)
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
Assessment of a high-order accurate Discontinuous Galerkin method for turbomachinery flows
NASA Astrophysics Data System (ADS)
Bassi, F.; Botti, L.; Colombo, A.; Crivellini, A.; Franchina, N.; Ghidoni, A.
2016-04-01
In this work the capabilities of a high-order Discontinuous Galerkin (DG) method applied to the computation of turbomachinery flows are investigated. The Reynolds averaged Navier-Stokes equations coupled with the two equations k-ω turbulence model are solved to predict the flow features, either in a fixed or rotating reference frame, to simulate the fluid flow around bodies that operate under an imposed steady rotation. To ensure, by design, the positivity of all thermodynamic variables at a discrete level, a set of primitive variables based on pressure and temperature logarithms is used. The flow fields through the MTU T106A low-pressure turbine cascade and the NASA Rotor 37 axial compressor have been computed up to fourth-order of accuracy and compared to the experimental and numerical data available in the literature.
A Weight-Averaged Interpolation Method for Coupling Time-Accurate Rarefied and Continuum Flows
NASA Astrophysics Data System (ADS)
Diaz, Steven William
A novel approach to coupling rarefied and continuum flow regimes as a single, hybrid model is introduced. The method borrows from techniques used in the simulation of spray flows to interpolate Lagrangian point-particles onto an Eulerian grid in a weight-averaged sense. A brief overview of traditional methods for modeling both rarefied and continuum domains is given, and a review of the literature regarding rarefied/continuum flow coupling is presented. Details of the theoretical development of the method of weighted interpolation are then described. The method evaluates macroscopic properties at the nodes of a CFD grid via the weighted interpolation of all simulated molecules in a set surrounding the node. The weight factor applied to each simulated molecule is the inverse of the linear distance between it and the given node. During development, the method was applied to several preliminary cases, including supersonic flow over an airfoil, subsonic flow over tandem airfoils, and supersonic flow over a backward facing step; all at low Knudsen numbers. The main thrust of the research centered on the time-accurate expansion of a rocket plume into a near-vacuum. The method proves flexible enough to be used with various flow solvers, demonstrated by the use of Fluent as the continuum solver for the preliminary cases and a NASA-developed Large Eddy Simulation research code, WRLES, for the full lunar model. The method is applicable to a wide range of Mach numbers and is completely grid independent, allowing the rarefied and continuum solvers to be optimized for their respective domains without consideration of the other. The work presented demonstrates the validity, and flexibility of the method of weighted interpolation as a novel concept in the field of hybrid flow coupling. The method marks a significant divergence from current practices in the coupling of rarefied and continuum flow domains and offers a kernel on which to base an ongoing field of research. It has the
Modeling collisional processes in plasmas using discontinuous numerical methods
NASA Astrophysics Data System (ADS)
Miller, Sean
Fluid-based plasma models are typically applied to parameter regimes where a local thermal equilibrium is assumed. The applicability of this regime is valid for many plasmas, however, it is limited to plasma dynamics dominated by collisional effects. This study attempts to extend the validity of the collisional fluid regime using an anisotropic 13-moment fluid model derived from the Pearson type-IV probability distribution. The model explicitly evolves the heat flux hyperbolically alongside the density, momentum, and energy in order to capture dynamics usually restricted to costly kinetic models. Each particle species is modeled individually and collectively coupled through electromagnetic and collision operators. To remove electromagnetic divergence errors inherent to numerical representations of Maxwell's equations, both hyperbolic and parabolic cleaning methods are presented. The plasma models are implemented using high-order finite volume and discontinuous Galerkin numerical methods designed for unstructured meshes. The unstructured code framework, numerical methods, and plasma models were developed in the University of Washington's WARPXM code for use on heterogeneous accelerated clusters.
The instanton method and its numerical implementation in fluid mechanics
NASA Astrophysics Data System (ADS)
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
Adaptive and accurate color edge extraction method for one-shot shape acquisition
NASA Astrophysics Data System (ADS)
Yin, Wei; Cheng, Xiaosheng; Cui, Haihua; Li, Dawei; Zhou, Lei
2016-09-01
This paper presents an approach to extract accurate color edge information using encoded patterns in hue, saturation, and intensity (HSI) color space. This method is applied to one-shot shape acquisition. Theoretical analysis shows that the hue transition between primary and secondary colors in a color edge is based on light interference and diffraction. We set up a color transition model to illustrate the hue transition on an edge and then define the segmenting position of two stripes. By setting up an adaptive HSI color space, the colors of the stripes and subpixel edges are obtained precisely without a dark laboratory environment, in a low-cost processing algorithm. Since this method does not have any constraints for colors of neighboring stripes, the encoding is an easy procedure. The experimental results show that the edges of dense modulation patterns can be obtained under a complicated environment illumination, and the precision can ensure that the three-dimensional shape of the object is obtained reliably with only one image.
Joo, Jong Wha J; Kang, Eun Yong; Org, Elin; Furlotte, Nick; Parks, Brian; Hormozdiari, Farhad; Lusis, Aldons J; Eskin, Eleazar
2016-12-01
A typical genome-wide association study tests correlation between a single phenotype and each genotype one at a time. However, single-phenotype analysis might miss unmeasured aspects of complex biological networks. Analyzing many phenotypes simultaneously may increase the power to capture these unmeasured aspects and detect more variants. Several multivariate approaches aim to detect variants related to more than one phenotype, but these current approaches do not consider the effects of population structure. As a result, these approaches may result in a significant amount of false positive identifications. Here, we introduce a new methodology, referred to as GAMMA for generalized analysis of molecular variance for mixed-model analysis, which is capable of simultaneously analyzing many phenotypes and correcting for population structure. In a simulated study using data implanted with true genetic effects, GAMMA accurately identifies these true effects without producing false positives induced by population structure. In simulations with this data, GAMMA is an improvement over other methods which either fail to detect true effects or produce many false positive identifications. We further apply our method to genetic studies of yeast and gut microbiome from mice and show that GAMMA identifies several variants that are likely to have true biological mechanisms.
An Accurate Method for Measuring Airplane-Borne Conformal Antenna's Radar Cross Section
NASA Astrophysics Data System (ADS)
Guo, Shuxia; Zhang, Lei; Wang, Yafeng; Hu, Chufeng
2016-09-01
The airplane-borne conformal antenna attaches itself tightly with the airplane skin, so the conventional measurement method cannot determine the contribution of the airplane-borne conformal antenna to its radar cross section (RCS). This paper uses the 2D microwave imaging to isolate and extract the distribution of the reflectivity of the airplane-borne conformal antenna. It obtains the 2D spatial spectra of the conformal antenna through the wave spectral transform between the 2D spatial image and the 2D spatial spectrum. After the interpolation from the rectangular coordinate domain to the polar coordinate domain, the spectral domain data for the variation of the scatter of the conformal antenna with frequency and angle is obtained. The experimental results show that the measurement method proposed in this paper greatly enhances the airplane-borne conformal antenna's RCS measurement accuracy, essentially eliminates the influences caused by the airplane skin and more accurately reveals the airplane-borne conformal antenna's RCS scatter properties.
MASCG: Multi-Atlas Segmentation Constrained Graph method for accurate segmentation of hip CT images.
Chu, Chengwen; Bai, Junjie; Wu, Xiaodong; Zheng, Guoyan
2015-12-01
This paper addresses the issue of fully automatic segmentation of a hip CT image with the goal to preserve the joint structure for clinical applications in hip disease diagnosis and treatment. For this purpose, we propose a Multi-Atlas Segmentation Constrained Graph (MASCG) method. The MASCG method uses multi-atlas based mesh fusion results to initialize a bone sheetness based multi-label graph cut for an accurate hip CT segmentation which has the inherent advantage of automatic separation of the pelvic region from the bilateral proximal femoral regions. We then introduce a graph cut constrained graph search algorithm to further improve the segmentation accuracy around the bilateral hip joint regions. Taking manual segmentation as the ground truth, we evaluated the present approach on 30 hip CT images (60 hips) with a 15-fold cross validation. When the present approach was compared to manual segmentation, an average surface distance error of 0.30 mm, 0.29 mm, and 0.30 mm was found for the pelvis, the left proximal femur, and the right proximal femur, respectively. A further look at the bilateral hip joint regions demonstrated an average surface distance error of 0.16 mm, 0.21 mm and 0.20 mm for the acetabulum, the left femoral head, and the right femoral head, respectively.
Accurate computation of surface stresses and forces with immersed boundary methods
NASA Astrophysics Data System (ADS)
Goza, Andres; Liska, Sebastian; Morley, Benjamin; Colonius, Tim
2016-09-01
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluid-structure interaction problems, to obtain smooth and convergent stress distributions on the surface. To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose ill-posedness is the source of spurious oscillations in the stresses. We also demonstrate that for sufficiently smooth delta functions, the oscillations may be filtered out to obtain physically accurate surface stresses. The filtering is applied as a post-processing procedure, so that the convergence of the velocity field is unaffected. We demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems.
Eiber, Calvin D; Dokos, Socrates; Lovell, Nigel H; Suaning, Gregg J
2016-08-19
The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.
Methods for accurate cold-chain temperature monitoring using digital data-logger thermometers
NASA Astrophysics Data System (ADS)
Chojnacky, M. J.; Miller, W. M.; Strouse, G. F.
2013-09-01
Complete and accurate records of vaccine temperature history are vital to preserving drug potency and patient safety. However, previously published vaccine storage and handling guidelines have failed to indicate a need for continuous temperature monitoring in vaccine storage refrigerators. We evaluated the performance of seven digital data logger models as candidates for continuous temperature monitoring of refrigerated vaccines, based on the following criteria: out-of-box performance and compliance with manufacturer accuracy specifications over the range of use; measurement stability over extended, continuous use; proper setup in a vaccine storage refrigerator so that measurements reflect liquid vaccine temperatures; and practical methods for end-user validation and establishing metrological traceability. Data loggers were tested using ice melting point checks and by comparison to calibrated thermocouples to characterize performance over 0 °C to 10 °C. We also monitored logger performance in a study designed to replicate the range of vaccine storage and environmental conditions encountered at provider offices. Based on the results of this study, the Centers for Disease Control released new guidelines on proper methods for storage, handling, and temperature monitoring of vaccines for participants in its federally-funded Vaccines for Children Program. Improved temperature monitoring practices will ultimately decrease waste from damaged vaccines, improve consumer confidence, and increase effective inoculation rates.
Obtaining accurate amounts of mercury from mercury compounds via electrolytic methods
Grossman, Mark W.; George, William A.
1987-01-01
A process for obtaining pre-determined, accurate rate amounts of mercury. In one embodiment, predetermined, precise amounts of Hg are separated from HgO and plated onto a cathode wire. The method for doing this involves dissolving a precise amount of HgO which corresponds to a pre-determined amount of Hg desired in an electrolyte solution comprised of glacial acetic acid and H.sub.2 O. The mercuric ions are then electrolytically reduced and plated onto a cathode producing the required pre-determined quantity of Hg. In another embodiment, pre-determined, precise amounts of Hg are obtained from Hg.sub.2 Cl.sub.2. The method for doing this involves dissolving a precise amount of Hg.sub.2 Cl.sub.2 in an electrolyte solution comprised of concentrated HCl and H.sub.2 O. The mercurous ions in solution are then electrolytically reduced and plated onto a cathode wire producing the required, pre-determined quantity of Hg.
Obtaining accurate amounts of mercury from mercury compounds via electrolytic methods
Grossman, M.W.; George, W.A.
1987-07-07
A process is described for obtaining pre-determined, accurate rate amounts of mercury. In one embodiment, predetermined, precise amounts of Hg are separated from HgO and plated onto a cathode wire. The method for doing this involves dissolving a precise amount of HgO which corresponds to a pre-determined amount of Hg desired in an electrolyte solution comprised of glacial acetic acid and H[sub 2]O. The mercuric ions are then electrolytically reduced and plated onto a cathode producing the required pre-determined quantity of Hg. In another embodiment, pre-determined, precise amounts of Hg are obtained from Hg[sub 2]Cl[sub 2]. The method for doing this involves dissolving a precise amount of Hg[sub 2]Cl[sub 2] in an electrolyte solution comprised of concentrated HCl and H[sub 2]O. The mercurous ions in solution are then electrolytically reduced and plated onto a cathode wire producing the required, pre-determined quantity of Hg. 1 fig.
Open lung biopsy: a safe, reliable and accurate method for diagnosis in diffuse lung disease.
Shah, S S; Tsang, V; Goldstraw, P
1992-01-01
The ideal method for obtaining lung tissue for diagnosis should provide high diagnostic yield with low morbidity and mortality. We reviewed all 432 patients (mean age 55 years) who underwent an open lung biopsy at this hospital over a 10-year period. Twenty-four patients (5.5%) were immunocompromised. One hundred and twenty-five patients were on steroid therapy at the time of operation. Open lung biopsy provided a firm diagnosis in 410 cases overall (94.9%) and in 20 out of 24 patients in the immunocompromised group (83.3%). The commonest diagnosis was cryptogenic fibrosing alveolitis (173 patients). Twenty-two patients (5.1%) suffered complications following the procedure: wound infection 11 patients, pneumothorax 9 patients and haemothorax 1 patient. Thirteen patients (3.0%) died following open lung biopsy, but in only 1 patient was the death attributable to the procedure itself. We conclude that open lung biopsy is an accurate and safe method for establishing a diagnosis in diffuse lung disease with a high yield and minimal risk.
Methods for accurate estimation of net discharge in a tidal channel
Simpson, M.R.; Bland, R.
2000-01-01
Accurate estimates of net residual discharge in tidally affected rivers and estuaries are possible because of recently developed ultrasonic discharge measurement techniques. Previous discharge estimates using conventional mechanical current meters and methods based on stage/discharge relations or water slope measurements often yielded errors that were as great as or greater than the computed residual discharge. Ultrasonic measurement methods consist of: 1) the use of ultrasonic instruments for the measurement of a representative 'index' velocity used for in situ estimation of mean water velocity and 2) the use of the acoustic Doppler current discharge measurement system to calibrate the index velocity measurement data. Methods used to calibrate (rate) the index velocity to the channel velocity measured using the Acoustic Doppler Current Profiler are the most critical factors affecting the accuracy of net discharge estimation. The index velocity first must be related to mean channel velocity and then used to calculate instantaneous channel discharge. Finally, discharge is low-pass filtered to remove the effects of the tides. An ultrasonic velocity meter discharge-measurement site in a tidally affected region of the Sacramento-San Joaquin Rivers was used to study the accuracy of the index velocity calibration procedure. Calibration data consisting of ultrasonic velocity meter index velocity and concurrent acoustic Doppler discharge measurement data were collected during three time periods. Two sets of data were collected during a spring tide (monthly maximum tidal current) and one of data collected during a neap tide (monthly minimum tidal current). The relative magnitude of instrumental errors, acoustic Doppler discharge measurement errors, and calibration errors were evaluated. Calibration error was found to be the most significant source of error in estimating net discharge. Using a comprehensive calibration method, net discharge estimates developed from the three
Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies
Safta, Cosmin; Najm, Habib N.; Phipps, Eric Todd
2014-09-01
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
NASA Astrophysics Data System (ADS)
Sakuma, Hiroki; Okamoto, Atsushi; Shibukawa, Atsushi; Goto, Yuta; Tomita, Akihisa
2016-02-01
We propose a spatial mode generation technology using spatial cross modulation (SCM) for mode division multiplexing (MDM). The most well-known method for generating arbitrary complex amplitude fields is to display an off-axis computer-generated hologram (CGH) on a spatial light modulator (SLM). However, in this method, a desired complex amplitude field is obtained with first order diffraction light. This critically lowers the light utilization efficiency. On the other hand, in the SCM, the desired complex field is provided with zeroth order diffraction light. For this reason, our technology can generate spatial modes with large light utilization efficiency in addition to high accuracy. In this study, first, a numerical simulation was performed to verify that the SCM is applicable for spatial mode generation. Next, we made a comparison from two view points of the coupling efficiency and the light utilization between our technology and the technology using an off-axis amplitude hologram as a representative complex amplitude generation method. The simulation results showed that our technology can achieve considerably high light utilization efficiency while maintaining the enough coupling efficiency comparable to the technology using an off-axis amplitude hologram. Finally, we performed an experiment on spatial modes generation using the SCM. Experimental results showed that our technology has the great potential to realize the spatial mode generation with high accuracy.
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
NASA Astrophysics Data System (ADS)
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Lucas, D.S.
2004-10-03
This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.
Integrated numerical methods for hypersonic aircraft cooling systems analysis
NASA Technical Reports Server (NTRS)
Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.
1992-01-01
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
Borazjani, Iman; Westerdale, John; McMahon, Eileen M; Rajaraman, Prathish K; Heys, Jeffrey J; Belohlavek, Marek
2013-01-01
The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics.
Borazjani, Iman; Westerdale, John; McMahon, Eileen M.; Rajaraman, Prathish K.; Heys, Jeffrey J.
2013-01-01
The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics. PMID:23690874
Numerical method for evolving the projected Gross-Pitaevskii equation.
Blakie, P Blair
2008-08-01
In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and nonequilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Reynolds, Daniel R. . E-mail: drreynolds@ucsd.edu; Samtaney, Ravi . E-mail: samtaney@pppl.gov; Woodward, Carol S. . E-mail: cswoodward@llnl.gov
2006-11-20
We present a nonlinearly implicit, conservative numerical method for integration of the single-fluid resistive MHD equations. The method uses a high-order spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly in time, providing for increased interaction between physical processes as well as additional stability over explicit-time methods. A high-order adaptive time integration is employed, which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit CFL condition. We apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which challenge the efficiency of explicit methods. We provide computational evidence showing that for such problems the method is comparably accurate with explicit-time simulations, while providing a significant runtime improvement due to its increased temporal stability.
NASA Technical Reports Server (NTRS)
Russell, William S.; Roberts, William W., Jr.
1993-01-01
An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.; Jacobsen, S. E.
1986-01-01
An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
. This finding may lead to more comprehensive studies of the effect of the particle rotation on fluid–solid drag laws. It is also demonstrated that, when the third-order or the fourth-order Runge–Kutta scheme is used, the numerical stability of the present IB-LBM is better than that of all methods in the literature, including the previous IB-LBMs and also the methods with the combination of the IBM and the traditional incompressible Navier–Stokes solver. - Highlights: • The IBM is embedded in the LBM using Runge–Kutta time schemes. • The effectiveness of the present IB-LBM is validated by benchmark applications. • For the first time, the IB-LBM achieves the second-order accuracy. • The numerical stability of the present IB-LBM is better than previous methods.
Numerical integration of population models satisfying conservation laws: NSFD methods.
Mickens, Ronald E
2007-10-01
Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models.
Du, Qi-Shi; Wang, Cheng-Hua; Wang, Yu-Ting; Huang, Ri-Bo
2010-04-01
The electrostatic potential (ESP) is an important property of interactions within and between macromolecules, including those of importance in the life sciences. Semiempirical quantum chemical methods and classical Coulomb calculations fail to provide even qualitative ESP for many of these biomolecules. A new empirical ESP calculation method, namely, EM-ESP, is developed in this study, in which the traditional approach of point atomic charges and the classical Coulomb equation is discarded. In its place, the EM-ESP generates a three-dimensional electrostatic potential V(EM)(r) in molecular space that is the sum of contributions from all component atoms. The contribution of an atom k is formulated as a Gaussian function g(r(k);alpha(k),beta(k)) = alpha(k)/r(k)(betak) with two parameters (alpha(k) and beta(k)). The benchmark for the parameter optimization is the ESP obtained by using higher-level quantum chemical approaches (e.g., CCSD/TZVP). A set of atom-based parameters is optimized in a training set of common organic molecules. Calculated examples demonstrate that the EM-ESP approach is a vast improvement over the Coulombic approach in producing the molecular ESP contours that are comparable to the results obtained with higher-level quantum chemical methods. The atom-based parameters are shown to be transferrable between one part of closely related aromatic molecules. The atom-based ESP formulization and parametrization strategy can be extended to biological macromolecules, such as proteins, DNA, and RNA molecules. Since ESP is frequently used to rationalize and predict intermolecular interactions, we expect that the EM-ESP method will have important applications for studies of protein-ligand and protein-protein interactions in numerous areas of chemistry, molecular biology, and other life sciences.
