A Sensitivity Analysis of Circular Error Probable Approximation Techniques

DTIC Science & Technology

1992-03-01

SENSITIVITY ANALYSIS OF CIRCULAR ERROR PROBABLE APPROXIMATION TECHNIQUES THESIS Presented to the Faculty of the School of Engineering of the Air Force...programming skills. Major Paul Auclair patiently advised me in this endeavor, and Major Andy Howell added numerous insightful contributions. I thank my...techniques. The two ret(st accuratec techniiques require numerical integration and can take several hours to run ov a personal comlputer [2:1-2,4-6]. Some

Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

NASA Technical Reports Server (NTRS)

Fink, Patrick W.; Wilton, Donald R.; Khayat, Michael A.

2007-01-01

Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.

Numerical evaluation of the radiation from unbaffled, finite plates using the FFT

NASA Technical Reports Server (NTRS)

Williams, E. G.

1983-01-01

An iteration technique is described which numerically evaluates the acoustic pressure and velocity on and near unbaffled, finite, thin plates vibrating in air. The technique is based on Rayleigh's integral formula and its inverse. These formulas are written in their angular spectrum form so that the fast Fourier transform (FFT) algorithm may be used to evaluate them. As an example of the technique the pressure on the surface of a vibrating, unbaffled disk is computed and shown to be in excellent agreement with the exact solution using oblate spheroidal functions. Furthermore, the computed velocity field outside the disk shows the well-known singularity at the rim of the disk. The radiated fields from unbaffled flat sources of any geometry with prescribed surface velocity may be evaluated using this technique. The use of the FFT to perform the integrations in Rayleigh's formulas provides a great savings in computation time compared with standard integration algorithms, especially when an array processor can be used to implement the FFT.

Numerical simulation of the generation, propagation, and diffraction of nonlinear waves in a rectangular basin: A three-dimensional numerical wave tank

NASA Astrophysics Data System (ADS)

Darwiche, Mahmoud Khalil M.

The research presented herein is a contribution to the understanding of the numerical modeling of fully nonlinear, transient water waves. The first part of the work involves the development of a time-domain model for the numerical generation of fully nonlinear, transient waves by a piston type wavemaker in a three-dimensional, finite, rectangular tank. A time-domain boundary-integral model is developed for simulating the evolving fluid field. A robust nonsingular, adaptive integration technique for the assembly of the boundary-integral coefficient matrix is developed and tested. A parametric finite-difference technique for calculating the fluid- particle kinematics is also developed and tested. A novel compatibility and continuity condition is implemented to minimize the effect of the singularities that are inherent at the intersections of the various Dirichlet and/or Neumann subsurfaces. Results are presented which demonstrate the accuracy and convergence of the numerical model. The second portion of the work is a study of the interaction of the numerically-generated, fully nonlinear, transient waves with a bottom-mounted, surface-piercing, vertical, circular cylinder. The numerical model developed in the first part of this dissertation is extended to include the presence of the cylinder at the centerline of the basin. The diffraction of the numerically generated waves by the cylinder is simulated, and the particle kinematics of the diffracted flow field are calculated and reported. Again, numerical results showing the accuracy and convergence of the extended model are presented.

Density-matrix-based algorithm for solving eigenvalue problems

NASA Astrophysics Data System (ADS)

Polizzi, Eric

2009-03-01

A fast and stable numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques and takes its inspiration from the contour integration and density-matrix representation in quantum mechanics. It will be shown that this algorithm—named FEAST—exhibits high efficiency, robustness, accuracy, and scalability on parallel architectures. Examples from electronic structure calculations of carbon nanotubes are presented, and numerical performances and capabilities are discussed.

Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments.

PubMed

Sainath, Kamalesh; Teixeira, Fernando L; Donderici, Burkay

2014-01-01

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both its (complex) permittivity and permeability tensors. Among the salient features of our formulation are (i) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (ii) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly evanescent spectra contributions, and (iii) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena (e.g., mode coupling at interfaces and nonreciprocal mode propagation). Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

NASA Astrophysics Data System (ADS)

d'Aquino, M.; Capuano, F.; Coppola, G.; Serpico, C.; Mayergoyz, I. D.

2018-05-01

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

Numerical methods for engine-airframe integration

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

Murthy, S.N.B.; Paynter, G.C.

1986-01-01

Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison ofmore » full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.« less

Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

NASA Astrophysics Data System (ADS)

de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

2018-03-01

Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

Improving the numerical integration solution of satellite orbits in the presence of solar radiation pressure using modified back differences

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Feulner, M. R.; Abusali, P. A. M.; Ho, C. S.

1991-01-01

The method of modified back differences, a technique that significantly reduces the numerical integration errors associated with crossing shadow boundaries using a fixed-mesh multistep integrator without a significant increase in computer run time, is presented. While Hubbard's integral approach can produce significant improvements to the trajectory solution, the interpolation method provides the best overall results. It is demonstrated that iterating on the point mass term correction is also important for achieving the best overall results. It is also shown that the method of modified back differences can be implemented with only a small increase in execution time.

Experimental Mathematics and Mathematical Physics

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

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2009-06-26

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

Algorithms for computing the geopotential using a simple density layer

NASA Technical Reports Server (NTRS)

Morrison, F.

1976-01-01

Several algorithms have been developed for computing the potential and attraction of a simple density layer. These are numerical cubature, Taylor series, and a mixed analytic and numerical integration using a singularity-matching technique. A computer program has been written to combine these techniques for computing the disturbing acceleration on an artificial earth satellite. A total of 1640 equal-area, constant surface density blocks on an oblate spheroid are used. The singularity-matching algorithm is used in the subsatellite region, Taylor series in the surrounding zone, and numerical cubature on the rest of the earth.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Surface albedo from bidirectional reflectance

NASA Technical Reports Server (NTRS)

Ranson, K. J.; Irons, J. R.; Daughtry, C. S. T.

1991-01-01

The validity of integrating over discrete wavelength bands is examined to estimate total shortwave bidirectional reflectance of vegetated and bare soil surfaces. Methods for estimating albedo from multiple angle, discrete wavelength band radiometer measurements are studied. These methods include a numerical integration technique and the integration of an empirically derived equation for bidirectional reflectance. It is concluded that shortwave albedos estimated through both techniques agree favorably with the independent pyranometer measurements. Absolute rms errors are found to be 0.5 percent or less for both grass sod and bare soil surfaces.

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.

On performing of interference technique based on self-adjusting Zernike filters (SA-AVT method) to investigate flows and validate 3D flow numerical simulations

NASA Astrophysics Data System (ADS)

Pavlov, Al. A.; Shevchenko, A. M.; Khotyanovsky, D. V.; Pavlov, A. A.; Shmakov, A. S.; Golubev, M. P.

2017-10-01

We present a method for and results of determination of the field of integral density in the structure of flow corresponding to the Mach interaction of shock waves at Mach number M = 3. The optical diagnostics of flow was performed using an interference technique based on self-adjusting Zernike filters (SA-AVT method). Numerical simulations were carried out using the CFS3D program package for solving the Euler and Navier-Stokes equations. Quantitative data on the distribution of integral density on the path of probing radiation in one direction of 3D flow transillumination in the region of Mach interaction of shock waves were obtained for the first time.

Characterizing Exposures of Fish to Wastewater Treatment Plant Effluent: An Integrated Metabolite and Lipid Profiling Approach

EPA Science Inventory

Metabolite and lipid profiling are well established techniques for studying chemical-induced alterations to normal biological function in numerous organisms. These techniques have been used successfully to identify biomarkers of chemical exposure, screen for chemical potency, or ...

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.

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

S-matrix method for the numerical determination of bound states.

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Madan, R. N.

1973-01-01

A rapid numerical technique for the determination of bound states of a partial-wave-projected Schroedinger equation is presented. First, one needs to integrate the equation only outwards as in the scattering case, and second, the number of trials necessary to determine the eigenenergy and the corresponding eigenfunction is considerably less than in the usual method. As a nontrivial example of the technique, bound states are calculated in the exchange approximation for the e-/He+ system and l equals 1 partial wave.

The Making of a Government LSI - From Warfare Capability to Operational System

DTIC Science & Technology

2015-04-30

continues to evolve and implement Lead System Integrator (LSI) acquisition strategies, they have started to define numerous program initiatives that...employ more integrated engineering and management processes and techniques. These initiatives are developing varying acquisition approaches that define (1...government LSI transformation. Navy Systems Commands have begun adding a higher level of integration into their acquisition process with the

The gravitational potential of axially symmetric bodies from a regularized green kernel

NASA Astrophysics Data System (ADS)

Trova, A.; Huré, J.-M.; Hersant, F.

2011-12-01

The determination of the gravitational potential inside celestial bodies (rotating stars, discs, planets, asteroids) is a common challenge in numerical Astrophysics. Under axial symmetry, the potential is classically found from a two-dimensional integral over the body's meridional cross-section. Because it involves an improper integral, high accuracy is generally difficult to reach. We have discovered that, for homogeneous bodies, the singular Green kernel can be converted into a regular kernel by direct analytical integration. This new kernel, easily managed with standard techniques, opens interesting horizons, not only for numerical calculus but also to generate approximations, in particular for geometrically thin discs and rings.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

NASA Astrophysics Data System (ADS)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

NASA Astrophysics Data System (ADS)

Wang, Wei; Shen, Jianqi

2018-06-01

The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

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

Patel, Saumil S.; Fischer, Paul F.; Min, Misun

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

A study of the displacement of a Wankel rotary engine

NASA Astrophysics Data System (ADS)

Beard, J. E.; Pennock, G. R.

1993-03-01

The volumetric displacement of a Wankel rotary engine is a function of the trochoid ratio and the pin size ratio, assuming the engine has a unit depth and the number of lobes is specified. The mathematical expression which defines the displacement contains a function which can be evaluated directly and a normal elliptic integral of the second type which does not have an explicit solution. This paper focuses on the contribution of the elliptic integral to the total displacement of the engine. The influence of the elliptic integral is shown to account for as much as 20 percent of the total displacement, depending on the trochoid ratio and the pin size ratio. Two numerical integration techniques are compared in the paper, namely, the trapezoidal rule and Simpson's 1/3 rule. The bounds on the error, associated with each numerical method, are analyzed. The results indicate that the numerical method has a minimal effect on the accuracy of the calculated displacement for a practical number of integration steps. The paper also evaluates the influence of manufacturing tolerances on the calculated displacement and the actual displacement. Finally. a numerical example of the common three-lobed Wankel rotary engine is included for illustrative purposes.

A Novel Polygonal Finite Element Method: Virtual Node Method

NASA Astrophysics Data System (ADS)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Flexible Plasmonic Sensors

PubMed Central

Shir, Daniel; Ballard, Zachary S.; Ozcan, Aydogan

2016-01-01

Mechanical flexibility and the advent of scalable, low-cost, and high-throughput fabrication techniques have enabled numerous potential applications for plasmonic sensors. Sensitive and sophisticated biochemical measurements can now be performed through the use of flexible plasmonic sensors integrated into existing medical and industrial devices or sample collection units. More robust sensing schemes and practical techniques must be further investigated to fully realize the potentials of flexible plasmonics as a framework for designing low-cost, embedded and integrated sensors for medical, environmental, and industrial applications. PMID:27547023

Numerical methods in acoustics

NASA Astrophysics Data System (ADS)

Candel, S. M.

This paper presents a survey of some computational techniques applicable to acoustic wave problems. Recent advances in wave extrapolation methods, spectral methods and boundary integral methods are discussed and illustrated by specific calculations.

A linear circuit analysis program with stiff systems capability

NASA Technical Reports Server (NTRS)

Cook, C. H.; Bavuso, S. J.

1973-01-01

Several existing network analysis programs have been modified and combined to employ a variable topological approach to circuit translation. Efficient numerical integration techniques are used for transient analysis.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

Discrete distributed strain sensing of intelligent structures

NASA Technical Reports Server (NTRS)

Anderson, Mark S.; Crawley, Edward F.

1992-01-01

Techniques are developed for the design of discrete highly distributed sensor systems for use in intelligent structures. First the functional requirements for such a system are presented. Discrete spatially averaging strain sensors are then identified as satisfying the functional requirements. A variety of spatial weightings for spatially averaging sensors are examined, and their wave number characteristics are determined. Preferable spatial weightings are identified. Several numerical integration rules used to integrate such sensors in order to determine the global deflection of the structure are discussed. A numerical simulation is conducted using point and rectangular sensors mounted on a cantilevered beam under static loading. Gage factor and sensor position uncertainties are incorporated to assess the absolute error and standard deviation of the error in the estimated tip displacement found by numerically integrating the sensor outputs. An experiment is carried out using a statically loaded cantilevered beam with five point sensors. It is found that in most cases the actual experimental error is within one standard deviation of the absolute error as found in the numerical simulation.

Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation

NASA Astrophysics Data System (ADS)

Zavrazhina, T. V.

2007-10-01

A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ℝ2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.

Dictionary-based image reconstruction for superresolution in integrated circuit imaging.

PubMed

Cilingiroglu, T Berkin; Uyar, Aydan; Tuysuzoglu, Ahmet; Karl, W Clem; Konrad, Janusz; Goldberg, Bennett B; Ünlü, M Selim

2015-06-01

Resolution improvement through signal processing techniques for integrated circuit imaging is becoming more crucial as the rapid decrease in integrated circuit dimensions continues. Although there is a significant effort to push the limits of optical resolution for backside fault analysis through the use of solid immersion lenses, higher order laser beams, and beam apodization, signal processing techniques are required for additional improvement. In this work, we propose a sparse image reconstruction framework which couples overcomplete dictionary-based representation with a physics-based forward model to improve resolution and localization accuracy in high numerical aperture confocal microscopy systems for backside optical integrated circuit analysis. The effectiveness of the framework is demonstrated on experimental data.

Evaluation of analytical procedures for prediction of turbulent boundary layers on a porous wall

NASA Technical Reports Server (NTRS)

Towne, C. E.

1974-01-01

An analytical study has been made to determine how well current boundary layer prediction techniques work when there is mass transfer normal to the wall. The data that were considered in this investigation were for two-dimensional, incompressible, turbulent boundary layers with suction and blowing. Some of the bleed data were taken in an adverse pressure gradient. An integral prediction method was used three different porous wall skin friction relations, in addition to a solid-surface relation for the suction cases. A numerical prediction method was also used. Comparisons were made between theoretical and experimental skin friction coefficients, displacement and momentum thicknesses, and velocity profiles. The integral method with one of the porous wall skin friction laws gave very good agreement with data for most of the cases considered. The use of the solid-surface skin friction law caused the integral to overpredict the effectiveness of the bleed. The numerical techniques also worked well for most of the cases.

Analytic Method for Computing Instrument Pointing Jitter

NASA Technical Reports Server (NTRS)

Bayard, David

2003-01-01

A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation. The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor- output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration.

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.; Tang, Harry (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1979-01-01

The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

The numerical calculation of laminar boundary-layer separation

NASA Technical Reports Server (NTRS)

Klineberg, J. M.; Steger, J. L.

1974-01-01

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2000-01-01

A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.

Cubic spline numerical solution of an ablation problem with convective backface cooling

NASA Astrophysics Data System (ADS)

Lin, S.; Wang, P.; Kahawita, R.

1984-08-01

An implicit numerical technique using cubic splines is presented for solving an ablation problem on a thin wall with convective cooling. A non-uniform computational mesh with 6 grid points has been used for the numerical integration. The method has been found to be computationally efficient, providing for the care under consideration of an overall error of about 1 percent. The results obtained indicate that the convective cooling is an important factor in reducing the ablation thickness.

Integrated approaches to the application of advanced modeling technology in process development and optimization

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

Allgor, R.J.; Feehery, W.F.; Tolsma, J.E.

The batch process development problem serves as good candidate to guide the development of process modeling environments. It demonstrates that very robust numerical techniques are required within an environment that can collect, organize, and maintain the data and models required to address the batch process development problem. This paper focuses on improving the robustness and efficiency of the numerical algorithms required in such a modeling environment through the development of hybrid numerical and symbolic strategies.

Goddard trajectory determination subsystem: Mathematical specifications

NASA Technical Reports Server (NTRS)

Wagner, W. E. (Editor); Velez, C. E. (Editor)

1972-01-01

The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

Buckling Of Shells Of Revolution /BOSOR/ with various wall constructions

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1969-01-01

Computer program, using numerical integration and finite difference techniques, solves almost any buckling problem for shells exhibiting orthotropic behavior. Stability analyses can be performed with reasonable accuracy and without unduly restrictive approximations.

Use of simulated satellite radiances from a mesoscale numerical model to understand kinematic and dynamic processes

NASA Technical Reports Server (NTRS)

Kalb, Michael; Robertson, Franklin; Jedlovec, Gary; Perkey, Donald

1987-01-01

Techniques by which mesoscale numerical weather prediction model output and radiative transfer codes are combined to simulate the radiance fields that a given passive temperature/moisture satellite sensor would see if viewing the evolving model atmosphere are introduced. The goals are to diagnose the dynamical atmospheric processes responsible for recurring patterns in observed satellite radiance fields, and to develop techniques to anticipate the ability of satellite sensor systems to depict atmospheric structures and provide information useful for numerical weather prediction (NWP). The concept of linking radiative transfer and dynamical NWP codes is demonstrated with time sequences of simulated radiance imagery in the 24 TIROS vertical sounder channels derived from model integrations for March 6, 1982.

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1992-01-01

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

Experimenting with galaxies

NASA Technical Reports Server (NTRS)

Miller, Richard H.

1992-01-01

A study to demonstrate how the dynamics of galaxies may be investigated through the creation of galaxies within a computer model is presented. The numerical technique for simulating galaxies is shown to be both highly efficient and highly robust. Consideration is given to the anatomy of a galaxy, the gravitational N-body problem, numerical approaches to the N-body problem, use of the Poisson equation, and the symplectic integrator.

A parallel time integrator for noisy nonlinear oscillatory systems

NASA Astrophysics Data System (ADS)

Subber, Waad; Sarkar, Abhijit

2018-06-01

In this paper, we adapt a parallel time integration scheme to track the trajectories of noisy non-linear dynamical systems. Specifically, we formulate a parallel algorithm to generate the sample path of nonlinear oscillator defined by stochastic differential equations (SDEs) using the so-called parareal method for ordinary differential equations (ODEs). The presence of Wiener process in SDEs causes difficulties in the direct application of any numerical integration techniques of ODEs including the parareal algorithm. The parallel implementation of the algorithm involves two SDEs solvers, namely a fine-level scheme to integrate the system in parallel and a coarse-level scheme to generate and correct the required initial conditions to start the fine-level integrators. For the numerical illustration, a randomly excited Duffing oscillator is investigated in order to study the performance of the stochastic parallel algorithm with respect to a range of system parameters. The distributed implementation of the algorithm exploits Massage Passing Interface (MPI).

Depth Cue Integration in an Active Control Paradigm

NASA Technical Reports Server (NTRS)

Kaiser, Mary K.; Sweet, Barabara T.; Shafto, Meredith; Null, Cynthia H. (Technical Monitor)

1995-01-01

Numerous models of depth cue integration have been proposed. Of particular interest is how the visual system processes discrepent cues, as might arise when viewing synthetic displays. A powerful paradigm for examining this integration process can be adapted from manual control research. This methodology introduces independent disturbances in the candidate cues, then performs spectral analysis of subjects' resulting motoric responses (e.g., depth matching). We will describe this technique and present initial findings.

Composite use of numerical groundwater flow modeling and geoinformatics techniques for monitoring Indus Basin aquifer, Pakistan.

PubMed

Ahmad, Zulfiqar; Ashraf, Arshad; Fryar, Alan; Akhter, Gulraiz

2011-02-01

The integration of the Geographic Information System (GIS) with groundwater modeling and satellite remote sensing capabilities has provided an efficient way of analyzing and monitoring groundwater behavior and its associated land conditions. A 3-dimensional finite element model (Feflow) has been used for regional groundwater flow modeling of Upper Chaj Doab in Indus Basin, Pakistan. The approach of using GIS techniques that partially fulfill the data requirements and define the parameters of existing hydrologic models was adopted. The numerical groundwater flow model is developed to configure the groundwater equipotential surface, hydraulic head gradient, and estimation of the groundwater budget of the aquifer. GIS is used for spatial database development, integration with a remote sensing, and numerical groundwater flow modeling capabilities. The thematic layers of soils, land use, hydrology, infrastructure, and climate were developed using GIS. The Arcview GIS software is used as additive tool to develop supportive data for numerical groundwater flow modeling and integration and presentation of image processing and modeling results. The groundwater flow model was calibrated to simulate future changes in piezometric heads from the period 2006 to 2020. Different scenarios were developed to study the impact of extreme climatic conditions (drought/flood) and variable groundwater abstraction on the regional groundwater system. The model results indicated a significant response in watertable due to external influential factors. The developed model provides an effective tool for evaluating better management options for monitoring future groundwater development in the study area.

Modeling global vector fields of chaotic systems from noisy time series with the aid of structure-selection techniques.

PubMed

Xu, Daolin; Lu, Fangfang

2006-12-01

We address the problem of reconstructing a set of nonlinear differential equations from chaotic time series. A method that combines the implicit Adams integration and the structure-selection technique of an error reduction ratio is proposed for system identification and corresponding parameter estimation of the model. The structure-selection technique identifies the significant terms from a pool of candidates of functional basis and determines the optimal model through orthogonal characteristics on data. The technique with the Adams integration algorithm makes the reconstruction available to data sampled with large time intervals. Numerical experiment on Lorenz and Rossler systems shows that the proposed strategy is effective in global vector field reconstruction from noisy time series.

DE 102 - A numerically integrated ephemeris of the moon and planets spanning forty-four centuries

NASA Technical Reports Server (NTRS)

Newhall, X. X.; Standish, E. M.; Willams, J. G.

1983-01-01

It is pointed out that the 1960's were the turning point for the generation of lunar and planetary ephemerides. All previous measurements of the positions of solar system bodies were optical angular measurements. New technological improvements leading to immense changes in observational accuracy are related to developments concerning radar, Viking landers on Mars, and laser ranges to lunar corner cube retroreflectors. Suitable numerical integration techniques and more comprehensive physical models were developed to match the accuracy of the modern data types. The present investigation is concerned with the first integrated ephemeris, DE 102, which covers the entire span of the historical astronomical observations of usable accuracy which are known. The fit is made to modern data. The integration spans the time period from 1411 BC to 3002 AD.

Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics

NASA Technical Reports Server (NTRS)

Zhu, J. Z.; He, Guowei; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

Numerical simulation has now become an integral part of engineering design process. Critical design decisions are routinely made based on the simulation results and conclusions. Verification and validation of the reliability of the numerical simulation is therefore vitally important in the engineering design processes. We propose to develop theories and methodologies that can automatically provide quantitative information about the reliability of the numerical simulation by estimating numerical approximation error, computational model induced errors and the uncertainties contained in the mathematical models so that the reliability of the numerical simulation can be verified and validated. We also propose to develop and implement methodologies and techniques that can control the error and uncertainty during the numerical simulation so that the reliability of the numerical simulation can be improved.

Rotorcraft Brownout: Advanced Understanding, Control and Mitigation

DTIC Science & Technology

2008-12-31

the Gauss Seidel iterative method . The overall steps of SIMPLER algorithm can be summarized as: 1. Guess velocity field, 2. Calculate the momentum...techniques and numerical methods , and the team will begin to develop a methodology that is capable of integrating these solutions and highlighting...rotorcraft design optimization techniques will then be undertaken using the validated computational methods . 15. SUBJECT TERMS Rotorcraft

Structural dynamics payload loads estimates

NASA Technical Reports Server (NTRS)

Engels, R. C.

1982-01-01

Methods for the prediction of loads on large space structures are discussed. Existing approaches to the problem of loads calculation are surveyed. A full scale version of an alternate numerical integration technique to solve the response part of a load cycle is presented, and a set of short cut versions of the algorithm developed. The implementation of these techniques using the software package developed is discussed.

Numerical Simulation of Delamination Growth in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, P. P.; Davila, C. G.; Ambur, D. R.

2001-01-01

The use of decohesion elements for the simulation of delamination in composite materials is reviewed. The test methods available to measure the interfacial fracture toughness used in the formulation of decohesion elements are described initially. After a brief presentation of the virtual crack closure technique, the technique most widely used to simulate delamination growth, the formulation of interfacial decohesion elements is described. Problems related with decohesion element constitutive equations, mixed-mode crack growth, element numerical integration and solution procedures are discussed. Based on these investigations, it is concluded that the use of interfacial decohesion elements is a promising technique that avoids the need for a pre-existing crack and pre-defined crack paths, and that these elements can be used to simulate both delamination onset and growth.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

Regularization in Orbital Mechanics; Theory and Practice

NASA Astrophysics Data System (ADS)

Roa, Javier

2017-09-01

Regularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

Integral method for the calculation of Hawking radiation in dispersive media. I. Symmetric asymptotics.

PubMed

Robertson, Scott; Leonhardt, Ulf

2014-11-01

Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.

High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

NASA Astrophysics Data System (ADS)

He, Yang; Sun, Yajuan; Zhang, Ruili; Wang, Yulei; Liu, Jian; Qin, Hong

2016-09-01

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracy-enhancing processing technique, the explicit methods obtain high-order accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations.

Stress and Sealing Performance Analysis of Containment Vessel

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

WU, TSU-TE

2005-05-24

This paper presents a numerical technique for analyzing the containment vessel subjected to the combined loading of closure-bolt torque and internal pressure. The detailed stress distributions in the O-rings generated by both the torque load and the internal pressure can be evaluated by using this method. Consequently, the sealing performance of the O-rings can be determined. The material of the O-rings can be represented by any available constitutive equation for hyperelastic material. In the numerical calculation of this paper, the form of the Mooney-Rivlin strain energy potential is used. The technique treats both the preloading process of bolt tightening andmore » the application of internal pressure as slow dynamic loads. Consequently, the problem can be evaluated using explicit numerical integration scheme.« less

A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

NASA Astrophysics Data System (ADS)

Brovont, Aaron D.

The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

ParaExp Using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

NASA Astrophysics Data System (ADS)

Merkel, M.; Niyonzima, I.; Schöps, S.

2017-12-01

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strong ly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1985-01-01

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

Numerical simulation of liquid jet impact on a rigid wall

NASA Astrophysics Data System (ADS)

Aganin, A. A.; Guseva, T. S.

2016-11-01

Basic points of a numerical technique for computing high-speed liquid jet impact on a rigid wall are presented. In the technique the flows of the liquid and the surrounding gas are governed by the equations of gas dynamics in the density, velocity, and pressure, which are integrated by the CIP-CUP method on dynamically adaptive grids without explicitly tracking the gas-liquid interface. The efficiency of the technique is demonstrated by the results of computing the problems of impact of the liquid cone and the liquid wedge on a wall in the mode with the shockwave touching the wall by its edge. Numerical solutions of these problems are compared with the analytical solution of the problem of impact of the plane liquid flow on a wall. Applicability of the technique to the problems of the high-speed liquid jet impact on a wall is illustrated by the results of computing a problem of impact of a cylindrical liquid jet with the hemispherical end on a wall covered by a layer of the same liquid.

Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

PubMed Central

Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

Thermoviscoelastoplastic Deformation of Compound Shells of Revolution Made of a Damageable Material

NASA Astrophysics Data System (ADS)

Shevchenko, Yu. N.; Galishin, A. Z.; Babeshko, M. E.

2015-11-01

A technique for numerical analysis of the thermoviscoelastoplastic deformation of thin compound shells made of a damageable material in which a fracture front propagates is described. A procedure for automatic variation in the step of integration of the kinetic damage equation is developed. A two-layer cylindrical shell cooling by convection and subjected to internal pressure and tensile force is analyzed as an example. The numerical data are presented and analyzed

Full waveform inversion of combined towed streamer and limited OBS seismic data: a theoretical study

NASA Astrophysics Data System (ADS)

Yang, Huachen; Zhang, Jianzhong

2018-06-01

In marine seismic oil exploration, full waveform inversion (FWI) of towed-streamer data is used to reconstruct velocity models. However, the FWI of towed-streamer data easily converges to a local minimum solution due to the lack of low-frequency content. In this paper, we propose a new FWI technique using towed-streamer data, its integrated data sets and limited OBS data. Both integrated towed-streamer seismic data and OBS data have low-frequency components. Therefore, at early iterations in the new FWI technique, the OBS data combined with the integrated towed-streamer data sets reconstruct an appropriate background model. And the towed-streamer seismic data play a major role in later iterations to improve the resolution of the model. The new FWI technique is tested on numerical examples. The results show that when starting models are not accurate enough, the models inverted using the new FWI technique are superior to those inverted using conventional FWI.

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Electromagnetic Field Penetration Studies

NASA Technical Reports Server (NTRS)

Deshpande, M.D.