NASA Astrophysics Data System (ADS)
Parand, K.; Rad, J. A.; Ahmadi, M.
2016-09-01
Natural convective heat transfer in porous media which is of importance in the design of canisters for nuclear waste disposal has received considerable attention during the past few decades. This paper presents a comparison between two different analytical and numerical methods, i.e. pseudospectral and Adomian decomposition methods. The pseudospectral approach makes use of the orthogonal rational Jacobi functions; this method reduces the solution of the problem to a solution of a system of algebraic equations. Numerical results are compared with each other, showing that the pseudospectral method leads to more accurate results and is applicable on similar problems.
NASA Astrophysics Data System (ADS)
Marom, Noa; Knight, Joseph; Wang, Xiaopeng; Gallandi, Lukas; Dolgounitcheva, Olga; Ren, Xinguo; Ortiz, Vincent; Rinke, Patrick; Korzdorfer, Thomas
The performance of different GW methods is assessed for a set of 24 organic acceptors. Errors are evaluated with respect to coupled cluster singles, doubles, perturbative triples [CCSD(T)] reference data for the vertical ionization potentials (IPs) and electron affinities (EAs), extrapolated to the complete basis set limit. Additional comparisons are made to experimental data, where available. We consider fully self-consistent GW (scGW), partial self-consistency in the Green's function (scGW0) , non-self-consistent G0W0 based on several mean-field starting points, and a ``beyond GW'' second order screened exchange (SOSEX) correction to G0W0. The best performers overall are G0W0 + SOSEX and G0W0 based on an IP-tuned long range corrected hybrid functional with the former being more accurate for EAs and the latter for IPs. Both provide a balanced treatment of localized vs. delocalized states and valence spectra in good agreement with photoemission spectroscopy (PES) experiments.
McKellop, H; Clarke, I C; Markolf, K L; Amstutz, H C
1978-11-01
The wear of UHMW polyethylene bearing against 316 stainless steel or cobalt chrome alloy was measured using a 12-channel wear tester especially developed for the evaluation of candidate materials for prosthetic joints. The coefficient of friction and wear rate was determined as a function of lubricant, contact stress, and metallic surface roughness in tests lasting two to three million cycles, the equivalent of several years' use of a prosthesis. Wear was determined from the weight loss of the polyethylene specimens corrected for the effect of fluid absorption. The friction and wear processes in blood serum differed markedly from those in saline solution or distilled water. Only serum lubrication produced wear surfaces resembling those observed on removed prostheses. The experimental method provided a very accurate reproducible measurement of polyethylene wear. The long-term wear rates were proportional to load and sliding distance and were much lower than expected from previously published data. Although the polyethylene wear rate increased with increasing surface roughness, wear was not severe except with very coarse metal surfaces. The data obtained in these studies forms a basis for the subsequent comparative evaluation of potentially superior materials for prosthetic joints.
Method for accurate sizing of pulmonary vessels from 3D medical images
NASA Astrophysics Data System (ADS)
O'Dell, Walter G.
2015-03-01
Detailed characterization of vascular anatomy, in particular the quantification of changes in the distribution of vessel sizes and of vascular pruning, is essential for the diagnosis and management of a variety of pulmonary vascular diseases and for the care of cancer survivors who have received radiation to the thorax. Clinical estimates of vessel radii are typically based on setting a pixel intensity threshold and counting how many "On" pixels are present across the vessel cross-section. A more objective approach introduced recently involves fitting the image with a library of spherical Gaussian filters and utilizing the size of the best matching filter as the estimate of vessel diameter. However, both these approaches have significant accuracy limitations including mis-match between a Gaussian intensity distribution and that of real vessels. Here we introduce and demonstrate a novel approach for accurate vessel sizing using 3D appearance models of a tubular structure along a curvilinear trajectory in 3D space. The vessel branch trajectories are represented with cubic Hermite splines and the tubular branch surfaces represented as a finite element surface mesh. An iterative parameter adjustment scheme is employed to optimally match the appearance models to a patient's chest X-ray computed tomography (CT) scan to generate estimates for branch radii and trajectories with subpixel resolution. The method is demonstrated on pulmonary vasculature in an adult human CT scan, and on 2D simulated test cases.
Performance analysis of a mirror by numerical iterative method.
Park, Kwijong; Cho, Myung; Lee, Dae-Hee; Moon, Bongkon
2014-12-29
Zernike polynomials are generally used to predict the optical performance of a mirror. However, it can also be done by a numerical iterative method. As piston, tip, tilt, and defocus (P.T.T.F) aberrations can be easily removed by optical alignment, we iteratively used a rotation transformation and a paraboloid graph subtraction for removal of the aberrations from a raw deformation of the optical surface through a Finite Element Method (FEM). The results of a 30 cm concave circular mirror corrected by the iterative method were almost the same as those yielded by Zernike polynomial fitting, and the computational time was fast. In addition, a concave square mirror whose surface area is π was analyzed in order to visualize the deformation maps of a general mirror aperture shape. The iterative method can be applicable efficiently because it does not depend on the mirror aperture shape.
Numerical method for gas dynamics combining characteristic and conservation concepts
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1981-01-01
An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
NASA Astrophysics Data System (ADS)
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
may lead to more comprehensive studies of the effect of the particle rotation on fluid-solid drag laws. It is also demonstrated that, when the third-order or the fourth-order Runge-Kutta scheme is used, the numerical stability of the present IB-LBM is better than that of all methods in the literature, including the previous IB-LBMs and also the methods with the combination of the IBM and the traditional incompressible Navier-Stokes solver.
Computation of Nonlinear Backscattering Using a High-Order Numerical Method
NASA Technical Reports Server (NTRS)
Fibich, G.; Ilan, B.; Tsynkov, S.
2001-01-01
The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.
The numerical methods for the fluid flow of UCMCWS
Zhang Wenfu; Li Hui; Zhu Shuquan; Wang Zuna
1997-12-31
As an alternative for diesel oil for internal combustion engines, the fluid flow state of Ultra Clean Micronized Coal-Water Slurry (UCMCWS) in mini pipe and nozzle of a diesel engine must be known. In the laboratory three kinds of UCMCWS have been made with coal containing less than 0.8% ash, viscosity less than 600 mPa.s and concentration between 50% and 56%. Because the UCMCWS is a non-Newtonian fluid, there are no analytical resolution for pipe flow, especially in inlet and outlet sections. In this case using the numerical methods to research the flow state of UCMCWS is a useful method. Using the method of finite element, the flow state of UCMCWS in inlet and outlet sections (similar to a nozzle) have been studied. The distribution of velocity at different pressures of UCMCWS in outlet and inlet sections have been obtained. The result of the numerical methods is the efficient base for the pipe and nozzle design.
NASA Astrophysics Data System (ADS)
Westendorp, Hendrik; Nuver, Tonnis T.; Moerland, Marinus A.; Minken, André W.
2015-10-01
The geometry of a permanent prostate implant varies over time. Seeds can migrate and edema of the prostate affects the position of seeds. Seed movements directly influence dosimetry which relates to treatment quality. We present a method that tracks all individual seeds over time allowing quantification of seed movements. This linking procedure was tested on transrectal ultrasound (TRUS) and cone-beam CT (CBCT) datasets of 699 patients. These datasets were acquired intraoperatively during a dynamic implantation procedure, that combines both imaging modalities. The procedure was subdivided in four automatic linking steps. (I) The Hungarian Algorithm was applied to initially link seeds in CBCT and the corresponding TRUS datasets. (II) Strands were identified and optimized based on curvature and linefits: non optimal links were removed. (III) The positions of unlinked seeds were reviewed and were linked to incomplete strands if within curvature- and distance-thresholds. (IV) Finally, seeds close to strands were linked, also if the curvature-threshold was violated. After linking the seeds an affine transformation was applied. The procedure was repeated until the results were stable or the 6th iteration ended. All results were visually reviewed for mismatches and uncertainties. Eleven implants showed a mismatch and in 12 cases an uncertainty was identified. On average the linking procedure took 42 ms per case. This accurate and fast method has the potential to be used for other time spans, like Day 30, and other imaging modalities. It can potentially be used during a dynamic implantation procedure to faster and better evaluate the quality of the permanent prostate implant.
Numerical methods and measurement systems for nonlinear magnetic circuits (abstract)
NASA Astrophysics Data System (ADS)
Heitbrink, Axel; Dieter Storzer, Hans; Beyer, Adalbert
1994-05-01
In the past years an increasing interest in calculation methods of circuits containing magnetic nonlinearities could be observed. For this reason a new method was developed which makes it possible to calculate the steady state solution of such circuits by the help of an interactive cad program. The modular concept of the software allows to separate the circuit into nonlinear and linear subnetworks. When regarding nonlinear magnetic elements one can choose between several numerical models for the description of the hysteresis loops or an inbuilt realtime measurement system can be activated to get the dynamic hysteresis loops. The measurement system is also helpful for the parameter extraction for the numerical hysteresis models. A modified harmonic-balance algorithm and a set of iteration schemes is used for solving the network function. The combination of the realtime measurement system and modern numerical methods brings up a productive total concept for the exact calculation of nonlinear magnetic circuits. A special application class will be discussed which is given by earth-leakage circuit breakers. These networks contain a toroidal high permeable NiFe alloy and a relay as nonlinear elements (cells) and some resistors, inductors, and capacitors as linear elements. As input dc signals at the primary winding of the core any curveform must be regarded, especially 135° phasecutted pulses. These signals with extreme higher frequency components make it impossible to use numerical models for the description of the nonlinear behavior of the core and the relays. So for both elements the realtime measurement system must be used during the iteration process. During each iteration step the actual magnetization current is sent to the measurement system, which measures the dynamic hysteresis loop at the probe. These values flow back into the iteration process. A graphic subsystem allows a look at the waveforms of all voltages and current when the iterations take place. One
A numerical oil spill model based on a hybrid method.
Guo, W J; Wang, Y X
2009-05-01
The purpose of this paper is the development of a hybrid particle tracking/Eulerian-Lagrangian approach for the simulation of spilled oil in coastal areas. Oil discharge from the source is modeled by the release of particles. When the oil slick thickness or the oil concentration reaches a critical value, particles are mapped on slick thickness or node concentrations, and the calculations proceed in the Eulerian-Lagrangian mode. To acquire accurate environment information, the model is coupled with the 3-D free-surface hydrodynamics model (POM) and the third-generation wave model (SWAN). By simulating the oil processes of spreading, advection, turbulent diffusion, evaporation, emulsification, dissolution and shoreline deposition, it has the ability to predict the horizontal movement of surface oil slick, the vertical distribution of oil particles, the concentration in the water column and the mass balance of spilled oil. An accidental oil release near Dalian coastal waters is simulated to validate the developed model. Compared with the satellite images of oil slicks on the surface, the numerical results indicate that the model has a reasonable accuracy.
A comparison of numerical methods for non-Newtonian fluid flows in a sudden expansion
NASA Astrophysics Data System (ADS)
Ilio, G. Di; Chiappini, D.; Bella, G.
2016-06-01
A numerical study on incompressible laminar flow in symmetric channel with sudden expansion is conducted. In this work, Newtonian and non-Newtonian fluids are considered, where non-Newtonian fluids are described by the power-law model. Three different computational methods are employed, namely a semi-implicit Chorin projection method (SICPM), an explicit algorithm based on fourth-order Runge-Kutta method (ERKM) and a Lattice Boltzmann method (LBM). The aim of the work is to investigate on the capabilities of the LBM for the solution of complex flows through the comparison with traditional computational methods. In the range of Reynolds number investigated, excellent agreement with the literature results is found. In particular, the LBM is found to be accurate in the prediction of the fluid flow behavior for the problem under consideration.
Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.
Bell, John B; Garcia, Alejandro L; Williams, Sarah A
2007-07-01
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.
Numerical Analysis of a Finite Element/Volume Penalty Method
NASA Astrophysics Data System (ADS)
Maury, Bertrand
The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.
Comparison of four stable numerical methods for Abel's integral equation
NASA Technical Reports Server (NTRS)
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
The present numerical method for the solution of the isenthalpic form of the governing equations for compressible viscous and inviscid flows has its basis in the concept of flux vector splitting in its implicit form, and has been tested in the cases of several difficult viscous and inviscid configurations. An acceleration of time-marching to steady state is accomplished by implementing a multigrid procedure which effectively increases the convergence rate. The steady state results obtained are largely of good quality, and required only short computational times.
Numerical Methods for Computing Turbulence-Induced Noise
2005-12-16
consider the finite dimensional subspace Vhl C Vh . Let vhi -= phlu be the optimal representation of u in Vhl and phi : V+_+ Vhl be the appropriate...mapping. We consider the following numerical method which is obtained by replacing h with hi in (2.4). Find uhl E Vhi , such that B(whi, uhl) + M(whUhl, f...the same functional form of the model that leads to the optimal solution on Vh, also leads to the optimal solution on Vhi . Thus, requiring uhl = vh
Calculation of free-fall trajectories using numerical optimization methods.
NASA Technical Reports Server (NTRS)
Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.
1972-01-01
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
NASA Astrophysics Data System (ADS)
Hong, Youngjoon; Nicholls, David P.
2017-02-01
The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.
a Numerical Method for Scattering from Acoustically Soft and Hard Thin Bodies in Two Dimensions
NASA Astrophysics Data System (ADS)
YANG, S. A.
2002-03-01
This paper presents a numerical method for predicting the acoustic scattering from two-dimensional (2-D) thin bodies. Both the Dirichlet and Neumann problems are considered. Applying the thin-body formulation leads to the boundary integral equations involving weakly singular and hypersingular kernels. Completely regularizing these kinds of singular kernels is thus the main concern of this paper. The basic subtraction-addition technique is adopted. The purpose of incorporating a parametric representation of the boundary surface with the integral equations is two-fold. The first is to facilitate the numerical implementation for arbitrarily shaped bodies. The second one is to facilitate the expansion of the unknown function into a series of Chebyshev polynomials. Some of the resultant integrals are evaluated by using the Gauss-Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral. The numerical implementation basically includes only two parts, one for evaluating the ordinary integrals and the other for solving a system of algebraic equations. Thus, the current method is highly efficient and accurate because these two solution procedures are easy and straightforward. Numerical calculations consist of the acoustic scattering by flat and curved plates. Comparisons with analytical solutions for flat plates are made.
Numerical divergence effects of equivalence theory in the nodal expansion method
Zika, M.R.; Downar, T.J. )
1993-11-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible.
Numerical solution of flame sheet problems with and without multigrid methods
NASA Technical Reports Server (NTRS)
Douglas, Craig C.; Ern, Alexandre
1993-01-01
Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.
1986-01-01
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
Numerical modeling of spray combustion with an advanced VOF method
NASA Technical Reports Server (NTRS)
Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul
1995-01-01
This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.
Numerical Methods and Simulations of Complex Multiphase Flows
NASA Astrophysics Data System (ADS)
Brady, Peter
Multiphase flows are an important part of many natural and technological phenomena such as ocean-air coupling (which is important for climate modeling) and the atomization of liquid fuel jets in combustion engines. The unique challenges of multiphase flow often make analytical solutions to the governing equations impossible and experimental investigations very difficult. Thus, high-fidelity numerical simulations can play a pivotal role in understanding these systems. This dissertation describes numerical methods developed for complex multiphase flows and the simulations performed using these methods. First, the issue of multiphase code verification is addressed. Code verification answers the question "Is this code solving the equations correctly?" The method of manufactured solutions (MMS) is a procedure for generating exact benchmark solutions which can test the most general capabilities of a code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented, using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. Guidelines for the use of the MMS to help locate coding mistakes are also detailed. Three multiphase systems are then investigated: (1) the thermocapillary motion of three-dimensional and axisymmetric drops in a confined apparatus, (2) the flow of two immiscible fluids completely filling an enclosed cylinder and driven by the rotation of the bottom endwall, and (3) the atomization of a single drop subjected to a high shear turbulent flow. The systems are simulated numerically by solving the full multiphase Navier-Stokes equations coupled to the various equations of state and a level set interface tracking scheme based on the refined level set grid method. The codes have been parallelized using MPI in order to take advantage of today's very large parallel computational
Lin, W.L.; Carlson, K.D.; Chen, C.J. |
1999-05-01
In this study, a diagonal Cartesian method for thermal analysis is developed for simulation of conjugate heat transfer over complex boundaries. This method uses diagonal line segments in addition to Cartesian coordinates. The velocity fields are also modeled using the diagonal Cartesian method. The transport equations are discretized with the finite analytic (FA) method. The current work is validated by simulating a rotated lid-driven cavity flow with conjugate heat transfer, and accurate results are obtained.
Numerical methods for assessment of the ship's pollutant emissions
NASA Astrophysics Data System (ADS)
Jenaru, A.; Acomi, N.
2016-08-01
The maritime transportation sector constitutes a source of atmospheric pollution. To avoid or minimize ships pollutant emissions the first step is to assess them. Two methods of estimation of the ships’ emissions are proposed in this paper. These methods prove their utility for shipboard and shore based management personnel from the practical perspective. The methods were demonstrated for a product tanker vessel where a permanent monitoring system for the pollutant emissions has previously been fitted. The values of the polluting agents from the exhaust gas were determined for the ship from the shipyard delivery and were used as starting point. Based on these values, the paper aimed at numerical assessing of ship's emissions in order to determine the ways for avoiding environmental pollution: the analytical method of determining the concentrations of the exhaust gas components, by using computation program MathCAD, and the graphical method of determining the concentrations of the exhaust gas components, using variation diagrams of the parameters, where the results of the on board measurements were introduced, following the application of pertinent correction factors. The results should be regarded as a supporting tool during the decision making process linked to the reduction of ship's pollutant emissions.
Accurate measurement method of Fabry-Perot cavity parameters via optical transfer function
Bondu, Francois; Debieu, Olivier
2007-05-10
It is shown how the transfer function from frequency noise to a Pound-Drever-Hall signal for a Fabry-Perot cavity can be used to accurately measure cavity length, cavity linewidth, mirror curvature, misalignments, laser beam shape mismatching with resonant beam shape, and cavity impedance mismatching with respect to vacuum.
A time-accurate implicit method for chemical non-equilibrium flows at all speeds
NASA Technical Reports Server (NTRS)
Shuen, Jian-Shun
1992-01-01
A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.
A method for improving time-stepping numerics
NASA Astrophysics Data System (ADS)
Williams, P. D.
2012-04-01
In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.
Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods
NASA Technical Reports Server (NTRS)
Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark
2002-01-01
Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.
A Hybrid Numerical Analysis Method for Structural Health Monitoring
NASA Technical Reports Server (NTRS)
Forth, Scott C.; Staroselsky, Alexander
2001-01-01
A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.
Numerical Method of Characteristics for One-Dimensional Blood Flow.
Acosta, Sebastian; Puelz, Charles; Riviére, Béatrice; Penny, Daniel J; Rusin, Craig G
2015-08-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
Numerical method of characteristics for one-dimensional blood flow
NASA Astrophysics Data System (ADS)
Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-08-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
Space-time adaptive numerical methods for geophysical applications.
Castro, C E; Käser, M; Toro, E F
2009-11-28
In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost.
Numerical Method of Characteristics for One–Dimensional Blood Flow
Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-01-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant. PMID:25931614
Two Approaches in the Lunar Libration Theory: Analytical vs. Numerical Methods
NASA Astrophysics Data System (ADS)
Petrova, Natalia; Zagidullin, Arthur; Nefediev, Yurii; Kosulin, Valerii
2016-10-01
Observation of the physical libration of the Moon and the celestial bodies is one of the astronomical methods to remotely evaluate the internal structure of a celestial body without using expensive space experiments. Review of the results obtained due to the physical libration study, is presented in the report.The main emphasis is placed on the description of successful lunar laser ranging for libration determination and on the methods of simulating the physical libration. As a result, estimation of the viscoelastic and dissipative properties of the lunar body, of the lunar core parameters were done. The core's existence was confirmed by the recent reprocessing of seismic data Apollo missions. Attention is paid to the physical interpretation of the phenomenon of free libration and methods of its determination.A significant part of the report is devoted to describing the practical application of the most accurate to date the analytical tables of lunar libration built by comprehensive analytical processing of residual differences obtained when comparing the long-term series of laser observations with numerical ephemeris DE421 [1].In general, the basic outline of the report reflects the effectiveness of two approaches in the libration theory - numerical and analytical solution. It is shown that the two approaches complement each other for the study of the Moon in different aspects: numerical approach provides high accuracy of the theory necessary for adequate treatment of modern high-accurate observations and the analytic approach allows you to see the essence of the various kind manifestations in the lunar rotation, predict and interpret the new effects in observations of physical libration [2].[1] Rambaux, N., J. G. Williams, 2011, The Moon's physical librations and determination of their free modes, Celest. Mech. Dyn. Astron., 109, 85-100.[2] Petrova N., A. Zagidullin, Yu. Nefediev. Analysis of long-periodic variations of lunar libration parameters on the basis of
Hao, Hongxia; Zhou, Hong; Liu, Xiaopei; Zhang, Zhong; Yu, Zhongshan
2013-06-10
Carbon monoxide (CO) may be the cause of more than half the fatal poisonings reported in many countries, with some of these cases under-reported or misdiagnosed by medical professionals. Therefore, an accurate and reliable analytical method to measure blood carboxyhemoglobin level (COHb%), in the 1% to lethal range, is essential for correct diagnosis. Herein a method was established, i.e. head-space gas chromatography-mass spectrometry (HS/GC/MS) that has numerous advantages over other techniques, such as UV spectrometry, for determination of COHb%. There was a linear relationship (R(2)=0. 9995) between the peak area for CO and the COHb% in blood. Using a molecular sieve-packed column, CO levels in the air down to 0.01% and COHb% levels in small blood samples down to 0.2% could be quantitated rapidly and accurately. Furthermore, this method showed good reproducibility with a relative standard deviation for COHb% of <1%. Therefore, this technique provides an accurate and reliable method for determining CO and COHb% levels and may prove useful for investigation of deaths potentially related to CO exposure.
NASA Astrophysics Data System (ADS)
Cai, Can-Ying; Zeng, Song-Jun; Liu, Hong-Rong; Yang, Qi-Bin
2008-05-01
A completely different formulation for simulation of the high order Laue zone (HOLZ) diffractions is derived. It refers to the new method, i.e. the Taylor series (TS) method. To check the validity and accuracy of the TS method, we take polyvinglidene fluoride (PVDF) crystal as an example to calculate the exit wavefunction by the conventional multi-slice (CMS) method and the TS method. The calculated results show that the TS method is much more accurate than the CMS method and is independent of the slice thicknesses. Moreover, the pure first order Laue zone wavefunction by the TS method can reflect the major potential distribution of the first reciprocal plane.
A survey of numerical methods for shock physics applications
Hertel, E.S. Jr.
1997-10-01
Hydrocodes or more accurately, shock physics analysis packages, have been widely used in the US Department of Energy (DOE) laboratories and elsewhere around the world for over 30 years. Initial applications included weapons effects studies where the pressure levels were high enough to disregard the material strength, hence the term hydrocode. Over the last 30 years, Sandia has worked extensively to develop and apply advanced hydrocodes to armor/anti-armor interactions, warhead design, high explosive initiation, and nuclear weapon safety issues. The needs of the DOE have changed over the last 30 years, especially over the last decade. A much stronger emphasis is currently placed on the details of material deformation and high explosive initiation phenomena. The hydrocodes of 30 years ago have now evolved into sophisticated analysis tools that can replace testing in some situations and complement it in all situations. A brief history of the development of hydrocodes in the US will be given. The author also discusses and compares the four principal methods in use today for the solution of the conservation equations of mass, momentum, and energy for shock physics applications. The techniques discussed are the Eulerian methods currently employed by the Sandia multi-dimensional shock physics analysis package known as CTH; the element based Lagrangian method currently used by codes like DYNA; the element free Lagrangian method (also known as smooth particle hydrodynamics) used by codes like the Los Alamos code SPHINX; and the Arbitrary Lagrangian Eulerian methods used by codes like the Lawrence Livermore code CALE or the Sandia code ALEGRA.
NASA Technical Reports Server (NTRS)
Schneider, Harold
1959-01-01
This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.
Taylor, G.; Dong, C.; Sun, S.
2010-03-18
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.
NASA Technical Reports Server (NTRS)
Hu, Fang Q.
1994-01-01
It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.
A mathematical model and numerical method for thermoelectric DNA sequencing
NASA Astrophysics Data System (ADS)
Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong
2014-05-01
Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.
Numerical optimization method for packing regular convex polygons
NASA Astrophysics Data System (ADS)
Galiev, Sh. I.; Lisafina, M. S.
2016-08-01
An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.
Numerical simulation on snow melting phenomena by CIP method
NASA Astrophysics Data System (ADS)
Mizoe, H.; Yoon, Seong Y.; Josho, M.; Yabe, T.
2001-04-01
A numerical scheme based on the C-CUP method to simulate melting phenomena in snow is proposed. To calculate these complex phenomena we introduce the phase change, elastic-plastic model, porous model, and verify each model by using some simple examples. This scheme is applied to a practical model, such as the snow piled on the insulator of electrical transmission line, in which snow is modeled as a compound material composed of air, water, and ice, and is calculated by elastic-plastic model. The electric field between two electrodes is solved by the Poisson equation giving the Joule heating in the energy conservation that eventually leads to snow melting. Comparison is made by changing the fraction of water in the snow to see its effect on melting process for the cases of applied voltage of 50 and 500 kV on the two electrodes.
Tenon, Mathieu; Feuillère, Nicolas; Roller, Marc; Birtić, Simona
2017-04-15
Yucca GRAS-labelled saponins have been and are increasingly used in food/feed, pharmaceutical or cosmetic industries. Existing techniques presently used for Yucca steroidal saponin quantification remain either inaccurate and misleading or accurate but time consuming and cost prohibitive. The method reported here addresses all of the above challenges. HPLC/ELSD technique is an accurate and reliable method that yields results of appropriate repeatability and reproducibility. This method does not over- or under-estimate levels of steroidal saponins. HPLC/ELSD method does not require each and every pure standard of saponins, to quantify the group of steroidal saponins. The method is a time- and cost-effective technique that is suitable for routine industrial analyses. HPLC/ELSD methods yield a saponin fingerprints specific to the plant species. As the method is capable of distinguishing saponin profiles from taxonomically distant species, it can unravel plant adulteration issues.
Simultaneous source-mask optimization: a numerical combining method
NASA Astrophysics Data System (ADS)
Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.
2010-09-01
A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.
Device and method for accurately measuring concentrations of airborne transuranic isotopes
McIsaac, C.V.; Killian, E.W.; Grafwallner, E.G.; Kynaston, R.L.; Johnson, L.O.; Randolph, P.D.
1996-09-03
An alpha continuous air monitor (CAM) with two silicon alpha detectors and three sample collection filters is described. This alpha CAM design provides continuous sampling and also measures the cumulative transuranic (TRU), i.e., plutonium and americium, activity on the filter, and thus provides a more accurate measurement of airborne TRU concentrations than can be accomplished using a single fixed sample collection filter and a single silicon alpha detector. 7 figs.
Device and method for accurately measuring concentrations of airborne transuranic isotopes
McIsaac, Charles V.; Killian, E. Wayne; Grafwallner, Ervin G.; Kynaston, Ronnie L.; Johnson, Larry O.; Randolph, Peter D.
1996-01-01
An alpha continuous air monitor (CAM) with two silicon alpha detectors and three sample collection filters is described. This alpha CAM design provides continuous sampling and also measures the cumulative transuranic (TRU), i.e., plutonium and americium, activity on the filter, and thus provides a more accurate measurement of airborne TRU concentrations than can be accomplished using a single fixed sample collection filter and a single silicon alpha detector.
In the field of bioassessment, tolerance has traditionally referred to the degree to which organisms can withstand environmental degradation. This concept has been around for many years and its use is widespread. In numerous cases, tolerance values (TVs) have been assigned to i...
NASA Astrophysics Data System (ADS)
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.
NASA Astrophysics Data System (ADS)
Bekhoucha, Ferhat; Rechak, Said; Duigou, Laëtitia; Cadou, Jean-Marc
2015-05-01
This paper deals with the computation of backbone curves bifurcated from a Hopf bifurcation point in the framework of nonlinear free vibrations of a rotating flexible beams. The intrinsic and geometrical equations of motion for anisotropic beams subjected to large displacements are used and transformed with Galerkin and harmonic balance methods to one quadratic algebraic equation involving one parameter, the pulsation. The latter is treated with the asymptotic numerical method using Padé approximants. An algorithm, equivalent to the Lyapunov-Schmidt reduction is proposed, to compute the bifurcated branches accurately from a Hopf bifurcation point, with singularity of co-rank 2, related to a conservative and gyroscopic dynamical system steady state, toward a nonlinear periodic state. Numerical tests dealing with clamped, isotropic and composite, rotating beams show the reliability of the proposed method reinforced by accurate results.
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
Advanced numerical methods and software approaches for semiconductor device simulation
CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.
2000-03-23
In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.
Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation
Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.
2000-01-01
In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers
NASA Technical Reports Server (NTRS)
Kennedy, Christopher A.; Carpenter, Mark H.
1997-01-01
An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan; Venkatachari, Balaji Shankar; Cheng, Gary
2013-01-01
With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.
NASA Astrophysics Data System (ADS)
Lambert, J.; Josselin, E.; Ryde, N.; Faure, A.
2015-08-01
Context. The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to handle large-scale systems, such as molecular spectra emerging from, for example, cool stellar atmospheres. Aims: Our objective is to develop a new method, which aims to circumvent these problems, using nonstationary numerical techniques and taking advantage of parallel computers. Methods: The technique we develop may be seen as a generalization of the coupled escape probability method. It solves the statistical equilibrium equations in all layers of a discretized model simultaneously. The numerical scheme adopted is based on the generalized minimum residual method. Results: The code has already been applied to the special case of the water spectrum in a red supergiant stellar atmosphere. This demonstrates the fast convergence of this method, and opens the way to a wide variety of astrophysical problems.
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
Numerical modelling methods for predicting antenna performance on aircraft
NASA Astrophysics Data System (ADS)
Kubina, S. J.
1983-09-01
Typical case studies that involve the application of Moment Methods to the prediction of the radiation characteristics of antennas in the HF frequency band are examined. The examples consist of the analysis of a shorted transmission line HF antenna on a CHSS-2/Sea King helicopter, wire antennas on the CP-140/Aurora patrol aircraft and a long dipole antenna on the Space Shuttle Orbiter spacecraft. In each of these cases the guidelines for antenna modeling by the use of the program called the Numerical Electromagnetic Code are progressively applied and results are compared to measurements made by the use of scale-model techniques. In complex examples of this type comparisons based on individual radiation patterns are insufficient for the validation of computer models. A volumetric method of radiation pattern comparison is used based on criteria that result from pattern integration and that are related to communication system performance. This is supplemented by hidden-surface displays of an entire set of conical radiation patterns resulting from measurements and computations. Antenna coupling considerations are discussed for the case of the dual HF installation on the CP-140/Aurora aircraft.
Sun, Jiasong; Chen, Qian; Zhang, Yuzhen; Zuo, Chao
2016-03-15
In this Letter, an accurate and highly efficient numerical phase aberration compensation method is proposed for digital holographic microscopy. Considering that most parts of the phase aberration resides in the low spatial frequency domain, a Fourier-domain mask is introduced to extract the aberrated frequency components, while rejecting components that are unrelated to the phase aberration estimation. Principal component analysis (PCA) is then performed only on the reduced-sized spectrum, and the aberration terms can be extracted from the first principal component obtained. Finally, by oversampling the reduced-sized aberration terms, the precise phase aberration map is obtained and thus can be compensated by multiplying with its conjugation. Because the phase aberration is estimated from the limited but more relevant raw data, the compensation precision is improved and meanwhile the computation time can be significantly reduced. Experimental results demonstrate that our proposed technique could achieve both high compensating accuracy and robustness compared with other developed compensation methods.
Numerical Analysis of Maneuvering Rotorcraft Using Moving Overlapped Grid Method
NASA Astrophysics Data System (ADS)
Yang, Choongmo; Aoyama, Takashi
In transient flight, rotor wakes and tip vortex generated by unsteady blade air-loads and blade motions are fully unsteady and 3-dimensionally-aperiodic, giving rise to significant complicity in accurate analysis compared to steady flight. We propose a hybrid approach by splitting the motions of a maneuvering helicopter into translation and rotation. Translation is simulated using a non-inertial moving (translating) coordinate for which new governing equations are derived, and rotations are simulated by moving each grid in the frame. A flow simulation (CFD) code is constructed by using the hybrid approach, then two simple cases (accelerating/decelerating flight and right-turn flight) for maneuvering helicopter are calculated using the moving overlapped grid method, which is now one of the most advanced techniques for tip-vortex capture. The vortex bundling phenomena, which is a main characteristic of right-turn flight, is well captured by the simulation code. The results of the present study provide better understanding of the characteristics for maneuvering rotorcraft, which can be valuable in full helicopter design.
Simplified method for numerical modeling of fiber lasers.
Shtyrina, O V; Yarutkina, I A; Fedoruk, M P
2014-12-29
A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Vandoormaal, J. P.; Turan, A.; Raithby, G. D.
1986-01-01
The objective of the present study is to improve both the accuracy and computational efficiency of existing numerical techniques used to predict viscous recirculating flows in combustors. A review of the status of the study is presented along with some illustrative results. The effort to improve the numerical techniques consists of the following technical tasks: (1) selection of numerical techniques to be evaluated; (2) two dimensional evaluation of selected techniques; and (3) three dimensional evaluation of technique(s) recommended in Task 2.
Novel micelle PCR-based method for accurate, sensitive and quantitative microbiota profiling.
Boers, Stefan A; Hays, John P; Jansen, Ruud
2017-04-05
In the last decade, many researchers have embraced 16S rRNA gene sequencing techniques, which has led to a wealth of publications and documented differences in the composition of microbial communities derived from many different ecosystems. However, comparison between different microbiota studies is currently very difficult due to the lack of a standardized 16S rRNA gene sequencing protocol. Here we report on a novel approach employing micelle PCR (micPCR) in combination with an internal calibrator that allows for standardization of microbiota profiles via their absolute abundances. The addition of an internal calibrator allows the researcher to express the resulting operational taxonomic units (OTUs) as a measure of 16S rRNA gene copies by correcting the number of sequences of each individual OTU in a sample for efficiency differences in the NGS process. Additionally, accurate quantification of OTUs obtained from negative extraction control samples allows for the subtraction of contaminating bacterial DNA derived from the laboratory environment or chemicals/reagents used. Using equimolar synthetic microbial community samples and low biomass clinical samples, we demonstrate that the calibrated micPCR/NGS methodology possess a much higher precision and a lower limit of detection compared with traditional PCR/NGS, resulting in more accurate microbiota profiles suitable for multi-study comparison.
Novel micelle PCR-based method for accurate, sensitive and quantitative microbiota profiling
Boers, Stefan A.; Hays, John P.; Jansen, Ruud
2017-01-01
In the last decade, many researchers have embraced 16S rRNA gene sequencing techniques, which has led to a wealth of publications and documented differences in the composition of microbial communities derived from many different ecosystems. However, comparison between different microbiota studies is currently very difficult due to the lack of a standardized 16S rRNA gene sequencing protocol. Here we report on a novel approach employing micelle PCR (micPCR) in combination with an internal calibrator that allows for standardization of microbiota profiles via their absolute abundances. The addition of an internal calibrator allows the researcher to express the resulting operational taxonomic units (OTUs) as a measure of 16S rRNA gene copies by correcting the number of sequences of each individual OTU in a sample for efficiency differences in the NGS process. Additionally, accurate quantification of OTUs obtained from negative extraction control samples allows for the subtraction of contaminating bacterial DNA derived from the laboratory environment or chemicals/reagents used. Using equimolar synthetic microbial community samples and low biomass clinical samples, we demonstrate that the calibrated micPCR/NGS methodology possess a much higher precision and a lower limit of detection compared with traditional PCR/NGS, resulting in more accurate microbiota profiles suitable for multi-study comparison. PMID:28378789
gitter: a robust and accurate method for quantification of colony sizes from plate images.
Wagih, Omar; Parts, Leopold
2014-03-20
Colony-based screens that quantify the fitness of clonal populations on solid agar plates are perhaps the most important source of genome-scale functional information in microorganisms. The images of ordered arrays of mutants produced by such experiments can be difficult to process because of laboratory-specific plate features, morphed colonies, plate edges, noise, and other artifacts. Most of the tools developed to address this problem are optimized to handle a single setup and do not work out of the box in other settings. We present gitter, an image analysis tool for robust and accurate processing of images from colony-based screens. gitter works by first finding the grid of colonies from a preprocessed image and then locating the bounds of each colony separately. We show that gitter produces comparable colony sizes to other tools in simple cases but outperforms them by being able to handle a wider variety of screens and more accurately quantify colony sizes from difficult images. gitter is freely available as an R package from http://cran.r-project.org/web/packages/gitter under the LGPL. Tutorials and demos can be found at http://omarwagih.github.io/gitter.
McClarren, Ryan G. Lowrie, Robert B.
2008-12-01
Many hyperbolic systems of equations with stiff relaxation terms reduce to a parabolic description when relaxation dominates. An asymptotic-preserving numerical method is a discretization of the hyperbolic system that becomes a valid discretization of the parabolic system in the asymptotic limit. We explore the consequences of applying a slope limiter to the discontinuous Galerkin (DG) method, with linear elements, for hyperbolic systems with stiff relaxation terms. Without a limiter, the DG method gives an accurate discretization of the Chapman-Enskog approximation of the system when the relaxation length scale is not resolved. It is well known that the first-order upwind (or 'step') method fails to obtain the proper asymptotic limit. We show that using the minmod slope limiter also fails, but that using double minmod gives the proper asymptotic limit. Despite its effectiveness in the asymptotic limit, the double minmod limiter allows artificial extrema at cell interfaces, referred to as 'sawteeth'. We present a limiter that eliminates the sawteeth, but maintains the proper asymptotic limit. The systems that we analyze are the hyperbolic heat equation and the P{sub n} thermal radiation equations. Numerical examples are used to verify our analysis.
Simulation of intra-aneurysmal blood flow by different numerical methods.
Weichert, Frank; Walczak, Lars; Fisseler, Denis; Opfermann, Tobias; Razzaq, Mudassar; Münster, Raphael; Turek, Stefan; Grunwald, Iris; Roth, Christian; Veith, Christian; Wagner, Mathias
2013-01-01
The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms.