2000-01-01

A numerical method is presented to determine electromagnetic shielding effectiveness of rectangular enclosure with apertures on its wall used for input and output connections, control panels, visual-access windows, ventilation panels, etc. Expressing EM fields in terms of cavity Green's function inside the enclosure and the free space Green's function outside the enclosure, integral equations with aperture tangential electric fields as unknown variables are obtained by enforcing the continuity of tangential electric and magnetic fields across the apertures. Using the Method of Moments, the integral equations are solved for unknown aperture fields. From these aperture fields, the EM field inside a rectangular enclosure due to external electromagnetic sources are determined. Numerical results on electric field shielding of a rectangular cavity with a thin rectangular slot obtained using the present method are compared with the results obtained using simple transmission line technique for code validation. The present technique is applied to determine field penetration inside a Boeing-757 by approximating its passenger cabin as a rectangular cavity filled with a homogeneous medium and its passenger windows by rectangular apertures. Preliminary results for, two windows, one on each side of fuselage were considered. Numerical results for Boeing-757 at frequencies 26 MHz, 171-175 MHz, and 428-432 MHz are presented.

Efficient grid-based techniques for density functional theory

NASA Astrophysics Data System (ADS)

Rodriguez-Hernandez, Juan Ignacio

Understanding the chemical and physical properties of molecules and materials at a fundamental level often requires quantum-mechanical models for these substance's electronic structure. This type of many body quantum mechanics calculation is computationally demanding, hindering its application to substances with more than a few hundreds atoms. The supreme goal of many researches in quantum chemistry---and the topic of this dissertation---is to develop more efficient computational algorithms for electronic structure calculations. In particular, this dissertation develops two new numerical integration techniques for computing molecular and atomic properties within conventional Kohn-Sham-Density Functional Theory (KS-DFT) of molecular electronic structure. The first of these grid-based techniques is based on the transformed sparse grid construction. In this construction, a sparse grid is generated in the unit cube and then mapped to real space according to the pro-molecular density using the conditional distribution transformation. The transformed sparse grid was implemented in program deMon2k, where it is used as the numerical integrator for the exchange-correlation energy and potential in the KS-DFT procedure. We tested our grid by computing ground state energies, equilibrium geometries, and atomization energies. The accuracy on these test calculations shows that our grid is more efficient than some previous integration methods: our grids use fewer points to obtain the same accuracy. The transformed sparse grids were also tested for integrating, interpolating and differentiating in different dimensions (n = 1,2,3,6). The second technique is a grid-based method for computing atomic properties within QTAIM. It was also implemented in deMon2k. The performance of the method was tested by computing QTAIM atomic energies, charges, dipole moments, and quadrupole moments. For medium accuracy, our method is the fastest one we know of.

Acid rain: Microphysical model

NASA Technical Reports Server (NTRS)

Dingle, A. N.

1980-01-01

A microphysical model was used to simulate the case of a ground cloud without dilution by entrainment and without precipitation. The numerical integration techniques of the model are presented. The droplet size spectra versus time and the droplet molalities for each value of time are discussed.

Development of a GIS-based integrated framework for coastal seiches monitoring and forecasting: A North Jiangsu shoal case study

NASA Astrophysics Data System (ADS)

Qin, Rufu; Lin, Liangzhao

2017-06-01

Coastal seiches have become an increasingly important issue in coastal science and present many challenges, particularly when attempting to provide warning services. This paper presents the methodologies, techniques and integrated services adopted for the design and implementation of a Seiches Monitoring and Forecasting Integration Framework (SMAF-IF). The SMAF-IF is an integrated system with different types of sensors and numerical models and incorporates the Geographic Information System (GIS) and web techniques, which focuses on coastal seiche events detection and early warning in the North Jiangsu shoal, China. The in situ sensors perform automatic and continuous monitoring of the marine environment status and the numerical models provide the meteorological and physical oceanographic parameter estimates. A model outputs processing software was developed in C# language using ArcGIS Engine functions, which provides the capabilities of automatically generating visualization maps and warning information. Leveraging the ArcGIS Flex API and ASP.NET web services, a web based GIS framework was designed to facilitate quasi real-time data access, interactive visualization and analysis, and provision of early warning services for end users. The integrated framework proposed in this study enables decision-makers and the publics to quickly response to emergency coastal seiche events and allows an easy adaptation to other regional and scientific domains related to real-time monitoring and forecasting.

Conference on Complex Turbulent Flows: Comparison of Computation and Experiment, Stanford University, Stanford, CA, September 14-18, 1981, Proceedings. Volume 2 - Taxonomies, reporters' summaries, evaluation, and conclusions

NASA Technical Reports Server (NTRS)

Kline, S. J. (Editor); Cantwell, B. J. (Editor); Lilley, G. M.

1982-01-01

Computational techniques for simulating turbulent flows were explored, together with the results of experimental investigations. Particular attention was devoted to the possibility of defining a universal closure model, applicable for all turbulence situations; however, conclusions were drawn that zonal models, describing localized structures, were the most promising techniques to date. The taxonomy of turbulent flows was summarized, as were algebraic, differential, integral, and partial differential methods for numerical depiction of turbulent flows. Numerous comparisons of theoretically predicted and experimentally obtained data for wall pressure distributions, velocity profiles, turbulent kinetic energy profiles, Reynolds shear stress profiles, and flows around transonic airfoils were presented. Simplifying techniques for reducing the necessary computational time for modeling complex flowfields were surveyed, together with the industrial requirements and applications of computational fluid dynamics techniques.

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

An iterative analytical technique for the design of interplanetary direct transfer trajectories including perturbations

NASA Astrophysics Data System (ADS)

Parvathi, S. P.; Ramanan, R. V.

2018-06-01

An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed. The perturbations such as non-spherical gravity of Earth and the third body perturbations due to Sun and Moon are included in the analytical design process. In the design process, first the design is obtained using the iterative patched conic technique without including the perturbations and then modified to include the perturbations. The modification is based on, (i) backward analytical propagation of the state vector obtained from the iterative patched conic technique at the sphere of influence by including the perturbations, and (ii) quantification of deviations in the orbital elements at periapsis of the departure hyperbolic orbit. The orbital elements at the sphere of influence are changed to nullify the deviations at the periapsis. The analytical backward propagation is carried out using the linear approximation technique. The new analytical design technique, named as biased iterative patched conic technique, does not depend upon numerical integration and all computations are carried out using closed form expressions. The improved design is very close to the numerical design. The design analysis using the proposed technique provides a realistic insight into the mission aspects. Also, the proposed design is an excellent initial guess for numerical refinement and helps arrive at the four distinct design options for a given opportunity.

Integrated optical circuits for numerical computation

NASA Technical Reports Server (NTRS)

Verber, C. M.; Kenan, R. P.

1983-01-01

The development of integrated optical circuits (IOC) for numerical-computation applications is reviewed, with a focus on the use of systolic architectures. The basic architecture criteria for optical processors are shown to be the same as those proposed by Kung (1982) for VLSI design, and the advantages of IOCs over bulk techniques are indicated. The operation and fabrication of electrooptic grating structures are outlined, and the application of IOCs of this type to an existing 32-bit, 32-Mbit/sec digital correlator, a proposed matrix multiplier, and a proposed pipeline processor for polynomial evaluation is discussed. The problems arising from the inherent nonlinearity of electrooptic gratings are considered. Diagrams and drawings of the application concepts are provided.

Ensemble-type numerical uncertainty information from single model integrations

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

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

A study of methods to predict and measure the transmission of sound through the walls of light aircraft. Integration of certain singular boundary element integrals for applications in linear acoustics

NASA Technical Reports Server (NTRS)

Zimmerle, D.; Bernhard, R. J.

1985-01-01

An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.

Local numerical modelling of ultrasonic guided waves in linear and nonlinear media

NASA Astrophysics Data System (ADS)

Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.

Big data integration for regional hydrostratigraphic mapping

NASA Astrophysics Data System (ADS)

Friedel, M. J.

2013-12-01

Numerical models provide a way to evaluate groundwater systems, but determining the hydrostratigraphic units (HSUs) used in devising these models remains subjective, nonunique, and uncertain. A novel geophysical-hydrogeologic data integration scheme is proposed to constrain the estimation of continuous HSUs. First, machine-learning and multivariate statistical techniques are used to simultaneously integrate borehole hydrogeologic (lithology, hydraulic conductivity, aqueous field parameters, dissolved constituents) and geophysical (gamma, spontaneous potential, and resistivity) measurements. Second, airborne electromagnetic measurements are numerically inverted to obtain subsurface resistivity structure at randomly selected locations. Third, the machine-learning algorithm is trained using the borehole hydrostratigraphic units and inverted airborne resistivity profiles. The trained machine-learning algorithm is then used to estimate HSUs at independent resistivity profile locations. We demonstrate efficacy of the proposed approach to map the hydrostratigraphy of a heterogeneous surficial aquifer in northwestern Nebraska.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Leading singularities and off-shell conformal integrals

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

Drummond, James; Duhr, Claude; Eden, Burkhard

2013-08-29

The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certainmore » limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.« less

Computer program analyzes Buckling Of Shells Of Revolution with various wall construction, BOSOR

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1968-01-01

Computer program performs stability analyses for a wide class of shells without unduly restrictive approximations. The program uses numerical integration, finite difference of finite element techniques to solve with reasonable accuracy almost any buckling problem for shells exhibiting orthotropic behavior.

An integral-equation solution for TE radiation and scattering from conducting cylinders

NASA Technical Reports Server (NTRS)

Richmond, J. H.

1973-01-01

The piecewise-sinusoidal reaction technique is applied to low frequency radiation and scattering from noncircular cylinders with perfect or imperfect conductivity. This report presents the theory, computer programs and numerical results for these two-dimensional problems with the TE polarization.

Numerical methods for coupled fracture problems

NASA Astrophysics Data System (ADS)

Viesca, Robert C.; Garagash, Dmitry I.

2018-04-01

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

Recent advances in computational-analytical integral transforms for convection-diffusion problems

NASA Astrophysics Data System (ADS)

Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.; Almeida, A. P.

2017-10-01

An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

HARM processing techniques for MEMS and MOEMS devices using bonded SOI substrates and DRIE

NASA Astrophysics Data System (ADS)

Gormley, Colin; Boyle, Anne; Srigengan, Viji; Blackstone, Scott C.

2000-08-01

Silicon-on-Insulator (SOI) MEMS devices (1) are rapidly gaining popularity in realizing numerous solutions for MEMS, especially in the optical and inertia application fields. BCO recently developed a DRIE trench etch, utilizing the Bosch process, and refill process for high voltage dielectric isolation integrated circuits on thick SOI substrates. In this paper we present our most recently developed DRIE processes for MEMS and MOEMS devices. These advanced etch techniques are initially described and their integration with silicon bonding demonstrated. This has enabled process flows that are currently being utilized to develop optical router and filter products for fiber optics telecommunications and high precision accelerometers.

Efficient numerical evaluation of Feynman integrals

NASA Astrophysics Data System (ADS)

Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran

2016-03-01

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

A general numerical model for wave rotor analysis

NASA Technical Reports Server (NTRS)

Paxson, Daniel W.

1992-01-01

Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved.

Further studies of propellant sloshing under low-gravity conditions

NASA Technical Reports Server (NTRS)

Dodge, F. T.

1971-01-01

A variational integral is formulated from Hamilton's Principle and is proved to be equivalent to the usual differential equations of low-gravity sloshing in ellipsoidal tanks. It is shown that for a zero-degree contact angle the contact line boundary condition corresponds to the stuck condition, a result that is due to the linearization of the equations and the ambiguity in the definition of the wave height at the wall. The variational integral is solved by a Rayleigh-Ritz technique. Results for slosh frequency when the free surface is not bent-over compare well with previous numerical solutions. When the free surface is bent over, however, the results for slosh frequency are considerably larger than those predicted by previous finite-difference, numerical approaches: the difference may be caused by the use of a zero degree contact angle in the present theory in contrast to the nonzero contact angle used in the numerical approaches.

Enhancement Of Reading Accuracy By Multiple Data Integration

NASA Astrophysics Data System (ADS)

Lee, Kangsuk

1989-07-01

In this paper, a multiple sensor integration technique with neural network learning algorithms is presented which can enhance the reading accuracy of the hand-written numerals. Many document reading applications involve hand-written numerals in a predetermined location on a form, and in many cases, critical data is redundantly described. The amount of a personal check is one such case which is written redundantly in numerals and in alphabetical form. Information from two optical character recognition modules, one specialized for digits and one for words, is combined to yield an enhanced recognition of the amount. The combination can be accomplished by a decision tree with "if-then" rules, but by simply fusing two or more sets of sensor data in a single expanded neural net, the same functionality can be expected with a much reduced system cost. Experimental results of fusing two neural nets to enhance overall recognition performance using a controlled data set are presented.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Variational method for integrating radial gradient field

NASA Astrophysics Data System (ADS)

Legarda-Saenz, Ricardo; Brito-Loeza, Carlos; Rivera, Mariano; Espinosa-Romero, Arturo

2014-12-01

We propose a variational method for integrating information obtained from circular fringe pattern. The proposed method is a suitable choice for objects with radial symmetry. First, we analyze the information contained in the fringe pattern captured by the experimental setup and then move to formulate the problem of recovering the wavefront using techniques from calculus of variations. The performance of the method is demonstrated by numerical experiments with both synthetic and real data.

Diagram reduction in problem of critical dynamics of ferromagnets: 4-loop approximation

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts; Ivanova, E. V.; Kompaniets, M. V.; Vorobyeva, S. Ye

2018-04-01

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we perform a calculation of the critical exponent z of model A at 4-loop level, where our method allows one to reduce the number of integrals from 66 to 17. The way of constructing the integrand in a Feynman representation of such diagrams is discussed. Integrals were estimated numerically with a sector decomposition technique.

CSM solutions of rotating blade dynamics using integrating matrices

NASA Technical Reports Server (NTRS)

Lakin, William D.

1992-01-01

The dynamic behavior of flexible rotating beams continues to receive considerable research attention as it constitutes a fundamental problem in applied mechanics. Further, beams comprise parts of many rotating structures of engineering significance. A topic of particular interest at the present time involves the development of techniques for obtaining the behavior in both space and time of a rotor acted upon by a simple airload loading. Most current work on problems of this type use solution techniques based on normal modes. It is certainly true that normal modes cannot be disregarded, as knowledge of natural blade frequencies is always important. However, the present work has considered a computational structural mechanics (CSM) approach to rotor blade dynamics problems in which the physical properties of the rotor blade provide input for a direct numerical solution of the relevant boundary-and-initial-value problem. Analysis of the dynamics of a given rotor system may require solution of the governing equations over a long time interval corresponding to many revolutions of the loaded flexible blade. For this reason, most of the common techniques in computational mechanics, which treat the space-time behavior concurrently, cannot be applied to the rotor dynamics problem without a large expenditure of computational resources. By contrast, the integrating matrix technique of computational mechanics has the ability to consistently incorporate boundary conditions and 'remove' dependence on a space variable. For problems involving both space and time, this feature of the integrating matrix approach thus can generate a 'splitting' which forms the basis of an efficient CSM method for numerical solution of rotor dynamics problems.

The Development and Comparison of Molecular Dynamics Simulation and Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Chen, Jundong

2018-03-01

Molecular dynamics is an integrated technology that combines physics, mathematics and chemistry. Molecular dynamics method is a computer simulation experimental method, which is a powerful tool for studying condensed matter system. This technique not only can get the trajectory of the atom, but can also observe the microscopic details of the atomic motion. By studying the numerical integration algorithm in molecular dynamics simulation, we can not only analyze the microstructure, the motion of particles and the image of macroscopic relationship between them and the material, but can also study the relationship between the interaction and the macroscopic properties more conveniently. The Monte Carlo Simulation, similar to the molecular dynamics, is a tool for studying the micro-molecular and particle nature. In this paper, the theoretical background of computer numerical simulation is introduced, and the specific methods of numerical integration are summarized, including Verlet method, Leap-frog method and Velocity Verlet method. At the same time, the method and principle of Monte Carlo Simulation are introduced. Finally, similarities and differences of Monte Carlo Simulation and the molecular dynamics simulation are discussed.

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Downhole drilling network using burst modulation techniques

DOEpatents

Hall,; David R. , Fox; Joe, [Spanish Fork, UT

2007-04-03

A downhole drilling system is disclosed in one aspect of the present invention as including a drill string and a transmission line integrated into the drill string. Multiple network nodes are installed at selected intervals along the drill string and are adapted to communicate with one another through the transmission line. In order to efficiently allocate the available bandwidth, the network nodes are configured to use any of numerous burst modulation techniques to transmit data.

Statistical Mechanics and Dynamics of the Outer Solar System.I. The Jupiter/Saturn Zone

NASA Technical Reports Server (NTRS)

Grazier, K. R.; Newman, W. I.; Kaula, W. M.; Hyman, J. M.

1996-01-01

We report on numerical simulations designed to understand how the solar system evolved through a winnowing of planetesimals accreeted from the early solar nebula. This sorting process is driven by the energy and angular momentum and continues to the present day. We reconsider the existence and importance of stable niches in the Jupiter/Saturn Zone using greatly improved numerical techniques based on high-order optimized multi-step integration schemes coupled to roundoff error minimizing methods.

Numerical and experimental analysis of a ducted propeller designed by a fully automated optimization process under open water condition

NASA Astrophysics Data System (ADS)

Yu, Long; Druckenbrod, Markus; Greve, Martin; Wang, Ke-qi; Abdel-Maksoud, Moustafa

2015-10-01

A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The developed process allows the direct integration of a RANSE solver in the design stage. A practical ducted propeller design case study is carried out for validation. Numerical simulations and open water tests are fulfilled and proved that the optimum ducted propeller improves hydrodynamic performance as predicted.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Computer modeling of test particle acceleration at oblique shocks

NASA Technical Reports Server (NTRS)

Decker, Robert B.

1988-01-01

The present evaluation of the basic techniques and illustrative results of charged particle-modeling numerical codes suitable for particle acceleration at oblique, fast-mode collisionless shocks emphasizes the treatment of ions as test particles, calculating particle dynamics through numerical integration along exact phase-space orbits. Attention is given to the acceleration of particles at planar, infinitessimally thin shocks, as well as to plasma simulations in which low-energy ions are injected and accelerated at quasi-perpendicular shocks with internal structure.

Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations

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

Chen, Guangye; Chacon, Luis; Knoll, Dana Alan

2015-07-31

A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω peΔt >>1, and Δx >> λ D), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylovmore » (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.« less

Thin-plate spline quadrature of geodetic integrals

NASA Technical Reports Server (NTRS)

Vangysen, Herman

1989-01-01

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Experimental analysis and numerical modeling of mollusk shells as a three dimensional integrated volume.

PubMed

Faghih Shojaei, M; Mohammadi, V; Rajabi, H; Darvizeh, A

2012-12-01

In this paper, a new numerical technique is presented to accurately model the geometrical and mechanical features of mollusk shells as a three dimensional (3D) integrated volume. For this purpose, the Newton method is used to solve the nonlinear equations of shell surfaces. The points of intersection on the shell surface are identified and the extra interior parts are removed. Meshing process is accomplished with respect to the coordinate of each point of intersection. The final 3D generated mesh models perfectly describe the spatial configuration of the mollusk shells. Moreover, the computational model perfectly matches with the actual interior geometry of the shells as well as their exterior architecture. The direct generation technique is employed to generate a 3D finite element (FE) model in ANSYS 11. X-ray images are taken to show the close similarity of the interior geometry of the models and the actual samples. A scanning electron microscope (SEM) is used to provide information on the microstructure of the shells. In addition, a set of compression tests were performed on gastropod shell specimens to obtain their ultimate compressive strength. A close agreement between experimental data and the relevant numerical results is demonstrated. Copyright © 2012 Elsevier Ltd. All rights reserved.

On the energy integral for first post-Newtonian approximation

NASA Astrophysics Data System (ADS)

O'Leary, Joseph; Hill, James M.; Bennett, James C.

2018-07-01

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials W^j (j=1,2,3), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.

Suture Products and Techniques: What to Use, Where, and Why.

PubMed

Regula, Christie G; Yag-Howard, Cyndi

2015-10-01

There are an increasing number of wound closure materials and suturing techniques described in the dermatologic and surgery literature. A dermatologic surgeon's familiarity with these materials and techniques is important to supplement his or her already established practices and improve surgical outcomes. To perform a thorough literature review of wound closure materials (sutures, tissue adhesives, surgical tape, and staples) and suturing techniques and to outline how and when to use them. A literature review was conducted using PubMed and other online search engines. Keywords searched included suture, tissue adhesive, tissue glue, surgical tape, staples, dermatologic suturing, and suturing techniques. Numerous articles outline the utility of various sutures, surgical adhesives, surgical tape, and staples in dermatologic surgery. In addition, there are various articles describing classic and novel suturing techniques along with their specific uses in cutaneous surgery. Numerous factors must be considered when choosing a wound closure material and suturing technique. These include wound tension, desire for wound edge eversion/inversion, desired hemostasis, repair type, patient's ability to care for the wound and return for suture removal, skin integrity, and wound location. Careful consideration of these factors and proper execution of suturing techniques can lead to excellent cosmetic results.

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

NASA Technical Reports Server (NTRS)

Radhakrishnan, K.

1984-01-01

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Simulation tools for guided wave based structural health monitoring

NASA Astrophysics Data System (ADS)

Mesnil, Olivier; Imperiale, Alexandre; Demaldent, Edouard; Baronian, Vahan; Chapuis, Bastien

2018-04-01

Structural Health Monitoring (SHM) is a thematic derived from Non Destructive Evaluation (NDE) based on the integration of sensors onto or into a structure in order to monitor its health without disturbing its regular operating cycle. Guided wave based SHM relies on the propagation of guided waves in plate-like or extruded structures. Using piezoelectric transducers to generate and receive guided waves is one of the most widely accepted paradigms due to the low cost and low weight of those sensors. A wide range of techniques for flaw detection based on the aforementioned setup is available in the literature but very few of these techniques have found industrial applications yet. A major difficulty comes from the sensitivity of guided waves to a substantial number of parameters such as the temperature or geometrical singularities, making guided wave measurement difficult to analyze. In order to apply guided wave based SHM techniques to a wider spectrum of applications and to transfer those techniques to the industry, the CEA LIST develops novel numerical methods. These methods facilitate the evaluation of the robustness of SHM techniques for multiple applicative cases and ease the analysis of the influence of various parameters, such as sensors positioning or environmental conditions. The first numerical tool is the guided wave module integrated to the commercial software CIVA, relying on a hybrid modal-finite element formulation to compute the guided wave response of perturbations (cavities, flaws…) in extruded structures of arbitrary cross section such as rails or pipes. The second numerical tool is based on the spectral element method [2] and simulates guided waves in both isotropic (metals) and orthotropic (composites) plate like-structures. This tool is designed to match the widely accepted sparse piezoelectric transducer array SHM configuration in which each embedded sensor acts as both emitter and receiver of guided waves. This tool is under development and will be adapted to simulate complex real-life structures such as curved composite panels with stiffeners. This communication will present these numerical tools and their main functionalities.

A satellite digital controller or 'play that PID tune again, Sam'. [Position, Integral, Derivative feedback control algorithm for design strategy

NASA Technical Reports Server (NTRS)

Seltzer, S. M.

1976-01-01

The problem discussed is to design a digital controller for a typical satellite. The controlled plant is considered to be a rigid body acting in a plane. The controller is assumed to be a digital computer which, when combined with the proposed control algorithm, can be represented as a sampled-data system. The objective is to present a design strategy and technique for selecting numerical values for the control gains (assuming position, integral, and derivative feedback) and the sample rate. The technique is based on the parameter plane method and requires that the system be amenable to z-transform analysis.

A Gas Dynamics Method Based on The Spectral Deferred Corrections (SDC) Time Integration Technique and The Piecewise Parabolic Method (PPM)

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

Samet Y. Kadioglu

2011-12-01

We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge averaged quantities which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [17]. However, [17] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [17]. The method is fourth order (both in space and time) for smooth flows,more » and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.« less

An Empirical Evaluation of Five Circular Error Probable Estimation Techniques and a Method for Improving Them

DTIC Science & Technology

1993-03-10

template which runs a Romberg algorithm in the background to numerically integrate the BVN [12:257]. Appendix A als- lists the results from two other...for computing these values: a Taylor series expansion, the Romberg algorithm , and the CBN technique. Appendix A lists CEPpop. values for eleven...determining factor in this selection process. Of the 175 populations ex- amined in the experiment, the MathCAD version of the Romberg algorithm failed

All-optical signal processing using dynamic Brillouin gratings

PubMed Central

Santagiustina, Marco; Chin, Sanghoon; Primerov, Nicolay; Ursini, Leonora; Thévenaz, Luc

2013-01-01

The manipulation of dynamic Brillouin gratings in optical fibers is demonstrated to be an extremely flexible technique to achieve, with a single experimental setup, several all-optical signal processing functions. In particular, all-optical time differentiation, time integration and true time reversal are theoretically predicted, and then numerically and experimentally demonstrated. The technique can be exploited to process both photonic and ultra-wide band microwave signals, so enabling many applications in photonics and in radio science. PMID:23549159

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

PubMed

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

NASA Astrophysics Data System (ADS)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

A computerized symbolic integration technique for development of triangular and quadrilateral composite shallow-shell finite elements

NASA Technical Reports Server (NTRS)

Anderson, C. M.; Noor, A. K.

1975-01-01

Computerized symbolic integration was used in conjunction with group-theoretic techniques to obtain analytic expressions for the stiffness, geometric stiffness, consistent mass, and consistent load matrices of composite shallow shell structural elements. The elements are shear flexible and have variable curvature. A stiffness (displacement) formulation was used with the fundamental unknowns consisting of both the displacement and rotation components of the reference surface of the shell. The triangular elements have six and ten nodes; the quadrilateral elements have four and eight nodes and can have internal degrees of freedom associated with displacement modes which vanish along the edges of the element (bubble modes). The stiffness, geometric stiffness, consistent mass, and consistent load coefficients are expressed as linear combinations of integrals (over the element domain) whose integrands are products of shape functions and their derivatives. The evaluation of the elemental matrices is divided into two separate problems - determination of the coefficients in the linear combination and evaluation of the integrals. The integrals are performed symbolically by using the symbolic-and-algebraic-manipulation language MACSYMA. The efficiency of using symbolic integration in the element development is demonstrated by comparing the number of floating-point arithmetic operations required in this approach with those required by a commonly used numerical quadrature technique.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Reliability-Based Stability Analysis of Rock Slopes Using Numerical Analysis and Response Surface Method

NASA Astrophysics Data System (ADS)

Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.

2017-08-01

While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.

hp-Adaptive time integration based on the BDF for viscous flows

NASA Astrophysics Data System (ADS)

Hay, A.; Etienne, S.; Pelletier, D.; Garon, A.

2015-06-01

This paper presents a procedure based on the Backward Differentiation Formulas of order 1 to 5 to obtain efficient time integration of the incompressible Navier-Stokes equations. The adaptive algorithm performs both stepsize and order selections to control respectively the solution accuracy and the computational efficiency of the time integration process. The stepsize selection (h-adaptivity) is based on a local error estimate and an error controller to guarantee that the numerical solution accuracy is within a user prescribed tolerance. The order selection (p-adaptivity) relies on the idea that low-accuracy solutions can be computed efficiently by low order time integrators while accurate solutions require high order time integrators to keep computational time low. The selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize. Hence, it guarantees both that (1) the used method of integration operates inside of its stability region and (2) the time integration procedure is computationally efficient. The proposed time integration procedure also features a time-step rejection and quarantine mechanisms, a modified Newton method with a predictor and dense output techniques to compute solution at off-step points.

Efficient integration method for fictitious domain approaches

NASA Astrophysics Data System (ADS)

Duczek, Sascha; Gabbert, Ulrich

2015-10-01

In the current article, we present an efficient and accurate numerical method for the integration of the system matrices in fictitious domain approaches such as the finite cell method (FCM). In the framework of the FCM, the physical domain is embedded in a geometrically larger domain of simple shape which is discretized using a regular Cartesian grid of cells. Therefore, a spacetree-based adaptive quadrature technique is normally deployed to resolve the geometry of the structure. Depending on the complexity of the structure under investigation this method accounts for most of the computational effort. To reduce the computational costs for computing the system matrices an efficient quadrature scheme based on the divergence theorem (Gauß-Ostrogradsky theorem) is proposed. Using this theorem the dimension of the integral is reduced by one, i.e. instead of solving the integral for the whole domain only its contour needs to be considered. In the current paper, we present the general principles of the integration method and its implementation. The results to several two-dimensional benchmark problems highlight its properties. The efficiency of the proposed method is compared to conventional spacetree-based integration techniques.

From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics

NASA Astrophysics Data System (ADS)

Kreis, Karsten; Kremer, Kurt; Potestio, Raffaello; Tuckerman, Mark E.

2017-12-01

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

Confining potential in momentum space

NASA Technical Reports Server (NTRS)

Norbury, John W.; Kahana, David E.; Maung, Khin Maung

1992-01-01

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

A User's Applications of Imaging Techniques: The University of Maryland Historic Textile Database.