NASA Astrophysics Data System (ADS)
McClarren, Ryan G.; Lowrie, Robert B.
2008-12-01
Many hyperbolic systems of equations with stiff relaxation terms reduce to a parabolic description when relaxation dominates. An asymptotic-preserving numerical method is a discretization of the hyperbolic system that becomes a valid discretization of the parabolic system in the asymptotic limit. We explore the consequences of applying a slope limiter to the discontinuous Galerkin (DG) method, with linear elements, for hyperbolic systems with stiff relaxation terms. Without a limiter, the DG method gives an accurate discretization of the Chapman-Enskog approximation of the system when the relaxation length scale is not resolved. It is well known that the first-order upwind (or "step") method fails to obtain the proper asymptotic limit. We show that using the minmod slope limiter also fails, but that using double minmod gives the proper asymptotic limit. Despite its effectiveness in the asymptotic limit, the double minmod limiter allows artificial extrema at cell interfaces, referred to as "sawteeth". We present a limiter that eliminates the sawteeth, but maintains the proper asymptotic limit. The systems that we analyze are the hyperbolic heat equation and the Pn thermal radiation equations. Numerical examples are used to verify our analysis.
ERIC Educational Resources Information Center
Beare, R. A.
2008-01-01
Professional astronomers use specialized software not normally available to students to determine the rotation periods of asteroids from fragmented light curve data. This paper describes a simple yet accurate method based on Microsoft Excel[R] that enables students to find periods in asteroid light curve and other discontinuous time series data of…
Numerical Weather Predictions Evaluation Using Spatial Verification Methods
NASA Astrophysics Data System (ADS)
Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.
2014-12-01
During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain--Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is cofinanced by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007--2013).
NASA Astrophysics Data System (ADS)
Nikadat, Nooraddin; Fatehi Marji, Mohammad; Rahmannejad, Reza; Yarahmadi Bafghi, Alireza
2016-11-01
Different conditions may affect the stability of tunnels by the geometry (spacing and orientation) of joints in the surrounded rock mass. In this study, by comparing the results obtained by the three novel numerical methods i.e. finite element method (Phase2), discrete element method (UDEC) and indirect boundary element method (TFSDDM), the effects of joint spacing and joint dips on the stress distribution around rock tunnels are numerically studied. These comparisons indicate the validity of the stress analyses around circular rock tunnels. These analyses also reveal that for a semi-continuous environment, boundary element method gives more accurate results compared to the results of finite element and distinct element methods. In the indirect boundary element method, the displacements due to joints of different spacing and dips are estimated by using displacement discontinuity (DD) formulations and the total stress distribution around the tunnel are obtained by using fictitious stress (FS) formulations.
Augustin, Christoph M; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J; Niederer, Steven A; Haase, Gundolf; Plank, Gernot
2016-01-15
Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate
Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot
2016-01-01
Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate
NASA Astrophysics Data System (ADS)
Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot
2016-01-01
Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Numerical methods for incompressible viscous flows with engineering applications
NASA Technical Reports Server (NTRS)
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
Accurate surface tension measurement of glass melts by the pendant drop method.
Chang, Yao-Yuan; Wu, Ming-Ya; Hung, Yi-Lin; Lin, Shi-Yow
2011-05-01
A pendant drop tensiometer, coupled with image digitization technology and a best-fitting algorithm, was built to accurately measure the surface tension of glass melts at high temperatures. More than one thousand edge-coordinate points were obtained for a pendant glass drop. These edge points were fitted with the theoretical drop profiles derived from the Young-Laplace equation to determine the surface tension of glass melt. The uncertainty of the surface tension measurements was investigated. The measurement uncertainty (σ) could be related to a newly defined factor of drop profile completeness (Fc): the larger the Fc is, the smaller σ is. Experimental data showed that the uncertainty of the surface tension measurement when using this pendant drop tensiometer could be ±3 mN∕m for glass melts.
Numerical modeling of subsidence in saturated porous media: A mass conservative method
NASA Astrophysics Data System (ADS)
Asadi, Roza; Ataie-Ashtiani, Behzad
2016-11-01
In this paper, a second order accurate cell-centered finite volume method (FVM) is coupled with a finite element method (FEM) to solve the deformation of a saturated porous layer based on Biot's consolidation model. The proposed numerical technique is applied to the fully unstructured triangular grids to simulate actual geological formations. To reconstruct the pressure gradient at control volume faces, the diamond scheme is implemented as a multipoint flux approximation method. Also the least square algorithm is used to interpolate pressure at the vertices from the cell-center values. The stability of this numerical model is studied in comparison to the different FEMs through various examples. It is shown that, although the Taylor-Hood FEM has been introduced as a remedy for violation of the inf-sup condition, it does not entirely remove the non-physical oscillations. Contrary to the linear and Taylor-Hood FEMs, the proposed discretization model provides monotonic solution without imposing any restriction on the mesh or time step size. Compared to the mixed FEM, the method achieves local mass balance with fewer degrees of freedom. To couple the flow and mechanical sub-problems, the fixed-stress operator split is implemented as an iterative sequential method, due to its unconditional stability, accuracy and high rate of convergence. The accuracy of the proposed model is verified via a range of examples including analytical and numerical solutions. The performance of this methodology is assessed through modeling of subsidence in an aquifer-interbed system. This problem illustrates the capability of the model in providing stable solution in heterogeneous domains with complicated shapes.
NASA Astrophysics Data System (ADS)
Du, Xia; Zhao, Dong-Xia; Yang, Zhong-Zhi
2013-02-01
A new approach to characterize and measure bond strength has been developed. First, we propose a method to accurately calculate the potential acting on an electron in a molecule (PAEM) at the saddle point along a chemical bond in situ, denoted by Dpb. Then, a direct method to quickly evaluate bond strength is established. We choose some familiar molecules as models for benchmarking this method. As a practical application, the Dpb of base pairs in DNA along C-H and N-H bonds are obtained for the first time. All results show that C7-H of A-T and C8-H of G-C are the relatively weak bonds that are the injured positions in DNA damage. The significance of this work is twofold: (i) A method is developed to calculate Dpb of various sizable molecules in situ quickly and accurately; (ii) This work demonstrates the feasibility to quickly predict the bond strength in macromolecules.
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Yang, H. Q.
1989-01-01
The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.
Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods
NASA Astrophysics Data System (ADS)
Zhu, Honggeng; Zhang, Rentian; Deng, Dongsheng; Feng, Xusong; Yao, Linbi
2010-06-01
Since the flow in tubular pumping systems is basically along axial direction and passes symmetrically through the impeller, most satisfying the basic hypotheses in the design of impeller and having higher pumping system efficiency in comparison with vertical pumping system, they are being widely applied to low-head pumping engineering. In a pumping station, the fluctuation of water levels in the sump and discharge pool is most common and at most time the pumping system runs under off-design conditions. Hence, the operation of pump has to be flexibly regulated to meet the needs of flow rates, and the selection of regulation method is as important as that of pump to reduce operation cost and achieve economic operation. In this paper, the three dimensional time-averaged Navier-Stokes equations are closed by RNG κ-ɛ turbulent model, and two tubular pumping systems with different regulation methods, equipped with the same pump model but with different designed system structures, are numerically simulated respectively to predict the pumping system performances and analyze the influence of regulation device and help designers make final decision in the selection of design schemes. The computed results indicate that the pumping system with blade-adjusting device needs longer suction box, and the increased hydraulic loss will lower the pumping system efficiency in the order of 1.5%. The pumping system with permanent magnet motor, by means of variable speed regulation, obtains higher system efficiency partly for shorter suction box and partly for different structure design. Nowadays, the varied speed regulation is realized by varied frequency device, the energy consumption of which is about 3˜4% of output power of the motor. Hence, when the efficiency of variable frequency device is considered, the total pumping system efficiency will probably be lower.
Numerical study of reflectance imaging using a parallel Monte Carlo method.
Chen, Cheng; Lu, Jun Q; Li, Kai; Zhao, Suisheng; Brock, R Scott; Hu, Xin-Hua
2007-07-01
Reflectance imaging of biological tissues with visible and near-infrared light has the significant potential to provide a noninvasive and safe imaging modality for diagnosis of dysplastic and malignant lesions in the superficial tissue layers. The difficulty in the extraction of optical and structural parameters lies in the lack of efficient methods for accurate modeling of light scattering in biological tissues of turbid nature. We present a parallel Monte Carlo method for accurate and efficient modeling of reflectance images from turbid tissue phantoms. A parallel Monte Carlo code has been developed with the message passing interface and evaluated on a computing cluster with 16 processing elements. The code was validated against the solutions of the radiative transfer equation on the bidirectional reflection and transmission functions. With this code we investigated numerically the dependence of reflectance image on the imaging system and phantom parameters. The contrasts of reflectance images were found to be nearly independent of the numerical aperture (NA) of the imaging camera despite the fact that reflectance depends on the NA. This enables efficient simulations of the reflectance images using an NA at 1.00. Using heterogeneous tissue phantoms with an embedded region simulating a lesion, we investigated the correlation between the reflectance image profile or contrast and the phantom parameters. It has been shown that the image contrast approaches 0 when the single-scattering albedos of the two regions in the heterogeneous phantoms become matched. Furthermore, a zone of detection has been demonstrated for determination of the thickness of the embedded region and optical parameters from the reflectance image profile and contrast. Therefore, the utility of the reflectance imaging method with visible and near-infrared light has been firmly established. We conclude from these results that the optical parameters of the embedded region can be determined inversely
Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods
ERIC Educational Resources Information Center
Maase, Eric L.; High, Karen A.
2008-01-01
"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…
Alanazi, Hamdan O; Abdullah, Abdul Hanan; Qureshi, Kashif Naseer
2017-04-01
Recently, Artificial Intelligence (AI) has been used widely in medicine and health care sector. In machine learning, the classification or prediction is a major field of AI. Today, the study of existing predictive models based on machine learning methods is extremely active. Doctors need accurate predictions for the outcomes of their patients' diseases. In addition, for accurate predictions, timing is another significant factor that influences treatment decisions. In this paper, existing predictive models in medicine and health care have critically reviewed. Furthermore, the most famous machine learning methods have explained, and the confusion between a statistical approach and machine learning has clarified. A review of related literature reveals that the predictions of existing predictive models differ even when the same dataset is used. Therefore, existing predictive models are essential, and current methods must be improved.
Kolin, David L.; Ronis, David; Wiseman, Paul W.
2006-01-01
We present the theory and application of reciprocal space image correlation spectroscopy (kICS). This technique measures the number density, diffusion coefficient, and velocity of fluorescently labeled macromolecules in a cell membrane imaged on a confocal, two-photon, or total internal reflection fluorescence microscope. In contrast to r-space correlation techniques, we show kICS can recover accurate dynamics even in the presence of complex fluorophore photobleaching and/or “blinking”. Furthermore, these quantities can be calculated without nonlinear curve fitting, or any knowledge of the beam radius of the exciting laser. The number densities calculated by kICS are less sensitive to spatial inhomogeneity of the fluorophore distribution than densities measured using image correlation spectroscopy. We use simulations as a proof-of-principle to show that number densities and transport coefficients can be extracted using this technique. We present calibration measurements with fluorescent microspheres imaged on a confocal microscope, which recover Stokes-Einstein diffusion coefficients, and flow velocities that agree with single particle tracking measurements. We also show the application of kICS to measurements of the transport dynamics of α5-integrin/enhanced green fluorescent protein constructs in a transfected CHO cell imaged on a total internal reflection fluorescence microscope using charge-coupled device area detection. PMID:16861272
Thompson, A.P.; Swiler, L.P.; Trott, C.R.; Foiles, S.M.; Tucker, G.J.
2015-03-15
We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.
NASA Astrophysics Data System (ADS)
Thompson, A. P.; Swiler, L. P.; Trott, C. R.; Foiles, S. M.; Tucker, G. J.
2015-03-01
We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.
An Improved Method for Accurate and Rapid Measurement of Flight Performance in Drosophila
Babcock, Daniel T.; Ganetzky, Barry
2014-01-01
Drosophila has proven to be a useful model system for analysis of behavior, including flight. The initial flight tester involved dropping flies into an oil-coated graduated cylinder; landing height provided a measure of flight performance by assessing how far flies will fall before producing enough thrust to make contact with the wall of the cylinder. Here we describe an updated version of the flight tester with four major improvements. First, we added a "drop tube" to ensure that all flies enter the flight cylinder at a similar velocity between trials, eliminating variability between users. Second, we replaced the oil coating with removable plastic sheets coated in Tangle-Trap, an adhesive designed to capture live insects. Third, we use a longer cylinder to enable more accurate discrimination of flight ability. Fourth we use a digital camera and imaging software to automate the scoring of flight performance. These improvements allow for the rapid, quantitative assessment of flight behavior, useful for large datasets and large-scale genetic screens. PMID:24561810
NASA Astrophysics Data System (ADS)
Serag, Ahmed; Blesa, Manuel; Moore, Emma J.; Pataky, Rozalia; Sparrow, Sarah A.; Wilkinson, A. G.; MacNaught, Gillian; Semple, Scott I.; Boardman, James P.
2016-03-01
Accurate whole-brain segmentation, or brain extraction, of magnetic resonance imaging (MRI) is a critical first step in most neuroimage analysis pipelines. The majority of brain extraction algorithms have been developed and evaluated for adult data and their validity for neonatal brain extraction, which presents age-specific challenges for this task, has not been established. We developed a novel method for brain extraction of multi-modal neonatal brain MR images, named ALFA (Accurate Learning with Few Atlases). The method uses a new sparsity-based atlas selection strategy that requires a very limited number of atlases ‘uniformly’ distributed in the low-dimensional data space, combined with a machine learning based label fusion technique. The performance of the method for brain extraction from multi-modal data of 50 newborns is evaluated and compared with results obtained using eleven publicly available brain extraction methods. ALFA outperformed the eleven compared methods providing robust and accurate brain extraction results across different modalities. As ALFA can learn from partially labelled datasets, it can be used to segment large-scale datasets efficiently. ALFA could also be applied to other imaging modalities and other stages across the life course.
Serag, Ahmed; Blesa, Manuel; Moore, Emma J; Pataky, Rozalia; Sparrow, Sarah A; Wilkinson, A G; Macnaught, Gillian; Semple, Scott I; Boardman, James P
2016-03-24
Accurate whole-brain segmentation, or brain extraction, of magnetic resonance imaging (MRI) is a critical first step in most neuroimage analysis pipelines. The majority of brain extraction algorithms have been developed and evaluated for adult data and their validity for neonatal brain extraction, which presents age-specific challenges for this task, has not been established. We developed a novel method for brain extraction of multi-modal neonatal brain MR images, named ALFA (Accurate Learning with Few Atlases). The method uses a new sparsity-based atlas selection strategy that requires a very limited number of atlases 'uniformly' distributed in the low-dimensional data space, combined with a machine learning based label fusion technique. The performance of the method for brain extraction from multi-modal data of 50 newborns is evaluated and compared with results obtained using eleven publicly available brain extraction methods. ALFA outperformed the eleven compared methods providing robust and accurate brain extraction results across different modalities. As ALFA can learn from partially labelled datasets, it can be used to segment large-scale datasets efficiently. ALFA could also be applied to other imaging modalities and other stages across the life course.
A method of numerically controlled machine part programming
NASA Technical Reports Server (NTRS)
1970-01-01
Computer program is designed for automatically programmed tools. Preprocessor computes desired tool path and postprocessor computes actual commands causing machine tool to follow specific path. It is used on a Cincinnati ATC-430 numerically controlled machine tool.
Some numerical methods for dosimetry: Extremely low frequencies to microwave frequencies
NASA Astrophysics Data System (ADS)
Gandhi, Om P.
1995-01-01
This paper describes some of the numerical methods that have been developed for calculations of induced electric fields, current densities, and specific absorption rates for anatomically based heterogeneous models of the human body with increasingly finer resolutions. These methods, namely, the impedance method and the finite difference time domain (FDTD) method, have been used for dosimetric calculations for a number of bioelectromagnetic problems for whole-body or partial-body exposures, for far-field or near-field sources, and for CW or transient fields. The paper gives detailed calculations for some recent applications such as currents induced in the user's body by the electromagnetic fields (emfs) of electric blankets using the impedance method, coupling of an ultrawideband pulse using the frequency-dependent FDTD method incorporating dispersive properties of the various tissues, and specific absorption rate distributions in the head for emfs of cellular telephones. Because of accurate modeling of tissue heterogeneities and shapes, these methods are likely to play an increasing role in emerging technologies with bioelectromagnetic concerns.
Efficient numerical method for computation of thermohydrodynamics of laminar lubricating films
NASA Technical Reports Server (NTRS)
Elrod, Harold G.
1989-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. The procedure presented here is a sequel to one presented in Leeds in 1986 that was carried out for the one-dimensional case. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. The extent of computation required makes economy in numerical processing of utmost importance. In pursuit of such economy, we here use techniques similar to those for Gaussian quadrature. We show that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes well the transverse temperature distribution.
Basic numerical methods. [of unsteady and transonic flow
NASA Technical Reports Server (NTRS)
Steger, Joseph L.; Van Dalsem, William R.
1989-01-01
Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.
ERIC Educational Resources Information Center
Hughes, Stephen W.
2005-01-01
A little-known method of measuring the volume of small objects based on Archimedes' principle is described, which involves suspending an object in a water-filled container placed on electronic scales. The suspension technique is a variation on the hydrostatic weighing technique used for measuring volume. The suspension method was compared with two…
Calculation of accurate channel spacing of an AWG optical demultiplexer applying proportional method
NASA Astrophysics Data System (ADS)
Seyringer, D.; Hodzic, E.
2015-06-01
We present the proportional method to correct the channel spacing between the transmitted output channels of an AWG. The developed proportional method was applied to 64-channel, 50 GHz AWG and the achieved results confirm very good correlation between designed channel spacing (50 GHz) and the channel spacing calculated from simulated AWG transmission characteristics.
NASA Astrophysics Data System (ADS)
Hrubý, Jan
2012-04-01
Mathematical modeling of the non-equilibrium condensing transonic steam flow in the complex 3D geometry of a steam turbine is a demanding problem both concerning the physical concepts and the required computational power. Available accurate formulations of steam properties IAPWS-95 and IAPWS-IF97 require much computation time. For this reason, the modelers often accept the unrealistic ideal-gas behavior. Here we present a computation scheme based on a piecewise, thermodynamically consistent representation of the IAPWS-95 formulation. Density and internal energy are chosen as independent variables to avoid variable transformations and iterations. On the contrary to the previous Tabular Taylor Series Expansion Method, the pressure and temperature are continuous functions of the independent variables, which is a desirable property for the solution of the differential equations of the mass, energy, and momentum conservation for both phases.
Fully Implicit Numerical Methods for the Baroclinic Primitive Equations
NASA Technical Reports Server (NTRS)
Cohn, S. E.; Isaacson, E.
1984-01-01
A fully implicit code was developed to solve the three-dimensional primitive equations of atmospheric flow. The scheme is second order accurate in time and fourth order accurate in the horizontal and vertical directions. Furthermore, as a result of being fully implicit, the time step is not restricted by the mesh spacing near the poles, nor by the speed of inertia-gravity waves. Rather, the time step, deltat is determined simply by the requirement that it be small enough to adequately resolve the atmospheric flow of interest. The accuracy and efficiency of current models for fine grids should be significantly improved.
Methods for Applying Accurate Digital PCR Analysis on Low Copy DNA Samples
Whale, Alexandra S.; Cowen, Simon; Foy, Carole A.; Huggett, Jim F.