ERIC Educational Resources Information Center

Anderson, Clarita S.

1991-01-01

Describes the incorporation of textile images into the University of Maryland Historic Textile Database by a computer user rather than a computer expert. Selection of a database management system is discussed, and PICTUREPOWER, a system that integrates photographic quality images with text and numeric information in databases, is described. (three…

Transient well flow in vertically heterogeneous aquifers

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

A solution for the general problem of computing well flow in vertically heterogeneous aquifers is found by an integration of both analytical and numerical techniques. The radial component of flow is treated analytically; the drawdown is a continuous function of the distance to the well. The finite-difference technique is used for the vertical flow component only. The aquifer is discretized in the vertical dimension and the heterogeneous aquifer is considered to be a layered (stratified) formation with a finite number of homogeneous sublayers, where each sublayer may have different properties. The transient part of the differential equation is solved with Stehfest's algorithm, a numerical inversion technique of the Laplace transform. The well is of constant discharge and penetrates one or more of the sublayers. The effect of wellbore storage on early drawdown data is taken into account. In this way drawdowns are found for a finite number of sublayers as a continuous function of radial distance to the well and of time since the pumping started. The model is verified by comparing results with published analytical and numerical solutions for well flow in homogeneous and heterogeneous, confined and unconfined aquifers. Instantaneous and delayed drainage of water from above the water table are considered, combined with the effects of partially penetrating and finite-diameter wells. The model is applied to demonstrate that the transient effects of wellbore storage in unconfined aquifers are less pronounced than previous numerical experiments suggest. Other applications of the presented solution technique are given for partially penetrating wells in heterogeneous formations, including a demonstration of the effect of decreasing specific storage values with depth in an otherwise homogeneous aquifer. The presented solution can be a powerful tool for the analysis of drawdown from pumping tests, because hydraulic properties of layered heterogeneous aquifer systems with partially penetrating wells may be estimated without the need to construct transient numerical models. A computer program based on the hybrid analytical-numerical technique is available from the author.

Wavelet Algorithms for Illumination Computations

NASA Astrophysics Data System (ADS)

Schroder, Peter

One of the core problems of computer graphics is the computation of the equilibrium distribution of light in a scene. This distribution is given as the solution to a Fredholm integral equation of the second kind involving an integral over all surfaces in the scene. In the general case such solutions can only be numerically approximated, and are generally costly to compute, due to the geometric complexity of typical computer graphics scenes. For this computation both Monte Carlo and finite element techniques (or hybrid approaches) are typically used. A simplified version of the illumination problem is known as radiosity, which assumes that all surfaces are diffuse reflectors. For this case hierarchical techniques, first introduced by Hanrahan et al. (32), have recently gained prominence. The hierarchical approaches lead to an asymptotic improvement when only finite precision is required. The resulting algorithms have cost proportional to O(k^2 + n) versus the usual O(n^2) (k is the number of input surfaces, n the number of finite elements into which the input surfaces are meshed). Similarly a hierarchical technique has been introduced for the more general radiance problem (which allows glossy reflectors) by Aupperle et al. (6). In this dissertation we show the equivalence of these hierarchical techniques to the use of a Haar wavelet basis in a general Galerkin framework. By so doing, we come to a deeper understanding of the properties of the numerical approximations used and are able to extend the hierarchical techniques to higher orders. In particular, we show the correspondence of the geometric arguments underlying hierarchical methods to the theory of Calderon-Zygmund operators and their sparse realization in wavelet bases. The resulting wavelet algorithms for radiosity and radiance are analyzed and numerical results achieved with our implementation are reported. We find that the resulting algorithms achieve smaller and smoother errors at equivalent work.

A novel hybrid scattering order-dependent variance reduction method for Monte Carlo simulations of radiative transfer in cloudy atmosphere

NASA Astrophysics Data System (ADS)

Wang, Zhen; Cui, Shengcheng; Yang, Jun; Gao, Haiyang; Liu, Chao; Zhang, Zhibo

2017-03-01

We present a novel hybrid scattering order-dependent variance reduction method to accelerate the convergence rate in both forward and backward Monte Carlo radiative transfer simulations involving highly forward-peaked scattering phase function. This method is built upon a newly developed theoretical framework that not only unifies both forward and backward radiative transfer in scattering-order-dependent integral equation, but also generalizes the variance reduction formalism in a wide range of simulation scenarios. In previous studies, variance reduction is achieved either by using the scattering phase function forward truncation technique or the target directional importance sampling technique. Our method combines both of them. A novel feature of our method is that all the tuning parameters used for phase function truncation and importance sampling techniques at each order of scattering are automatically optimized by the scattering order-dependent numerical evaluation experiments. To make such experiments feasible, we present a new scattering order sampling algorithm by remodeling integral radiative transfer kernel for the phase function truncation method. The presented method has been implemented in our Multiple-Scaling-based Cloudy Atmospheric Radiative Transfer (MSCART) model for validation and evaluation. The main advantage of the method is that it greatly improves the trade-off between numerical efficiency and accuracy order by order.

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Introduction to Computational Physics for Undergraduates

NASA Astrophysics Data System (ADS)

Zubairi, Omair; Weber, Fridolin

2018-03-01

This is an introductory textbook on computational methods and techniques intended for undergraduates at the sophomore or junior level in the fields of science, mathematics, and engineering. It provides an introduction to programming languages such as FORTRAN 90/95/2000 and covers numerical techniques such as differentiation, integration, root finding, and data fitting. The textbook also entails the use of the Linux/Unix operating system and other relevant software such as plotting programs, text editors, and mark up languages such as LaTeX. It includes multiple homework assignments.

Active Vibration damping of Smart composite beams based on system identification technique

NASA Astrophysics Data System (ADS)

Bendine, Kouider; Satla, Zouaoui; Boukhoulda, Farouk Benallel; Nouari, Mohammed

2018-03-01

In the present paper, the active vibration control of a composite beam using piezoelectric actuator is investigated. The space state equation is determined using system identification technique based on the structure input output response provided by ANSYS APDL finite element package. The Linear Quadratic (LQG) control law is designed and integrated into ANSYS APDL to perform closed loop simulations. Numerical examples for different types of excitation loads are presented to test the efficiency and the accuracy of the proposed model.

Analysis of real-time numerical integration methods applied to dynamic clamp experiments.

PubMed

Butera, Robert J; McCarthy, Maeve L

2004-12-01

Real-time systems are frequently used as an experimental tool, whereby simulated models interact in real time with neurophysiological experiments. The most demanding of these techniques is known as the dynamic clamp, where simulated ion channel conductances are artificially injected into a neuron via intracellular electrodes for measurement and stimulation. Methodologies for implementing the numerical integration of the gating variables in real time typically employ first-order numerical methods, either Euler or exponential Euler (EE). EE is often used for rapidly integrating ion channel gating variables. We find via simulation studies that for small time steps, both methods are comparable, but at larger time steps, EE performs worse than Euler. We derive error bounds for both methods, and find that the error can be characterized in terms of two ratios: time step over time constant, and voltage measurement error over the slope factor of the steady-state activation curve of the voltage-dependent gating variable. These ratios reliably bound the simulation error and yield results consistent with the simulation analysis. Our bounds quantitatively illustrate how measurement error restricts the accuracy that can be obtained by using smaller step sizes. Finally, we demonstrate that Euler can be computed with identical computational efficiency as EE.

A Pressure Plate-Based Method for the Automatic Assessment of Foot Strike Patterns During Running.

PubMed

Santuz, Alessandro; Ekizos, Antonis; Arampatzis, Adamantios

2016-05-01

The foot strike pattern (FSP, description of how the foot touches the ground at impact) is recognized to be a predictor of both performance and injury risk. The objective of the current investigation was to validate an original foot strike pattern assessment technique based on the numerical analysis of foot pressure distribution. We analyzed the strike patterns during running of 145 healthy men and women (85 male, 60 female). The participants ran on a treadmill with integrated pressure plate at three different speeds: preferred (shod and barefoot 2.8 ± 0.4 m/s), faster (shod 3.5 ± 0.6 m/s) and slower (shod 2.3 ± 0.3 m/s). A custom-designed algorithm allowed the automatic footprint recognition and FSP evaluation. Incomplete footprints were simultaneously identified and corrected from the software itself. The widely used technique of analyzing high-speed video recordings was checked for its reliability and has been used to validate the numerical technique. The automatic numerical approach showed a good conformity with the reference video-based technique (ICC = 0.93, p < 0.01). The great improvement in data throughput and the increased completeness of results allow the use of this software as a powerful feedback tool in a simple experimental setup.

Finite element based simulation on friction stud welding of metal matrix composites to steel

NASA Astrophysics Data System (ADS)

Hynes, N. Rajesh Jesudoss; Tharmaraj, R.; Velu, P. Shenbaga; Kumar, R.

2016-05-01

Friction welding is a solid state joining technique used for joining similar and dissimilar materials with high integrity. This new technique is being successfully applied to the aerospace, automobile, and ship building industries, and is attracting more and more research interest. The quality of Friction Stud Welded joints depends on the frictional heat generated at the interface. Hence, thermal analysis on friction stud welding of stainless steel (AISI 304) and aluminium silicon carbide (AlSiC) combination is carried out in the present work. In this study, numerical simulation is carried out using ANSYS software and the temperature profiles are predicted at various increments of time. The developed numerical model is found to be adequate to predict temperature distribution of friction stud weld aluminium silicon carbide/stainless steel joints.

Analysis and testing of numerical formulas for the initial value problem

NASA Technical Reports Server (NTRS)

Brown, R. L.; Kovach, K. R.; Popyack, J. L.

1980-01-01

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Automated monitor and control for deep space network subsystems

NASA Technical Reports Server (NTRS)

Smyth, P.

1989-01-01

The problem of automating monitor and control loops for Deep Space Network (DSN) subsystems is considered and an overview of currently available automation techniques is given. The use of standard numerical models, knowledge-based systems, and neural networks is considered. It is argued that none of these techniques alone possess sufficient generality to deal with the demands imposed by the DSN environment. However, it is shown that schemes that integrate the better aspects of each approach and are referenced to a formal system model show considerable promise, although such an integrated technology is not yet available for implementation. Frequent reference is made to the receiver subsystem since this work was largely motivated by experience in developing an automated monitor and control loop for the advanced receiver.

A novel approach to evaluation of pest insect abundance in the presence of noise.

PubMed

Embleton, Nina; Petrovskaya, Natalia

2014-03-01

Evaluation of pest abundance is an important task of integrated pest management. It has recently been shown that evaluation of pest population size from discrete sampling data can be done by using the ideas of numerical integration. Numerical integration of the pest population density function is a computational technique that readily gives us an estimate of the pest population size, where the accuracy of the estimate depends on the number of traps installed in the agricultural field to collect the data. However, in a standard mathematical problem of numerical integration, it is assumed that the data are precise, so that the random error is zero when the data are collected. This assumption does not hold in ecological applications. An inherent random error is often present in field measurements, and therefore it may strongly affect the accuracy of evaluation. In our paper, we offer a novel approach to evaluate the pest insect population size under the assumption that the data about the pest population include a random error. The evaluation is not based on statistical methods but is done using a spatially discrete method of numerical integration where the data obtained by trapping as in pest insect monitoring are converted to values of the population density. It will be discussed in the paper how the accuracy of evaluation differs from the case where the same evaluation method is employed to handle precise data. We also consider how the accuracy of the pest insect abundance evaluation can be affected by noise when the data available from trapping are sparse. In particular, we show that, contrary to intuitive expectations, noise does not have any considerable impact on the accuracy of evaluation when the number of traps is small as is conventional in ecological applications.

Hydroforming Of Patchwork Blanks — Numerical Modeling And Experimental Validation

NASA Astrophysics Data System (ADS)

Lamprecht, Klaus; Merklein, Marion; Geiger, Manfred

2005-08-01

In comparison to the commonly applied technology of tailored blanks the concept of patchwork blanks offers a number of additional advantages. Potential application areas for patchwork blanks in automotive industry are e.g. local reinforcements of automotive closures, structural reinforcements of rails and pillars as well as shock towers. But even if there is a significant application potential for patchwork blanks in automobile production, industrial realization of this innovative technique is decelerated due to a lack of knowledge regarding the forming behavior and the numerical modeling of patchwork blanks. Especially for the numerical simulation of hydroforming processes, where one part of the forming tool is replaced by a fluid under pressure, advanced modeling techniques are required to ensure an accurate prediction of the blanks' forming behavior. The objective of this contribution is to provide an appropriate model for the numerical simulation of patchwork blanks' forming processes. Therefore, different finite element modeling techniques for patchwork blanks are presented. In addition to basic shell element models a combined finite element model consisting of shell and solid elements is defined. Special emphasis is placed on the modeling of the weld seam. For this purpose the local mechanical properties of the weld metal, which have been determined by means of Martens-hardness measurements and uniaxial tensile tests, are integrated in the finite element models. The results obtained from the numerical simulations are compared to experimental data from a hydraulic bulge test. In this context the focus is laid on laser- and spot-welded patchwork blanks.

From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element method

PubMed Central

Bolis, A; Cantwell, C D; Kirby, R M; Sherwin, S J

2014-01-01

We investigate the relative performance of a second-order Adams–Bashforth scheme and second-order and fourth-order Runge–Kutta schemes when time stepping a 2D linear advection problem discretised using a spectral/hp element technique for a range of different mesh sizes and polynomial orders. Numerical experiments explore the effects of short (two wavelengths) and long (32 wavelengths) time integration for sets of uniform and non-uniform meshes. The choice of time-integration scheme and discretisation together fixes a CFL limit that imposes a restriction on the maximum time step, which can be taken to ensure numerical stability. The number of steps, together with the order of the scheme, affects not only the runtime but also the accuracy of the solution. Through numerical experiments, we systematically highlight the relative effects of spatial resolution and choice of time integration on performance and provide general guidelines on how best to achieve the minimal execution time in order to obtain a prescribed solution accuracy. The significant role played by higher polynomial orders in reducing CPU time while preserving accuracy becomes more evident, especially for uniform meshes, compared with what has been typically considered when studying this type of problem.© 2014. The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons, Ltd. PMID:25892840

A reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows

NASA Astrophysics Data System (ADS)

Meldi, M.; Poux, A.

2017-10-01

A Kalman filter based sequential estimator is presented in this work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state integrating available observation in the CFD model, naturally preserving a zero-divergence condition for the velocity field. Because of the prohibitive costs associated with a complete Kalman Filter application, two model reduction strategies have been proposed and assessed. These strategies dramatically reduce the increase in computational costs of the model, which can be quantified in an augmentation of 10%- 15% with respect to the classical numerical simulation. In addition, an extended analysis of the behavior of the numerical model covariance Q has been performed. Optimized values are strongly linked to the truncation error of the discretization procedure. The estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity, including turbulent flow configurations. The results show that the augmented flow successfully improves the prediction of the physical quantities investigated, even when the observation is provided in a limited region of the physical domain. In addition, the present work suggests that these Data Assimilation techniques, which are at an embryonic stage of development in CFD, may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation.

An integrated approach to improving noisy speech perception

NASA Astrophysics Data System (ADS)

Koval, Serguei; Stolbov, Mikhail; Smirnova, Natalia; Khitrov, Mikhail

2002-05-01

For a number of practical purposes and tasks, experts have to decode speech recordings of very poor quality. A combination of techniques is proposed to improve intelligibility and quality of distorted speech messages and thus facilitate their comprehension. Along with the application of noise cancellation and speech signal enhancement techniques removing and/or reducing various kinds of distortions and interference (primarily unmasking and normalization in time and frequency fields), the approach incorporates optimal listener expert tactics based on selective listening, nonstandard binaural listening, accounting for short-term and long-term human ear adaptation to noisy speech, as well as some methods of speech signal enhancement to support speech decoding during listening. The approach integrating the suggested techniques ensures high-quality ultimate results and has successfully been applied by Speech Technology Center experts and by numerous other users, mainly forensic institutions, to perform noisy speech records decoding for courts, law enforcement and emergency services, accident investigation bodies, etc.

Integrated computational study of ultra-high heat flux cooling using cryogenic micro-solid nitrogen spray

NASA Astrophysics Data System (ADS)

Ishimoto, Jun; Oh, U.; Tan, Daisuke

2012-10-01

A new type of ultra-high heat flux cooling system using the atomized spray of cryogenic micro-solid nitrogen (SN2) particles produced by a superadiabatic two-fluid nozzle was developed and numerically investigated for application to next generation super computer processor thermal management. The fundamental characteristics of heat transfer and cooling performance of micro-solid nitrogen particulate spray impinging on a heated substrate were numerically investigated and experimentally measured by a new type of integrated computational-experimental technique. The employed Computational Fluid Dynamics (CFD) analysis based on the Euler-Lagrange model is focused on the cryogenic spray behavior of atomized particulate micro-solid nitrogen and also on its ultra-high heat flux cooling characteristics. Based on the numerically predicted performance, a new type of cryogenic spray cooling technique for application to a ultra-high heat power density device was developed. In the present integrated computation, it is clarified that the cryogenic micro-solid spray cooling characteristics are affected by several factors of the heat transfer process of micro-solid spray which impinges on heated surface as well as by atomization behavior of micro-solid particles. When micro-SN2 spraying cooling was used, an ultra-high cooling heat flux level was achieved during operation, a better cooling performance than that with liquid nitrogen (LN2) spray cooling. As micro-SN2 cooling has the advantage of direct latent heat transport which avoids the film boiling state, the ultra-short time scale heat transfer in a thin boundary layer is more possible than in LN2 spray. The present numerical prediction of the micro-SN2 spray cooling heat flux profile can reasonably reproduce the measurement results of cooling wall heat flux profiles. The application of micro-solid spray as a refrigerant for next generation computer processors is anticipated, and its ultra-high heat flux technology is expected to result in an extensive improvement in the effective cooling performance of large scale supercomputer systems.

Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational

DOE PAGES

Ellison, C. L.; Burby, J. W.; Qin, H.

2015-11-01

One popular technique for the numerical time advance of charged particles interacting with electric and magnetic fields according to the Lorentz force law [1], [2], [3] and [4] is the Boris algorithm. Its popularity stems from simple implementation, rapid iteration, and excellent long-term numerical fidelity [1] and [5]. Excellent long-term behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6]. Moreover, without conserved quantities to constrain the numerical dynamics, algorithms typically dissipate or accumulate important observables such as energy and momentum over long periods of simulated time [6]. Identification of themore » conservative properties of an algorithm is important for establishing rigorous expectations on the long-term behavior; energy-preserving, symplectic, and volume-preserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].« less

GNSS-based multi-sensor system for structural monitoring applications

NASA Astrophysics Data System (ADS)

Bogusz, Janusz; Figurski, Mariusz; Nykiel, Grzegorz; Szolucha, Marcin; Wrona, Maciej

2012-03-01

In 2007 the Centre of Applied Geomatics of the Military University of Technology started measurements aimed at the monitoring of the dynamic state of the engineering structures using GNSS. The complexity of the problem forced us to apply an integrated system architecture. This concept is based on simultaneous measuring some selected elements of the structure using various types of sensors. Measurement information from numerous instruments is numerically integrated for determining the investigated parameter, e.g., the displacement vector. The CAG team performed the tests using such a system on the two permanent 500-meters long bridges, the temporary bridge crossing for military purposes and the 300-meters high chimney of the CHP station. The information about displacement vector together with the characteristic frequencies of the structure were determined using different techniques for increasing of its reliability. This paper presents the results of such tests, gives description of the integrated system designed in the CAG and brings forward with the plans for the future.

Materials-by-design: computation, synthesis, and characterization from atoms to structures

NASA Astrophysics Data System (ADS)

Yeo, Jingjie; Jung, Gang Seob; Martín-Martínez, Francisco J.; Ling, Shengjie; Gu, Grace X.; Qin, Zhao; Buehler, Markus J.

2018-05-01

In the 50 years that succeeded Richard Feynman’s exposition of the idea that there is ‘plenty of room at the bottom’ for manipulating individual atoms for the synthesis and manufacturing processing of materials, the materials-by-design paradigm is being developed gradually through synergistic integration of experimental material synthesis and characterization with predictive computational modeling and optimization. This paper reviews how this paradigm creates the possibility to develop materials according to specific, rational designs from the molecular to the macroscopic scale. We discuss promising techniques in experimental small-scale material synthesis and large-scale fabrication methods to manipulate atomistic or macroscale structures, which can be designed by computational modeling. These include recombinant protein technology to produce peptides and proteins with tailored sequences encoded by recombinant DNA, self-assembly processes induced by conformational transition of proteins, additive manufacturing for designing complex structures, and qualitative and quantitative characterization of materials at different length scales. We describe important material characterization techniques using numerous methods of spectroscopy and microscopy. We detail numerous multi-scale computational modeling techniques that complements these experimental techniques: DFT at the atomistic scale; fully atomistic and coarse-grain molecular dynamics at the molecular to mesoscale; continuum modeling at the macroscale. Additionally, we present case studies that utilize experimental and computational approaches in an integrated manner to broaden our understanding of the properties of two-dimensional materials and materials based on silk and silk-elastin-like proteins.

An integrated Navier-Stokes - full potential - free wake method for rotor flows

NASA Astrophysics Data System (ADS)

Berkman, Mert Enis

1998-12-01

The strong wake shed from rotary wings interacts with almost all components of the aircraft, and alters the flow field thus causing performance and noise problems. Understanding and modeling the behavior of this wake, and its effect on the aerodynamics and acoustics of helicopters have remained as challenges. This vortex wake and its effect should be accurately accounted for in any technique that aims to predict rotor flow field and performance. In this study, an advanced and efficient computational technique for predicting three-dimensional unsteady viscous flows over isolated helicopter rotors in hover and in forward flight is developed. In this hybrid technique, the advantages of various existing methods have been combined to accurately and efficiently study rotor flows with a single numerical method. The flow field is viewed in three parts: (i) an inner zone surrounding each blade where the wake and viscous effects are numerically captured, (ii) an outer zone away from the blades where wake is modeled, and (iii) a Lagrangean wake which induces wake effects in the outer zone. This technique was coded in a flow solver and compared with experimental data for hovering and advancing rotors including a two-bladed rotor, the UH-60A rotor and a tapered tip rotor. Detailed surface pressure, integrated thrust and torque, sectional thrust, and tip vortex position predictions compared favorably against experimental data. Results indicated that the hybrid solver provided accurate flow details and performance information typically in one-half to one-eighth cost of complete Navier-Stokes methods.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

NASA Technical Reports Server (NTRS)

Drummond, Mark; Fox, Mark; Tate, Austin; Zweben, Monte

1992-01-01

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques.

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.

Side-branch resonators modelling with Green's function methods

NASA Astrophysics Data System (ADS)

Perrey-Debain, E.; Maréchal, R.; Ville, J. M.

2014-09-01

This paper deals with strategies for computing efficiently the propagation of sound waves in ducts containing passive components. In many cases of practical interest, these components are acoustic cavities which are connected to the duct. Though standard Finite Element software could be used for the numerical prediction of sound transmission through such a system, the method is known to be extremely demanding, both in terms of data preparation and computation, especially in the mid-frequency range. To alleviate this, a numerical technique that exploits the benefit of the FEM and the BEM approach has been devised. First, a set of eigenmodes is computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. By choosing an appropriate Green's function for the duct, the integration procedure is limited to the duct-cavity interface only. This allows an accurate computation of the scattering matrix of such an acoustic system with a numerical complexity that grows very mildly with the frequency. Typical applications involving Helmholtz and Herschel-Quincke resonators are presented.

Numerical Modeling of the Lake Mary Road Bridge for Foundation Reuse Assessment

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

Sitek, M. A.; Bojanowski, C.; Lottes, S. A.

This project uses numerical techniques to assess the structural integrity and capacity of the bridge foundations and, as a result, reduces the risk associated with reusing the same foundation for a new superstructure. Nondestructive test methods of different types were used in combination with the numerical modeling and analysis. The onsite tests included visual inspection, tomography, ground penetrating radar, drilling boreholes and coreholes, and the laboratory tests on recovered samples. The results were utilized to identify the current geometry of the structure with foundation, including the hidden geometry of the abutments and piers, and soil and foundation material properties. Thismore » data was used to build the numerical models and run computational analyses on a high performance computer cluster to assess the structural integrity of the bridge and foundations including the suitability of the foundation for reuse with a new superstructure and traffic that will increase the load on the foundations. Computational analysis is more cost-effective and gives an advantage of getting more detailed knowledge about the structural response. It also enables to go beyond non-destructive testing and find the failure conditions without destroying the structure under consideration.« less

A novel method for calculating relative free energy of similar molecules in two environments

NASA Astrophysics Data System (ADS)

Farhi, Asaf; Singh, Bipin

2017-03-01

Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy, simple implementation, robustness and efficiency, which prevent the calculations from being automated and limit their use. Here we present an exact and complete decoupling analysis in which the partition functions of the compared systems decompose into the partition functions of the common and different subsystems. This decoupling analysis is applicable to submolecules with coupled degrees of freedom such as the methyl group and to any potential function (including the typical dihedral potentials), enabling to remove less terms in the transformation which results in a more efficient calculation. Then we show mathematically, in the context of partition function decoupling, that the two compared systems can be simulated separately, eliminating the need to design a composite system. We demonstrate the decoupling analysis and the separate transformations in a relative free energy calculation using MD simulations for a general force field and compare to another calculation and to experimental results. We present a unified soft-core technique that ensures the monotonicity of the numerically integrated function (analytical proof) which is important for the selection of intermediates. We show mathematically that in this soft-core technique the numerically integrated function can be non-steep only when we transform the systems separately, which can simplify the numerical integration. Finally, we show that when the systems have rugged energy landscape they can be equilibrated without introducing another sampling dimension which can also enable to use the simulation results for other free energy calculations.

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

A path integral approach to asset-liability management

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann; Goovaerts, Marc

2006-05-01

Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of asset-liability management. We work with a representation of cash flows by means of a two-dimensional delta-function perturbation, in the case of a Brownian model and a geometric Brownian model. We derive closed-form solutions for a finite horizon ALM policy. The results are numerically and graphically illustrated.

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

NASA Technical Reports Server (NTRS)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element

PubMed Central

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667

CW deuterium fluoride chemical laser with reactant combination C2H4/NF3

NASA Astrophysics Data System (ADS)

Jiang, Zhongfu; Hua, Weihong

1998-05-01

The characters of combustion driven cw deuterium fluoride (DF) chemical laser with C2H4/NF3 reactant were numerically investigated. The numerical simulation was carried out using compressibility scaling method--a finite difference technique for the numerical integration of the steady and unsteady Navier-stokes equations for reactive flow. The small signal gain and the flow field were calculated. The numerical results shown that active zone length of the cw DF chemical laser with C2H4/NF3 is very long, which is about 6 cm, and the average cavity pressure is about 7 torr as the combustion pressure is about 1.5 atm. These results shown that the DF chemical laser with C2H4/NF3 is suitable for high cavity pressure performance.

Two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography

NASA Astrophysics Data System (ADS)

Rahmouni, Lyes; Mitharwal, Rajendra; Andriulli, Francesco P.

2017-11-01

This work presents two new volume integral equations for the Electroencephalography (EEG) forward problem which, differently from the standard integral approaches in the domain, can handle heterogeneities and anisotropies of the head/brain conductivity profiles. The new formulations translate to the quasi-static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems. This has been obtained by extending, to the volume case, the two classical surface integral formulations used in EEG imaging and by introducing an extra surface equation, in addition to the volume ones, to properly handle boundary conditions. Numerical results corroborate theoretical treatments, showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction

NASA Astrophysics Data System (ADS)

Ammari, Habib; Qiu, Lingyun; Santosa, Fadil; Zhang, Wenlong

2017-12-01

In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with data acquired from diffusion tensor imaging. Magneto-acoustic tomography with magnetic induction (MAT-MI) is a hybrid, non-invasive medical imaging technique to produce conductivity images with improved spatial resolution and accuracy. Diffusion tensor imaging (DTI) is also a non-invasive technique for characterizing the diffusion properties of water molecules in tissues. We propose a model for anisotropic conductivity in which the conductivity is proportional to the diffusion tensor. Under this assumption, we propose an optimal control approach for reconstructing the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy and feasibility.

Assessment of numerical techniques for unsteady flow calculations

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung

1989-01-01

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

NPSS Multidisciplinary Integration and Analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Rasche, Joseph; Simons, Todd A.; Hoyniak, Daniel

2006-01-01

The objective of this task was to enhance the capability of the Numerical Propulsion System Simulation (NPSS) by expanding its reach into the high-fidelity multidisciplinary analysis area. This task investigated numerical techniques to convert between cold static to hot running geometry of compressor blades. Numerical calculations of blade deformations were iteratively done with high fidelity flow simulations together with high fidelity structural analysis of the compressor blade. The flow simulations were performed with the Advanced Ducted Propfan Analysis (ADPAC) code, while structural analyses were performed with the ANSYS code. High fidelity analyses were used to evaluate the effects on performance of: variations in tip clearance, uncertainty in manufacturing tolerance, variable inlet guide vane scheduling, and the effects of rotational speed on the hot running geometry of the compressor blades.