2013-01-01
Digital PCR (dPCR) is a highly accurate molecular approach, capable of precise measurements, offering a number of unique opportunities. However, in its current format dPCR can be limited by the amount of sample that can be analysed and consequently additional considerations such as performing multiplex reactions or pre-amplification can be considered. This study investigated the impact of duplexing and pre-amplification on dPCR analysis by using three different assays targeting a model template (a portion of the Arabidopsis thaliana alcohol dehydrogenase gene). We also investigated the impact of different template types (linearised plasmid clone and more complex genomic DNA) on measurement precision using dPCR. We were able to demonstrate that duplex dPCR can provide a more precise measurement than uniplex dPCR, while applying pre-amplification or varying template type can significantly decrease the precision of dPCR. Furthermore, we also demonstrate that the pre-amplification step can introduce measurement bias that is not consistent between experiments for a sample or assay and so could not be compensated for during the analysis of this data set. We also describe a model for estimating the prevalence of molecular dropout and identify this as a source of dPCR imprecision. Our data have demonstrated that the precision afforded by dPCR at low sample concentration can exceed that of the same template post pre-amplification thereby negating the need for this additional step. Our findings also highlight the technical differences between different templates types containing the same sequence that must be considered if plasmid DNA is to be used to assess or control for more complex templates like genomic DNA. PMID:23472156
Is photometry an accurate and reliable method to assess boar semen concentration?
Camus, A; Camugli, S; Lévêque, C; Schmitt, E; Staub, C
2011-02-01
Sperm concentration assessment is a key point to insure appropriate sperm number per dose in species subjected to artificial insemination (AI). The aim of the present study was to evaluate the accuracy and reliability of two commercially available photometers, AccuCell™ and AccuRead™ pre-calibrated for boar semen in comparison to UltiMate™ boar version 12.3D, NucleoCounter SP100 and Thoma hemacytometer. For each type of instrument, concentration was measured on 34 boar semen samples in quadruplicate and agreement between measurements and instruments were evaluated. Accuracy for both photometers was illustrated by mean of percentage differences to the general mean. It was -0.6% and 0.5% for Accucell™ and Accuread™ respectively, no significant differences were found between instrument and mean of measurement among all equipment. Repeatability for both photometers was 1.8% and 3.2% for AccuCell™ and AccuRead™ respectively. Low differences were observed between instruments (confidence interval 3%) except when hemacytometer was used as a reference. Even though hemacytometer is considered worldwide as the gold standard, it is the more variable instrument (confidence interval 7.1%). The conclusion is that routine photometry measures of raw semen concentration are reliable, accurate and precise using AccuRead™ or AccuCell™. There are multiple steps in semen processing that can induce sperm loss and therefore increase differences between theoretical and real sperm numbers in doses. Potential biases that depend on the workflow but not on the initial photometric measure of semen concentration are discussed.
Mackie, Iain D; Dilabio, Gino A
2010-06-21
B971, PBE and PBE1 density functionals with 6-31G(d) basis sets are shown to accurately describe the binding in dispersion bound dimers. This is achieved through the use of dispersion-correcting potentials (DCPs) in conjunction with counterpoise corrections. DCPs resemble and are applied like conventional effective core potentials that can be used with most computational chemistry programs without code modification. Rather, DCPs are implemented by simple appendage to the input files for these types of programs. Binding energies are predicted to within ca. 11% and monomer separations to within ca. 0.06 A of high-level wavefunction data using B971/6-31G(d)-DCP. Similar results are obtained for PBE and PBE1 with the 6-31G(d) basis sets and DCPs. Although results found using the 3-21G(d) are not as impressive, they never-the-less show promise as a means of initial study for a wide variety of dimers, including those dominated by dispersion, hydrogen-bonding and a mixture of interactions. Notable improvement is found in comparison to M06-2X/6-31G(d) data, e.g., mean absolute deviations for the S22-set of dimers of ca. 13.6 and 16.5% for B971/6-31G(d)-DCP and M06-2X, respectively. However, it should be pointed out that the latter data were obtained using a larger integration grid size since a smaller grid results in different binding energies and geometries for simple dispersion-bound dimers such as methane and ethene.
Accurate Hf isotope determinations of complex zircons using the "laser ablation split stream" method
NASA Astrophysics Data System (ADS)
Fisher, Christopher M.; Vervoort, Jeffery D.; DuFrane, S. Andrew
2014-01-01
The "laser ablation split stream" (LASS) technique is a powerful tool for mineral-scale isotope analyses and in particular, for concurrent determination of age and Hf isotope composition of zircon. Because LASS utilizes two independent mass spectrometers, a large range of masses can be measured during a single ablation, and thus, the same sample volume can be analyzed for multiple geochemical systems. This paper describes a simple analytical setup using a laser ablation system coupled to a single-collector (for U-Pb age determination) and a multicollector (for Hf isotope analyses) inductively coupled plasma mass spectrometer (MC-ICPMS). The ability of the LASS for concurrent Hf + age technique to extract meaningful Hf isotope compositions in isotopically zoned zircon is demonstrated using zircons from two Proterozoic gneisses from northern Idaho, USA. These samples illustrate the potential problems associated with inadvertently sampling multiple age and Hf components in zircons, as well as the potential of LASS to recover meaningful Hf isotope compositions. We suggest that such inadvertent sampling of differing age and Hf components can be a significant cause of excess scatter in Hf isotope analyses and demonstrate that the LASS approach offers a robust solution to these issues. The veracity of the approach is demonstrated by accurate analyses of 10 reference zircons with well-characterized age and Hf isotopic composition, using laser spot diameters of 30 and 40 µm. In order to expand the database of high-precision Lu-Hf isotope analyses of reference zircons, we present 27 new isotope dilution-MC-ICPMS Lu-Hf isotope measurements of five U-Pb zircon standards: FC1, Temora, R33, QGNG, and 91500.
Accurate Simulation of MPPT Methods Performance When Applied to Commercial Photovoltaic Panels
2015-01-01
A new, simple, and quick-calculation methodology to obtain a solar panel model, based on the manufacturers' datasheet, to perform MPPT simulations, is described. The method takes into account variations on the ambient conditions (sun irradiation and solar cells temperature) and allows fast MPPT methods comparison or their performance prediction when applied to a particular solar panel. The feasibility of the described methodology is checked with four different MPPT methods applied to a commercial solar panel, within a day, and under realistic ambient conditions. PMID:25874262
A flux monitoring method for easy and accurate flow rate measurement in pressure-driven flows.
Siria, Alessandro; Biance, Anne-Laure; Ybert, Christophe; Bocquet, Lydéric
2012-03-07
We propose a low-cost and versatile method to measure flow rate in microfluidic channels under pressure-driven flows, thereby providing a simple characterization of the hydrodynamic permeability of the system. The technique is inspired by the current monitoring method usually employed to characterize electro-osmotic flows, and makes use of the measurement of the time-dependent electric resistance inside the channel associated with a moving salt front. We have successfully tested the method in a micrometer-size channel, as well as in a complex microfluidic channel with a varying cross-section, demonstrating its ability in detecting internal shape variations.
Accurate simulation of MPPT methods performance when applied to commercial photovoltaic panels.
Cubas, Javier; Pindado, Santiago; Sanz-Andrés, Ángel
2015-01-01
A new, simple, and quick-calculation methodology to obtain a solar panel model, based on the manufacturers' datasheet, to perform MPPT simulations, is described. The method takes into account variations on the ambient conditions (sun irradiation and solar cells temperature) and allows fast MPPT methods comparison or their performance prediction when applied to a particular solar panel. The feasibility of the described methodology is checked with four different MPPT methods applied to a commercial solar panel, within a day, and under realistic ambient conditions.
Three-Signal Method for Accurate Measurements of Depolarization Ratio with Lidar
NASA Technical Reports Server (NTRS)
Reichardt, Jens; Baumgart, Rudolf; McGee, Thomsa J.
2003-01-01
A method is presented that permits the determination of atmospheric depolarization-ratio profiles from three elastic-backscatter lidar signals with different sensitivity to the state of polarization of the backscattered light. The three-signal method is insensitive to experimental errors and does not require calibration of the measurement, which could cause large systematic uncertainties of the results, as is the case in the lidar technique conventionally used for the observation of depolarization ratios.
A Fast Numerical Method for a Nonlinear Black-Scholes Equation
NASA Astrophysics Data System (ADS)
Koleva, Miglena N.; Vulkov, Lubin G.
2009-11-01
In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.
NASA Astrophysics Data System (ADS)
Ying, Teh Yuan; Yaacob, Nazeeruddin
2013-04-01
In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed. The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluations at each integration step and it gives accuracy of order ten. In addition, GKLM(7,10)-IIIA has stage order seven and being A-stable. Numerical experiments compare the accuracy between GKLM(7,10)-IIIA and the classical 5-stage tenth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKLM(7,10)-IIIA is more accurate than the 5-stage tenth order Gauss-Legendre method because GKLM(7,10)-IIIA has higher stage order.
NASA Astrophysics Data System (ADS)
Ying, Teh Yuan; Yaacob, Nazeeruddin
2013-04-01
In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.
Dahdouh, S; Varsier, N; Nunez Ochoa, M A; Wiart, J; Peyman, A; Bloch, I
2016-02-21
Numerical dosimetry studies require the development of accurate numerical 3D models of the human body. This paper proposes a novel method for building 3D heterogeneous young children models combining results obtained from a semi-automatic multi-organ segmentation algorithm and an anatomy deformation method. The data consist of 3D magnetic resonance images, which are first segmented to obtain a set of initial tissues. A deformation procedure guided by the segmentation results is then developed in order to obtain five young children models ranging from the age of 5 to 37 months. By constraining the deformation of an older child model toward a younger one using segmentation results, we assure the anatomical realism of the models. Using the proposed framework, five models, containing thirteen tissues, are built. Three of these models are used in a prospective dosimetry study to analyze young child exposure to radiofrequency electromagnetic fields. The results lean to show the existence of a relationship between age and whole body exposure. The results also highlight the necessity to specifically study and develop measurements of child tissues dielectric properties.
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Govers, Gerard
2015-07-01
The stream power equation is commonly used to model river incision into bedrock. Although specific conditions allow an analytical approach, finite difference methods (FDMs) are most frequently used to solve this equation. FDMs inevitably suffer from numerical smearing which may affect their suitability for transient river incision modeling. We propose the use of a finite volume method (FVM) which is total variation diminishing (TVD) to simulate river incision in a more accurate way. The TVD_FVM is designed to simulate sharp discontinuities, making it very suitable to simulate river incision pulses. We show that the TVD_FVM is much better capable of preserving propagating knickpoints than FDMs, using Niagara Falls as an example. Comparison of numerical results obtained using the TVD_FVM with analytical solutions shows a very good agreement. Furthermore, the uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. The high accuracy of the TVD_FDM allows correct simulation of transient incision waves as a consequence of older uplift pulses. This implies that the TVD_FVM is much more suitable than FDMs to reconstruct regional uplift histories from current river profile morphology and to simulate river incision processes in general.
NASA Astrophysics Data System (ADS)
Dahdouh, S.; Varsier, N.; Nunez Ochoa, M. A.; Wiart, J.; Peyman, A.; Bloch, I.
2016-02-01
Numerical dosimetry studies require the development of accurate numerical 3D models of the human body. This paper proposes a novel method for building 3D heterogeneous young children models combining results obtained from a semi-automatic multi-organ segmentation algorithm and an anatomy deformation method. The data consist of 3D magnetic resonance images, which are first segmented to obtain a set of initial tissues. A deformation procedure guided by the segmentation results is then developed in order to obtain five young children models ranging from the age of 5 to 37 months. By constraining the deformation of an older child model toward a younger one using segmentation results, we assure the anatomical realism of the models. Using the proposed framework, five models, containing thirteen tissues, are built. Three of these models are used in a prospective dosimetry study to analyze young child exposure to radiofrequency electromagnetic fields. The results lean to show the existence of a relationship between age and whole body exposure. The results also highlight the necessity to specifically study and develop measurements of child tissues dielectric properties.
NASA Astrophysics Data System (ADS)
Russo, A.; Zuccarello, B.
2007-07-01
The paper presents a theoretical-numerical hybrid method for determining the stresses distribution in composite laminates containing a circular hole and subjected to uniaxial tensile loading. The method is based upon an appropriate corrective function allowing a simple and rapid evaluation of stress distributions in a generic plate of finite width with a hole based on the theoretical stresses distribution in an infinite plate with the same hole geometry and material. In order to verify the accuracy of the method proposed, various numerical and experimental tests have been performed by considering different laminate lay-ups; in particular, the experimental results have shown that a combined use of the method proposed and the well-know point-stress criterion leads to reliable strength predictions for GFRP or CFRP laminates with a circular hole.
A numerical analysis method for evaluating rod lenses using the Monte Carlo method.
Yoshida, Shuhei; Horiuchi, Shuma; Ushiyama, Zenta; Yamamoto, Manabu
2010-12-20
We propose a numerical analysis method for evaluating GRIN lenses using the Monte Carlo method. Actual measurements of the modulation transfer function (MTF) of a GRIN lens using this method closely match those made by conventional methods. Experimentally, the MTF is measured using a square wave chart, and is then calculated based on the distribution of output strength on the chart. In contrast, the general method using computers evaluates the MTF based on a spot diagram made by an incident point light source. However the results differ greatly from those from experiments. We therefore developed an evaluation method similar to the experimental system based on the Monte Carlo method and verified that it more closely matches the experimental results than the conventional method.
NASA Technical Reports Server (NTRS)
Desmarais, R. N.
1982-01-01
The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.
A mass conserving level set method for detailed numerical simulation of liquid atomization
Luo, Kun; Shao, Changxiao; Yang, Yue; Fan, Jianren
2015-10-01
An improved mass conserving level set method for detailed numerical simulations of liquid atomization is developed to address the issue of mass loss in the existing level set method. This method introduces a mass remedy procedure based on the local curvature at the interface, and in principle, can ensure the absolute mass conservation of the liquid phase in the computational domain. Three benchmark cases, including Zalesak's disk, a drop deforming in a vortex field, and the binary drop head-on collision, are simulated to validate the present method, and the excellent agreement with exact solutions or experimental results is achieved. It is shown that the present method is able to capture the complex interface with second-order accuracy and negligible additional computational cost. The present method is then applied to study more complex flows, such as a drop impacting on a liquid film and the swirling liquid sheet atomization, which again, demonstrates the advantages of mass conservation and the capability to represent the interface accurately.
Mikesell, T. Dylan; Malcolm, Alison E.; Yang, Di; Haney, Matthew M.
2015-01-01
Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here, we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We illustrate the differences of all three methods compared to one another using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has better time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements. DTW is a new tool that may find new applications in seismology and other geophysical methods (e.g., as a waveform inversion misfit function).
SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS
NASA Technical Reports Server (NTRS)
Frisch, H. P.
1994-01-01
SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any
Zhang, Jie; Draxl, Caroline; Hopson, Thomas; Monache, Luca Delle; Vanvyve, Emilie; Hodge, Bri-Mathias
2015-10-01
Numerical weather prediction (NWP) models have been widely used for wind resource assessment. Model runs with higher spatial resolution are generally more accurate, yet extremely computational expensive. An alternative approach is to use data generated by a low resolution NWP model, in conjunction with statistical methods. In order to analyze the accuracy and computational efficiency of different types of NWP-based wind resource assessment methods, this paper performs a comparison of three deterministic and probabilistic NWP-based wind resource assessment methodologies: (i) a coarse resolution (0.5 degrees x 0.67 degrees) global reanalysis data set, the Modern-Era Retrospective Analysis for Research and Applications (MERRA); (ii) an analog ensemble methodology based on the MERRA, which provides both deterministic and probabilistic predictions; and (iii) a fine resolution (2-km) NWP data set, the Wind Integration National Dataset (WIND) Toolkit, based on the Weather Research and Forecasting model. Results show that: (i) as expected, the analog ensemble and WIND Toolkit perform significantly better than MERRA confirming their ability to downscale coarse estimates; (ii) the analog ensemble provides the best estimate of the multi-year wind distribution at seven of the nine sites, while the WIND Toolkit is the best at one site; (iii) the WIND Toolkit is more accurate in estimating the distribution of hourly wind speed differences, which characterizes the wind variability, at five of the available sites, with the analog ensemble being best at the remaining four locations; and (iv) the analog ensemble computational cost is negligible, whereas the WIND Toolkit requires large computational resources. Future efforts could focus on the combination of the analog ensemble with intermediate resolution (e.g., 10-15 km) NWP estimates, to considerably reduce the computational burden, while providing accurate deterministic estimates and reliable probabilistic assessments.
Yoshidome, Takashi; Ekimoto, Toru; Matubayasi, Nobuyuki; Harano, Yuichi; Kinoshita, Masahiro; Ikeguchi, Mitsunori
2015-05-07
The hydration free energy (HFE) is a crucially important physical quantity to discuss various chemical processes in aqueous solutions. Although an explicit-solvent computation with molecular dynamics (MD) simulations is a preferable treatment of the HFE, huge computational load has been inevitable for large, complex solutes like proteins. In the present paper, we propose an efficient computation method for the HFE. In our method, the HFE is computed as a sum of 〈UUV〉/2 (〈UUV〉 is the ensemble average of the sum of pair interaction energy between solute and water molecule) and the water reorganization term mainly reflecting the excluded volume effect. Since 〈UUV〉 can readily be computed through a MD of the system composed of solute and water, an efficient computation of the latter term leads to a reduction of computational load. We demonstrate that the water reorganization term can quantitatively be calculated using the morphometric approach (MA) which expresses the term as the linear combinations of the four geometric measures of a solute and the corresponding coefficients determined with the energy representation (ER) method. Since the MA enables us to finish the computation of the solvent reorganization term in less than 0.1 s once the coefficients are determined, the use of the MA enables us to provide an efficient computation of the HFE even for large, complex solutes. Through the applications, we find that our method has almost the same quantitative performance as the ER method with substantial reduction of the computational load.
Highly effective and accurate weak point monitoring method for advanced design rule (1x nm) devices
NASA Astrophysics Data System (ADS)
Ahn, Jeongho; Seong, ShiJin; Yoon, Minjung; Park, Il-Suk; Kim, HyungSeop; Ihm, Dongchul; Chin, Soobok; Sivaraman, Gangadharan; Li, Mingwei; Babulnath, Raghav; Lee, Chang Ho; Kurada, Satya; Brown, Christine; Galani, Rajiv; Kim, JaeHyun
2014-04-01
Historically when we used to manufacture semiconductor devices for 45 nm or above design rules, IC manufacturing yield was mainly determined by global random variations and therefore the chip manufacturers / manufacturing team were mainly responsible for yield improvement. With the introduction of sub-45 nm semiconductor technologies, yield started to be dominated by systematic variations, primarily centered on resolution problems, copper/low-k interconnects and CMP. These local systematic variations, which have become decisively greater than global random variations, are design-dependent [1, 2] and therefore designers now share the responsibility of increasing yield with manufacturers / manufacturing teams. A widening manufacturing gap has led to a dramatic increase in design rules that are either too restrictive or do not guarantee a litho/etch hotspot-free design. The semiconductor industry is currently limited to 193 nm scanners and no relief is expected from the equipment side to prevent / eliminate these systematic hotspots. Hence we have seen a lot of design houses coming up with innovative design products to check hotspots based on model based lithography checks to validate design manufacturability, which will also account for complex two-dimensional effects that stem from aggressive scaling of 193 nm lithography. Most of these hotspots (a.k.a., weak points) are especially seen on Back End of the Line (BEOL) process levels like Mx ADI, Mx Etch and Mx CMP. Inspecting some of these BEOL levels can be extremely challenging as there are lots of wafer noises or nuisances that can hinder an inspector's ability to detect and monitor the defects or weak points of interest. In this work we have attempted to accurately inspect the weak points using a novel broadband plasma optical inspection approach that enhances defect signal from patterns of interest (POI) and precisely suppresses surrounding wafer noises. This new approach is a paradigm shift in wafer inspection
NASA Astrophysics Data System (ADS)
Shukla, K.; Wang, Y.; Jaiswal, P.
2014-12-01
In a porous medium the seismic energy not only propagates through matrix but also through pore-fluids. The differential movement between sediment grains of the matrix and interstitial fluid generates a diffusive wave which is commonly referred to as the slow P-wave. A combined system of equation which includes both elastic and diffusive phases is known as the poroelasticity. Analyzing seismic data through poroelastic modeling results in accurate interpretation of amplitude and separation of wave modes, leading to more accurate estimation of geomehanical properties of rocks. Despite its obvious multi-scale application, from sedimentary reservoir characterization to deep-earth fractured crust, poroelasticity remains under-developed primarily due to the complex nature of its constituent equations. We present a detail formulation of poroleastic wave equations for isotropic media by combining the Biot's and Newtonian mechanics. System of poroelastic wave equation constitutes for eight time dependent hyperbolic PDEs in 2D whereas in case of 3D number goes up to thirteen. Eigen decomposition of Jacobian of these systems confirms the presence of an additional slow-P wave phase with velocity lower than shear wave, posing stability issues on numerical scheme. To circumvent the issue, we derived a numerical scheme using nodal discontinuous Galerkin approach by adopting the triangular meshes in 2D which is extended to tetrahedral for 3D problems. In our nodal DG approach the basis function over a triangular element is interpolated using Legendre-Gauss-Lobatto (LGL) function leading to a more accurate local solutions than in the case of simple DG. We have tested the numerical scheme for poroelastic media in 1D and 2D case, and solution obtained for the systems offers high accuracy in results over other methods such as finite difference , finite volume and pseudo-spectral. The nodal nature of our approach makes it easy to convert the application into a multi-threaded algorithm
An Accurate Method for Free Vibration Analysis of Structures with Application to Plates
NASA Astrophysics Data System (ADS)
KEVORKIAN, S.; PASCAL, M.
2001-10-01
In this work, the continuous element method which has been used as an alternative to the finite element method of vibration analysis of frames is applied to more general structures like 3-D continuum and rectangular plates. The method is based on the concept of the so-called impedance matrix giving in the frequency domain, the linear relation between the generalized displacements of the boundaries and the generalized forces exerted on these boundaries. For a 3-D continuum, the concept of impedance matrix is introduced assuming a particular kind of boundary conditions. For rectangular plates, this new development leads to the solution of vibration problems for boundary conditions other than the simply supported ones.
A new method based on the subpixel Gaussian model for accurate estimation of asteroid coordinates
NASA Astrophysics Data System (ADS)
Savanevych, V. E.; Briukhovetskyi, O. B.; Sokovikova, N. S.; Bezkrovny, M. M.; Vavilova, I. B.; Ivashchenko, Yu. M.; Elenin, L. V.; Khlamov, S. V.; Movsesian, Ia. S.; Dashkova, A. M.; Pogorelov, A. V.
2015-08-01
We describe a new iteration method to estimate asteroid coordinates, based on a subpixel Gaussian model of the discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational space (the set of pixel potentials) of the CCD frame. In this model, the kind of coordinate distribution of the photons hitting a pixel of the CCD frame is known a priori, while the associated parameters are determined from a real digital object image. The method that is developed, which is flexible in adapting to any form of object image, has a high measurement accuracy along with a low calculating complexity, due to the maximum-likelihood procedure that is implemented to obtain the best fit instead of a least-squares method and Levenberg-Marquardt algorithm for minimization of the quadratic form. Since 2010, the method has been tested as the basis of our Collection Light Technology (COLITEC) software, which has been installed at several observatories across the world with the aim of the automatic discovery of asteroids and comets in sets of CCD frames. As a result, four comets (C/2010 X1 (Elenin), P/2011 NO1(Elenin), C/2012 S1 (ISON) and P/2013 V3 (Nevski)) as well as more than 1500 small Solar system bodies (including five near-Earth objects (NEOs), 21 Trojan asteroids of Jupiter and one Centaur object) have been discovered. We discuss these results, which allowed us to compare the accuracy parameters of the new method and confirm its efficiency. In 2014, the COLITEC software was recommended to all members of the Gaia-FUN-SSO network for analysing observations as a tool to detect faint moving objects in frames.
NASA Astrophysics Data System (ADS)
Barenbrug, Theo M. A. O. M.; Peters, E. A. J. F. (Frank); Schieber, Jay D.
2002-11-01
In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common "naı̈ve simulation method" accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naı̈ve method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Öttinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the "corrected simulation method" to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces.
Modeling supersonic combustion using a fully-implicit numerical method
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Wilson, Gregory J.
1990-01-01
A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.
A novel method to accurately locate and count large numbers of steps by photobleaching
Tsekouras, Konstantinos; Custer, Thomas C.; Jashnsaz, Hossein; Walter, Nils G.; Pressé, Steve
2016-01-01
Photobleaching event counting is a single-molecule fluorescence technique that is increasingly being used to determine the stoichiometry of protein and RNA complexes composed of many subunits in vivo as well as in vitro. By tagging protein or RNA subunits with fluorophores, activating them, and subsequently observing as the fluorophores photobleach, one obtains information on the number of subunits in a complex. The noise properties in a photobleaching time trace depend on the number of active fluorescent subunits. Thus, as fluorophores stochastically photobleach, noise properties of the time trace change stochastically, and these varying noise properties have created a challenge in identifying photobleaching steps in a time trace. Although photobleaching steps are often detected by eye, this method only works for high individual fluorophore emission signal-to-noise ratios and small numbers of fluorophores. With filtering methods or currently available algorithms, it is possible to reliably identify photobleaching steps for up to 20–30 fluorophores and signal-to-noise ratios down to ∼1. Here we present a new Bayesian method of counting steps in photobleaching time traces that takes into account stochastic noise variation in addition to complications such as overlapping photobleaching events that may arise from fluorophore interactions, as well as on-off blinking. Our method is capable of detecting ≥50 photobleaching steps even for signal-to-noise ratios as low as 0.1, can find up to ≥500 steps for more favorable noise profiles, and is computationally inexpensive. PMID:27654946
Technology Transfer Automated Retrieval System (TEKTRAN)
The rapid advances in analytical chromatography equipment have made the reliable and reproducible measurement of a wide range of plant chemical components possible. Full chemical characterization of a given plant material is possible with the new mass spectrometers currently available. New methods a...
A Robust Method of Vehicle Stability Accurate Measurement Using GPS and INS
NASA Astrophysics Data System (ADS)
Miao, Zhibin; Zhang, Hongtian; Zhang, Jinzhu
2015-12-01
With the development of the vehicle industry, controlling stability has become more and more important. Techniques of evaluating vehicle stability are in high demand. Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is a very practical method to get high-precision measurement data. Usually, the Kalman filter is used to fuse the data from GPS and INS. In this paper, a robust method is used to measure vehicle sideslip angle and yaw rate, which are two important parameters for vehicle stability. First, a four-wheel vehicle dynamic model is introduced, based on sideslip angle and yaw rate. Second, a double level Kalman filter is established to fuse the data from Global Positioning System and Inertial Navigation System. Then, this method is simulated on a sample vehicle, using Carsim software to test the sideslip angle and yaw rate. Finally, a real experiment is made to verify the advantage of this approach. The experimental results showed the merits of this method of measurement and estimation, and the approach can meet the design requirements of the vehicle stability controller.
A new noninvasive method for the accurate and precise assessment of varicose vein diameters.
Baldassarre, Damiano; Pustina, Linda; Castelnuovo, Samuela; Bondioli, Alighiero; Carlà, Matteo; Sirtori, Cesare R
2003-01-01
The feasibility and reproducibility of a new ultrasonic method for the direct assessment of maximal varicose vein diameter (VVD) were evaluated. A study was also performed to demonstrate the capacity of the method to detect changes in venous diameter induced by a pharmacologic treatment. Patients with varicose vein disease were recruited. A method that allows the precise positioning of patient and transducer and performance of scans in a gel-bath was developed. Maximal VVD was recorded both in the standing and supine positions. The intraassay reproducibility was determined by replicate scans made within 15 minutes in both positions. The interobserver variability was assessed by comparing VVDs measured during the first phase baseline examination with those obtained during baseline examinations in the second phase of the study. The error in reproducibility of VVD determinations was 5.3% when diameters were evaluated in the standing position and 6.4% when assessed in the supine position. The intramethod agreement was high, with a bias between readings of 0.06 +/- 0.18 mm and of -0.02 +/- 0.19 mm, respectively, in standing and supine positions. Correlation coefficients were better than 0.99 in both positions. The method appears to be sensitive enough to detect small changes in VVDs induced by treatments. The proposed technique provides a tool of potential valid use in the detection and in vivo monitoring of VVD changes in patients with varicose vein disease. The method offers an innovative approach to obtain a quantitative assessment of varicose vein progression and of treatment effects, thus providing a basis for epidemiologic surveys.
Swamidass, S. Joshua; Azencott, Chloé-Agathe; Lin, Ting-Wan; Gramajo, Hugo; Tsai, Sheryl; Baldi, Pierre
2009-01-01
Given activity training data from Hight-Throughput Screening (HTS) experiments, virtual High-Throughput Screening (vHTS) methods aim to predict in silico the activity of untested chemicals. We present a novel method, the Influence Relevance Voter (IRV), specifically tailored for the vHTS task. The IRV is a low-parameter neural network which refines a k-nearest neighbor classifier by non-linearly combining the influences of a chemical's neighbors in the training set. Influences are decomposed, also non-linearly, into a relevance component and a vote component. The IRV is benchmarked using the data and rules of two large, open, competitions, and its performance compared to the performance of other participating methods, as well as of an in-house Support Vector Machine (SVM) method. On these benchmark datasets, IRV achieves state-of-the-art results, comparable to the SVM in one case, and significantly better than the SVM in the other, retrieving three times as many actives in the top 1% of its prediction-sorted list. The IRV presents several other important advantages over SVMs and other methods: (1) the output predictions have a probabilistic semantic; (2) the underlying inferences are interpretable; (3) the training time is very short, on the order of minutes even for very large data sets; (4) the risk of overfitting is minimal, due to the small number of free parameters; and (5) additional information can easily be incorporated into the IRV architecture. Combined with its performance, these qualities make the IRV particularly well suited for vHTS. PMID:19391629
Application of numerical methods to planetary radiowave scattering
NASA Technical Reports Server (NTRS)
Simpson, Richard A.; Tyler, G. Leonard
1987-01-01
Existing numerical techniques for the solution of scattering problems were investigated to determine those which might be applicable to planetary surface studies, with the goal of improving the interpretation of radar data from Venus, Mars, the Moon, and icy satellites. The general characteristics of the models are described along with computational concerns. In particular, the Numerical Electrogmatics Code (NEC) developed at the Lawrence Livermore Laboratory is discussed. Though not developed for random rough surfaces, the NEC contains elements which may be generalized and which could be valuable in the study of scattering by planetary surfaces.
The Design of CAL Packages for Teaching Numerical Methods to Chemistry Students.
ERIC Educational Resources Information Center
Norris, A. C.
1979-01-01
Discusses the design of computational exercises useful for a course in numerical methods for chemists. Some of the exercises make use of available programs while others require the student to write programs incorporating numerical routines. The emphasis throughout is on the use of numerical methods to solve chemical problems. (Author)
Exact kinetic energy enables accurate evaluation of weak interactions by the FDE-vdW method
Sinha, Debalina; Pavanello, Michele
2015-08-28
The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term the Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.
Exact kinetic energy enables accurate evaluation of weak interactions by the FDE-vdW method.
Sinha, Debalina; Pavanello, Michele
2015-08-28
The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term the Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.
A Variable Coefficient Method for Accurate Monte Carlo Simulation of Dynamic Asset Price
NASA Astrophysics Data System (ADS)
Li, Yiming; Hung, Chih-Young; Yu, Shao-Ming; Chiang, Su-Yun; Chiang, Yi-Hui; Cheng, Hui-Wen
2007-07-01
In this work, we propose an adaptive Monte Carlo (MC) simulation technique to compute the sample paths for the dynamical asset price. In contrast to conventional MC simulation with constant drift and volatility (μ,σ), our MC simulation is performed with variable coefficient methods for (μ,σ) in the solution scheme, where the explored dynamic asset pricing model starts from the formulation of geometric Brownian motion. With the method of simultaneously updated (μ,σ), more than 5,000 runs of MC simulation are performed to fulfills basic accuracy of the large-scale computation and suppresses statistical variance. Daily changes of stock market index in Taiwan and Japan are investigated and analyzed.
NASA Technical Reports Server (NTRS)
Kemp, James Herbert (Inventor); Talukder, Ashit (Inventor); Lambert, James (Inventor); Lam, Raymond (Inventor)
2008-01-01
A computer-implemented system and method of intra-oral analysis for measuring plaque removal is disclosed. The system includes hardware for real-time image acquisition and software to store the acquired images on a patient-by-patient basis. The system implements algorithms to segment teeth of interest from surrounding gum, and uses a real-time image-based morphing procedure to automatically overlay a grid onto each segmented tooth. Pattern recognition methods are used to classify plaque from surrounding gum and enamel, while ignoring glare effects due to the reflection of camera light and ambient light from enamel regions. The system integrates these components into a single software suite with an easy-to-use graphical user interface (GUI) that allows users to do an end-to-end run of a patient record, including tooth segmentation of all teeth, grid morphing of each segmented tooth, and plaque classification of each tooth image.
Methods to achieve accurate projection of regional and global raster databases
Usery, E.L.; Seong, J.C.; Steinwand, D.R.; Finn, M.P.
2002-01-01
This research aims at building a decision support system (DSS) for selecting an optimum projection considering various factors, such as pixel size, areal extent, number of categories, spatial pattern of categories, resampling methods, and error correction methods. Specifically, this research will investigate three goals theoretically and empirically and, using the already developed empirical base of knowledge with these results, develop an expert system for map projection of raster data for regional and global database modeling. The three theoretical goals are as follows: (1) The development of a dynamic projection that adjusts projection formulas for latitude on the basis of raster cell size to maintain equal-sized cells. (2) The investigation of the relationships between the raster representation and the distortion of features, number of categories, and spatial pattern. (3) The development of an error correction and resampling procedure that is based on error analysis of raster projection.
Krokhotin, Andrey; Dokholyan, Nikolay V
2015-01-01
Computational methods can provide significant insights into RNA structure and dynamics, bridging the gap in our understanding of the relationship between structure and biological function. Simulations enrich and enhance our understanding of data derived on the bench, as well as provide feasible alternatives to costly or technically challenging experiments. Coarse-grained computational models of RNA are especially important in this regard, as they allow analysis of events occurring in timescales relevant to RNA biological function, which are inaccessible through experimental methods alone. We have developed a three-bead coarse-grained model of RNA for discrete molecular dynamics simulations. This model is efficient in de novo prediction of short RNA tertiary structure, starting from RNA primary sequences of less than 50 nucleotides. To complement this model, we have incorporated additional base-pairing constraints and have developed a bias potential reliant on data obtained from hydroxyl probing experiments that guide RNA folding to its correct state. By introducing experimentally derived constraints to our computer simulations, we are able to make reliable predictions of RNA tertiary structures up to a few hundred nucleotides. Our refined model exemplifies a valuable benefit achieved through integration of computation and experimental methods.
EEMD based pitch evaluation method for accurate grating measurement by AFM
NASA Astrophysics Data System (ADS)
Li, Changsheng; Yang, Shuming; Wang, Chenying; Jiang, Zhuangde
2016-09-01
The pitch measurement and AFM calibration precision are significantly influenced by the grating pitch evaluation method. This paper presents the ensemble empirical mode decomposition (EEMD) based pitch evaluation method to relieve the accuracy deterioration caused by high and low frequency components of scanning profile during pitch evaluation. The simulation analysis shows that the application of EEMD can improve the pitch accuracy of the FFT-FT algorithm. The pitch error is small when the iteration number of the FFT-FT algorithms was 8. The AFM measurement of the 500 nm-pitch one-dimensional grating shows that the EEMD based pitch evaluation method could improve the pitch precision, especially the grating line position precision, and greatly expand the applicability of the gravity center algorithm when particles and impression marks were distributed on the sample surface. The measurement indicates that the nonlinearity was stable, and the nonlinearity of x axis and forward scanning was much smaller than their counterpart. Finally, a detailed pitch measurement uncertainty evaluation model suitable for commercial AFMs was demonstrated and a pitch uncertainty in the sub-nanometer range was achieved. The pitch uncertainty was reduced about 10% by EEMD.
Numerical Analysis of Hydrodynamics for Bionic Oscillating Hydrofoil Based on Panel Method.
Xue, Gang; Liu, Yanjun; Zhang, Muqun; Ding, Hongpeng
2016-01-01
The kinematics model based on the Slender-Body theory is proposed from the bionic movement of real fish. The Panel method is applied to the hydrodynamic performance analysis innovatively, with the Gauss-Seidel method to solve the Navier-Stokes equations additionally, to evaluate the flexible deformation of fish in swimming accurately when satisfying the boundary conditions. A physical prototype to mimic the shape of tuna is developed with the revolutionized technology of rapid prototyping manufacturing. The hydrodynamic performance for rigid oscillating hydrofoil is analyzed with the proposed method, and it shows good coherence with the cases analyzed by the commercial software Fluent and the experimental data from robofish. Furthermore, the hydrodynamic performance of coupled hydrofoil, which consisted of flexible fish body and rigid caudal fin, is analyzed with the proposed method. It shows that the caudal fin has great influence on trailing vortex shedding and the phase angle is the key factor on hydrodynamic performance. It is verified that the shape of trailing vortex is similar to the image of the motion curve at the trailing edge as the assumption of linear vortex plane under the condition of small downwash velocity. The numerical analysis of hydrodynamics for bionic movement based on the Panel method has certain value to reveal the fish swimming mechanism.
Numerical Analysis of Hydrodynamics for Bionic Oscillating Hydrofoil Based on Panel Method
2016-01-01
The kinematics model based on the Slender-Body theory is proposed from the bionic movement of real fish. The Panel method is applied to the hydrodynamic performance analysis innovatively, with the Gauss-Seidel method to solve the Navier-Stokes equations additionally, to evaluate the flexible deformation of fish in swimming accurately when satisfying the boundary conditions. A physical prototype to mimic the shape of tuna is developed with the revolutionized technology of rapid prototyping manufacturing. The hydrodynamic performance for rigid oscillating hydrofoil is analyzed with the proposed method, and it shows good coherence with the cases analyzed by the commercial software Fluent and the experimental data from robofish. Furthermore, the hydrodynamic performance of coupled hydrofoil, which consisted of flexible fish body and rigid caudal fin, is analyzed with the proposed method. It shows that the caudal fin has great influence on trailing vortex shedding and the phase angle is the key factor on hydrodynamic performance. It is verified that the shape of trailing vortex is similar to the image of the motion curve at the trailing edge as the assumption of linear vortex plane under the condition of small downwash velocity. The numerical analysis of hydrodynamics for bionic movement based on the Panel method has certain value to reveal the fish swimming mechanism. PMID:27578959
Numerical modeling of shallow magma intrusions with finite element method
NASA Astrophysics Data System (ADS)
Chen, Tielin; Cheng, Shaozhen; Fang, Qian; Zhou, Cheng
2017-03-01
A numerical approach for simulation of magma intrusion process, considering the couplings of the stress distribution, the viscous fluid flow of magma, and the fracturing of host rock, has been developed to investigate the mechanisms of fracture initiation and propagation in host rock during magma intrusion without pre-placing a set of fractures. The study focused on the dike intrusions filled with injected viscous magma in shallow sediments. A series of numerical modellings were carried out to simulate the process of magma intrusion in host rocks, with particular attention on the magma propagation processes and the formation of intrusion shapes. The model materials were Mohr-Coulomb materials with tension failure and shear failure. The scenarios of both stochastically heterogeneous host rocks and layered host rocks were analyzed. The injected magma formed intrusions shapes of (a) dyke, (b) sill, (c) cup-shaped intrusion, (d) saucer-shaped intrusion. The numerical results were in agreement with the experimental and field observed results, which confirmed the adequacy and the power of the numerical approach.