Vector analogues of the Maggi-Rubinowicz theory of edge diffraction

NASA Astrophysics Data System (ADS)

Meneghini, R.; Shu, P.; Bay, J.

1980-10-01

The Maggi-Rubinowicz technique for scalar and electromagnetic fields is interpreted as a transformation of an integral over an open surface to a line integral around its rim. Maggi-Rubinowicz analogues are found for several vector physical optics representations. For diffraction from a circular aperture, a numerical comparison between these formulations shows the two methods are in agreement. To circumvent certain convergence difficulties in the Maggi-Rubinowicz integrals that occur as the observer approaches the shadow boundary, a variable mesh integration is used. For the examples considered, where the ratio of the aperture diameter to wavelength is about ten, the Maggi-Rubinowicz formulation yields an 8 to 10 fold decrease in computation time relative to the physical optics formulation.

Vector analogues of the Maggi-Rubinowicz theory of edge diffraction

NASA Technical Reports Server (NTRS)

Meneghini, R.; Shu, P.; Bay, J.

1980-01-01

The Maggi-Rubinowicz technique for scalar and electromagnetic fields is interpreted as a transformation of an integral over an open surface to a line integral around its rim. Maggi-Rubinowicz analogues are found for several vector physical optics representations. For diffraction from a circular aperture, a numerical comparison between these formulations shows the two methods are in agreement. To circumvent certain convergence difficulties in the Maggi-Rubinowicz integrals that occur as the observer approaches the shadow boundary, a variable mesh integration is used. For the examples considered, where the ratio of the aperture diameter to wavelength is about ten, the Maggi-Rubinowicz formulation yields an 8 to 10 fold decrease in computation time relative to the physical optics formulation.

Non-invasive studies of multiphase flow in process equipment. Positron emission particle tracking technique

NASA Astrophysics Data System (ADS)

Balakin, B. V.; Adamsen, T. C. H.; Chang, Y.-F.; Kosinski, P.; Hoffmann, A. C.

2017-01-01

Positron emission particle tracking (PEPT) is a novel experimental technique for non-invasive inspection of industrial fluid/particle flows. The method is based on the dynamic positioning of a positron-emitting, flowing object (particle) performed through the sensing of annihilation events and subsequent numerical treatment to determine the particle position. The present paper shows an integrated overview of PEPT studies which were carried out using a new PET scanner in the Bergen University Hospital to study multiphase flows in different geometric configurations.

Multiclass Bayes error estimation by a feature space sampling technique

NASA Technical Reports Server (NTRS)

Mobasseri, B. G.; Mcgillem, C. D.

1979-01-01

A general Gaussian M-class N-feature classification problem is defined. An algorithm is developed that requires the class statistics as its only input and computes the minimum probability of error through use of a combined analytical and numerical integration over a sequence simplifying transformations of the feature space. The results are compared with those obtained by conventional techniques applied to a 2-class 4-feature discrimination problem with results previously reported and 4-class 4-feature multispectral scanner Landsat data classified by training and testing of the available data.

Manufacturing engineering: Principles for optimization

NASA Astrophysics Data System (ADS)

Koenig, Daniel T.

Various subjects in the area of manufacturing engineering are addressed. The topics considered include: manufacturing engineering organization concepts and management techniques, factory capacity and loading techniques, capital equipment programs, machine tool and equipment selection and implementation, producibility engineering, methods, planning and work management, and process control engineering in job shops. Also discussed are: maintenance engineering, numerical control of machine tools, fundamentals of computer-aided design/computer-aided manufacture, computer-aided process planning and data collection, group technology basis for plant layout, environmental control and safety, and the Integrated Productivity Improvement Program.

Improving the trust in results of numerical simulations and scientific data analytics

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

Cappello, Franck; Constantinescu, Emil; Hovland, Paul

This white paper investigates several key aspects of the trust that a user can give to the results of numerical simulations and scientific data analytics. In this document, the notion of trust is related to the integrity of numerical simulations and data analytics applications. This white paper complements the DOE ASCR report on Cybersecurity for Scientific Computing Integrity by (1) exploring the sources of trust loss; (2) reviewing the definitions of trust in several areas; (3) providing numerous cases of result alteration, some of them leading to catastrophic failures; (4) examining the current notion of trust in numerical simulation andmore » scientific data analytics; (5) providing a gap analysis; and (6) suggesting two important research directions and their respective research topics. To simplify the presentation without loss of generality, we consider that trust in results can be lost (or the results’ integrity impaired) because of any form of corruption happening during the execution of the numerical simulation or the data analytics application. In general, the sources of such corruption are threefold: errors, bugs, and attacks. Current applications are already using techniques to deal with different types of corruption. However, not all potential corruptions are covered by these techniques. We firmly believe that the current level of trust that a user has in the results is at least partially founded on ignorance of this issue or the hope that no undetected corruptions will occur during the execution. This white paper explores the notion of trust and suggests recommendations for developing a more scientifically grounded notion of trust in numerical simulation and scientific data analytics. We first formulate the problem and show that it goes beyond previous questions regarding the quality of results such as V&V, uncertainly quantification, and data assimilation. We then explore the complexity of this difficult problem, and we sketch complementary general approaches to address it. This paper does not focus on the trust that the execution will actually complete. The product of simulation or of data analytic executions is the final element of a potentially long chain of transformations, where each stage has the potential to introduce harmful corruptions. These corruptions may produce results that deviate from the user-expected accuracy without notifying the user of this deviation. There are many potential sources of corruption before and during the execution; consequently, in this white paper we do not focus on the protection of the end result after the execution.« less

Topographic gravity modeling for global Bouguer maps to degree 2160: Validation of spectral and spatial domain forward modeling techniques at the 10 microGal level

NASA Astrophysics Data System (ADS)

Hirt, Christian; Reußner, Elisabeth; Rexer, Moritz; Kuhn, Michael

2016-09-01

Over the past years, spectral techniques have become a standard to model Earth's global gravity field to 10 km scales, with the EGM2008 geopotential model being a prominent example. For some geophysical applications of EGM2008, particularly Bouguer gravity computation with spectral techniques, a topographic potential model of adequate resolution is required. However, current topographic potential models have not yet been successfully validated to degree 2160, and notable discrepancies between spectral modeling and Newtonian (numerical) integration well beyond the 10 mGal level have been reported. Here we accurately compute and validate gravity implied by a degree 2160 model of Earth's topographic masses. Our experiments are based on two key strategies, both of which require advanced computational resources. First, we construct a spectrally complete model of the gravity field which is generated by the degree 2160 Earth topography model. This involves expansion of the topographic potential to the 15th integer power of the topography and modeling of short-scale gravity signals to ultrahigh degree of 21,600, translating into unprecedented fine scales of 1 km. Second, we apply Newtonian integration in the space domain with high spatial resolution to reduce discretization errors. Our numerical study demonstrates excellent agreement (8 μGgal RMS) between gravity from both forward modeling techniques and provides insight into the convergence process associated with spectral modeling of gravity signals at very short scales (few km). As key conclusion, our work successfully validates the spectral domain forward modeling technique for degree 2160 topography and increases the confidence in new high-resolution global Bouguer gravity maps.

Efficient Trajectory Propagation for Orbit Determination Problems

NASA Technical Reports Server (NTRS)

Roa, Javier; Pelaez, Jesus

2015-01-01

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

Determining integral density distribution in the mach reflection of shock waves

NASA Astrophysics Data System (ADS)

Shevchenko, A. M.; Golubev, M. P.; Pavlov, A. A.; Pavlov, Al. A.; Khotyanovsky, D. V.; Shmakov, A. S.

2017-05-01

We present a method for and results of determination of the field of integral density in the structure of flow corresponding to the Mach interaction of shock waves at Mach number M = 3. The optical diagnostics of flow was performed using an interference technique based on self-adjusting Zernike filters (SA-AVT method). Numerical simulations were carried out using the CFS3D program package for solving the Euler and Navier-Stokes equations. Quantitative data on the distribution of integral density on the path of probing radiation in one direction of 3D flow transillumination in the region of Mach interaction of shock waves were obtained for the first time.

A test of a vortex method for the computation of flap side edge noise

NASA Technical Reports Server (NTRS)

Martin, James E.

1995-01-01

Upon approach to landing, a major source location of airframe noise occurs at the side edges of the part span, trailing edge flaps. In the vicinity of these flaps, a complex arrangement of spanwise flow with primary and secondary tip vortices may form. Each of these vortices is observed to become fully three-dimensional. In the present study, a numerical model is developed to investigate the noise radiated from the side edge of a flap. The inherent three-dimensionality of this flow forces us to carefully consider a numerical scheme which will be both accurate in its prediction of the flow acoustics and also computationally efficient. Vortex methods have offered a fast and efficient means of simulating many two and three-dimensional, vortex dominated flows. In vortex methods, the time development of the flow is tracked by following exclusively the vorticity containing regions. Through the Biot-Savart law, knowledge of the vorticity field enables one to obtain flow quantities at any desired location during the flow evolution. In the present study, a numerical procedure has been developed which incorporates the Lagrangian approach of vortex methods into a calculation for the noise radiated by a flow-surface interaction. In particular, the noise generated by a vortex in the presence of a flat half plane is considered. This problem serves as a basic model of flap edge flow. It also permits the direct comparison between our computed results and previous acoustic analyses performed for this problem. In our numerical simulations, the mean flow is represented by the complex potential W(z) = Aiz(exp l/2), which is obtained through conformal mapping techniques. The magnitude of the mean flow is controlled by the parameter A. This mean flow has been used in the acoustic analysis by Hardin and is considered a reasonable model of the flow field in the vicinity of the edge and away from the leading and trailing edges of the flap. To represent the primary vortex which occurs near the flap, a point vortex is introduced just below the flat half plane. Using a technique from panel methods, boundary conditions on the flap surface are satisfied by the introduction of a row of stationary point vortices along the extent of the flap. At each time step in the calculation, the strength of these vortices is chosen to eliminate the normal velocity at intermediary collocation points. The time development of the overall flow field is then tracked using standard techniques from vortex methods. Vortex trajectories obtained through this computation are in good agreement with those predicted by the analytical solution given by Hardin, thus verifying the viability of this procedure for more complex flow arrangements. For the flow acoustics, the Ffowcs Williams-Hawkings equation is numerically integrated. This equation supplies the far field acoustic pressure based upon pressures occurring along the flap surface. With our vortex method solution, surface pressures may be obtained with exceptional resolution. The Ffowcs Williams-Hawkings equation is integrated using a spatially fourth order accurate Simpson's rule. Rational function interpolation is used to obtain the surface pressures at the appropriate retarded times. Comparisons between our numerical results for the acoustic pressure and those predicted by the Hardin analysis have been made. Preliminary results indicate the need for an improved integration technique. In the future, the numerical procedure developed in this study will be applied to the case of a rectangular flap of finite thickness and ultimately modified for application to the fully three-dimensional problem.

Severe weather investigation using GNSS signals - a new dimension of GNSS meteorology

NASA Astrophysics Data System (ADS)

Rohm, W.; Zhang, K.; Choy, S.; Kuleshov, Y.; Bosy, J.; Kroszczyński, K.

2012-04-01

The Global Navigation Satellite Systems (GNSS) signals transmitted from satellites are subjected to atmospheric delays since the signals have to propagate through different layers of the atmosphere before GNSS receiver receives them. Two major distinctive effects according to the nature of the impact on the signal propagation are the ionosphere which is a dispersive media and the troposphere which is a non-dispersive layer. In this study, our focus of research is concentrated on the troposphere and the severe weather phenomena caused by midlatitude cyclonic storms. GNSS tomography technique is used to investigate both the spatial and temporal structures of a cyclonic storm. New algorithms will be developed based on optimal integrations of various observation techniques, such as ground-based meteorological measurements, radiosonde data, numerical weather prediction (NWP) models, GNSS radio occultation (RO) profiles. Our initial results suggest that the ground-based GNSS CORS stations will play a major role in the integration process. The structure and distribution of the GNSS CORS network and satellite constellations in context of size and resolution of tomography model are investigated along with the a priori information required, observation and estimation time interval and precision and accuracy needs. A number of numerical analyses are carried out using actual measurements in different parts of the world to evaluate the new algorithms developed through international collaboration. It is expected that GNSS tomography with a number of integrated measurements will provide an important insight into the vertical as well as the horizontal structure of different kinds of severe weather phenomena. It is also expected that GNSS tomography will become an important tool for the study of the severe weather processes, such as the development, maturation, and dissipation stages, which is complementary to other meteorological techniques such as weather radars and microwave radiometers. Potential usages of the new technique in real and/or near-real time would provide an exciting opportunity to launch monitoring and warning services that are able to offer vital information for community and decision makers.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

A two-dimensional numerical simulation of a supersonic, chemically reacting mixing layer

NASA Technical Reports Server (NTRS)

Drummond, J. Philip

1988-01-01

Research has been undertaken to achieve an improved understanding of physical phenomena present when a supersonic flow undergoes chemical reaction. A detailed understanding of supersonic reacting flows is necessary to successfully develop advanced propulsion systems now planned for use late in this century and beyond. In order to explore such flows, a study was begun to create appropriate physical models for describing supersonic combustion, and to develop accurate and efficient numerical techniques for solving the governing equations that result from these models. From this work, two computer programs were written to study reacting flows. Both programs were constructed to consider the multicomponent diffusion and convection of important chemical species, the finite rate reaction of these species, and the resulting interaction of the fluid mechanics and the chemistry. The first program employed a finite difference scheme for integrating the governing equations, whereas the second used a hybrid Chebyshev pseudospectral technique for improved accuracy.

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Ash, Robert L.

1992-01-01

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

A VAS-numerical model impact study using the Gal-Chen variational approach. [Visible Infrared Spin-Scan Radiometer Atmospheric Sounder (VAS)

NASA Technical Reports Server (NTRS)

Aune, Robert M.; Uccellini, Louis W.; Peterson, Ralph A.; Tuccillo, James J.

1987-01-01

Numerical experiments to assess the impact of incorporating temperature data from the VISSR Atmospheric Sounder (VAS) using the assimilation technique developed by Gal-Chen (1986) modified for use in the Mesoscale Atmospheric Simulation System (MASS) model were conducted. The scheme is designed to utilize the high temporal and horizontal resolution of satellite retrievals while maintaining the fine vertical structure generated by the model. This is accomplished by adjusting the model lapse rates to reflect thicknesses retrieved from VAS and applying a three-dimensional variational that preserves the distribution of the geopotential fields in the model. A nudging technique whereby the model temperature fields are gradually adjusted toward the updated temperature fields during model integration is also tested. An adiabatic version of MASS is used in all experiments to better isolate mass-momentum imbalances. The method has a sustained impact over an 18 hr model simulation.

Identification of individual foothill yellow-legged frogs (Rana boylii) using chin pattern photographs: a non-invasive and effective method for small population studies

Treesearch

K.R. Marlow; K.D. Wiseman; Clara Wheeler; J.E.  Drennan; R.E.  Jackman

2016-01-01

The ability to identify individual animals is a valuable tool in the study of amphibian population dynamics, movement ecology, social behavior, and habitat use. Numerous methods of marking amphibians have been employed including the use of passive integrated transponder (PIT) tags, radio-transmitters, elastomers, branding, and mutilation techniques such as toe...

Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Hsieh, Shang-Hsien

1993-01-01

The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.

Molecular andrology as related to sperm DNA fragmentation/sperm chromatin biotechnology.

PubMed

Shafik, A; Shafik, A A; Shafik, I; El Sibai, O

2006-01-01

Genetic male infertility occurs throughout the life cycle from genetic traits carried by the sperm, to fertilization and post-fertilization genome alterations, and subsequent developmental changes in the blastocyst and fetus as well as errors in meiosis and abnormalities in spermatogenesis/spermatogenesis. Genes encoding proteins for normal development include SRY, SOX9, INSL3 and LGR8. Genetic abnormalities affect spermatogenesis whereas polymorphisms affect receptor affinity and hormone bioactivity. Transgenic animal models, the human genome project, and other techniques have identified numerous genes related to male fertility. Several techniques have been developed to measure the amount of sperm DNA damage in an effort to identify more objective parameters for evaluation of infertile men. The integrity of sperm DNA influences a couple's fertility and helps predict the chances of pregnancy and its successful outcome. The available tests of sperm DNA damage require additional large-scale clinical trials before their integration into routine clinical practice. The physiological/molecular integrity of sperm DNA is a novel parameter of semen quality and a potential fertility predictor. Although DNA integrity assessment appears to be a logical biomarker of sperm quality, it is not being assessed as a routine part of semen analysis by clinical andrologists. Extensive investigation has been conducted for the comparative evaluation of these techniques. However, some of these techniques require expensive instrumentation for optimal and unbiased analysis, are labor intensive, or require the use of enzymes whose activity and accessibility to DNA breaks may be irregular. Thus, these techniques are recommended for basic research rather than for routine andrology laboratories.

A self-diagnostic adhesive for monitoring bonded joints in aerospace structures

NASA Astrophysics Data System (ADS)

Zhuang, Yitao; Li, Yu-hung; Kopsaftopoulos, Fotis; Chang, Fu-Kuo

2016-04-01

Bondline integrity is still one of the most critical concerns in the design of aircraft structures up to date. Due to the lack of confidence on the integrity of the bondline both during fabrication and service, the industry standards and regulations still require assembling the composite using conventional fasteners. Furthermore, current state-of-the-art non-destructive evaluation (NDE) and structural health monitoring (SHM) techniques are incapable of offering mature solutions on the issue of bondline integrity monitoring. Therefore, the objective of this work is the development of an intelligent adhesive film with integrated micro-sensors for monitoring the integrity of the bondline interface. The proposed method makes use of an electromechanical-impedance (EMI) based method, which is a rapidly evolving approach within the SHM family. Furthermore, an innovative screen-printing technique to fabricate piezoelectric ceramic sensors with minimal thickness has been developed at Stanford. The approach presented in this study is based on the use of (i) micro screen-printed piezoelectric sensors integrated into adhesive leaving a minimal footprint on the material, (ii) numerical and analytical modeling of the EMI spectrum of the adhesive bondline, (iii) novel diagnostic algorithms for monitoring the bondline integrity based on advanced signal processing techniques, and (iv) the experimental assessment via prototype adhesively bonded structures in static (varying loads) and dynamic (fatigue) environments. The proposed method will provide a huge confidence on the use of bonded joints for aerospace structures and lead to a paradigm change in their design by enabling enormous weight savings while maximizing the economic and performance efficiency.

Model reference tracking control of an aircraft: a robust adaptive approach

NASA Astrophysics Data System (ADS)

Tanyer, Ilker; Tatlicioglu, Enver; Zergeroglu, Erkan

2017-05-01

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.

Quantum Mechanics, Path Integrals and Option Pricing:. Reducing the Complexity of Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani

2003-04-01

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.

Synthetic Biology and Microbial Fuel Cells: Towards Self-Sustaining Life Support Systems

NASA Technical Reports Server (NTRS)

Hogan, John Andrew

2014-01-01

NASA ARC and the J. Craig Venter Institute (JCVI) collaborated to investigate the development of advanced microbial fuels cells (MFCs) for biological wastewater treatment and electricity production (electrogenesis). Synthetic biology techniques and integrated hardware advances were investigated to increase system efficiency and robustness, with the intent of increasing power self-sufficiency and potential product formation from carbon dioxide. MFCs possess numerous advantages for space missions, including rapid processing, reduced biomass and effective removal of organics, nitrogen and phosphorus. Project efforts include developing space-based MFC concepts, integration analyses, increasing energy efficiency, and investigating novel bioelectrochemical system applications

Analysis of airfoil leading edge separation bubbles

NASA Technical Reports Server (NTRS)

Carter, J. E.; Vatsa, V. N.

1982-01-01

A local inviscid-viscous interaction technique was developed for the analysis of low speed airfoil leading edge transitional separation bubbles. In this analysis an inverse boundary layer finite difference analysis is solved iteratively with a Cauchy integral representation of the inviscid flow which is assumed to be a linear perturbation to a known global viscous airfoil analysis. Favorable comparisons with data indicate the overall validity of the present localized interaction approach. In addition numerical tests were performed to test the sensitivity of the computed results to the mesh size, limits on the Cauchy integral, and the location of the transition region.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

A full three dimensional Navier-Stokes numerical simulation of flow field inside a power plant Kaplan turbine using some model test turbine hill chart points

NASA Astrophysics Data System (ADS)

Hosseinalipour, S. M.; Raja, A.; Hajikhani, S.

2012-06-01

A full three dimensional Navier - Stokes numerical simulation has been performed for performance analysis of a Kaplan turbine which is installed in one of the Irans south dams. No simplifications have been enforced in the simulation. The numerical results have been evaluated using some integral parameters such as the turbine efficiency via comparing the results with existing experimental data from the prototype Hill chart. In part of this study the numerical simulations were performed in order to calculate the prototype turbine efficiencies in some specific points which comes from the scaling up of the model efficiency that are available in the model experimental Hill chart. The results are very promising which shows the good ability of the numerical techniques for resolving the flow characteristics in these kind of complex geometries. A parametric study regarding the evaluation of turbine performance in three different runner angles of the prototype is also performed and the results are cited in this paper.

Simulation and analysis of a geopotential research mission

NASA Technical Reports Server (NTRS)

Schutz, B. E.

1987-01-01

Computer simulations were performed for a Geopotential Research Mission (GRM) to enable the study of the gravitational sensitivity of the range rate measurements between the two satellites and to provide a set of simulated measurements to assist in the evaluation of techniques developed for the determination of the gravity field. The simulations were conducted with two satellites in near circular, frozen orbits at 160 km altitudes separated by 300 km. High precision numerical integration of the polar orbits were used with a gravitational field complete to degree and order 360. The set of simulated data for a mission duration of about 32 days was generated on a Cray X-MP computer. The results presented cover the most recent simulation, S8703, and includes a summary of the numerical integration of the simulated trajectories, a summary of the requirements to compute nominal reference trajectories to meet the initial orbit determination requirements for the recovery of the geopotential, an analysis of the nature of the one way integrated Doppler measurements associated with the simulation, and a discussion of the data set to be made available.

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

NASA Technical Reports Server (NTRS)

Pratt, D. T.; Radhakrishnan, K.

1986-01-01

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Modeling of ion acceleration through drift and diffusion at interplanetary shocks

NASA Technical Reports Server (NTRS)

Decker, R. B.; Vlahos, L.

1986-01-01

A test particle simulation designed to model ion acceleration through drift and diffusion at interplanetary shocks is described. The technique consists of integrating along exact particle orbits in a system where the angle between the shock normal and mean upstream magnetic field, the level of magnetic fluctuations, and the energy of injected particles can assume a range of values. The technique makes it possible to study time-dependent shock acceleration under conditions not amenable to analytical techniques. To illustrate the capability of the numerical model, proton acceleration was considered under conditions appropriate for interplanetary shocks at 1 AU, including large-amplitude transverse magnetic fluctuations derived from power spectra of both ambient and shock-associated MHD waves.

Nonparametric probability density estimation by optimization theoretic techniques

NASA Technical Reports Server (NTRS)

Scott, D. W.

1976-01-01

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Fibre Optic Sensors for Structural Health Monitoring of Aircraft Composite Structures: Recent Advances and Applications

PubMed Central

Di Sante, Raffaella

2015-01-01

In-service structural health monitoring of composite aircraft structures plays a key role in the assessment of their performance and integrity. In recent years, Fibre Optic Sensors (FOS) have proved to be a potentially excellent technique for real-time in-situ monitoring of these structures due to their numerous advantages, such as immunity to electromagnetic interference, small size, light weight, durability, and high bandwidth, which allows a great number of sensors to operate in the same system, and the possibility to be integrated within the material. However, more effort is still needed to bring the technology to a fully mature readiness level. In this paper, recent research and applications in structural health monitoring of composite aircraft structures using FOS have been critically reviewed, considering both the multi-point and distributed sensing techniques. PMID:26263987

Fibre Optic Sensors for Structural Health Monitoring of Aircraft Composite Structures: Recent Advances and Applications.

PubMed

Di Sante, Raffaella

2015-07-30

In-service structural health monitoring of composite aircraft structures plays a key role in the assessment of their performance and integrity. In recent years, Fibre Optic Sensors (FOS) have proved to be a potentially excellent technique for real-time in-situ monitoring of these structures due to their numerous advantages, such as immunity to electromagnetic interference, small size, light weight, durability, and high bandwidth, which allows a great number of sensors to operate in the same system, and the possibility to be integrated within the material. However, more effort is still needed to bring the technology to a fully mature readiness level. In this paper, recent research and applications in structural health monitoring of composite aircraft structures using FOS have been critically reviewed, considering both the multi-point and distributed sensing techniques.

Numerical analysis for the stick-slip vibration of a transversely moving beam in contact with a frictional wall

NASA Astrophysics Data System (ADS)

Won, Hong-In; Chung, Jintai

2018-04-01

This paper presents a numerical analysis for the stick-slip vibration of a transversely moving beam, considering both stick-slip transition and friction force discontinuity. The dynamic state of the beam was separated into the stick state and the slip state, and boundary conditions were defined for both. By applying the finite element method, two matrix-vector equations were derived: one for stick state and the other for slip state. However, the equations have different degrees of freedom depending on whether the end of a beam sticks or slips, so we encountered difficulties in time integration. To overcome the difficulties, we proposed a new numerical technique to alternatively use the matrix-vector equations with different matrix sizes. In addition, to eliminate spurious high-frequency responses, we applied the generalized-α time integration method with appropriate value of high-frequency numerical dissipation. Finally, the dynamic responses of stick-slip vibration were analyzed in time and frequency domains: the dynamic behavior of the beam was explained to facilitate understanding of the stick-slip motion, and frequency characteristics of the stick-slip vibration were investigated in relation to the natural frequencies of the beam. The effects of the axial load and the moving speed upon the dynamic response were also examined.

An evaluation of analog and numerical techniques for unsteady heat transfer measurement with thin-film gauges in transient facilities

NASA Technical Reports Server (NTRS)

George, William K.; Rae, William J.; Woodward, Scott H.

1991-01-01

The importance of frequency response considerations in the use of thin-film gages for unsteady heat transfer measurements in transient facilities is considered, and methods for evaluating it are proposed. A departure frequency response function is introduced and illustrated by an existing analog circuit. A Fresnel integral temperature which possesses the essential features of the film temperature in transient facilities is introduced and is used to evaluate two numerical algorithms. Finally, criteria are proposed for the use of finite-difference algorithms for the calculation of the unsteady heat flux from a sampled temperature signal.

A numerical method for determination of source time functions for general three-dimensional rupture propagation

NASA Technical Reports Server (NTRS)

Das, S.

1979-01-01

A method to determine the displacement and the stress on the crack plane for a three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane is presented. The main idea of the method is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. As a test of the accuracy of the numerical technique, the results are compared with known solutions for two simple cases.

Three Dimensional Imaging of the Nucleon

NASA Astrophysics Data System (ADS)

More, Jai; Mukherjee, Asmita; Nair, Sreeraj

2018-05-01

We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin -1/2 state of quark dressed with a gluon. This state allows us to calculate the quark and gluon Wigner distributions analytically in terms of LFWFs using Hamiltonian perturbation theory. We analyze numerically the Wigner distributions of quark and gluon and report their nature in the contour plots. We use an improved numerical technique to remove the cutoff dependence of the Fourier transformed integral over \\varvec{Δ}_\\perp.

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

Manteuffel, T.A.

The objective of this project is the development of numerical solution techniques for deterministic models of the transport of neutral and charged particles and the demonstration of their effectiveness in both a production environment and on advanced architecture computers. The primary focus is on various versions of the linear Boltzman equation. These equations are fundamental in many important applications. This project is an attempt to integrate the development of numerical algorithms with the process of developing production software. A major thrust of this reject will be the implementation of these algorithms on advanced architecture machines that reside at the Advancedmore » Computing Laboratory (ACL) at Los Alamos National Laboratories (LANL).« less

Stress evaluation in displacement-based 2D nonlocal finite element method

NASA Astrophysics Data System (ADS)

Pisano, Aurora Angela; Fuschi, Paolo

2018-06-01

The evaluation of the stress field within a nonlocal version of the displacement-based finite element method is addressed. With the aid of two numerical examples it is shown as some spurious oscillations of the computed nonlocal stresses arise at sections (or zones) of macroscopic inhomogeneity of the examined structures. It is also shown how the above drawback, which renders the stress numerical solution unreliable, can be viewed as the so-called locking in FEM, a subject debated in the early seventies. It is proved that a well known remedy for locking, i.e. the reduced integration technique, can be successfully applied also in the nonlocal elasticity context.

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1971-01-01

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Integrated analysis of particle interactions at hadron colliders Report of research activities in 2010-2015

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

Nadolsky, Pavel M.

2015-08-31

The report summarizes research activities of the project ”Integrated analysis of particle interactions” at Southern Methodist University, funded by 2010 DOE Early Career Research Award DE-SC0003870. The goal of the project is to provide state-of-the-art predictions in quantum chromodynamics in order to achieve objectives of the LHC program for studies of electroweak symmetry breaking and new physics searches. We published 19 journal papers focusing on in-depth studies of proton structure and integration of advanced calculations from different areas of particle phenomenology: multi-loop calculations, accurate long-distance hadronic functions, and precise numerical programs. Methods for factorization of QCD cross sections were advancedmore » in order to develop new generations of CTEQ parton distribution functions (PDFs), CT10 and CT14. These distributions provide the core theoretical input for multi-loop perturbative calculations by LHC experimental collaborations. A novel ”PDF meta-analysis” technique was invented to streamline applications of PDFs in numerous LHC simulations and to combine PDFs from various groups using multivariate stochastic sampling of PDF parameters. The meta-analysis will help to bring the LHC perturbative calculations to the new level of accuracy, while reducing computational efforts. The work on parton distributions was complemented by development of advanced perturbative techniques to predict observables dependent on several momentum scales, including production of massive quarks and transverse momentum resummation at the next-to-next-to-leading order in QCD.« less

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

New Computer Automated Holo-Photoelastic Method For Measuring Planar Principal Stress Magnitudes And Orientation

NASA Astrophysics Data System (ADS)

Brown, G. M.; Sullivan, J. L.

1987-09-01

A complete experimental determination of the stress and strain fields in an arbitrary deformed structure is generally unavailable. However, for two dimensional elasticity problems, such determinations are possible since in those cases one needs only to solve for three stresses (two normal and one shear). In fact, such determinations have been conducted quite often. By using isochromatic and isoclinic photoelastic data, the shear difference and numerical iteration techniques (1) and the least squares techniques (2) have been successfully used for complete stress field determinations of two dimensional elasticity problems. Though the shear difference technique can be particularly sensitive to cumulative errors resulting from numerical integration, the least squares technique is not affected by this and appears to yield better accuracy. The methods just cited use both experimental data and one or more mechanics conditions(e.g., the equations of equilibrium) to determine the stress field. However, the stress field can also be obtained from experimental data alone for planar elasticity problems, if there is enough of it to solve for the three stresses. For example, the Moire* technique or the combination of isochromatic, isoclinic, and isopachic data (for transparent models) can be used for such determinations. Further, with the marriage of advanced image processing equipment to computers, such analyses using this type of data can be conveniently conducted. It is even possible that such analyses could be more accurate than those using the combined experimental/numerical techniques cited above. The purposes of this report are two fold: i) to describe a single apparatus for obtaining isochromatic, isopachic, and isoclinic results for complete stress field determinations of two dimensional transparent models, and ii) to compare experimental and theoretical stress field values for an antisymmetrically loaded beam obtained using that apparatus.

The Numerical Technique for the Landslide Tsunami Simulations Based on Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Kozelkov, A. S.

2017-12-01

The paper presents an integral technique simulating all phases of a landslide-driven tsunami. The technique is based on the numerical solution of the system of Navier-Stokes equations for multiphase flows. The numerical algorithm uses a fully implicit approximation method, in which the equations of continuity and momentum conservation are coupled through implicit summands of pressure gradient and mass flow. The method we propose removes severe restrictions on the time step and allows simulation of tsunami propagation to arbitrarily large distances. The landslide origin is simulated as an individual phase being a Newtonian fluid with its own density and viscosity and separated from the water and air phases by an interface. The basic formulas of equation discretization and expressions for coefficients are presented, and the main steps of the computation procedure are described in the paper. To enable simulations of tsunami propagation across wide water areas, we propose a parallel algorithm of the technique implementation, which employs an algebraic multigrid method. The implementation of the multigrid method is based on the global level and cascade collection algorithms that impose no limitations on the paralleling scale and make this technique applicable to petascale systems. We demonstrate the possibility of simulating all phases of a landslide-driven tsunami, including its generation, propagation and uprush. The technique has been verified against the problems supported by experimental data. The paper describes the mechanism of incorporating bathymetric data to simulate tsunamis in real water areas of the world ocean. Results of comparison with the nonlinear dispersion theory, which has demonstrated good agreement, are presented for the case of a historical tsunami of volcanic origin on the Montserrat Island in the Caribbean Sea.

Analytical approximation of a distorted reflector surface defined by a discrete set of points

NASA Technical Reports Server (NTRS)

Acosta, Roberto J.; Zaman, Afroz A.

1988-01-01

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Tension Cutoff and Parameter Identification for the Viscoplastic Cap Model.

DTIC Science & Technology

1983-04-01

computer program "VPDRVR" which employs a Crank-Nicolson time integration scheme and a Newton-Raphson iterative solution procedure. Numerical studies were...parameters was illustrated for triaxial stress and uniaxial strain loading for a well- studied sand material (McCormick Ranch Sand). Lastly, a finite element...viscoplastic tension-cutoff cri- terion and to establish parameter identification techniques with experimental data. Herein lies the impetus of this study

Target-in-the-loop remote sensing of laser beam and atmospheric turbulence characteristics.

PubMed

Vorontsov, Mikhail A; Lachinova, Svetlana L; Majumdar, Arun K

2016-07-01

A new target-in-the-loop (TIL) atmospheric sensing concept for in situ remote measurements of major laser beam characteristics and atmospheric turbulence parameters is proposed and analyzed numerically. The technique is based on utilization of an integral relationship between complex amplitudes of the counterpropagating optical waves known as overlapping integral or interference metric, whose value is preserved along the propagation path. It is shown that the interference metric can be directly measured using the proposed TIL sensing system composed of a single-mode fiber-based optical transceiver and a remotely located retro-target. The measured signal allows retrieval of key beam and atmospheric turbulence characteristics including scintillation index and the path-integrated refractive index structure parameter.

Light-modulating pressure sensor with integrated flexible organic light-emitting diode.

PubMed

Cheneler, D; Vervaeke, M; Thienpont, H

2014-05-01

Organic light-emitting diodes (OLEDs) are used almost exclusively for display purposes. Even when implemented as a sensing component, it is rarely in a manner that exploits the possible compliance of the OLED. Here it is shown that OLEDs can be integrated into compliant mechanical micro-devices making a new range of applications possible. A light-modulating pressure sensor is considered, whereby the OLED is integrated with a silicon membrane. It is shown that such devices have potential and advantages over current measurement techniques. An analytical model has been developed that calculates the response of the device. Ray tracing numerical simulations verify the theory and show that the design can be optimized to maximize the resolution of the sensor.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

Extraction of Urban Trees from Integrated Airborne Based Digital Image and LIDAR Point Cloud Datasets - Initial Results

NASA Astrophysics Data System (ADS)

Dogon-yaro, M. A.; Kumar, P.; Rahman, A. Abdul; Buyuksalih, G.

2016-10-01

Timely and accurate acquisition of information on the condition and structural changes of urban trees serves as a tool for decision makers to better appreciate urban ecosystems and their numerous values which are critical to building up strategies for sustainable development. The conventional techniques used for extracting tree features include; ground surveying and interpretation of the aerial photography. However, these techniques are associated with some constraint, such as labour intensive field work, a lot of financial requirement, influences by weather condition and topographical covers which can be overcome by means of integrated airborne based LiDAR and very high resolution digital image datasets. This study presented a semi-automated approach for extracting urban trees from integrated airborne based LIDAR and multispectral digital image datasets over Istanbul city of Turkey. The above scheme includes detection and extraction of shadow free vegetation features based on spectral properties of digital images using shadow index and NDVI techniques and automated extraction of 3D information about vegetation features from the integrated processing of shadow free vegetation image and LiDAR point cloud datasets. The ability of the developed algorithms shows a promising result as an automated and cost effective approach to estimating and delineated 3D information of urban trees. The research also proved that integrated datasets is a suitable technology and a viable source of information for city managers to be used in urban trees management.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

Numerical computation of gravitational field of general extended body and its application to rotation curve study of galaxies

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2017-06-01

Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface mass density distribution. Fortran 90 subroutines to execute these methods and their test programs and sample outputs are available from the author's WEB site: https://www.researchgate.net/profile/Toshio_Fukushima/

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

Continuous state-space representation of a bucket-type rainfall-runoff model: a case study with the GR4 model using state-space GR4 (version 1.0)

NASA Astrophysics Data System (ADS)

Santos, Léonard; Thirel, Guillaume; Perrin, Charles

2018-04-01

In many conceptual rainfall-runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called operator splitting. As a result, only the solutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall-runoff model explicit and to solve them continuously. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which makes the structural analysis of the model more complex, could be removed. In this state-space representation, the lag functions (unit hydrographs), which are frequent in rainfall-runoff models and make the resolution of the representation difficult, are first replaced by a so-called Nash cascade and then solved with a robust numerical integration technique. To illustrate this methodology, the GR4J model is taken as an example. The substitution of the unit hydrographs with a Nash cascade, even if it modifies the model behaviour when solved using operator splitting, does not modify it when the state-space representation is solved using an implicit integration technique. Indeed, the flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The use of a robust numerical technique that approximates a continuous-time model also improves the lag parameter consistency across time steps and provides a more time-consistent model with time-independent parameters.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

Highly efficient full-wave electromagnetic analysis of 3-D arbitrarily shaped waveguide microwave devices using an integral equation technique

NASA Astrophysics Data System (ADS)

Vidal, A.; San-Blas, A. A.; Quesada-Pereira, F. D.; Pérez-Soler, J.; Gil, J.; Vicente, C.; Gimeno, B.; Boria, V. E.

2015-07-01

A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RME technique. The developed tool also provides an accurate computation of the electromagnetic fields at an arbitrary observation point of the considered device, so it can be used for predicting high-power breakdown phenomena. In order to validate the accuracy and efficiency of this novel approach, several new designs of band-pass waveguides filters are presented. The obtained results (S-parameters and electromagnetic fields) are successfully compared both to experimental data and to numerical simulations provided by a commercial software based on the finite element technique. The results obtained show that the new technique is specially suitable for the efficient full-wave analysis of complex waveguide devices considering an integrated coaxial excitation, where the coaxial probes may be in contact with the metallic insets of the component.

Graphical and PC-software analysis of volcano eruption precursors according to the Materials Failure Forecast Method (FFM)

NASA Astrophysics Data System (ADS)

Cornelius, Reinold R.; Voight, Barry

1995-03-01

The Materials Failure Forecasting Method for volcanic eruptions (FFM) analyses the rate of precursory phenomena. Time of eruption onset is derived from the time of "failure" implied by accelerating rate of deformation. The approach attempts to fit data, Ω, to the differential relationship Ω¨=AΩ˙, where the dot superscript represents the time derivative, and the data Ω may be any of several parameters describing the accelerating deformation or energy release of the volcanic system. Rate coefficients, A and α, may be derived from appropriate data sets to provide an estimate of time to "failure". As the method is still an experimental technique, it should be used with appropriate judgment during times of volcanic crisis. Limitations of the approach are identified and discussed. Several kinds of eruption precursory phenomena, all simulating accelerating creep during the mechanical deformation of the system, can be used with FFM. Among these are tilt data, slope-distance measurements, crater fault movements and seismicity. The use of seismic coda, seismic amplitude-derived energy release and time-integrated amplitudes or coda lengths are examined. Usage of cumulative coda length directly has some practical advantages to more rigorously derived parameters, and RSAM and SSAM technologies appear to be well suited to real-time applications. One graphical and four numerical techniques of applying FFM are discussed. The graphical technique is based on an inverse representation of rate versus time. For α = 2, the inverse rate plot is linear; it is concave upward for α < 2 and concave downward for α > 2. The eruption time is found by simple extrapolation of the data set toward the time axis. Three numerical techniques are based on linear least-squares fits to linearized data sets. The "linearized least-squares technique" is most robust and is expected to be the most practical numerical technique. This technique is based on an iterative linearization of the given rate-time series. The hindsight technique is disadvantaged by a bias favouring a too early eruption time in foresight applications. The "log rate versus log acceleration technique", utilizing a logarithmic representation of the fundamental differential equation, is disadvantaged by large data scatter after interpolation of accelerations. One further numerical technique, a nonlinear least-squares fit to rate data, requires special and more complex software. PC-oriented computer codes were developed for data manipulation, application of the three linearizing numerical methods, and curve fitting. Separate software is required for graphing purposes. All three linearizing techniques facilitate an eruption window based on a data envelope according to the linear least-squares fit, at a specific level of confidence, and an estimated rate at time of failure.

The application of quaternions and other spatial representations to the reconstruction of re-entry vehicle motion.

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

De Sapio, Vincent

2010-09-01

The analysis of spacecraft kinematics and dynamics requires an efficient scheme for spatial representation. While the representation of displacement in three dimensional Euclidean space is straightforward, orientation in three dimensions poses particular challenges. The unit quaternion provides an approach that mitigates many of the problems intrinsic in other representation approaches, including the ill-conditioning that arises from computing many successive rotations. This report focuses on the computational utility of unit quaternions and their application to the reconstruction of re-entry vehicle (RV) motion history from sensor data. To this end they will be used in conjunction with other kinematic and data processingmore » techniques. We will present a numerical implementation for the reconstruction of RV motion solely from gyroscope and accelerometer data. This will make use of unit quaternions due to their numerical efficacy in dealing with the composition of many incremental rotations over a time series. In addition to signal processing and data conditioning procedures, algorithms for numerical quaternion-based integration of gyroscope data will be addressed, as well as accelerometer triangulation and integration to yield RV trajectory. Actual processed flight data will be presented to demonstrate the implementation of these methods.« less

A comparative study of integrated pest management strategies based on impulsive control.

PubMed

Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan

2018-12-01

The paper presents a comprehensive numerical study of mathematical models used to describe complex biological systems in the framework of integrated pest management. Our study considers two specific ecosystems that describe the application of control mechanisms based on pesticides and natural enemies, implemented in an impulsive and periodic manner, due to which the considered models belong to the class of impulsive differential equations. The present work proposes a numerical approach to study such type of models in detail, via the application of path-following (continuation) techniques for nonsmooth dynamical systems, via the novel continuation platform COCO (Dankowicz and Schilder). In this way, a detailed study focusing on the influence of selected system parameters on the effectiveness of the pest control scheme is carried out for both ecological scenarios. Furthermore, a comparative study is presented, with special emphasis on the mechanisms upon which a pest outbreak can occur in the considered ecosystems. Our study reveals that such outbreaks are determined by the presence of a branching point found during the continuation analysis. The numerical investigation concludes with an in-depth study of the state-dependent pesticide mortality considered in one of the ecological scenarios.

Assessing land cover performance in Senegal, West Africa using 1-km integrated NDVI and local variance analysis

USGS Publications Warehouse

Budde, M.E.; Tappan, G.; Rowland, James; Lewis, J.; Tieszen, L.L.

2004-01-01

The researchers calculated seasonal integrated normalized difference vegetation index (NDVI) for each of 7 years using a time-series of 1-km data from the Advanced Very High Resolution Radiometer (AVHRR) (1992-93, 1995) and SPOT Vegetation (1998-2001) sensors. We used a local variance technique to identify each pixel as normal or either positively or negatively anomalous when compared to its surroundings. We then summarized the number of years that a given pixel was identified as an anomaly. The resulting anomaly maps were analysed using Landsat TM imagery and extensive ground knowledge to assess the results. This technique identified anomalies that can be linked to numerous anthropogenic impacts including agricultural and urban expansion, maintenance of protected areas and increased fallow. Local variance analysis is a reliable method for assessing vegetation degradation resulting from human pressures or increased land productivity from natural resource management practices. ?? 2004 Published by Elsevier Ltd.

Nonlinear integral sliding mode control design of photovoltaic pumping system: Real time implementation.

PubMed

Chihi, Asma; Ben Azza, Hechmi; Jemli, Mohamed; Sellami, Anis

2017-09-01

The aim of this paper is to provide high performance control of pumping system. The proposed method is designed by an indirect field oriented control based on Sliding Mode (SM) technique. The first contribution of this work is to design modified switching surfaces which presented by adding an integral action to the considered controlled variables. Then, in order to prevent the chattering phenomenon, modified nonlinear component is developed. The SM concept and a Lyapunov function are combined to compute the Sliding Mode Control (SMC) gains. Besides, the motor performance is validated by numeric simulations and real time implementation using a dSpace system with DS1104 controller board. Also, to show the effectiveness of the proposed approach, the obtained results are compared with other techniques such as conventional PI, Proportional Sliding Mode (PSM) and backstepping controls. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Arbitrary Lagrangian-Eulerian Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics

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

Anderson, R W; Pember, R B; Elliott, N S

2001-10-22

A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less

On coarse projective integration for atomic deposition in amorphous systems

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

Chuang, Claire Y., E-mail: yungc@seas.upenn.edu, E-mail: meister@unm.edu, E-mail: zepedaruiz1@llnl.gov; Sinno, Talid, E-mail: talid@seas.upenn.edu; Han, Sang M., E-mail: yungc@seas.upenn.edu, E-mail: meister@unm.edu, E-mail: zepedaruiz1@llnl.gov

2015-10-07

Direct molecular dynamics simulation of atomic deposition under realistic conditions is notoriously challenging because of the wide range of time scales that must be captured. Numerous simulation approaches have been proposed to address the problem, often requiring a compromise between model fidelity, algorithmic complexity, and computational efficiency. Coarse projective integration, an example application of the “equation-free” framework, offers an attractive balance between these constraints. Here, periodically applied, short atomistic simulations are employed to compute time derivatives of slowly evolving coarse variables that are then used to numerically integrate differential equations over relatively large time intervals. A key obstacle to themore » application of this technique in realistic settings is the “lifting” operation in which a valid atomistic configuration is recreated from knowledge of the coarse variables. Using Ge deposition on amorphous SiO{sub 2} substrates as an example application, we present a scheme for lifting realistic atomistic configurations comprised of collections of Ge islands on amorphous SiO{sub 2} using only a few measures of the island size distribution. The approach is shown to provide accurate initial configurations to restart molecular dynamics simulations at arbitrary points in time, enabling the application of coarse projective integration for this morphologically complex system.« less

On Coarse Projective Integration for Atomic Deposition in Amorphous Systems

DOE PAGES

Chuang, Claire Y.; Han, Sang M.; Zepeda-Ruiz, Luis A.; ...

2015-10-02

Direct molecular dynamics simulation of atomic deposition under realistic conditions is notoriously challenging because of the wide range of timescales that must be captured. Numerous simulation approaches have been proposed to address the problem, often requiring a compromise between model fidelity, algorithmic complexity and computational efficiency. Coarse projective integration, an example application of the ‘equation-free’ framework, offers an attractive balance between these constraints. Here, periodically applied, short atomistic simulations are employed to compute gradients of slowly-evolving coarse variables that are then used to numerically integrate differential equations over relatively large time intervals. A key obstacle to the application of thismore » technique in realistic settings is the ‘lifting’ operation in which a valid atomistic configuration is recreated from knowledge of the coarse variables. Using Ge deposition on amorphous SiO 2 substrates as an example application, we present a scheme for lifting realistic atomistic configurations comprised of collections of Ge islands on amorphous SiO 2 using only a few measures of the island size distribution. In conclusion, the approach is shown to provide accurate initial configurations to restart molecular dynamics simulations at arbitrary points in time, enabling the application of coarse projective integration for this morphologically complex system.« less

Formulation of aerodynamic prediction techniques for hypersonic configuration design

NASA Technical Reports Server (NTRS)

1979-01-01

An investigation of approximate theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at moderate hypersonic speeds was performed. Emphasis was placed on approaches that would be responsive to preliminary configuration design level of effort. Supersonic second order potential theory was examined in detail to meet this objective. Shock layer integral techniques were considered as an alternative means of predicting gross aerodynamic characteristics. Several numerical pilot codes were developed for simple three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the second order computations indicated good agreement with higher order solutions and experimental results for a variety of wing like shapes and values of the hypersonic similarity parameter M delta approaching one.

Singular boundary method for global gravity field modelling

NASA Astrophysics Data System (ADS)

Cunderlik, Robert

2014-05-01

The singular boundary method (SBM) and method of fundamental solutions (MFS) are meshless boundary collocation techniques that use the fundamental solution of a governing partial differential equation (e.g. the Laplace equation) as their basis functions. They have been developed to avoid singular numerical integration as well as mesh generation in the traditional boundary element method (BEM). SBM have been proposed to overcome a main drawback of MFS - its controversial fictitious boundary outside the domain. The key idea of SBM is to introduce a concept of the origin intensity factors that isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques. Consequently, the source points can be placed directly on the real boundary and coincide with the collocation nodes. In this study we deal with SBM applied for high-resolution global gravity field modelling. The first numerical experiment presents a numerical solution to the fixed gravimetric boundary value problem. The achieved results are compared with the numerical solutions obtained by MFS or the direct BEM indicating efficiency of all methods. In the second numerical experiments, SBM is used to derive the geopotential and its first derivatives from the Tzz components of the gravity disturbing tensor observed by the GOCE satellite mission. A determination of the origin intensity factors allows to evaluate the disturbing potential and gravity disturbances directly on the Earth's surface where the source points are located. To achieve high-resolution numerical solutions, the large-scale parallel computations are performed on the cluster with 1TB of the distributed memory and an iterative elimination of far zones' contributions is applied.

Analysis of Well-Clear Boundary Models for the Integration of UAS in the NAS

NASA Technical Reports Server (NTRS)

Upchurch, Jason M.; Munoz, Cesar A.; Narkawicz, Anthony J.; Chamberlain, James P.; Consiglio, Maria C.

2014-01-01

The FAA-sponsored Sense and Avoid Workshop for Unmanned Aircraft Systems (UAS) defnes the concept of sense and avoid for remote pilots as "the capability of a UAS to remain well clear from and avoid collisions with other airborne traffic." Hence, a rigorous definition of well clear is fundamental to any separation assurance concept for the integration of UAS into civil airspace. This paper presents a family of well-clear boundary models based on the TCAS II Resolution Advisory logic. Analytical techniques are used to study the properties and relationships satisfied by the models. Some of these properties are numerically quantifed using statistical methods.

Diamondlike carbon applications in infrared optics and microelectronics

NASA Technical Reports Server (NTRS)

Woollam, John A.; De, Bhola N.; Orzeszko, S.; Ianno, N. J.; Snyder, Paul G.; Alterovitz, Samuel A.; Pouch, John J.; Wu, R. L. C.; Ingram, D. C.

1990-01-01

The use of diamondlike carbon (DLC) as a protective coating in harsh environments is addressed. There are three topics presented. The first is a description of the preparation of DLC on seven different infrared transmitting materials, and the possibility of using DLC as an antireflecting coating at commonly used wavelengths. DLC doesn't bond easily to all materials, and special techniques for bonding are presented. The second topic deals with how well DLC will protect a substrate from moisture penetration. This is an important aspect in numerous uses of DLC, including both infrared optics and integrated circuits. The third topic is the effect of particulate impact on film performance and integrity.

Penny-shaped crack in a fiber-reinforced matrix. [elastostatics

NASA Technical Reports Server (NTRS)

Narayanan, T. V.; Erdogan, F.

1974-01-01

Using a slender inclusion model developed earlier, the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles, the problem was reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given, and distribution of the stress intensity factor along the crack border was obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Applications of Laplace transform methods to airfoil motion and stability calculations

NASA Technical Reports Server (NTRS)

Edwards, J. W.

1979-01-01

This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

Numerical prediction of marine propeller noise in non-uniform inflow

NASA Astrophysics Data System (ADS)

Pan, Yu-cun; Zhang, Huai-xin

2013-03-01

A numerical study on the acoustic radiation of a propeller interacting with non-uniform inflow has been conducted. Real geometry of a marine propeller DTMB 4118 is used in the calculation, and sliding mesh technique is adopted to deal with the rotational motion of the propeller. The performance of the DES (Detached Eddy Simulation) approach at capturing the unsteady forces and moments on the propeller is compared with experiment. Far-field sound radiation is predicted by the formation 1A developed by Farassat, an integral solution of FW-H (Ffowcs Williams-Hawkings) equation in time domain. The sound pressure and directivity patterns of the propeller operating in two specific velocity distributions are discussed.

Penny-shaped crack in a fiber-reinforced matrix

NASA Technical Reports Server (NTRS)

Narayanan, T. V.; Erdogan, F.

1975-01-01

Using the slender inclusion model developed earlier the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles the problem is reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given and distribution of the stress intensity factor along the crack border is obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Finite volume model for two-dimensional shallow environmental flow

USGS Publications Warehouse

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Hybrid real-code ant colony optimisation for constrained mechanical design

NASA Astrophysics Data System (ADS)

Pholdee, Nantiwat; Bureerat, Sujin

2016-01-01

This paper proposes a hybrid meta-heuristic based on integrating a local search simplex downhill (SDH) method into the search procedure of real-code ant colony optimisation (ACOR). This hybridisation leads to five hybrid algorithms where a Monte Carlo technique, a Latin hypercube sampling technique (LHS) and a translational propagation Latin hypercube design (TPLHD) algorithm are used to generate an initial population. Also, two numerical schemes for selecting an initial simplex are investigated. The original ACOR and its hybrid versions along with a variety of established meta-heuristics are implemented to solve 17 constrained test problems where a fuzzy set theory penalty function technique is used to handle design constraints. The comparative results show that the hybrid algorithms are the top performers. Using the TPLHD technique gives better results than the other sampling techniques. The hybrid optimisers are a powerful design tool for constrained mechanical design problems.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Diagnostic imaging of infertility

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

Winfield, A.C.; Wentz, A.C.

1987-01-01

This text presents a review of all the imaging modalities available in the diagnosis of infertility. This book integrates the perspectives of experts in ob/gyn, radiology, reproductive endocrinology, and urology. It's a one-of-a-kind ''how to'' guide to hysterosalpinography and infertility evaluation, providing complete clinical information on the techniques, pitfalls, problems encountered and differential diagnosis. Detailed descriptions accompany numerous high-quality illustrations to help correlate findings and give meaning to the radiographic and ultrasound images.

Transient Effects in Planar Solidification of Dilute Binary Alloys

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Volz, Martin P.

2008-01-01

The initial transient during planar solidification of dilute binary alloys is studied in the framework of the boundary integral method that leads to the non-linear Volterra integral governing equation. An analytical solution of this equation is obtained for the case of a constant growth rate which constitutes the well-known Tiller's formula for the solute transient. The more physically relevant, constant ramping down temperature case has been studied both numerically and analytically. In particular, an asymptotic analytical solution is obtained for the initial transient behavior. A numerical technique to solve the non-linear Volterra equation is developed and the solution is obtained for a family of the governing parameters. For the rapid solidification condition, growth rate spikes have been observed even for the infinite kinetics model. When recirculating fluid flow is included into the analysis, the spike feature is dramatically diminished. Finally, we have investigated planar solidification with a fluctuating temperature field as a possible mechanism for frequently observed solute trapping bands.

On the development of OpenFOAM solvers based on explicit and implicit high-order Runge-Kutta schemes for incompressible flows with heat transfer

NASA Astrophysics Data System (ADS)

D'Alessandro, Valerio; Binci, Lorenzo; Montelpare, Sergio; Ricci, Renato

2018-01-01

Open-source CFD codes provide suitable environments for implementing and testing low-dissipative algorithms typically used to simulate turbulence. In this research work we developed CFD solvers for incompressible flows based on high-order explicit and diagonally implicit Runge-Kutta (RK) schemes for time integration. In particular, an iterated PISO-like procedure based on Rhie-Chow correction was used to handle pressure-velocity coupling within each implicit RK stage. For the explicit approach, a projected scheme was used to avoid the "checker-board" effect. The above-mentioned approaches were also extended to flow problems involving heat transfer. It is worth noting that the numerical technology available in the OpenFOAM library was used for space discretization. In this work, we additionally explore the reliability and effectiveness of the proposed implementations by computing several unsteady flow benchmarks; we also show that the numerical diffusion due to the time integration approach is completely canceled using the solution techniques proposed here.

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

NASA Technical Reports Server (NTRS)

Womble, M. E.; Potter, J. E.

1975-01-01

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

Monitoring concept for structural integration of PZT-fiber arrays in metal sheets: a numerical and experimental study

NASA Astrophysics Data System (ADS)

Drossel, Welf-Guntram; Schubert, Andreas; Putz, Matthias; Koriath, Hans-Joachim; Wittstock, Volker; Hensel, Sebastian; Pierer, Alexander; Müller, Benedikt; Schmidt, Marek

2018-01-01

The technique joining by forming allows the structural integration of piezoceramic fibers into locally microstructured metal sheets without any elastic interlayers. A high-volume production of the joining partners causes in statistical deviations from the nominal dimensions. A numerical simulation on geometric process sensitivity shows that the deviations have a high significant influence on the resulting fiber stresses after the joining by forming operation and demonstrate the necessity of a monitoring concept. On this basis, the electromechanical behavior of piezoceramic array transducers is investigated experimentally before, during and after the joining process. The piezoceramic array transducer consists of an arrangement of five electrical interconnected piezoceramic fibers. The findings show that the impedance spectrum depends on the fiber stresses and can be used for in-process monitoring during the joining process. Based on the impedance values the preload state of the interconnected piezoceramic fibers can be specifically controlled and a fiber overload.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Screening of groundwater remedial alternatives for brownfield sites: a comprehensive method integrated MCDA with numerical simulation.