Numerical Simulation of Turbulent Combustion Using Vortex Methods
1990-01-08
Electric Co., Schenectady, October 1988. 2. DOD and EPA Tyndall Conference on Halon, the Ozone Layer and Research on Alternative Chemicals, Tyndall...26th Aerospace Sciences Meetin , January 11-14, Reno, Nevada, AIAA-88-0729. 13. Ghoniem A.F., and Ng K.K., Numerical study of a forced shear layet
Investigation of the Dynamic Contact Angle Using a Direct Numerical Simulation Method.
Zhu, Guangpu; Yao, Jun; Zhang, Lei; Sun, Hai; Li, Aifen; Shams, Bilal
2016-11-15
A large amount of residual oil, which exists as isolated oil slugs, remains trapped in reservoirs after water flooding. Numerous numerical studies are performed to investigate the fundamental flow mechanism of oil slugs to improve flooding efficiency. Dynamic contact angle models are usually introduced to simulate an accurate contact angle and meniscus displacement of oil slugs under a high capillary number. Nevertheless, in the oil slug flow simulation process, it is unnecessary to introduce the dynamic contact angle model because of a negligible change in the meniscus displacement after using the dynamic contact angle model when the capillary number is small. Therefore, a critical capillary number should be introduced to judge whether the dynamic contact model should be incorporated into simulations. In this study, a direct numerical simulation method is employed to simulate the oil slug flow in a capillary tube at the pore scale. The position of the interface between water and the oil slug is determined using the phase-field method. The capacity and accuracy of the model are validated using a classical benchmark: a dynamic capillary filling process. Then, different dynamic contact angle models and the factors that affect the dynamic contact angle are analyzed. The meniscus displacements of oil slugs with a dynamic contact angle and a static contact angle (SCA) are obtained during simulations, and the relative error between them is calculated automatically. The relative error limit has been defined to be 5%, beyond which the dynamic contact angle model needs to be incorporated into the simulation to approach the realistic displacement. Thus, the desired critical capillary number can be determined. A three-dimensional universal chart of critical capillary number, which functions as static contact angle and viscosity ratio, is given to provide a guideline for oil slug simulation. Also, a fitting formula is presented for ease of use.
Numerical methods for multiphysics, multiphase, and multicomponent models for fuel cells
NASA Astrophysics Data System (ADS)
Xue, Guangri
In this dissertation, we design and analyze efficient numerical methods for obtaining accurate solutions to model problems arising in fuel cells. A basic fuel cell model consists of five principles of conservation, namely, mass, momentum, species, charges (electrons and ions), and thermal energy. Overall, transport equations couple with electrochemical processes through source terms to describe reaction kinetics and electro-osmotic drag in the polymer electrolyte. To model multiphase species transport in the porous media and the gas channel of fuel cells, we consider a multiphase mixture model framework. The diffusivity of the two-phase mixture water conservation equation in this model is nonlinear, discontinuous, and degenerate. To handle this difficulty, we developed efficient and fast nonlinear iterative solvers based on the Kirchhoff transformation and nonlinear Dirichlet-Neumann domain decomposition methods. To model the coupling between the multiphase flow in the porous media and the viscous flow in the gas channel of fuel cells, we consider the Darcy-Stokes-Brinkman model, which treats both the Darcy equation and the Stokes equation in a single form of partial differential equation (PDE) but with strongly discontinuous viscosity and permeability coefficients. For this model, we develop robust finite element methods that are uniformly stable with respect to the highly discontinuous coefficients and their jumps. Finally, we develop new numerical methods for the full steady-state 3D multi-physics simulation of liquid-feed direct methanol fuel cells (DMFC), consisting of five fundamental conservation equations: mass, momentum, species, charges, and thermal energy. Fast convergence of nonlinear iteration is achieved in our method.
An Accurate Calibration Method Based on Velocity in a Rotational Inertial Navigation System.
Zhang, Qian; Wang, Lei; Liu, Zengjun; Feng, Peide
2015-07-28
Rotation modulation is an effective method to enhance the accuracy of an inertial navigation system (INS) by modulating the gyroscope drifts and accelerometer bias errors into periodically varying components. The typical RINS drives the inertial measurement unit (IMU) rotation along the vertical axis and the horizontal sensors' errors are modulated, however, the azimuth angle error is closely related to vertical gyro drift, and the vertical gyro drift also should be modulated effectively. In this paper, a new rotation strategy in a dual-axis rotational INS (RINS) is proposed and the drifts of three gyros could be modulated, respectively. Experimental results from a real dual-axis RINS demonstrate that the maximum azimuth angle error is decreased from 0.04° to less than 0.01° during 1 h. Most importantly, the changing of rotation strategy leads to some additional errors in the velocity which is unacceptable in a high-precision INS. Then the paper studies the basic reason underlying horizontal velocity errors in detail and a relevant new calibration method is designed. Experimental results show that after calibration and compensation, the fluctuation and stages in the velocity curve disappear and velocity precision is improved.
Boyle, John J.; Kume, Maiko; Wyczalkowski, Matthew A.; Taber, Larry A.; Pless, Robert B.; Xia, Younan; Genin, Guy M.; Thomopoulos, Stavros
2014-01-01
When mechanical factors underlie growth, development, disease or healing, they often function through local regions of tissue where deformation is highly concentrated. Current optical techniques to estimate deformation can lack precision and accuracy in such regions due to challenges in distinguishing a region of concentrated deformation from an error in displacement tracking. Here, we present a simple and general technique for improving the accuracy and precision of strain estimation and an associated technique for distinguishing a concentrated deformation from a tracking error. The strain estimation technique improves accuracy relative to other state-of-the-art algorithms by directly estimating strain fields without first estimating displacements, resulting in a very simple method and low computational cost. The technique for identifying local elevation of strain enables for the first time the successful identification of the onset and consequences of local strain concentrating features such as cracks and tears in a highly strained tissue. We apply these new techniques to demonstrate a novel hypothesis in prenatal wound healing. More generally, the analytical methods we have developed provide a simple tool for quantifying the appearance and magnitude of localized deformation from a series of digital images across a broad range of disciplines. PMID:25165601
Wang, Jia-Nan; Jin, Jun-Ling; Geng, Yun; Sun, Shi-Ling; Xu, Hong-Liang; Lu, Ying-Hua; Su, Zhong-Min
2013-03-15
Recently, the extreme learning machine neural network (ELMNN) as a valid computing method has been proposed to predict the nonlinear optical property successfully (Wang et al., J. Comput. Chem. 2012, 33, 231). In this work, first, we follow this line of work to predict the electronic excitation energies using the ELMNN method. Significantly, the root mean square deviation of the predicted electronic excitation energies of 90 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) derivatives between the predicted and experimental values has been reduced to 0.13 eV. Second, four groups of molecule descriptors are considered when building the computing models. The results show that the quantum chemical descriptions have the closest intrinsic relation with the electronic excitation energy values. Finally, a user-friendly web server (EEEBPre: Prediction of electronic excitation energies for BODIPY dyes), which is freely accessible to public at the web site: http://202.198.129.218, has been built for prediction. This web server can return the predicted electronic excitation energy values of BODIPY dyes that are high consistent with the experimental values. We hope that this web server would be helpful to theoretical and experimental chemists in related research.
An Accurate Calibration Method Based on Velocity in a Rotational Inertial Navigation System
Zhang, Qian; Wang, Lei; Liu, Zengjun; Feng, Peide
2015-01-01
Rotation modulation is an effective method to enhance the accuracy of an inertial navigation system (INS) by modulating the gyroscope drifts and accelerometer bias errors into periodically varying components. The typical RINS drives the inertial measurement unit (IMU) rotation along the vertical axis and the horizontal sensors’ errors are modulated, however, the azimuth angle error is closely related to vertical gyro drift, and the vertical gyro drift also should be modulated effectively. In this paper, a new rotation strategy in a dual-axis rotational INS (RINS) is proposed and the drifts of three gyros could be modulated, respectively. Experimental results from a real dual-axis RINS demonstrate that the maximum azimuth angle error is decreased from 0.04° to less than 0.01° during 1 h. Most importantly, the changing of rotation strategy leads to some additional errors in the velocity which is unacceptable in a high-precision INS. Then the paper studies the basic reason underlying horizontal velocity errors in detail and a relevant new calibration method is designed. Experimental results show that after calibration and compensation, the fluctuation and stages in the velocity curve disappear and velocity precision is improved. PMID:26225983
A novel method for more accurately mapping the surface temperature of ultrasonic transducers.
Axell, Richard G; Hopper, Richard H; Jarritt, Peter H; Oxley, Chris H
2011-10-01
This paper introduces a novel method for measuring the surface temperature of ultrasound transducer membranes and compares it with two standard measurement techniques. The surface temperature rise was measured as defined in the IEC Standard 60601-2-37. The measurement techniques were (i) thermocouple, (ii) thermal camera and (iii) novel infra-red (IR) "micro-sensor." Peak transducer surface measurements taken with the thermocouple and thermal camera were -3.7 ± 0.7 (95% CI)°C and -4.3 ± 1.8 (95% CI)°C, respectively, within the limits of the IEC Standard. Measurements taken with the novel IR micro-sensor exceeded these limits by 3.3 ± 0.9 (95% CI)°C. The ambiguity between our novel method and the standard techniques could have direct patient safety implications because the IR micro-sensor measurements were beyond set limits. The spatial resolution of the measurement technique is not well defined in the IEC Standard and this has to be taken into consideration when selecting which measurement technique is used to determine the maximum surface temperature.
A method for the accurate and smooth approximation of standard thermodynamic functions
NASA Astrophysics Data System (ADS)
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
Practical implementation of an accurate method for multilevel design sensitivity analysis
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.
1987-01-01
Solution techniques for handling large scale engineering optimization problems are reviewed. Potentials for practical applications as well as their limited capabilities are discussed. A new solution algorithm for design sensitivity is proposed. The algorithm is based upon the multilevel substructuring concept to be coupled with the adjoint method of sensitivity analysis. There are no approximations involved in the present algorithm except the usual approximations introduced due to the discretization of the finite element model. Results from the six- and thirty-bar planar truss problems show that the proposed multilevel scheme for sensitivity analysis is more effective (in terms of computer incore memory and the total CPU time) than a conventional (one level) scheme even on small problems. The new algorithm is expected to perform better for larger problems and its applications on the new generation of computer hardwares with 'parallel processing' capability is very promising.
Zhang, Wei; Ma, Hong; Yang, Simon X
2016-03-18
In this research, an improved psychrometer is developed to solve practical issues arising in the relative humidity measurement of challenging drying environments for meat manufacturing in agricultural and agri-food industries. The design in this research focused on the structure of the improved psychrometer, signal conversion, and calculation methods. The experimental results showed the effect of varying psychrometer structure on relative humidity measurement accuracy. An industrial application to dry-cured meat products demonstrated the effective performance of the improved psychrometer being used as a relative humidity measurement sensor in meat-drying rooms. In a drying environment for meat manufacturing, the achieved measurement accuracy for relative humidity using the improved psychrometer was ±0.6%. The system test results showed that the improved psychrometer can provide reliable and long-term stable relative humidity measurements with high accuracy in the drying system of meat products.
An accurate heart beat detection method in the EKG recorded in fMRI system.
Oh, Sung Suk; Chung, Jun-Young; Yoon, Hyo Woon; Park, HyunWook
2007-01-01
The simultaneous recording of functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) provides an efficient signal for the high spatiotemporal brain mapping because each modality provides complementary information. The peak detection in the EEG signal measured in the MR scanner is necessary for removal of the ballistocardiac artifact. Especially, it would be affected by the quality of the EKG signal and the variation of the heart beat rate. Therefore, we propose the peak detection method using a K-teager energy operator (K-TEO) as well as further refinement processes in order to detect precise peaks. We applied this technique to the analysis of simulation waves with random noise and abrupt heat beat changes.
Zhang, Wei; Ma, Hong; Yang, Simon X.
2016-01-01
In this research, an improved psychrometer is developed to solve practical issues arising in the relative humidity measurement of challenging drying environments for meat manufacturing in agricultural and agri-food industries. The design in this research focused on the structure of the improved psychrometer, signal conversion, and calculation methods. The experimental results showed the effect of varying psychrometer structure on relative humidity measurement accuracy. An industrial application to dry-cured meat products demonstrated the effective performance of the improved psychrometer being used as a relative humidity measurement sensor in meat-drying rooms. In a drying environment for meat manufacturing, the achieved measurement accuracy for relative humidity using the improved psychrometer was ±0.6%. The system test results showed that the improved psychrometer can provide reliable and long-term stable relative humidity measurements with high accuracy in the drying system of meat products. PMID:26999161
Accurate treatment of total photoabsorption cross sections by an ab initio time-dependent method
NASA Astrophysics Data System (ADS)
Daud, Mohammad Noh
2014-09-01
A detailed discussion of parallel and perpendicular transitions required for the photoabsorption of a molecule is presented within a time-dependent view. Total photoabsorption cross sections for the first two ultraviolet absorption bands of the N2O molecule corresponding to transitions from the X1 A' state to the 21 A' and 11 A'' states are calculated to test the reliability of the method. By fully considering the property of the electric field polarization vector of the incident light, the method treats the coupling of angular momentum and the parity differently for two kinds of transitions depending on the direction of the vector whether it is: (a) situated parallel in a molecular plane for an electronic transition between states with the same symmetry; (b) situated perpendicular to a molecular plane for an electronic transition between states with different symmetry. Through this, for those transitions, we are able to offer an insightful picture of the dynamics involved and to characterize some new aspects in the photoabsorption process of N2O. Our calculations predicted that the parallel transition to the 21 A' state is the major dissociation pathway which is in qualitative agreement with the experimental observations. Most importantly, a significant improvement in the absolute value of the total cross section over previous theoretical results [R. Schinke, J. Chem. Phys. 134, 064313 (2011), M.N. Daud, G.G. Balint-Kurti, A. Brown, J. Chem. Phys. 122, 054305 (2005), S. Nanbu, M.S. Johnson, J. Phys. Chem. A 108, 8905 (2004)] was obtained.
Accurate treatment of total photoabsorption cross sections by an ab initio time-dependent method
NASA Astrophysics Data System (ADS)
Noh Daud, Mohammad
2014-09-01
A detailed discussion of parallel and perpendicular transitions required for the photoabsorption of a molecule is presented within a time-dependent view. Total photoabsorption cross sections for the first two ultraviolet absorption bands of the N2O molecule corresponding to transitions from the X1A' state to the 21A' and 11A'' states are calculated to test the reliability of the method. By fully considering the property of the electric field polarization vector of the incident light, the method treats the coupling of angular momentum and the parity differently for two kinds of transitions depending on the direction of the vector whether it is: (a) situated parallel in a molecular plane for an electronic transition between states with the same symmetry; (b) situated perpendicular to a molecular plane for an electronic transition between states with different symmetry. Through this, for those transitions, we are able to offer an insightful picture of the dynamics involved and to characterize some new aspects in the photoabsorption process of N2O. Our calculations predicted that the parallel transition to the 21A' state is the major dissociation pathway which is in qualitative agreement with the experimental observations. Most importantly, a significant improvement in the absolute value of the total cross section over previous theoretical results [R. Schinke, J. Chem. Phys. 134, 064313 (2011), M.N. Daud, G.G. Balint-Kurti, A. Brown, J. Chem. Phys. 122, 054305 (2005), S. Nanbu, M.S. Johnson, J. Phys. Chem. A 108, 8905 (2004)] was obtained.
DiScRIBinATE: a rapid method for accurate taxonomic classification of metagenomic sequences
2010-01-01
Background In metagenomic sequence data, majority of sequences/reads originate from new or partially characterized genomes, the corresponding sequences of which are absent in existing reference databases. Since taxonomic assignment of reads is based on their similarity to sequences from known organisms, the presence of reads originating from new organisms poses a major challenge to taxonomic binning methods. The recently published SOrt-ITEMS algorithm uses an elaborate work-flow to assign reads originating from hitherto unknown genomes with significant accuracy and specificity. Nevertheless, a significant proportion of reads still get misclassified. Besides, the use of an alignment-based orthology step (for improving the specificity of assignments) increases the total binning time of SOrt-ITEMS. Results In this paper, we introduce a rapid binning approach called DiScRIBinATE (Distance Score Ratio for Improved Binning And Taxonomic Estimation). DiScRIBinATE replaces the orthology approach of SOrt-ITEMS with a quicker 'alignment-free' approach. We demonstrate that incorporating this approach reduces binning time by half without any loss in the specificity and accuracy of assignments. Besides, a novel reclassification strategy incorporated in DiScRIBinATE results in reducing the overall misclassification rate to around 3 - 7%. This misclassification rate is 1.5 - 3 times lower as compared to that by SOrt-ITEMS, and 3 - 30 times lower as compared to that by MEGAN. Conclusions A significant reduction in binning time, coupled with a superior assignment accuracy (as compared to existing binning methods), indicates the immense applicability of the proposed algorithm in rapidly mapping the taxonomic diversity of large metagenomic samples with high accuracy and specificity. Availability The program is available on request from the authors. PMID:21106121
NASA Technical Reports Server (NTRS)
Kory, Carol L.
1999-01-01
The phenomenal growth of commercial communications has created a great demand for traveling-wave tube (TWT) amplifiers. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to accurately analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. For the first time, an accurate three-dimensional helical model was developed that allows accurate prediction of TWT cold-test characteristics including operating frequency, interaction impedance, and attenuation. This computational model, which was developed at the NASA Lewis Research Center, allows TWT designers to obtain a more accurate value of interaction impedance than is possible using experimental methods. Obtaining helical slow-wave circuit interaction impedance is an important part of the design process for a TWT because it is related to the gain and efficiency of the tube. This impedance cannot be measured directly; thus, conventional methods involve perturbing a helical circuit with a cylindrical dielectric rod placed on the central axis of the circuit and obtaining the difference in resonant frequency between the perturbed and unperturbed circuits. A mathematical relationship has been derived between this frequency difference and the interaction impedance (ref. 1). However, because of the complex configuration of the helical circuit, deriving this relationship involves several approximations. In addition, this experimental procedure is time-consuming and expensive, but until recently it was widely accepted as the most accurate means of determining interaction impedance. The advent of an accurate three-dimensional helical circuit model (ref. 2) made it possible for Lewis researchers to fully investigate standard approximations made in deriving the relationship between measured perturbation data and interaction impedance. The most prominent approximations made
Mansilla Alvarez, Luis; Blanco, Pablo; Bulant, Carlos; Dari, Enzo; Veneziani, Alessandro; Feijóo, Raúl
2017-04-01
In this work, we present a novel approach tailored to approximate the Navier-Stokes equations to simulate fluid flow in three-dimensional tubular domains of arbitrary cross-sectional shape. The proposed methodology is aimed at filling the gap between (cheap) one-dimensional and (expensive) three-dimensional models, featuring descriptive capabilities comparable with the full and accurate 3D description of the problem at a low computational cost. In addition, this methodology can easily be tuned or even adapted to address local features demanding more accuracy. The numerical strategy employs finite (pipe-type) elements that take advantage of the pipe structure of the spatial domain under analysis. While low order approximation is used for the longitudinal description of the physical fields, transverse approximation is enriched using high order polynomials. Although our application of interest is computational hemodynamics and its relevance to pathological dynamics like atherosclerosis, the approach is quite general and can be applied in any internal fluid dynamics problem in pipe-like domains. Numerical examples covering academic cases as well as patient-specific coronary arterial geometries demonstrate the potentialities of the developed methodology and its performance when compared against traditional finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.