PubMed

Li, Wei; Zhang, Min; Wang, Mingyu; Han, Zhantao; Liu, Jiankai; Chen, Zhezhou; Liu, Bo; Yan, Yan; Liu, Zhu

2018-06-01

Brownfield sites pollution and remediation is an urgent environmental issue worldwide. The screening and assessment of remedial alternatives is especially complex owing to its multiple criteria that involves technique, economy, and policy. To help the decision-makers selecting the remedial alternatives efficiently, the criteria framework conducted by the U.S. EPA is improved and a comprehensive method that integrates multiple criteria decision analysis (MCDA) with numerical simulation is conducted in this paper. The criteria framework is modified and classified into three categories: qualitative, semi-quantitative, and quantitative criteria, MCDA method, AHP-PROMETHEE (analytical hierarchy process-preference ranking organization method for enrichment evaluation) is used to determine the priority ranking of the remedial alternatives and the solute transport simulation is conducted to assess the remedial efficiency. A case study was present to demonstrate the screening method in a brownfield site in Cangzhou, northern China. The results show that the systematic method provides a reliable way to quantify the priority of the remedial alternatives.

Study on the influence of ground and satellite observations on the numerical air-quality for PM10 over Romanian territory

NASA Astrophysics Data System (ADS)

Dumitrache, Rodica Claudia; Iriza, Amalia; Maco, Bogdan Alexandru; Barbu, Cosmin Danut; Hirtl, Marcus; Mantovani, Simone; Nicola, Oana; Irimescu, Anisoara; Craciunescu, Vasile; Ristea, Alina; Diamandi, Andrei

2016-10-01

The numerical forecast of particulate matter concentrations in general, and PM10 in particular is a theme of high socio-economic relevance. The aim of this study was to investigate the impact of ground and satellite data assimilation of PM10 observations into the Weather Research and Forecasting model coupled with Chemistry (WRF-CHEM) numerical air quality model for Romanian territory. This is the first initiative of the kind for this domain of interest. Assimilation of satellite information - e.g. AOT's in air quality models is of interest due to the vast spatial coverage of the observations. Support Vector Regression (SVR) techniques are used to estimate the PM content from heterogeneous data sources, including EO products (Aerosol Optical Thickness), ground measurements and numerical model data (temperature, humidity, wind, etc.). In this study we describe the modeling framework employed and present the evaluation of the impact from the data assimilation of PM10 observations on the forecast of the WRF-CHEM model. Integrations of the WRF-CHEM model in data assimilation enabled/disabled configurations allowed the evaluation of satellite and ground data assimilation impact on the PM10 forecast performance for the Romanian territory. The model integration and evaluation were performed for two months, one in winter conditions (January 2013) and one in summer conditions (June 2013).

A hybrid method combining the surface integral equation method and ray tracing for the numerical simulation of high frequency diffraction involved in ultrasonic NDT

NASA Astrophysics Data System (ADS)

Bonnet, M.; Collino, F.; Demaldent, E.; Imperiale, A.; Pesudo, L.

2018-05-01

Ultrasonic Non-Destructive Testing (US NDT) has become widely used in various fields of applications to probe media. Exploiting the surface measurements of the ultrasonic incident waves echoes after their propagation through the medium, it allows to detect potential defects (cracks and inhomogeneities) and characterize the medium. The understanding and interpretation of those experimental measurements is performed with the help of numerical modeling and simulations. However, classical numerical methods can become computationally very expensive for the simulation of wave propagation in the high frequency regime. On the other hand, asymptotic techniques are better suited to model high frequency scattering over large distances but nevertheless do not allow accurate simulation of complex diffraction phenomena. Thus, neither numerical nor asymptotic methods can individually solve high frequency diffraction problems in large media, as those involved in UNDT controls, both quickly and accurately, but their advantages and limitations are complementary. Here we propose a hybrid strategy coupling the surface integral equation method and the ray tracing method to simulate high frequency diffraction under speed and accuracy constraints. This strategy is general and applicable to simulate diffraction phenomena in acoustic or elastodynamic media. We provide its implementation and investigate its performances for the 2D acoustic diffraction problem. The main features of this hybrid method are described and results of 2D computational experiments discussed.

Design and fabrication of planar structures with graded electromagnetic properties

NASA Astrophysics Data System (ADS)

Good, Brandon Lowell

Successfully integrating electromagnetic properties in planar structures offers numerous benefits to the microwave and optical communities. This work aims at formulating new analytic and optimized design methods, creating new fabrication techniques for achieving those methods, and matching appropriate implementation of methods to fabrication techniques. The analytic method consists of modifying an approach that realizes perfect antireflective properties from graded profiles. This method is shown for all-dielectric and magneto-dielectric grading profiles. The optimized design methods are applied to transformer (discrete) or taper (continuous) designs. From these methods, a subtractive and an additive manufacturing technique were established and are described. The additive method, dry powder dot deposition, enables three dimensional varying electromagnetic properties in a structural composite. Combining the methods and fabrication is shown in two applied methodologies. The first uses dry powder dot deposition to design one dimensionally graded electromagnetic profiles in a planar fiberglass composite. The second method simultaneously applies antireflective properties and adjusts directivity through a slab through the use of subwavelength structures to achieve a flat antireflective lens. The end result of this work is a complete set of methods, formulations, and fabrication techniques to achieve integrated electromagnetic properties in planar structures.

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

From LIDAR Scanning to 3d FEM Analysis for Complex Surface and Underground Excavations

NASA Astrophysics Data System (ADS)

Chun, K.; Kemeny, J.

2017-12-01

Light detection and ranging (LIDAR) has been a prevalent remote-sensing technology applied in the geological fields due to its high precision and ease to use. One of the major applications is to use the detailed geometrical information of underground structures as a basis for the generation of three-dimensional numerical model that can be used in FEM analysis. To date, however, straightforward techniques in reconstructing numerical model from the scanned data of underground structures have not been well established or tested. In this paper, we propose a comprehensive approach integrating from LIDAR scanning to finite element numerical analysis, specifically converting LIDAR 3D point clouds of object containing complex surface geometry into finite element model. This methodology has been applied to the Kartchner Caverns in Arizona for the stability analysis. Numerical simulations were performed using the finite element code ABAQUS. The results indicate that the highlights of our technologies obtained from LIDAR is effective and provide reference for other similar engineering project in practice.

Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2) k Theory Using the Truncated Conformal Spectrum Approach

DOE PAGES

Konik, R. M.; Palmai, T.; Takacs, G.; ...

2015-08-24

We study the SU(2) k Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at k » 1. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, λ. Moreover for λ >more » 0 this behavior depends on whether k is even or odd. With k even, we find definitive evidence that the model at low energies is equivalent to the massive O(3) sigma model. For k odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.« less

Uncovering the structure of (super)conformal field theories

NASA Astrophysics Data System (ADS)

Liendo, Pedro

Conformal field theories (CFTs) are of central importance in modern theoretical physics, with applications that range from condensed matter physics to particle theory phenomenology. In this Ph.D. thesis we study CFTs from two somehow orthogonal (but complementary) points of view. In the first approach we concentrate our efforts in two specific examples: the Veneziano limit of N = 2 and N = 1 superconformal QCD. The addition of supersymmetry makes these theories amenable to analytical analysis. In particular, we use the correspondence between single trace operators and states of a spin chain to study the integrability properties of each theory. Our results indicate that these theories are not completely integrable, but they do contain some subsectors in which integrability might hold. In the second approach, we consider the so-called "bootstrap program'', which is the ambitious idea that the restrictions imposed by conformal symmetry (crossing symmetry in particular) are so powerful that starting from a few basic assumptions one should be able to fix the form of a theory. In this thesis we apply bootstrap techniques to CFTs in the presence of a boundary. We study two-point functions using analytical and numerical methods. One-loop results were re-obtained from crossing symmetry alone and a variety of numerical bounds for conformal dimensions of operators were obtained. These bounds are quite general and valid for any CFT in the presence of a boundary, in contrast to our first approach where a specific set of theories was studied. A natural continuation of this work is to apply bootstrap techniques to supersymmetric theories. Some preliminary results along these lines are presented.

Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence

PubMed Central

Schöniger, Anneli; Wöhling, Thomas; Samaniego, Luis; Nowak, Wolfgang

2014-01-01

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. PMID:25745272

An integrated approach to monitoring the calibration stability of operational dual-polarization radars

DOE PAGES

Vaccarono, Mattia; Bechini, Renzo; Chandrasekar, Chandra V.; ...

2016-11-08

The stability of weather radar calibration is a mandatory aspect for quantitative applications, such as rainfall estimation, short-term weather prediction and initialization of numerical atmospheric and hydrological models. Over the years, calibration monitoring techniques based on external sources have been developed, specifically calibration using the Sun and calibration based on ground clutter returns. In this paper, these two techniques are integrated and complemented with a self-consistency procedure and an intercalibration technique. The aim of the integrated approach is to implement a robust method for online monitoring, able to detect significant changes in the radar calibration. The physical consistency of polarimetricmore » radar observables is exploited using the self-consistency approach, based on the expected correspondence between dual-polarization power and phase measurements in rain. This technique allows a reference absolute value to be provided for the radar calibration, from which eventual deviations may be detected using the other procedures. In particular, the ground clutter calibration is implemented on both polarization channels (horizontal and vertical) for each radar scan, allowing the polarimetric variables to be monitored and hardware failures to promptly be recognized. The Sun calibration allows monitoring the calibration and sensitivity of the radar receiver, in addition to the antenna pointing accuracy. It is applied using observations collected during the standard operational scans but requires long integration times (several days) in order to accumulate a sufficient amount of useful data. Finally, an intercalibration technique is developed and performed to compare colocated measurements collected in rain by two radars in overlapping regions. The integrated approach is performed on the C-band weather radar network in northwestern Italy, during July–October 2014. The set of methods considered appears suitable to establish an online tool to monitor the stability of the radar calibration with an accuracy of about 2 dB. In conclusion, this is considered adequate to automatically detect any unexpected change in the radar system requiring further data analysis or on-site measurements.« less

[Inheritance and evolution of acupuncture manipulation techniques of Zhejiang acupuncture masters in modern times].

PubMed

Yu, Daxiong; Ma, Ruijie; Fang, Jianqiao

2015-05-01

There are many eminent acupuncture masters in modern times in the regions of Zhejiang province, which has developed the acupuncture schools of numerous characteristics and induces the important impacts at home and abroad. Through the literature collection on the acupuncture schools in Zhejiang and the interviews to the parties involved, it has been discovered that the acupuncture manipulation techniques of acupuncture masters in modern times are specifically featured. Those techniques are developed on the basis of Neijing (Internal Classic), Jinzhenfu (Ode to Gold Needle) and Zhenjiu Dacheng (Great Compendium of Acupuncture and Moxibustion). No matter to obey the old maxim or study by himself, every master lays the emphasis on the research and interpretation of classical theories and integrates the traditional with the modern. In the paper, the acupuncture manipulation techniques of Zhejiang acupuncture masters in modern times are stated from four aspects, named needling techniques in Internal Classic, feijingzouqi needling technique, penetrating needling technique and innovation of acupuncture manipulation.

Simulation of laser generated ultrasound with application to defect detection

NASA Astrophysics Data System (ADS)

Pantano, A.; Cerniglia, D.

2008-06-01

Laser generated ultrasound holds substantial promise for use as a tool for defect detection in remote inspection thanks to its ability to produce frequencies in the MHz range, enabling fine spatial resolution of defects. Despite the potential impact of laser generated ultrasound in many areas of science and industry, robust tools for studying the phenomenon are lacking and thus limit the design and optimization of non-destructive testing and evaluation techniques. The laser generated ultrasound propagation in complex structures is an intricate phenomenon and is extremely hard to analyze. Only simple geometries can be studied analytically. Numerical techniques found in the literature have proved to be limited in their applicability, by the frequencies in the MHz range and very short wavelengths. The objective of this research is to prove that by using an explicit integration rule together with diagonal element mass matrices, instead of the almost universally adopted implicit integration rule to integrate the equations of motion in a dynamic analysis, it is possible to efficiently and accurately solve ultrasound wave propagation problems with frequencies in the MHz range travelling in relatively large bodies. Presented results on NDE testing of rails demonstrate that the proposed FE technique can provide a valuable tool for studying the laser generated ultrasound propagation.

Integrated Optics for Planar imaging and Optical Signal Processing

NASA Astrophysics Data System (ADS)

Song, Qi

Silicon photonics is a subject of growing interest with the potential of delivering planar electro-optical devices with chip scale integration. Silicon-on-insulator (SOI) technology has provided a marvelous platform for photonics industry because of its advantages in integration capability in CMOS circuit and countless nonlinearity applications in optical signal processing. This thesis is focused on the investigation of planar imaging techniques on SOI platform and potential applications in ultra-fast optical signal processing. In the first part, a general review and background introduction about integrated photonics circuit and planar imaging technique are provided. In chapter 2, planar imaging platform is realized by a silicon photodiode on SOI chip. Silicon photodiode on waveguide provides a high numerical aperture for an imaging transceiver pixel. An erbium doped Y2O3 particle is excited by 1550nm Laser and the fluorescent image is obtained with assistance of the scanning system. Fluorescence image is reconstructed by using image de-convolution technique. Under photovoltaic mode, we use an on-chip photodiode and an external PIN photodiode to realize similar resolution as 5μm. In chapter 3, a time stretching technique is developed to a spatial domain to realize a 2D imaging system as an ultrafast imaging tool. The system is evaluated based on theoretical calculation. The experimental results are shown for a verification of system capability to imaging a micron size particle or a finger print. Meanwhile, dynamic information for a moving object is also achieved by correlation algorithm. In chapter 4, the optical leaky wave antenna based on SOI waveguide has been utilized for imaging applications and extensive numerical studied has been conducted. and the theoretical explanation is supported by leaky wave theory. The highly directive radiation has been obtained from the broadside with 15.7 dB directivity and a 3dB beam width of ΔØ 3dB ≈ 1.65° in free space environment when β -1 = 2.409 × 105/m, α=4.576 ×103/m. At the end, electronics beam-steering principle has been studied and the comprehensive model has been built to explain carrier transformation behavior in a PIN junction as individual silicon perturbation. Results show that 1019/cm3 is possible obtained with electron injection mechanism. Although the radiation modulation based on carrier injection of 1019/cm3 gives 0.5dB variation, resonant structure, such as Fabry Perrot Cavity, can be integrated with LOWAs to enhance modulation effect.

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

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

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

DOE PAGES

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

2016-10-12

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

Integrated and differential accuracy in resummed cross sections

DOE PAGES

Bertolini, Daniele; Solon, Mikhail P.; Walsh, Jonathan R.

2017-03-30

Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant. Here in this paper we propose a method, which we call the σ-improved scheme, to resolve this issue. It consists of two steps: (i) include higher-order terms in the spectrum to improve the agreement with the cumulant central value, and (ii) employ profile scales that encode correlations between different points to give robust uncertainty estimates for the integrated spectrum. We provide a generic algorithm for determining suchmore » profile scales, and show the application to the thrust distribution in e +e - collisions at NLL'+NLO and NNLL'+NNLO.« less

Simulating the cold dark matter-neutrino dipole with TianNu

DOE PAGES

Inman, Derek; Yu, Hao-Ran; Zhu, Hong-Ming; ...

2017-04-20

Measurements of neutrino mass in cosmological observations rely on two-point statistics that are hindered by significant degeneracies with the optical depth and galaxy bias. The relative velocity effect between cold dark matter and neutrinos induces a large scale dipole in the matter density field and may be able to provide orthogonal constraints to standard techniques. In this paper, we numerically investigate this dipole in the TianNu simulation, which contains cold dark matter and 50 meV neutrinos. We first compute the dipole using a new linear response technique where we treat the displacement caused by the relative velocity as a phasemore » in Fourier space and then integrate the matter power spectrum over redshift. Then, we compute the dipole numerically in real space using the simulation density and velocity fields. We find excellent agreement between the linear response and N-body methods. Finally, utilizing the dipole as an observational tool requires two tracers of the matter distribution that are differently biased with respect to the neutrino density.« less

Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems

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

Jia, Jun; Jingfang, Huang

2008-01-01

In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\\bf \\it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving amore » decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.« less

Using remote sensing and GIS techniques to estimate discharge and recharge fluxes for the Death Valley regional groundwater flow system, USA

USGS Publications Warehouse

D'Agnese, F. A.; Faunt, C.C.; Turner, A.K.; ,

1996-01-01

The recharge and discharge components of the Death Valley regional groundwater flow system were defined by techniques that integrated disparate data types to develop a spatially complex representation of near-surface hydrological processes. Image classification methods were applied to multispectral satellite data to produce a vegetation map. The vegetation map was combined with ancillary data in a GIS to delineate different types of wetlands, phreatophytes and wet playa areas. Existing evapotranspiration-rate estimates were used to calculate discharge volumes for these area. An empirical method of groundwater recharge estimation was modified to incorporate data describing soil-moisture conditions, and a recharge potential map was produced. These discharge and recharge maps were readily converted to data arrays for numerical modelling codes. Inverse parameter estimation techniques also used these data to evaluate the reliability and sensitivity of estimated values.The recharge and discharge components of the Death Valley regional groundwater flow system were defined by remote sensing and GIS techniques that integrated disparate data types to develop a spatially complex representation of near-surface hydrological processes. Image classification methods were applied to multispectral satellite data to produce a vegetation map. This map provided a basis for subsequent evapotranspiration and infiltration estimations. The vegetation map was combined with ancillary data in a GIS to delineate different types of wetlands, phreatophytes and wet playa areas. Existing evapotranspiration-rate estimates were then used to calculate discharge volumes for these areas. A previously used empirical method of groundwater recharge estimation was modified by GIS methods to incorporate data describing soil-moisture conditions, and a recharge potential map was produced. These discharge and recharge maps were readily converted to data arrays for numerical modelling codes. Inverse parameter estimation techniques also used these data to evaluate the reliability and sensitivity of estimated values.

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

Bailey, David

In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard! If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100more » correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the book are provided, both in an appendix to the book and on a website. In the process, the authors take the reader on a wide-ranging tour of modern numerical mathematics, with enough background material so that even readers with little or no training in numerical analysis can follow. Here is a list of just a few of the topics visited: numerical quadrature (i.e., numerical integration), series summation, sequence extrapolation, contour integration, Fourier integrals, high-precision arithmetic, interval arithmetic, symbolic computing, numerical linear algebra, perturbation theory, Euler-Maclaurin summation, global minimization, eigenvalue methods, evolutionary algorithms, matrix preconditioning, random walks, special functions, elliptic functions, Monte-Carlo methods, and numerical differentiation.« less

Numerical investigations of internal stresses on carbon steel based on ultrasonic LCR waves

NASA Astrophysics Data System (ADS)

Ramasamy, R.; Ibrahim, Z.; Chai, H. K.

2017-10-01

Internal stresses or residual stresses in the structural elements are very crucial in carrying out in-service evaluations and fitness-for-purpose assessments. The generation of these internal stresses can occur as result of the fabrication of the steel members, installation sequence or other ad-hoc events such as accidents or impact. The accurate prediction of the internal stresses will contribute towards estimating the integrity state of the structural elements, with respect to their material allowable stresses. This paper investigates the explicit FE based numerical modelling of the ultrasonic based non-destructive technique, utilising the measurable longitudinal critical refracted wave (LCR) and relating these to the internal stresses within the structural elements by the evaluation of the material dependent acoustoelastic factors. The subsurface travel path of the LCR wave inside the structural elements makes it a sub-surface stress measurement technique and the linearised relationship with corresponding internal stresses can be systematically applied repeatedly. The numerical results are compared against laboratory tests data to correlate the findings and to establish modelling feasibility for future proof-of-concepts. It can be concluded from this numerical investigation, that the subsurface ultrasonic LCR wave has great potential to be implemented for in-situ structural residual stress measurements, as compared to other available surface measurements such as strain gauges or x-ray diffraction.

Explosion localization and characterization via infrasound using numerical modeling

NASA Astrophysics Data System (ADS)

Fee, D.; Kim, K.; Iezzi, A. M.; Matoza, R. S.; Jolly, A. D.; De Angelis, S.; Diaz Moreno, A.; Szuberla, C.

2017-12-01

Numerous methods have been applied to locate, detect, and characterize volcanic and anthropogenic explosions using infrasound. Far-field localization techniques typically use back-azimuths from multiple arrays (triangulation) or Reverse Time Migration (RTM, or back-projection). At closer ranges, networks surrounding a source may use Time Difference of Arrival (TDOA), semblance, station-pair double difference, etc. However, at volcanoes and regions with topography or obstructions that block the direct path of sound, recent studies have shown that numerical modeling is necessary to provide an accurate source location. A heterogeneous and moving atmosphere (winds) may also affect the location. The time reversal mirror (TRM) application of Kim et al. (2015) back-propagates the wavefield using a Finite Difference Time Domain (FDTD) algorithm, with the source corresponding to the location of peak convergence. Although it provides high-resolution source localization and can account for complex wave propagation, TRM is computationally expensive and limited to individual events. Here we present a new technique, termed RTM-FDTD, which integrates TRM and FDTD. Travel time and transmission loss information is computed from each station to the entire potential source grid from 3-D Green's functions derived via FDTD. The wave energy is then back-projected and stacked at each grid point, with the maximum corresponding to the likely source. We apply our method to detect and characterize thousands of explosions from Yasur Volcano, Vanuatu and Etna Volcano, Italy, which both provide complex wave propagation and multiple source locations. We compare our results with those from more traditional methods (e.g. semblance), and suggest our method is preferred as it is computationally less expensive than TRM but still integrates numerical modeling. RTM-FDTD could be applied to volcanic other anthropogenic sources at a wide variety of ranges and scenarios. Kim, K., Lees, J.M., 2015. Imaging volcanic infrasound sources using time reversal mirror algorithm. Geophysical Journal International 202, 1663-1676.

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.

Analytic model for a weakly dissipative shallow-water undular bore.

PubMed

El, G A; Grimshaw, R H J; Kamchatnov, A M

2005-09-01

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell-Segur (AKNS) scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.

Numerical Analysis of Dusty-Gas Flows

NASA Astrophysics Data System (ADS)

Saito, T.

2002-02-01

This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.

An efficient HZETRN (a galactic cosmic ray transport code)

NASA Technical Reports Server (NTRS)

Shinn, Judy L.; Wilson, John W.

1992-01-01

An accurate and efficient engineering code for analyzing the shielding requirements against the high-energy galactic heavy ions is needed. The HZETRN is a deterministic code developed at Langley Research Center that is constantly under improvement both in physics and numerical computation and is targeted for such use. One problem area connected with the space-marching technique used in this code is the propagation of the local truncation error. By improving the numerical algorithms for interpolation, integration, and grid distribution formula, the efficiency of the code is increased by a factor of eight as the number of energy grid points is reduced. The numerical accuracy of better than 2 percent for a shield thickness of 150 g/cm(exp 2) is found when a 45 point energy grid is used. The propagating step size, which is related to the perturbation theory, is also reevaluated.

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

An adaptive gridless methodology in one dimension

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

Snyder, N.T.; Hailey, C.E.

1996-09-01

Gridless numerical analysis offers great potential for accurately solving for flow about complex geometries or moving boundary problems. Because gridless methods do not require point connection, the mesh cannot twist or distort. The gridless method utilizes a Taylor series about each point to obtain the unknown derivative terms from the current field variable estimates. The governing equation is then numerically integrated to determine the field variables for the next iteration. Effects of point spacing and Taylor series order on accuracy are studied, and they follow similar trends of traditional numerical techniques. Introducing adaption by point movement using a spring analogymore » allows the solution method to track a moving boundary. The adaptive gridless method models linear, nonlinear, steady, and transient problems. Comparison with known analytic solutions is given for these examples. Although point movement adaption does not provide a significant increase in accuracy, it helps capture important features and provides an improved solution.« less

Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges

NASA Astrophysics Data System (ADS)

Blas, Harold; Callisaya, Hector Flores

2018-02-01

We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities, split into two infinite towers of conserved and asymptotically conserved charges. For two-solitons without definite parity under space-reflection symmetry (kink-kink and kink-antikink scatterings with unequal and opposite velocities) our numerical results show the existence of the asymptotically conserved charges only. However, we show that in the center-of-mass reference frame of the two solitons the parity symmetries and their associated set of exactly conserved charges can be restored. Moreover, the positive parity breather-like (kink-antikink bound state) solution exhibits a tower of exactly conserved charges and a subset of charges which are periodic in time. We back up our results with extensive numerical simulations which also demonstrate the existence of long lived breather-like states in these models. The time evolution has been simulated by the 4th order Runge-Kutta method supplied with non-reflecting boundary conditions.

Integrating numerical computation into the undergraduate education physics curriculum using spreadsheet excel

NASA Astrophysics Data System (ADS)

Fauzi, Ahmad

2017-11-01

Numerical computation has many pedagogical advantages: it develops analytical skills and problem-solving skills, helps to learn through visualization, and enhances physics education. Unfortunately, numerical computation is not taught to undergraduate education physics students in Indonesia. Incorporate numerical computation into the undergraduate education physics curriculum presents many challenges. The main challenges are the dense curriculum that makes difficult to put new numerical computation course and most students have no programming experience. In this research, we used case study to review how to integrate numerical computation into undergraduate education physics curriculum. The participants of this research were 54 students of the fourth semester of physics education department. As a result, we concluded that numerical computation could be integrated into undergraduate education physics curriculum using spreadsheet excel combined with another course. The results of this research become complements of the study on how to integrate numerical computation in learning physics using spreadsheet excel.

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

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

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less

Time-distance domain transformation for Acoustic Emission source localization in thin metallic plates.

PubMed

Grabowski, Krzysztof; Gawronski, Mateusz; Baran, Ireneusz; Spychalski, Wojciech; Staszewski, Wieslaw J; Uhl, Tadeusz; Kundu, Tribikram; Packo, Pawel

2016-05-01

Acoustic Emission used in Non-Destructive Testing is focused on analysis of elastic waves propagating in mechanical structures. Then any information carried by generated acoustic waves, further recorded by a set of transducers, allow to determine integrity of these structures. It is clear that material properties and geometry strongly impacts the result. In this paper a method for Acoustic Emission source localization in thin plates is presented. The approach is based on the Time-Distance Domain Transform, that is a wavenumber-frequency mapping technique for precise event localization. The major advantage of the technique is dispersion compensation through a phase-shifting of investigated waveforms in order to acquire the most accurate output, allowing for source-sensor distance estimation using a single transducer. The accuracy and robustness of the above process are also investigated. This includes the study of Young's modulus value and numerical parameters influence on damage detection. By merging the Time-Distance Domain Transform with an optimal distance selection technique, an identification-localization algorithm is achieved. The method is investigated analytically, numerically and experimentally. The latter involves both laboratory and large scale industrial tests. Copyright © 2016 Elsevier B.V. All rights reserved.

Laser fringe anemometry for aero engine components

NASA Technical Reports Server (NTRS)

Strazisar, A. J.

1986-01-01

Advances in flow measurement techniques in turbomachinery continue to be paced by the need to obtain detailed data for use in validating numerical predictions of the flowfield and for use in the development of empirical models for those flow features which cannot be readily modelled numerically. The use of laser anemometry in turbomachinery research has grown over the last 14 years in response to these needs. Based on past applications and current developments, this paper reviews the key issues which are involved when considering the application of laser anemometry to the measurement of turbomachinery flowfields. Aspects of laser fringe anemometer optical design which are applicable to turbomachinery research are briefly reviewed. Application problems which are common to both laser fringe anemometry (LFA) and laser transit anemometry (LTA) such as seed particle injection, optical access to the flowfield, and measurement of rotor rotational position are covered. The efficiency of various data acquisition schemes is analyzed and issues related to data integrity and error estimation are addressed. Real-time data analysis techniques aimed at capturing flow physics in real time are discussed. Finally, data reduction and analysis techniques are discussed and illustrated using examples taken from several LFA turbomachinery applications.

Impact energy and retained dose uniformity in enhanced glow discharge plasma immersion ion implantation

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

Lu, Q. Y.; Fu, Ricky K. Y.; Chu, Paul K.

2009-08-10

The implantation energy and retained dose uniformity in enhanced glow discharge plasma immersion ion implantation (EGD-PIII) is investigated numerically and experimentally. Depth profiles obtained from different samples processed by EGD-PIII and traditional PIII are compared. The retained doses under different pulse widths are calculated by integrating the area under the depth profiles. Our results indicate that the improvement in the impact energy and retained dose uniformity by this technique is remarkable.

Numeric stratigraphic modeling: Testing sequence Numeric stratigraphic modeling: Testing sequence stratigraphic concepts using high resolution geologic examples

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

Armentrout, J.M.; Smith-Rouch, L.S.; Bowman, S.A.

1996-08-01

Numeric simulations based on integrated data sets enhance our understanding of depositional geometry and facilitate quantification of depositional processes. Numeric values tested against well-constrained geologic data sets can then be used in iterations testing each variable, and in predicting lithofacies distributions under various depositional scenarios using the principles of sequence stratigraphic analysis. The stratigraphic modeling software provides a broad spectrum of techniques for modeling and testing elements of the petroleum system. Using well-constrained geologic examples, variations in depositional geometry and lithofacies distributions between different tectonic settings (passive vs. active margin) and climate regimes (hothouse vs. icehouse) can provide insight tomore » potential source rock and reservoir rock distribution, maturation timing, migration pathways, and trap formation. Two data sets are used to illustrate such variations: both include a seismic reflection profile calibrated by multiple wells. The first is a Pennsylvanian mixed carbonate-siliciclastic system in the Paradox basin, and the second a Pliocene-Pleistocene siliciclastic system in the Gulf of Mexico. Numeric simulations result in geometry and facies distributions consistent with those interpreted using the integrated stratigraphic analysis of the calibrated seismic profiles. An exception occurs in the Gulf of Mexico study where the simulated sediment thickness from 3.8 to 1.6 Ma within an upper slope minibasin was less than that mapped using a regional seismic grid. Regional depositional patterns demonstrate that this extra thickness was probably sourced from out of the plane of the modeled transect, illustrating the necessity for three-dimensional constraints on two-dimensional modeling.« less

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Vezewski, D. J.

1980-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1979-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Finite-element numerical modeling of atmospheric turbulent boundary layer

NASA Technical Reports Server (NTRS)

Lee, H. N.; Kao, S. K.

1979-01-01

A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

Beam shaping of laser diode radiation by waveguides with arbitrary cladding geometry written with fs-laser radiation.

PubMed

Beckmann, Dennis; Schnitzler, Daniel; Schaefer, Dagmar; Gottmann, Jens; Kelbassa, Ingomar

2011-12-05

Waveguides with arbitrary cross sections are written in the volume of Al(2)O(3)-crystals using tightly focused femtosecond laser radiation. Utilizing a scanning system with large numerical aperture, complex cladding geometries are realized with a precision around 0.5 µm and a scanning speed up to 100 mm/s. Individual beam and mode shaping of laser diode radiation is demonstrated by varying the design of the waveguide cladding. The influence of the writing parameters on the waveguide properties are investigated resulting in a numerical aperture of the waveguides in the range of 0.1. This direct laser writing technique enables optical devices which could possibly replace bulky beam shaping setups with an integrated solution.

A stability study of asteroid families near the 3:1 and 5:2 resonance with Jupiter

NASA Astrophysics Data System (ADS)

Hahn, G.; Lagerkvist, C.-I.; Lindblad, B. A.

1993-06-01

The stability and homogeneity of three asteroid families from Lindblad's list (1992) are studied using numerical integration techniques. These families include the Maria family, which lies close to the 3:1 mean motion resonance with Jupiter, the Oppavia-Gefion, and Dora families which are close to the 5:2 resonance. The study is based on a simplified solar system model, which takes into account the perturbations only by Jupiter and Saturn, and Everhart's variable stepsize integrator RA15. Preliminary results indicate that the stability of the orbits of all family members are not affected by the proximity to the 3:1 and 5:2 mean motion resonance with Jupiter.

Numerical modelling of surface plasmonic polaritons

NASA Astrophysics Data System (ADS)

Mansoor, Riyadh; AL-Khursan, Amin Habbeb

2018-06-01

Extending optoelectronics into the nano-regime seems problematic due to the relatively long wavelengths of light. The conversion of light into plasmons is a possible way to overcome this problem. Plasmon's wavelengths are much shorter than that of light which enables the propagation of signals in small size components. In this paper, a 3D simulation of surface plasmon polariton (SPP) excitation is performed. The Finite integration technique was used to solve Maxwell's equations in the dielectric-metal interface. The results show how the surface plasmon polariton was generated at the grating assisted dielectric-metal interface. SPP is a good candidate for signal confinement in small size optoelectronics which allow high density optical integrated circuits in all optical networks.

Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

NASA Astrophysics Data System (ADS)

Li, G. Q.; Zhu, Z. H.

2015-12-01

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Finite element techniques applied to cracks interacting with selected singularities

NASA Technical Reports Server (NTRS)

Conway, J. C.

1975-01-01

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

Real time estimation of ship motions using Kalman filtering techniques

NASA Technical Reports Server (NTRS)

Triantafyllou, M. S.; Bodson, M.; Athans, M.

1983-01-01

The estimation of the heave, pitch, roll, sway, and yaw motions of a DD-963 destroyer is studied, using Kalman filtering techniques, for application in VTOL aircraft landing. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A detailed numerical application for a DD-963 destroyer is presented and simulations of the estimations obtained from Kalman filters are discussed.

Design of vibration isolation systems using multiobjective optimization techniques

NASA Technical Reports Server (NTRS)

Rao, S. S.

1984-01-01

The design of vibration isolation systems is considered using multicriteria optimization techniques. The integrated values of the square of the force transmitted to the main mass and the square of the relative displacement between the main mass and the base are taken as the performance indices. The design of a three degrees-of-freedom isolation system with an exponentially decaying type of base disturbance is considered for illustration. Numerical results are obtained using the global criterion, utility function, bounded objective, lexicographic, goal programming, goal attainment and game theory methods. It is found that the game theory approach is superior in finding a better optimum solution with proper balance of the various objective functions.

Chaotic coordinates for the Large Helical Device

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

Hudson, S. R., E-mail: shudson@pppl.gov; Suzuki, Y.

The theory of quadratic-flux-minimizing (QFM) surfaces is reviewed, and numerical techniques that allow high-order QFM surfaces to be efficiently constructed for experimentally relevant, non-integrable magnetic fields are described. As a practical example, the chaotic edge of the magnetic field in the Large Helical Device (LHD) is examined. A precise technique for finding the boundary surface is implemented, the hierarchy of partial barriers associated with the near-critical cantori is constructed, and a coordinate system, which we call chaotic coordinates, that is based on a selection of QFM surfaces is constructed that simplifies the description of the magnetic field, so that fluxmore » surfaces become “straight” and islands become “square.”.« less

Fuzzy logic and neural networks in artificial intelligence and pattern recognition

NASA Astrophysics Data System (ADS)

Sanchez, Elie

1991-10-01

With the use of fuzzy logic techniques, neural computing can be integrated in symbolic reasoning to solve complex real world problems. In fact, artificial neural networks, expert systems, and fuzzy logic systems, in the context of approximate reasoning, share common features and techniques. A model of Fuzzy Connectionist Expert System is introduced, in which an artificial neural network is designed to construct the knowledge base of an expert system from, training examples (this model can also be used for specifications of rules in fuzzy logic control). Two types of weights are associated with the synaptic connections in an AND-OR structure: primary linguistic weights, interpreted as labels of fuzzy sets, and secondary numerical weights. Cell activation is computed through min-max fuzzy equations of the weights. Learning consists in finding the (numerical) weights and the network topology. This feedforward network is described and first illustrated in a biomedical application (medical diagnosis assistance from inflammatory-syndromes/proteins profiles). Then, it is shown how this methodology can be utilized for handwritten pattern recognition (characters play the role of diagnoses): in a fuzzy neuron describing a number for example, the linguistic weights represent fuzzy sets on cross-detecting lines and the numerical weights reflect the importance (or weakness) of connections between cross-detecting lines and characters.

Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites

NASA Technical Reports Server (NTRS)

Arenz, R. J.; Landel, R. F.

1989-01-01

Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.

Development of numerical methods for overset grids with applications for the integrated Space Shuttle vehicle

NASA Technical Reports Server (NTRS)

Chan, William M.

1995-01-01

Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation.

Light in diagnosis, therapy and surgery

PubMed Central

Yun, Seok Hyun; Kwok, Sheldon J. J.

2016-01-01

Light and optical techniques have made profound impacts on modern medicine, with numerous lasers and optical devices being currently used in clinical practice to assess health and treat disease. Recent advances in biomedical optics have enabled increasingly sophisticated technologies — in particular those that integrate photonics with nanotechnology, biomaterials and genetic engineering. In this Review, we revisit the fundamentals of light–matter interactions, describe the applications of light in imaging, diagnosis, therapy and surgery, overview their clinical use, and discuss the promise of emerging light-based technologies. PMID:28649464

Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions

NASA Technical Reports Server (NTRS)

Poole, L. R.

1972-01-01

A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.

ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

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

Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Integrating vegetation index time series and meteorological data to understand the effect of the land use/land cover (LULC) in the climatic seasonality of the Brazilian Cerrado

NASA Astrophysics Data System (ADS)

Lins, D. B.; Zullo, J.; Friedel, M. J.

2013-12-01

The Cerrado (savanna ecosystem) of São Paulo state (Brazil) represent a complex mosaic of different typologies of uses, actors and biophysical and social restrictions. Originally, 14% of the state of São Paulo area was covered by the diversity of Cerrado phytophysiognomies. Currently, only 1% of this original composition remains fragmented into numerous relicts of biodiversity, mainly concentrated in the central-eastern of the state. A relevant part of the fragments are found in areas of intense coverage change by human activities, whereas the greatest pressure comes from sugar cane cultivation, either by direct replacement of Cerrado vegetation or occupying pasture areas in the fragments edges. As a result, new local level dynamics has been introduced, directly or indirectly, affecting the established of processes in climate systems. In this study, the main goal is analyzing the relationship between the Cerrado landscape changing and the climate dynamics in regional and local areas. The multi-temporal MODIS 250 m Vegetation Index (VI) datasets (period of 2000 to 2012) are integrated with precipitation data of the correspondent period (http://www.agritempo.gov.br/),one of the most important variable of the spatial phytophysiognomies distribution. The integration of meteorological data enable the development of an integrated approach to understand the relationship between climatic seasonality and the changes in the spatial patterns. A procedure to congregated diverse dynamics information is the Self Organizing Map (SOM, Kohonen, 2001), a technique that relies on unsupervised competitive learning (Kohonen and Somervuo 2002) to recognize patterns. In this approach, high-dimensional data are represented on two dimensions, making possible to obtain patterns that takes into account information from different natures. Observed advances will contribute to bring machine-learning techniques as a valid tool to provide improve in land use/land cover (LULC) analyzes at different hierarchical scales to support numerous science and policy applications.

Non destructive technique for cracks detection by an eddy current in differential mode for steel frames

NASA Astrophysics Data System (ADS)

Harzalla, S.; Belgacem, F. Bin Muhammad; Chabaat, M.

2014-12-01

In this paper, a nondestructive technique is used as a tool to control cracks and microcracks in materials. A simulation by a numerical approach such as the finite element method is employed to detect cracks and eventually; to study their propagation using a crucial parameter such as the stress intensity factor. This approach has been used in the aircraft industry to control cracks. Besides, it makes it possible to highlight the defects of parts while preserving the integrity of the controlled products. On the other side, it is proven that the reliability of the control of defects gives convincing results for the improvement of the quality and the safety of the material. Eddy current testing (ECT) is a standard technique in industry for the detection of surface breaking flaws in magnetic materials such as steels. In this context, simulation tools can be used to improve the understanding of experimental signals, optimize the design of sensors or evaluate the performance of ECT procedures. CEA-LIST has developed for many years semi-analytical models embedded into the simulation platform CIVA dedicated to non-destructive testing. The developments presented herein address the case of flaws located inside a planar and magnetic medium. Simulation results are obtained through the application of the Volume Integral Method (VIM). When considering the ECT of a single flaw, a system of two differential equations is derived from Maxwell equations. The numerical resolution of the system is carried out using the classical Galerkin variant of the Method of Moments. Besides, a probe response is calculated by application of the Lorentz reciprocity theorem. Finally, the approach itself as well as comparisons between simulation results and measured data are presented.

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.

Development of a GNSS water vapour tomography system using algebraic reconstruction techniques

NASA Astrophysics Data System (ADS)

Bender, Michael; Dick, Galina; Ge, Maorong; Deng, Zhiguo; Wickert, Jens; Kahle, Hans-Gert; Raabe, Armin; Tetzlaff, Gerd

2011-05-01

A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.

An overview assessment of the effectiveness and global popularity of some methods used in measuring riverbank filtration

NASA Astrophysics Data System (ADS)

Umar, Da'u. Abba; Ramli, Mohammad Firuz; Aris, Ahmad Zaharin; Sulaiman, Wan Nor Azmin; Kura, Nura Umar; Tukur, Abubakar Ibrahim

2017-07-01

This paper presents an overview assessment of the effectiveness and popularity of some methods adopted in measuring river bank filtration (RBF). The review is aim at understanding some of the appropriate methods used in measuring riverbank filtration, their frequencies of use, and their spatial applications worldwide. The most commonly used methods and techniques in riverbank filtration studies are: Geographical Information System (GIS) (site suitability/surface characterization), Geophysical, Pumping Test and borehole logging (sub-surface), Hydrochemical, Geochemical, and Statistical techniques (hydrochemistry of water), Numerical modelling, Tracer techniques and Stable Isotope Approaches (degradation and contaminants attenuation processes). From the summary in Table 1, hydrochemical, numerical modelling and pumping test are the frequently used and popular methods, while geophysical, GIS and statistical techniques are the less attractive. However, many researchers prefer integrated approach especially that riverbank filtration studies involve diverse and interrelated components. In term of spatial popularity and successful implementation of riverbank filtration, it is explicitly clear that the popularity and success of the technology is more pronounced in developed countries like U.S. and most European countries. However, it is gradually gaining ground in Asia and Africa, although it is not far from its infancy state in Africa, where the technology could be more important considering the economic status of the region and its peculiarity when it comes to water resources predicaments.

Integrating the Gradient of the Thin Wire Kernel

NASA Technical Reports Server (NTRS)

Champagne, Nathan J.; Wilton, Donald R.

2008-01-01

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Monte Carlo methods for multidimensional integration for European option pricing

NASA Astrophysics Data System (ADS)

Todorov, V.; Dimov, I. T.

2016-10-01

In this paper, we illustrate examples of highly accurate Monte Carlo and quasi-Monte Carlo methods for multiple integrals related to the evaluation of European style options. The idea is that the value of the option is formulated in terms of the expectation of some random variable; then the average of independent samples of this random variable is used to estimate the value of the option. First we obtain an integral representation for the value of the option using the risk neutral valuation formula. Then with an appropriations change of the constants we obtain a multidimensional integral over the unit hypercube of the corresponding dimensionality. Then we compare a specific type of lattice rules over one of the best low discrepancy sequence of Sobol for numerical integration. Quasi-Monte Carlo methods are compared with Adaptive and Crude Monte Carlo techniques for solving the problem. The four approaches are completely different thus it is a question of interest to know which one of them outperforms the other for evaluation multidimensional integrals in finance. Some of the advantages and disadvantages of the developed algorithms are discussed.

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Towards a generalized computational fluid dynamics technique for all Mach numbers

NASA Technical Reports Server (NTRS)

Walters, R. W.; Slack, D. C.; Godfrey, A. G.

1993-01-01

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Self-aligned quadruple patterning using spacer on spacer integration optimization for N5

NASA Astrophysics Data System (ADS)

Thibaut, Sophie; Raley, Angélique; Mohanty, Nihar; Kal, Subhadeep; Liu, Eric; Ko, Akiteru; O'Meara, David; Tapily, Kandabara; Biolsi, Peter

2017-04-01

To meet scaling requirements, the semiconductor industry has extended 193nm immersion lithography beyond its minimum pitch limitation using multiple patterning schemes such as self-aligned double patterning, self-aligned quadruple patterning and litho-etch / litho etch iterations. Those techniques have been declined in numerous options in the last few years. Spacer on spacer pitch splitting integration has been proven to show multiple advantages compared to conventional pitch splitting approach. Reducing the number of pattern transfer steps associated with sacrificial layers resulted in significant decrease of cost and an overall simplification of the double pitch split technique. While demonstrating attractive aspects, SAQP spacer on spacer flow brings challenges of its own. Namely, material set selections and etch chemistry development for adequate selectivities, mandrel shape and spacer shape engineering to improve edge placement error (EPE). In this paper we follow up and extend upon our previous learning and proceed into more details on the robustness of the integration in regards to final pattern transfer and full wafer critical dimension uniformity. Furthermore, since the number of intermediate steps is reduced, one will expect improved uniformity and pitch walking control. This assertion will be verified through a thorough pitch walking analysis.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 3.0)

NASA Technical Reports Server (NTRS)

Epton, Michael A.; Magnus, Alfred E.

1990-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the Panel Aerodynamics (PAN AIR) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformation, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments. Principal revisions to version 3.0 are the following: (1) appendices H and K more fully describe the Aerodynamic Influence Coefficient (AIC) construction; (2) appendix L now provides a complete description of the AIC solution process; (3) appendix P is new and discusses the theory for the new FDP module (which calculates streamlines and offbody points); and (4) numerous small corrections and revisions reflecting the MAG module rewrite.

The leaking mode problem in atmospheric acoustic-gravity wave propagation

NASA Technical Reports Server (NTRS)

Kinney, W. A.; Pierce, A. D.

1976-01-01

The problem of predicting the transient acoustic pressure pulse at long horizontal distances from large explosions in the atmosphere is examined. Account is taken of poles off the real axis and of branch line integrals in the general integral governing the transient waveform. Perturbation techniques are described for the computation of the imaginary ordinate of the poles and numerical studies are described for a model atmosphere terminated by a halfspace with c = 478 m/sec above 125 km. For frequencies less than 0.0125 rad/sec, the GR sub 1 mode, for example, is found to have a frequency dependent amplitude decay of the order of 0.0001 nepers/km. Examples of numerically synthesized transient waveforms are exhibited with and without the inclusion of leaking modes. The inclusion of leaking modes results in waveforms with a more marked beginning rather than a low frequency oscillating precursor of gradually increasing amplitude. Also, the revised computations indicate that waveforms invariably begin with a pressure rise, a result supported by other theoretical considerations and by experimental data.

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

Liao, Haitao, E-mail: liaoht@cae.ac.cn

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results inmore » an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.« less

Efficient sensitivity analysis method for chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Liao, Haitao

2016-05-01

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

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

Vaccarono, Mattia; Bechini, Renzo; Chandrasekar, Chandra V.

The stability of weather radar calibration is a mandatory aspect for quantitative applications, such as rainfall estimation, short-term weather prediction and initialization of numerical atmospheric and hydrological models. Over the years, calibration monitoring techniques based on external sources have been developed, specifically calibration using the Sun and calibration based on ground clutter returns. In this paper, these two techniques are integrated and complemented with a self-consistency procedure and an intercalibration technique. The aim of the integrated approach is to implement a robust method for online monitoring, able to detect significant changes in the radar calibration. The physical consistency of polarimetricmore » radar observables is exploited using the self-consistency approach, based on the expected correspondence between dual-polarization power and phase measurements in rain. This technique allows a reference absolute value to be provided for the radar calibration, from which eventual deviations may be detected using the other procedures. In particular, the ground clutter calibration is implemented on both polarization channels (horizontal and vertical) for each radar scan, allowing the polarimetric variables to be monitored and hardware failures to promptly be recognized. The Sun calibration allows monitoring the calibration and sensitivity of the radar receiver, in addition to the antenna pointing accuracy. It is applied using observations collected during the standard operational scans but requires long integration times (several days) in order to accumulate a sufficient amount of useful data. Finally, an intercalibration technique is developed and performed to compare colocated measurements collected in rain by two radars in overlapping regions. The integrated approach is performed on the C-band weather radar network in northwestern Italy, during July–October 2014. The set of methods considered appears suitable to establish an online tool to monitor the stability of the radar calibration with an accuracy of about 2 dB. In conclusion, this is considered adequate to automatically detect any unexpected change in the radar system requiring further data analysis or on-site measurements.« less

Lateral conduction effects on heat-transfer data obtained with the phase-change paint technique

NASA Technical Reports Server (NTRS)

Maise, G.; Rossi, M. J.

1974-01-01

A computerized tool, CAPE, (Conduction Analysis Program using Eigenvalues) has been developed to account for lateral heat conduction in wind tunnel models in the data reduction of the phase-change paint technique. The tool also accounts for the effects of finite thickness (thin wings) and surface curvature. A special reduction procedure using just one time of melt is also possible on leading edges. A novel iterative numerical scheme was used, with discretized spatial coordinates but analytic integration in time, to solve the inverse conduction problem involved in the data reduction. A yes-no chart is provided which tells the test engineer when various corrections are large enough so that CAPE should be used. The accuracy of the phase-change paint technique in the presence of finite thickness and lateral conduction is also investigated.

Staggered solution procedures for multibody dynamics simulation

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.; Downer, J. D.

1990-01-01

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Two dimensional fully nonlinear numerical wave tank based on the BEM

NASA Astrophysics Data System (ADS)

Sun, Zhe; Pang, Yongjie; Li, Hongwei

2012-12-01

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

Implementation of a partitioned algorithm for simulation of large CSI problems

NASA Technical Reports Server (NTRS)

Alvin, Kenneth F.; Park, K. C.

1991-01-01

The implementation of a partitioned numerical algorithm for determining the dynamic response of coupled structure/controller/estimator finite-dimensional systems is reviewed. The partitioned approach leads to a set of coupled first and second-order linear differential equations which are numerically integrated with extrapolation and implicit step methods. The present software implementation, ACSIS, utilizes parallel processing techniques at various levels to optimize performance on a shared-memory concurrent/vector processing system. A general procedure for the design of controller and filter gains is also implemented, which utilizes the vibration characteristics of the structure to be solved. Also presented are: example problems; a user's guide to the software; the procedures and algorithm scripts; a stability analysis for the algorithm; and the source code for the parallel implementation.

Application of advanced grid generation techniques for flow field computations about complex configurations

NASA Technical Reports Server (NTRS)

Kathong, Monchai; Tiwari, Surendra N.

1988-01-01

In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.

Towards a new multiscale air quality transport model using the fully unstructured anisotropic adaptive mesh technology of Fluidity (version 4.1.9)

NASA Astrophysics Data System (ADS)

Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.

2015-10-01

An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection-diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.

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

Robert P. Lucht

Laser-induced polarization spectroscopy (LIPS), degenerate four-wave mixing (DFWM), and electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman scattering (CARS) are techniques that shows great promise for sensitive measurements of transient gas-phase species, and diagnostic applications of these techniques are being pursued actively at laboratories throughout the world. However, significant questions remain regarding strategies for quantitative concentration measurements using these techniques. The primary objective of this research program is to develop and test strategies for quantitative concentration measurements in flames and plasmas using these nonlinear optical techniques. Theoretically, we are investigating the physics of these processes by direct numerical integration (DNI) of the time-dependentmore » density matrix equations that describe the wave-mixing interaction. Significantly fewer restrictive assumptions are required when the density matrix equations are solved using this DNI approach compared with the assumptions required to obtain analytical solutions. For example, for LIPS calculations, the Zeeman state structure and hyperfine structure of the resonance and effects such as Doppler broadening can be included. There is no restriction on the intensity of the pump and probe beams in these nonperturbative calculations, and both the pump and probe beam intensities can be high enough to saturate the resonance. As computer processing speeds have increased, we have incorporated more complicated physical models into our DNI codes. During the last project period we developed numerical methods for nonperturbative calculations of the two-photon absorption process. Experimentally, diagnostic techniques are developed and demonstrated in gas cells and/or well-characterized flames for ease of comparison with model results. The techniques of two-photon, two-color H-atom LIPS and three-laser ERE CARS for NO and C{sub 2}H{sub 2} were demonstrated during the project period, and nonperturbative numerical models of both of these techniques were developed. In addition, we developed new single-mode, injection-seeded optical parametric laser sources (OPLSs) that will be used to replace multi-mode commercial dye lasers in our experimental measurements. The use of single-mode laser radiation in our experiments will increase significantly the rigor with which theory and experiment are compared.« less

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Hasanyan, Davresh; Librescu, iviu; Qin, Zhanming

2005-01-01

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

On-chip optical transduction scheme for graphene nano-electro-mechanical systems in silicon-photonic platform.

PubMed

Dash, Aneesh; Selvaraja, S K; Naik, A K

2018-02-15

We present a scheme for on-chip optical transduction of strain and displacement of graphene-based nano-electro-mechanical systems (NEMS). A detailed numerical study on the feasibility of three silicon-photonic integrated circuit configurations is presented: the Mach-Zehnder interferometer (MZI), the micro-ring resonator, and the ring-loaded MZI. An index sensing based technique using an MZI loaded with a ring resonator with a moderate Q-factor of 2400 can yield a sensitivity of 28  fm/Hz and 6.5×10 -6 %/Hz for displacement and strain, respectively. Though any phase-sensitive integrated-photonic device could be used for optical transduction, here we show that optimal sensitivity is achievable by combining resonance with phase sensitivity.

On-chip optical transduction scheme for graphene nano-electro-mechanical systems in silicon-photonic platform

NASA Astrophysics Data System (ADS)

Dash, Aneesh; Selvaraja, S. K.; Naik, A. K.

2018-02-01

We present a scheme for on-chip optical transduction of strain and displacement of Graphene-based Nano-Electro-Mechanical Systems (NEMS). A detailed numerical study on the feasibility of three silicon-photonic integrated circuit configurations is presented: Mach-Zehnder Interferometer(MZI), micro-ring resonator and ring-loaded MZI. An index-sensing based technique using a Mach-Zehnder Interferometer loaded with a ring resonator with a moderate Q-factor of 2400 can yield a sensitivity of 28 fm/sqrt(Hz), and 6.5E-6 %/sqrt(Hz) for displacement and strain respectively. Though any phase sensitive integrated photonic device could be used for optical transduction, here we show that optimal sensitivity is achievable by combining resonance with phase sensitivity.

Application of Numerical Integration and Data Fusion in Unit Vector Method

NASA Astrophysics Data System (ADS)

Zhang, J.

2012-01-01

The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of available observation apparatus. Compare with the classical differential improvement with the numerical integration, its calculation speed is also improved obviously. (2) After data fusion method has been introduced into the UVM, weighted distribution accords rationally with the accuracy of different kinds of data, all data are fully used and the new method is also good at numerical stability and rational weighted distribution.

Robust numerical electromagnetic eigenfunction expansion algorithms

NASA Astrophysics Data System (ADS)

Sainath, Kamalesh

This thesis summarizes developments in rigorous, full-wave, numerical spectral-domain (integral plane wave eigenfunction expansion [PWE]) evaluation algorithms concerning time-harmonic electromagnetic (EM) fields radiated by generally-oriented and positioned sources within planar and tilted-planar layered media exhibiting general anisotropy, thickness, layer number, and loss characteristics. The work is motivated by the need to accurately and rapidly model EM fields radiated by subsurface geophysical exploration sensors probing layered, conductive media, where complex geophysical and man-made processes can lead to micro-laminate and micro-fractured geophysical formations exhibiting, at the lower (sub-2MHz) frequencies typically employed for deep EM wave penetration through conductive geophysical media, bulk-scale anisotropic (i.e., directional) electrical conductivity characteristics. When the planar-layered approximation (layers of piecewise-constant material variation and transversely-infinite spatial extent) is locally, near the sensor region, considered valid, numerical spectral-domain algorithms are suitable due to their strong low-frequency stability characteristic, and ability to numerically predict time-harmonic EM field propagation in media with response characterized by arbitrarily lossy and (diagonalizable) dense, anisotropic tensors. If certain practical limitations are addressed, PWE can robustly model sensors with general position and orientation that probe generally numerous, anisotropic, lossy, and thick layers. The main thesis contributions, leading to a sensor and geophysical environment-robust numerical modeling algorithm, are as follows: (1) Simple, rapid estimator of the region (within the complex plane) containing poles, branch points, and branch cuts (critical points) (Chapter 2), (2) Sensor and material-adaptive azimuthal coordinate rotation, integration contour deformation, integration domain sub-region partition and sub-region-dependent integration order (Chapter 3), (3) Integration partition-extrapolation-based (Chapter 3) and Gauss-Laguerre Quadrature (GLQ)-based (Chapter 4) evaluations of the deformed, semi-infinite-length integration contour tails, (4) Robust in-situ-based (i.e., at the spectral-domain integrand level) direct/homogeneous-medium field contribution subtraction and analytical curbing of the source current spatial spectrum function's ill behavior (Chapter 5), and (5) Analytical re-casting of the direct-field expressions when the source is embedded within a NBAM, short for non-birefringent anisotropic medium (Chapter 6). The benefits of these contributions are, respectively, (1) Avoiding computationally intensive critical-point location and tracking (computation time savings), (2) Sensor and material-robust curbing of the integrand's oscillatory and slow decay behavior, as well as preventing undesirable critical-point migration within the complex plane (computation speed, precision, and instability-avoidance benefits), (3) sensor and material-robust reduction (or, for GLQ, elimination) of integral truncation error, (4) robustly stable modeling of scattered fields and/or fields radiated from current sources modeled as spatially distributed (10 to 1000-fold compute-speed acceleration also realized for distributed-source computations), and (5) numerically stable modeling of fields radiated from sources within NBAM layers. Having addressed these limitations, are PWE algorithms applicable to modeling EM waves in tilted planar-layered geometries too? This question is explored in Chapter 7 using a Transformation Optics-based approach, allowing one to model wave propagation through layered media that (in the sensor's vicinity) possess tilted planar interfaces. The technique leads to spurious wave scattering however, whose induced computation accuracy degradation requires analysis. Mathematical exhibition, and exhaustive simulation-based study and analysis of the limitations of, this novel tilted-layer modeling formulation is Chapter 7's main contribution.