Chan, Eugene; Rose, L R Francis; Wang, Chun H
2015-05-01
Existing damage imaging algorithms for detecting and quantifying structural defects, particularly those based on diffraction tomography, assume far-field conditions for the scattered field data. This paper presents a major extension of diffraction tomography that can overcome this limitation and utilises a near-field multi-static data matrix as the input data. This new algorithm, which employs numerical solutions of the dynamic Green's functions, makes it possible to quantitatively image laminar damage even in complex structures for which the dynamic Green's functions are not available analytically. To validate this new method, the numerical Green's functions and the multi-static data matrix for laminar damage in flat and stiffened isotropic plates are first determined using finite element models. Next, these results are time-gated to remove boundary reflections, followed by discrete Fourier transform to obtain the amplitude and phase information for both the baseline (damage-free) and the scattered wave fields. Using these computationally generated results and experimental verification, it is shown that the new imaging algorithm is capable of accurately determining the damage geometry, size and severity for a variety of damage sizes and shapes, including multi-site damage. Some aspects of minimal sensors requirement pertinent to image quality and practical implementation are also briefly discussed.
NASA Astrophysics Data System (ADS)
Pendota, Premchand
Many physical phenomena and industrial applications involve multiphase fluid flows and hence it is of high importance to be able to simulate various aspects of these flows accurately. The Dynamic Contact Angles (DCA) and the contact lines at the wall boundaries are a couple of such important aspects. In the past few decades, many mathematical models were developed for predicting the contact angles of the inter-face with the wall boundary under various flow conditions. These models are used to incorporate the physics of DCA and contact line motion in numerical simulations using various interface capturing/tracking techniques. In the current thesis, a simple approach to incorporate the static and dynamic contact angle boundary conditions using the level set method is developed and implemented in multiphase CFD codes, LIT (Level set Interface Tracking) (Herrmann (2008)) and NGA (flow solver) (Desjardins et al (2008)). Various DCA models and associated boundary conditions are reviewed. In addition, numerical aspects such as the occurrence of a stress singularity at the contact lines and grid convergence of macroscopic interface shape are dealt with in the context of the level set approach.
Beare, Richard; Brown, Michael J. I.; Pimbblet, Kevin
2014-12-20
We describe an accurate new method for determining absolute magnitudes, and hence also K-corrections, that is simpler than most previous methods, being based on a quadratic function of just one suitably chosen observed color. The method relies on the extensive and accurate new set of 129 empirical galaxy template spectral energy distributions from Brown et al. A key advantage of our method is that we can reliably estimate random errors in computed absolute magnitudes due to galaxy diversity, photometric error and redshift error. We derive K-corrections for the five Sloan Digital Sky Survey filters and provide parameter tables for use by the astronomical community. Using the New York Value-Added Galaxy Catalog, we compare our K-corrections with those from kcorrect. Our K-corrections produce absolute magnitudes that are generally in good agreement with kcorrect. Absolute griz magnitudes differ by less than 0.02 mag and those in the u band by ∼0.04 mag. The evolution of rest-frame colors as a function of redshift is better behaved using our method, with relatively few galaxies being assigned anomalously red colors and a tight red sequence being observed across the whole 0.0 < z < 0.5 redshift range.
NASA Astrophysics Data System (ADS)
Öz, E.; Batsch, F.; Muggli, P.
2016-09-01
A method to accurately measure the density of Rb vapor is described. We plan on using this method for the Advanced Wakefield (AWAKE) (Assmann et al., 2014 [1]) project at CERN , which will be the world's first proton driven plasma wakefield experiment. The method is similar to the hook (Marlow, 1967 [2]) method and has been described in great detail in the work by Hill et al. (1986) [3]. In this method a cosine fit is applied to the interferogram to obtain a relative accuracy on the order of 1% for the vapor density-length product. A single-mode, fiber-based, Mach-Zenhder interferometer will be built and used near the ends of the 10 meter-long AWAKE plasma source to be able to make accurate relative density measurement between these two locations. This can then be used to infer the vapor density gradient along the AWAKE plasma source and also change it to the value desired for the plasma wakefield experiment. Here we describe the plan in detail and show preliminary results obtained using a prototype 8 cm long novel Rb vapor cell.
Korth, Martin; Thiel, Walter
2011-09-13
Semiempirical quantum mechanical (SQM) methods offer a fast approximate treatment of the electronic structure and the properties of large molecules. Careful benchmarks are required to establish their accuracy. Here, we report a validation of standard SQM methods using a subset of the comprehensive GMTKN24 database for general main group thermochemistry, kinetics, and noncovalent interactions, which has recently been introduced to evaluate density functional theory (DFT) methods ( J. Chem. Theory Comput. 2010 , 6 , 107 ). For all SQM methods considered presently, parameters are available for the elements H, C, N, and O, and consequently, we have extracted from the GMTKN24 database all species containing only these four elements (excluding multireference cases). The resulting GMTKN24-hcno database has 370 entries (derived from 593 energies) compared with 715 entries (derived from 1033 energies) in the original GMTKN24 database. The current benchmark covers established standard SQM methods (AM1, PM6), more recent approaches with orthogonalization corrections (OM1, OM2, OM3), and the self-consistent-charge density functional tight binding method (SCC-DFTB). The results are compared against each other and against DFT results using standard functionals. We find that the OMx methods outperform AM1, PM6, and SCC-DFTB by a significant margin, with a substantial gain in accuracy especially for OM2 and OM3. These latter methods are quite accurate even in comparison with DFT, with an overall mean absolute deviation of 6.6 kcal/mol for PBE and 7.9 kcal/mol for OM3. The OMx methods are also remarkably robust with regard to the unusual bonding situations encountered in the "mindless" MB08-165 test set, for which all other SQM methods fail badly.
Some variance reduction methods for numerical stochastic homogenization.
Blanc, X; Le Bris, C; Legoll, F
2016-04-28
We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.
A hybrid method for efficient and accurate simulations of diffusion compartment imaging signals
NASA Astrophysics Data System (ADS)
Rensonnet, Gaëtan; Jacobs, Damien; Macq, Benoît; Taquet, Maxime
2015-12-01
Diffusion-weighted imaging is sensitive to the movement of water molecules through the tissue microstructure and can therefore be used to gain insight into the tissue cellular architecture. While the diffusion signal arising from simple geometrical microstructure is known analytically, it remains unclear what diffusion signal arises from complex microstructural configurations. Such knowledge is important to design optimal acquisition sequences, to understand the limitations of diffusion-weighted imaging and to validate novel models of the brain microstructure. We present a novel framework for the efficient simulation of high-quality DW-MRI signals based on the hybrid combination of exact analytic expressions in simple geometric compartments such as cylinders and spheres and Monte Carlo simulations in more complex geometries. We validate our approach on synthetic arrangements of parallel cylinders representing the geometry of white matter fascicles, by comparing it to complete, all-out Monte Carlo simulations commonly used in the literature. For typical configurations, equal levels of accuracy are obtained with our hybrid method in less than one fifth of the computational time required for Monte Carlo simulations.
Hemmati, Roholla; Gharipour, Mojgan; Khosravi, Alireza; Jozan, Mahnaz
2013-01-01
Background. The purpose of this study was to answer the question whether a single testing for microalbuminuria results in a reliable conclusion leading costs saving. Methods. This current cross-sectional study included a total of 126 consecutive persons. Microalbuminuria was assessed by collection of two fasting random urine specimens on arrival to the clinic as well as one week later in the morning. Results. In overall, 17 out of 126 participants suffered from microalbuminuria that, among them, 12 subjects were also diagnosed as microalbuminuria once assessing this factor with a sensitivity of 70.6%, a specificity of 100%, a PPV of 100%, a NPV of 95.6%, and an accuracy of 96.0%. The measured sensitivity, specificity, PVV, NPV, and accuracy in hypertensive patients were 73.3%, 100%, 100%, 94.8%, and 95.5%, respectively. Also, these rates in nonhypertensive groups were 50.0%, 100%, 100%, 97.3%, and 97.4%, respectively. According to the ROC curve analysis, a single measurement of UACR had a high value for discriminating defected from normal renal function state (c = 0.989). Urinary albumin concentration in a single measurement had also high discriminative value for diagnosis of damaged kidney (c = 0.995). Conclusion. The single testing of both UACR and urine albumin level rather frequent testing leads to high diagnostic sensitivity, specificity, and accuracy as well as high predictive values in total population and also in hypertensive subgroups.
An efficient method for accurate segmentation of LV in contrast-enhanced cardiac MR images
NASA Astrophysics Data System (ADS)
Suryanarayana K., Venkata; Mitra, Abhishek; Srikrishnan, V.; Jo, Hyun Hee; Bidesi, Anup
2016-03-01
Segmentation of left ventricle (LV) in contrast-enhanced cardiac MR images is a challenging task because of high variability in the image intensity. This is due to a) wash-in and wash-out of the contrast agent over time and b) poor contrast around the epicardium (outer wall) region. Current approaches for segmentation of the endocardium (inner wall) usually involve application of a threshold within the region of interest, followed by refinement techniques like active contours. A limitation of this method is under-segmentation of the inner wall because of gradual loss of contrast at the wall boundary. On the other hand, the challenge in outer wall segmentation is the lack of reliable boundaries because of poor contrast. There are four main contributions in this paper to address the aforementioned issues. First, a seed image is selected using variance based approach on 4D time-frame images over which initial endocardium and epicardium is segmented. Secondly, we propose a patch based feature which overcomes the problem of gradual contrast loss for LV endocardium segmentation. Third, we propose a novel Iterative-Edge-Refinement (IER) technique for epicardium segmentation. Fourth, we propose a greedy search algorithm for propagating the initial contour segmented on seed-image across other time frame images. We have experimented our technique on five contrast-enhanced cardiac MR Datasets (4D) having a total of 1097 images. The segmentation results for all 1097 images have been visually inspected by a clinical expert and have shown good accuracy.
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2015-12-02
We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less
NASA Astrophysics Data System (ADS)
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2016-03-01
We present the Clenshaw-Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw-Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. Finally, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.
Method for accurately positioning a device at a desired area of interest
Jones, Gary D.; Houston, Jack E.; Gillen, Kenneth T.
2000-01-01
A method for positioning a first device utilizing a surface having a viewing translation stage, the surface being movable between a first position where the viewing stage is in operational alignment with a first device and a second position where the viewing stage is in operational alignment with a second device. The movable surface is placed in the first position and an image is produced with the first device of an identifiable characteristic of a calibration object on the viewing stage. The moveable surface is then placed in the second position and only the second device is moved until an image of the identifiable characteristic in the second device matches the image from the first device. The calibration object is then replaced on the stage of the surface with a test object, and the viewing translation stage is adjusted until the second device images the area of interest. The surface is then moved to the first position where the test object is scanned with the first device to image the area of interest. An alternative embodiment where the devices move is also disclosed.
Quach, D.T.; Sakoulas, G.; Nizet, V.; Pogliano, J.; Pogliano, K.
2016-01-01
Successful treatment of bacterial infections requires the timely administration of appropriate antimicrobial therapy. The failure to initiate the correct therapy in a timely fashion results in poor clinical outcomes, longer hospital stays, and higher medical costs. Current approaches to antibiotic susceptibility testing of cultured pathogens have key limitations ranging from long run times to dependence on prior knowledge of genetic mechanisms of resistance. We have developed a rapid antimicrobial susceptibility assay for Staphylococcus aureus based on bacterial cytological profiling (BCP), which uses quantitative fluorescence microscopy to measure antibiotic induced changes in cellular architecture. BCP discriminated between methicillin-susceptible (MSSA) and -resistant (MRSA) clinical isolates of S. aureus (n = 71) within 1–2 h with 100% accuracy. Similarly, BCP correctly distinguished daptomycin susceptible (DS) from daptomycin non-susceptible (DNS) S. aureus strains (n = 20) within 30 min. Among MRSA isolates, BCP further identified two classes of strains that differ in their susceptibility to specific combinations of beta-lactam antibiotics. BCP provides a rapid and flexible alternative to gene-based susceptibility testing methods for S. aureus, and should be readily adaptable to different antibiotics and bacterial species as new mechanisms of resistance or multidrug-resistant pathogens evolve and appear in mainstream clinical practice. PMID:26981574
Variable inertia method: A novel numerical method for mantle convection simulation
NASA Astrophysics Data System (ADS)
Takeyama, Kosuke; Saitoh, Takayuki R.; Makino, Junichiro
2017-01-01
3D numerical simulations have been very useful for the understanding of mantle convection of the earth. In almost all previous simulations of mantle convection, the (extended) Boussinesq approximation has been used. This method is implicit in the sense that buoyancy force and viscosity are balanced, and allows the use of long timesteps that are not limited by the CFL condition. However, the resulting matrix is ill-conditioned, in particular since the viscosity strongly depends on the temperature. It is not well-suited to modern large-scale parallel machines. In this paper, we propose an explicit method which can be used to solve the mantle convection problem. If we can reduce the sound speed without changing the characteristics of the flow, we can increase the timestep and thus can use the explicit method. In order to reduce the sound speed, we multiplied the inertia term of the equation of motion by a large and viscosity-dependent coefficient. Theoretically, we can expect that this modification would not change the flow as long as the Reynolds number and the Mach number are sufficiently smaller than unity. We call this method the variable inertia method (VIM). We have performed an extensive set of numerical tests of the proposed method for thermal convection, and concluded that it works well. In particular, it can handle differences in viscosity of more than five orders of magnitude.
NASA Astrophysics Data System (ADS)
Brown, Sandra E.; Mandelshtam, Vladimir A.
2016-12-01
The self-consistent phonons (SCP) method is a practical approach for computing structural and dynamical properties of a general quantum or classical many-body system while incorporating anharmonic effects. However, a convincing demonstration of the accuracy of SCP and its advantages over the standard harmonic approximation is still lacking. Here we apply SCP to classical Lennard-Jones (LJ) clusters and compare with numerically exact results. The close agreement between the two reveals that SCP accurately describes structural properties of the classical LJ clusters from zero-temperature (where the method is exact) up to the temperatures at which the chosen cluster conformation becomes unstable. Given the similarities between thermal and quantum fluctuations, both physically and within the SCP ansatz, the accuracy of classical SCP over a range of temperatures suggests that quantum SCP is also accurate over a range of quantum de Boer parameter Λ = ℏ / (σ√{ mε }) , which describes the degree of quantum character of the system.
Algorithms for the Fractional Calculus: A Selection of Numerical Methods
NASA Technical Reports Server (NTRS)
Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.
2003-01-01
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.
Methods, Software and Tools for Three Numerical Applications. Final report
E. R. Jessup
2000-03-01
This is a report of the results of the authors work supported by DOE contract DE-FG03-97ER25325. They proposed to study three numerical problems. They are: (1) the extension of the PMESC parallel programming library; (2) the development of algorithms and software for certain generalized eigenvalue and singular value (SVD) problems, and (3) the application of techniques of linear algebra to an information retrieval technique known as latent semantic indexing (LSI).
NASA Astrophysics Data System (ADS)
Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.
2014-03-01
A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.
Overview: Applications of numerical optimization methods to helicopter design problems
NASA Technical Reports Server (NTRS)
Miura, H.
1984-01-01
There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.
NASA Astrophysics Data System (ADS)
Butet, J.; Bernasconi, G. D.; Yang, K.-Y.; Martin, O. J. F.
2016-09-01
During the last decade, important attention has been devoted to the observation of nonlinear optical processes in plasmonic nanosystems, giving rise to a new field of research called nonlinear plasmonics. The cornerstone of nonlinear plasmonics is the use of the large field enhancement associated with the excitation of localized surface plasmon resonances to reach high nonlinear conversion yields. Among all the nonlinear optical processes, second harmonic generation (SHG), the process whereby two photons at the fundamental frequency are converted into one photon at the second harmonic frequency, is undoubtedly the most studied one due to the relative simplicity of its experimental observation. However, the physical origin of SHG from plasmonic nanostructures hides a lot of subtleties, which are mainly related to its particular behavior upon inversion symmetry. In order to catch all the peculiarities of SHG, it is mandatory to develop dedicated numerical methods able to accurately describe all the underlying physical processes and the influence of the initial assumptions needs to be well-characterized. In this presentation, we discuss and compare different methods (namely full-wave computations based on the surface integral equations method, mode analysis, the Miller's rule, and the effective nonlinear susceptibility method) proposed for the evaluation of the SHG from plasmonic nanoparticles emphasizing their limitations and advantages. In particular, the design of double resonant antennas for efficient nonlinear conversion at the nanoscale is addressed in detail.
NASA Technical Reports Server (NTRS)
Wie, Yong-Sun
1990-01-01
A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.
NASA Astrophysics Data System (ADS)
Shirey, S. B.
2002-05-01
Gem-quality diamond contains such low abundances of parent-daughter radionuclides that dating the diamond lattice directly by isotopic measurements has been and will be impossible. Absolute ages on diamonds typically are obtained through measurements of their syngenetic mineral inclusions: Rb-Sr in garnet; Sm-Nd in garnet and pyroxene; Re-Os and U-Th-Pb in sulfide; K-Ar in pyroxene; and U-Pb in zircon. The application of the first two isotope schemes in the list requires putting together many inclusions from many diamonds whereas the latter isotope schemes permit ages on single diamonds. The key limitations on the application of these decay pairs are the availability and size of the inclusions, the abundance levels of the radionuclides, and instrumental sensitivity. Practical complications of radioisotope dating of inclusions are fatal to the application of the technique for diamond provenance. In all mines, the ratio of gem-quality diamonds to stones with datable inclusions is very high. Thus there is no way to date the valuable, marketable stones that are part of the conflict diamond problem, just their rare, flawed cousins. Each analysis destroys the diamond host plus the inclusion and can only be carried out in research labs by highly trained scientists. Thus, these methods can not be automated or applied to the bulk of diamond production. The geological problems with age dating are equally fatal to its application to diamond provenance. From the geological perspective, for age determination to work as a tool for diamond provenance studies, diamond ages would have to be specific to particular kimberlites or kimberlite fields and different between fields. The southern African Kaapvaal-Zimbabwe Craton and Limpopo Mobile Belt is the only cratonic region where age determinations have been applied on a large enough scale to a number of kimberlites to illustrate the geological problems in age measurements for diamond provenance. However, this southern African example
Sokkar, T Z N; El-Farahaty, K A; El-Bakary, M A; Omar, E Z; Hamza, A A
2016-05-01
A modified method was suggested to improve the performance of the Pluta microscope in its nonduplicated mode in the calculation of the areal craze density especially, for relatively low draw ratio (low areal craze density). This method decreases the error that is resulted from the similarity between the formed crazes and the dark fringes of the interference pattern. Furthermore, an accurate method to calculate the birefringence and the orientation function of the drawn fibers via nonduplicated Pluta polarizing interference microscope for high areal craze density (high draw ratio) was suggested. The advantage of the suggested method is to relate the optomechanical properties of the tested fiber with the areal craze density, for the same region of the fiber material.