Simulating and quantifying legacy topographic data uncertainty: an initial step to advancing topographic change analyses

NASA Astrophysics Data System (ADS)

Wasklewicz, Thad; Zhu, Zhen; Gares, Paul

2017-12-01

Rapid technological advances, sustained funding, and a greater recognition of the value of topographic data have helped develop an increasing archive of topographic data sources. Advances in basic and applied research related to Earth surface changes require researchers to integrate recent high-resolution topography (HRT) data with the legacy datasets. Several technical challenges and data uncertainty issues persist to date when integrating legacy datasets with more recent HRT data. The disparate data sources required to extend the topographic record back in time are often stored in formats that are not readily compatible with more recent HRT data. Legacy data may also contain unknown error or unreported error that make accounting for data uncertainty difficult. There are also cases of known deficiencies in legacy datasets, which can significantly bias results. Finally, scientists are faced with the daunting challenge of definitively deriving the extent to which a landform or landscape has or will continue to change in response natural and/or anthropogenic processes. Here, we examine the question: how do we evaluate and portray data uncertainty from the varied topographic legacy sources and combine this uncertainty with current spatial data collection techniques to detect meaningful topographic changes? We view topographic uncertainty as a stochastic process that takes into consideration spatial and temporal variations from a numerical simulation and physical modeling experiment. The numerical simulation incorporates numerous topographic data sources typically found across a range of legacy data to present high-resolution data, while the physical model focuses on more recent HRT data acquisition techniques. Elevation uncertainties observed from anchor points in the digital terrain models are modeled using "states" in a stochastic estimator. Stochastic estimators trace the temporal evolution of the uncertainties and are natively capable of incorporating sensor measurements observed at various times in history. The geometric relationship between the anchor point and the sensor measurement can be approximated via spatial correlation even when a sensor does not directly observe an anchor point. Findings from a numerical simulation indicate the estimated error coincides with the actual error using certain sensors (Kinematic GNSS, ALS, TLS, and SfM-MVS). Data from 2D imagery and static GNSS did not perform as well at the time the sensor is integrated into estimator largely as a result of the low density of data added from these sources. The estimator provides a history of DEM estimation as well as the uncertainties and cross correlations observed on anchor points. Our work provides preliminary evidence that our approach is valid for integrating legacy data with HRT and warrants further exploration and field validation. [Figure not available: see fulltext.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

NNLO computational techniques: The cases H→γγ and H→gg

NASA Astrophysics Data System (ADS)

Actis, Stefano; Passarino, Giampiero; Sturm, Christian; Uccirati, Sandro

2009-04-01

A large set of techniques needed to compute decay rates at the two-loop level are derived and systematized. The main emphasis of the paper is on the two Standard Model decays H→γγ and H→gg. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple recipes for handling internal unstable particles in two-loop processes; they illustrate simple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Furthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electroweak contributions to different physical (pseudo-)observables, showing how they can be transformed in a way that allows for a stable numerical integration. Numerical results for the two-loop percentage corrections to H→γγ,gg are presented and discussed. When applied to the process pp→gg+X→H+X, the results show that the electroweak scaling factor for the cross section is between -4% and +6% in the range 100 GeV

Comparisons of Particle Tracking Techniques and Galerkin Finite Element Methods in Flow Simulations on Watershed Scales

NASA Astrophysics Data System (ADS)

Shih, D.; Yeh, G.

2009-12-01

This paper applies two numerical approximations, the particle tracking technique and Galerkin finite element method, to solve the diffusive wave equation in both one-dimensional and two-dimensional flow simulations. The finite element method is one of most commonly approaches in numerical problems. It can obtain accurate solutions, but calculation times may be rather extensive. The particle tracking technique, using either single-velocity or average-velocity tracks to efficiently perform advective transport, could use larger time-step sizes than the finite element method to significantly save computational time. Comparisons of the alternative approximations are examined in this poster. We adapt the model WASH123D to examine the work. WASH123D is an integrated multimedia, multi-processes, physics-based computational model suitable for various spatial-temporal scales, was first developed by Yeh et al., at 1998. The model has evolved in design capability and flexibility, and has been used for model calibrations and validations over the course of many years. In order to deliver a locally hydrological model in Taiwan, the Taiwan Typhoon and Flood Research Institute (TTFRI) is working with Prof. Yeh to develop next version of WASH123D. So, the work of our preliminary cooperationx is also sketched in this poster.

Inviscid, nonadiabatic flow fields over blunt, sonic corner bodies for outer planet entry conditions by a method of integral relations

NASA Technical Reports Server (NTRS)

Gnoffo, P. A.

1978-01-01

An investigation has been made into the ability of a method of integral relations to calculate inviscid zero degree angle of attack, radiative heating distributions over blunt, sonic corner bodies for some representative outer planet entry conditions is investigated. Comparisons have been made with a more detailed numerical method, a time asymptotic technique, using the same equilibrium chemistry and radiation transport subroutines. An effort to produce a second order approximation (two-strip) method of integral relations code to aid in this investigation is also described and a modified two-strip routine is presented. Results indicate that the one-strip method of integral relations cannot be used to obtain accurate estimates of the radiative heating distribution because of its inability to resolve thermal gradients near the wall. The two-strip method can sometimes be used to improve these estimates; however, the two-strip method has only a small range of conditions over which it will yield significant improvement over the one-strip method.

The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?

PubMed

Goličnik, Marko

2013-08-01

A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.

Microsoft C#.NET program and electromagnetic depth sounding for large loop source

NASA Astrophysics Data System (ADS)

Prabhakar Rao, K.; Ashok Babu, G.

2009-07-01

A program, in the C# (C Sharp) language with Microsoft.NET Framework, is developed to compute the normalized vertical magnetic field of a horizontal rectangular loop source placed on the surface of an n-layered earth. The field can be calculated either inside or outside the loop. Five C# classes with member functions in each class are, designed to compute the kernel, Hankel transform integral, coefficients for cubic spline interpolation between computed values and the normalized vertical magnetic field. The program computes the vertical magnetic field in the frequency domain using the integral expressions evaluated by a combination of straightforward numerical integration and the digital filter technique. The code utilizes different object-oriented programming (OOP) features. It finally computes the amplitude and phase of the normalized vertical magnetic field. The computed results are presented for geometric and parametric soundings. The code is developed in Microsoft.NET visual studio 2003 and uses various system class libraries.

An Integrated Development Environment for Adiabatic Quantum Programming

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

Humble, Travis S; McCaskey, Alex; Bennink, Ryan S

2014-01-01

Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present an adiabatic quantum programming environment called JADE that provides control over all the steps taken during program development. JADE captures the workflow needed to rigorously benchmark performance while also allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation enginemore » that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its use for benchmarking adiabatic quantum programs.« less

Multi-format all-optical processing based on a large-scale, hybridly integrated photonic circuit.

PubMed

Bougioukos, M; Kouloumentas, Ch; Spyropoulou, M; Giannoulis, G; Kalavrouziotis, D; Maziotis, A; Bakopoulos, P; Harmon, R; Rogers, D; Harrison, J; Poustie, A; Maxwell, G; Avramopoulos, H

2011-06-06

We investigate through numerical studies and experiments the performance of a large scale, silica-on-silicon photonic integrated circuit for multi-format regeneration and wavelength-conversion. The circuit encompasses a monolithically integrated array of four SOAs inside two parallel Mach-Zehnder structures, four delay interferometers and a large number of silica waveguides and couplers. Exploiting phase-incoherent techniques, the circuit is capable of processing OOK signals at variable bit rates, DPSK signals at 22 or 44 Gb/s and DQPSK signals at 44 Gbaud. Simulation studies reveal the wavelength-conversion potential of the circuit with enhanced regenerative capabilities for OOK and DPSK modulation formats and acceptable quality degradation for DQPSK format. Regeneration of 22 Gb/s OOK signals with amplified spontaneous emission (ASE) noise and DPSK data signals degraded with amplitude, phase and ASE noise is experimentally validated demonstrating a power penalty improvement up to 1.5 dB.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms.

PubMed

Nosal, Eva-Marie; Hodgson, Murray; Ashdown, Ian

2004-08-01

This paper explores acoustical (or time-dependent) radiosity--a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms

NASA Astrophysics Data System (ADS)

Nosal, Eva-Marie; Hodgson, Murray; Ashdown, Ian

2004-08-01

This paper explores acoustical (or time-dependent) radiosity-a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

An accurate European option pricing model under Fractional Stable Process based on Feynman Path Integral

NASA Astrophysics Data System (ADS)

Ma, Chao; Ma, Qinghua; Yao, Haixiang; Hou, Tiancheng

2018-03-01

In this paper, we propose to use the Fractional Stable Process (FSP) for option pricing. The FSP is one of the few candidates to directly model a number of desired empirical properties of asset price risk neutral dynamics. However, pricing the vanilla European option under FSP is difficult and problematic. In the paper, built upon the developed Feynman Path Integral inspired techniques, we present a novel computational model for option pricing, i.e. the Fractional Stable Process Path Integral (FSPPI) model under a general fractional stable distribution that tackles this problem. Numerical and empirical experiments show that the proposed pricing model provides a correction of the Black-Scholes pricing error - overpricing long term options, underpricing short term options; overpricing out-of-the-money options, underpricing in-the-money options without any additional structures such as stochastic volatility and a jump process.

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

Real-time Retrieving Atmospheric Parameters from Multi-GNSS Constellations

NASA Astrophysics Data System (ADS)

Li, X.; Zus, F.; Lu, C.; Dick, G.; Ge, M.; Wickert, J.; Schuh, H.

2016-12-01

The multi-constellation GNSS (e.g. GPS, GLONASS, Galileo, and BeiDou) bring great opportunities and challenges for real-time retrieval of atmospheric parameters for supporting numerical weather prediction (NWP) nowcasting or severe weather event monitoring. In this study, the observations from different GNSS are combined together for atmospheric parameter retrieving based on the real-time precise point positioning technique. The atmospheric parameters retrieved from multi-GNSS observations, including zenith total delay (ZTD), integrated water vapor (IWV), horizontal gradient (especially high-resolution gradient estimates) and slant total delay (STD), are carefully analyzed and evaluated by using the VLBI, radiosonde, water vapor radiometer and numerical weather model to independently validate the performance of individual GNSS and also demonstrate the benefits of multi-constellation GNSS for real-time atmospheric monitoring. Numerous results show that the multi-GNSS processing can provide real-time atmospheric products with higher accuracy, stronger reliability and better distribution, which would be beneficial for atmospheric sounding systems, especially for nowcasting of extreme weather.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

NASA Astrophysics Data System (ADS)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

3D fluid-structure modelling and vibration analysis for fault diagnosis of Francis turbine using multiple ANN and multiple ANFIS

NASA Astrophysics Data System (ADS)

Saeed, R. A.; Galybin, A. N.; Popov, V.

2013-01-01

This paper discusses condition monitoring and fault diagnosis in Francis turbine based on integration of numerical modelling with several different artificial intelligence (AI) techniques. In this study, a numerical approach for fluid-structure (turbine runner) analysis is presented. The results of numerical analysis provide frequency response functions (FRFs) data sets along x-, y- and z-directions under different operating load and different position and size of faults in the structure. To extract features and reduce the dimensionality of the obtained FRF data, the principal component analysis (PCA) has been applied. Subsequently, the extracted features are formulated and fed into multiple artificial neural networks (ANN) and multiple adaptive neuro-fuzzy inference systems (ANFIS) in order to identify the size and position of the damage in the runner and estimate the turbine operating conditions. The results demonstrated the effectiveness of this approach and provide satisfactory accuracy even when the input data are corrupted with certain level of noise.

Structural characterization and numerical simulations of flow properties of standard and reservoir carbonate rocks using micro-tomography

NASA Astrophysics Data System (ADS)

Islam, Amina; Chevalier, Sylvie; Sassi, Mohamed

2018-04-01

With advances in imaging techniques and computational power, Digital Rock Physics (DRP) is becoming an increasingly popular tool to characterize reservoir samples and determine their internal structure and flow properties. In this work, we present the details for imaging, segmentation, as well as numerical simulation of single-phase flow through a standard homogenous Silurian dolomite core plug sample as well as a heterogeneous sample from a carbonate reservoir. We develop a procedure that integrates experimental results into the segmentation step to calibrate the porosity. We also look into using two different numerical tools for the simulation; namely Avizo Fire Xlab Hydro that solves the Stokes' equations via the finite volume method and Palabos that solves the same equations using the Lattice Boltzmann Method. Representative Elementary Volume (REV) and isotropy studies are conducted on the two samples and we show how DRP can be a useful tool to characterize rock properties that are time consuming and costly to obtain experimentally.

Distance Measurement Error in Time-of-Flight Sensors Due to Shot Noise

PubMed Central

Illade-Quinteiro, Julio; Brea, Víctor M.; López, Paula; Cabello, Diego; Doménech-Asensi, Gines

2015-01-01

Unlike other noise sources, which can be reduced or eliminated by different signal processing techniques, shot noise is an ever-present noise component in any imaging system. In this paper, we present an in-depth study of the impact of shot noise on time-of-flight sensors in terms of the error introduced in the distance estimation. The paper addresses the effect of parameters, such as the size of the photosensor, the background and signal power or the integration time, and the resulting design trade-offs. The study is demonstrated with different numerical examples, which show that, in general, the phase shift determination technique with two background measurements approach is the most suitable for pixel arrays of large resolution. PMID:25723141

GPU-accelerated computational tool for studying the effectiveness of asteroid disruption techniques

NASA Astrophysics Data System (ADS)

Zimmerman, Ben J.; Wie, Bong

2016-10-01

This paper presents the development of a new Graphics Processing Unit (GPU) accelerated computational tool for asteroid disruption techniques. Numerical simulations are completed using the high-order spectral difference (SD) method. Due to the compact nature of the SD method, it is well suited for implementation with the GPU architecture, hence solutions are generated at orders of magnitude faster than the Central Processing Unit (CPU) counterpart. A multiphase model integrated with the SD method is introduced, and several asteroid disruption simulations are conducted, including kinetic-energy impactors, multi-kinetic energy impactor systems, and nuclear options. Results illustrate the benefits of using multi-kinetic energy impactor systems when compared to a single impactor system. In addition, the effectiveness of nuclear options is observed.

An integrated optics microfluidic device for detecting single DNA molecules.

PubMed

Krogmeier, Jeffrey R; Schaefer, Ian; Seward, George; Yantz, Gregory R; Larson, Jonathan W

2007-12-01

A fluorescence-based integrated optics microfluidic device is presented, capable of detecting single DNA molecules in a high throughput and reproducible manner. The device integrates microfluidics for DNA stretching with two optical elements for single molecule detection (SMD): a plano-aspheric refractive lens for fluorescence excitation (illuminator) and a solid parabolic reflective mirror for fluorescence collection (collector). Although miniaturized in size, both optical components were produced and assembled onto the microfluidic device by readily manufacturable fabrication techniques. The optical resolution of the device is determined by the small and relatively low numerical aperture (NA) illuminator lens (0.10 effective NA, 4.0 mm diameter) that delivers excitation light to a diffraction limited 2.0 microm diameter spot at full width half maximum within the microfluidic channel. The collector (0.82 annular NA, 15 mm diameter) reflects the fluorescence over a large collection angle, representing 71% of a hemisphere, toward a single photon counting module in an infinity-corrected scheme. As a proof-of-principle experiment for this simple integrated device, individual intercalated lambda-phage DNA molecules (48.5 kb) were stretched in a mixed elongational-shear microflow, detected, and sized with a fluorescence signal to noise ratio of 9.9 +/-1.0. We have demonstrated that SMD does not require traditional high numerical aperture objective lenses and sub-micron positioning systems conventionally used in many applications. Rather, standard manufacturing processes can be combined in a novel way that promises greater accessibility and affordability for microfluidic-based single molecule applications.

Physically based modeling in catchment hydrology at 50: Survey and outlook

NASA Astrophysics Data System (ADS)

Paniconi, Claudio; Putti, Mario

2015-09-01

Integrated, process-based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection-dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science.

Accurate Critical Stress Intensity Factor Griffith Crack Theory Measurements by Numerical Techniques

PubMed Central

Petersen, Richard C.

2014-01-01

Critical stress intensity factor (KIc) has been an approximation for fracture toughness using only load-cell measurements. However, artificial man-made cracks several orders of magnitude longer and wider than natural flaws have required a correction factor term (Y) that can be up to about 3 times the recorded experimental value [1-3]. In fact, over 30 years ago a National Academy of Sciences advisory board stated that empirical KIc testing was of serious concern and further requested that an accurate bulk fracture toughness method be found [4]. Now that fracture toughness can be calculated accurately by numerical integration from the load/deflection curve as resilience, work of fracture (WOF) and strain energy release (SIc) [5, 6], KIc appears to be unnecessary. However, the large body of previous KIc experimental test results found in the literature offer the opportunity for continued meta analysis with other more practical and accurate fracture toughness results using energy methods and numerical integration. Therefore, KIc is derived from the classical Griffith Crack Theory [6] to include SIc as a more accurate term for strain energy release rate (𝒢Ic), along with crack surface energy (γ), crack length (a), modulus (E), applied stress (σ), Y, crack-tip plastic zone defect region (rp) and yield strength (σys) that can all be determined from load and deflection data. Polymer matrix discontinuous quartz fiber-reinforced composites to accentuate toughness differences were prepared for flexural mechanical testing comprising of 3 mm fibers at different volume percentages from 0-54.0 vol% and at 28.2 vol% with different fiber lengths from 0.0-6.0 mm. Results provided a new correction factor and regression analyses between several numerical integration fracture toughness test methods to support KIc results. Further, bulk KIc accurate experimental values are compared with empirical test results found in literature. Also, several fracture toughness mechanisms are discussed especially for fiber-reinforced composites. PMID:25620817

A multiple hypotheses uncertainty analysis in hydrological modelling: about model structure, landscape parameterization, and numerical integration

NASA Astrophysics Data System (ADS)

Pilz, Tobias; Francke, Till; Bronstert, Axel

2016-04-01

Until today a large number of competing computer models has been developed to understand hydrological processes and to simulate and predict streamflow dynamics of rivers. This is primarily the result of a lack of a unified theory in catchment hydrology due to insufficient process understanding and uncertainties related to model development and application. Therefore, the goal of this study is to analyze the uncertainty structure of a process-based hydrological catchment model employing a multiple hypotheses approach. The study focuses on three major problems that have received only little attention in previous investigations. First, to estimate the impact of model structural uncertainty by employing several alternative representations for each simulated process. Second, explore the influence of landscape discretization and parameterization from multiple datasets and user decisions. Third, employ several numerical solvers for the integration of the governing ordinary differential equations to study the effect on simulation results. The generated ensemble of model hypotheses is then analyzed and the three sources of uncertainty compared against each other. To ensure consistency and comparability all model structures and numerical solvers are implemented within a single simulation environment. First results suggest that the selection of a sophisticated numerical solver for the differential equations positively affects simulation outcomes. However, already some simple and easy to implement explicit methods perform surprisingly well and need less computational efforts than more advanced but time consuming implicit techniques. There is general evidence that ambiguous and subjective user decisions form a major source of uncertainty and can greatly influence model development and application at all stages.

The coupling of high-speed high resolution experimental data and LES through data assimilation techniques

NASA Astrophysics Data System (ADS)

Harris, S.; Labahn, J. W.; Frank, J. H.; Ihme, M.

2017-11-01

Data assimilation techniques can be integrated with time-resolved numerical simulations to improve predictions of transient phenomena. In this study, optimal interpolation and nudging are employed for assimilating high-speed high-resolution measurements obtained for an inert jet into high-fidelity large-eddy simulations. This experimental data set was chosen as it provides both high spacial and temporal resolution for the three-component velocity field in the shear layer of the jet. Our first objective is to investigate the impact that data assimilation has on the resulting flow field for this inert jet. This is accomplished by determining the region influenced by the data assimilation and corresponding effect on the instantaneous flow structures. The second objective is to determine optimal weightings for two data assimilation techniques. The third objective is to investigate how the frequency at which the data is assimilated affects the overall predictions. Graduate Research Assistant, Department of Mechanical Engineering.

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.

1995-01-01

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.

Fast secant methods for the iterative solution of large nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Deuflhard, Peter; Freund, Roland; Walter, Artur

1990-01-01

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

Applications of Tol2 Transposon-Mediated Gene Transfer for Stable Integration and Conditional Expression of Electroporated Genes in Chicken Embryos

NASA Astrophysics Data System (ADS)

Sato, Yuki; Takahashi, Yoshiko

Because of the high accessibility to developing embryos, avian embryos (chicken and quail) have long been used as a good model animal to study embryogenesis in vertebrates, especially amniotes (reviewed in Wolpert, 2004). The techniques used for “classical” avian embryology included tissue transplantations, tissue ablations, and cell-labeling by vital dye. At the end of the last century, the in ovo electropora tion technique was developed by Nakamura and his colleagues, and this modern method opened a way to study the roles of developmental genes directly in living embryos (Funahashi et al., 1999) reviewed in (Nakamura et al., 2004; Yasuda et al., 2000; Yasugi and Nakamura, 2000). This powerful technique allows us to introduce genes (DNA, RNA, morpholino) into embryos in a tissue-specific way by targeting a restricted area of embryonic tissues. Thus, the electroporation technique using chickens has provided numerous novel insights into the understanding of early development in vertebrates, making the chicken a unique model animal.

A comparison of the energy use of in situ product recovery techniques for the Acetone Butanol Ethanol fermentation.

PubMed

Outram, Victoria; Lalander, Carl-Axel; Lee, Jonathan G M; Davis, E Timothy; Harvey, Adam P

2016-11-01

The productivity of the Acetone Butanol Ethanol (ABE) fermentation can be significantly increased by application of various in situ product recovery (ISPR) techniques. There are numerous technically viable processes, but it is not clear which is the most economically viable in practice. There is little available information about the energy requirements and economics of ISPR for the ABE fermentation. This work compares various ISPR techniques based on UniSim process simulations of the ABE fermentation. The simulations provide information on the process energy and separation efficiency, which is fed into an economic assessment. Perstraction was the only technique to reduce the energy demand below that of a batch process, by approximately 5%. Perstraction also had the highest profit increase over a batch process, by 175%. However, perstraction is an immature technology, so would need significant development before being integrated to an industrial process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Department of the Navy Supporting Data for Fiscal Year 1984 Budget Estimates Descriptive Summaries Submitted to Congress January 1983. Research, Development, Test and Evaluation, Navy. Book 1. Technology Base, Advanced Technology Development, Strategic Programs.

DTIC Science & Technology

1983-01-01

altioser access (2) Asesss maturity of on-gotnR efforts and integrate appropriate development Into an effective globally dftjtributod .command spport...numerical techniques for nonlinear media.structure shock Interaction inrluding effects of elastic-plastic deformation have bee.a developed and used to...shtittle flight; develop camera payload for SPARTAN (free flyer) flight f rom shuttle. Develop detailed Interpretivesystem capablity~ for global ultraviolet

Spintronic logic: from switching devices to computing systems

NASA Astrophysics Data System (ADS)

Friedman, Joseph S.

2017-09-01

Though numerous spintronic switching devices have been proposed or demonstrated, there has been significant difficulty in translating these advances into practical computing systems. The challenge of cascading has impeded the integration of multiple devices into a logic family, and several proposed solutions potentially overcome these challenges. Here, the cascading techniques by which the output of each spintronic device can drive the input of another device are described for several logic families, including spin-diode logic (in particular, all-carbon spin logic), complementary magnetic tunnel junction logic (CMAT), and emitter-coupled spin-transistor logic (ECSTL).

Stress-intensity factors of r-cracks in fiber-reinforced composites under thermal and mechanical loading

NASA Astrophysics Data System (ADS)

Mueller, W. H.; Schmauder, S.

1993-02-01

The plane stress/plane strain problem of radial matrix cracking in fiber-reinforced composites, due to thermal mismatch and externally applied stress is solved numerically in the framework of linear elasticity, using Erdogan's integral equation technique. It is shown that, in order to obtain the results of the combined loading case, the solutions of purely thermal and purely mechanical loading can simply be superimposed. Stress-intensity factors are calculated for various lengths and distances of the crack from the interface for each of these loading conditions.

Technical Note for 8D Likelihood Effective Higgs Couplings Extraction Framework in the Golden Channel

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

Chen, Yi; Di Marco, Emanuele; Lykken, Joe

2014-10-17

In this technical note we present technical details on various aspects of the framework introduced in arXiv:1401.2077 aimed at extracting effective Higgs couplings in themore » $$h\\to 4\\ell$$ `golden channel'. Since it is the primary feature of the framework, we focus in particular on the convolution integral which takes us from `truth' level to `detector' level and the numerical and analytic techniques used to obtain it. We also briefly discuss other aspects of the framework.« less

Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics

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

Tian, Bailing; Zuo, Zongyu; Wang, Hong

The leader-follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations.

Compact self-aligning assemblies with refractive microlens arrays made by contactless embossing

NASA Astrophysics Data System (ADS)

Schulze, Jens; Ehrfeld, Wolfgang; Mueller, Holger; Picard, Antoni

1998-04-01

The hybrid integration of microlenses and arrays of microlenses in micro-optical systems is simplified using contactless embossing of microlenses (CEM) in combination with LIGA microfabrication. CEM is anew fabrication technique for the production of precise refractive microlens arrays. A high precision matrix of holes made by LIGA technique is used as a compression molding tool to form the microlenses. The tool is pressed onto a thermoplastic sample which is heated close to the glass transformation temperature of the material. The material bulges into the openings of the molding tool due to the applied pressure and forms lens-like spherical structures. The name refers to the fact that the surface of the microlens does not get in contact with the compression molding tool during the shaping process and optical quality of the surface is maintained. Microlenses and arrays of microlenses with lens diameters from 30 micrometers up to 700 micrometers and numerical aperture values of up to 0.25 have been fabricated in different materials. Cost-effectiveness in the production process, excellent optical performance and the feature of easy replication are the main advantages of this technique. The most promising feature of this method is the possibility to obtain self- aligned assemblies then can be further integrated into a micro-optical bench setup. The CEM fabrication method in combination with LIGA microfabrication considerably enhances the hybrid integration in micro-optical devices which results in a more cost-effective production of compact micro-opto-electro-mechanical systems.

Davidenko’s Method for the Solution of Nonlinear Operator Equations.

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), OPERATORS(MATHEMATICS), BANACH SPACE , MAPPING (TRANSFORMATIONS), NUMERICAL METHODS AND PROCEDURES, INTEGRALS, SET THEORY, CONVERGENCE, MATRICES(MATHEMATICS)

Fluid-structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; Boben, Joseph; Kostov, Nikolay; Boswell, Cody; Buscher, Austin

2013-12-01

To increase aerodynamic performance, the geometric porosity of a ringsail spacecraft parachute canopy is sometimes increased, beyond the "rings" and "sails" with hundreds of "ring gaps" and "sail slits." This creates extra computational challenges for fluid-structure interaction (FSI) modeling of clusters of such parachutes, beyond those created by the lightness of the canopy structure, geometric complexities of hundreds of gaps and slits, and the contact between the parachutes of the cluster. In FSI computation of parachutes with such "modified geometric porosity," the flow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the Homogenized Modeling of Geometric Porosity (HMGP), which was introduced to deal with the hundreds of gaps and slits. The flow needs to be actually resolved. All these computational challenges need to be addressed simultaneously in FSI modeling of clusters of spacecraft parachutes with modified geometric porosity. The core numerical technology is the Stabilized Space-Time FSI (SSTFSI) technique, and the contact between the parachutes is handled with the Surface-Edge-Node Contact Tracking (SENCT) technique. In the computations reported here, in addition to the SSTFSI and SENCT techniques and HMGP, we use the special techniques we have developed for removing the numerical spinning component of the parachute motion and for restoring the mesh integrity without a remesh. We present results for 2- and 3-parachute clusters with two different payload models.

The measurements of water flow rates in the straight microchannel based on the scanning micro-PIV technique

NASA Astrophysics Data System (ADS)

Wang, H. L.; Han, W.; Xu, M.

2011-12-01

Measurement of the water flow rate in microchannel has been one of the hottest points in the applications of microfluidics, medical, biological, chemical analyses and so on. In this study, the scanning microscale particle image velocimetry (scanning micro-PIV) technique is used for the measurements of water flow rates in a straight microchannel of 200μm width and 60μm depth under the standard flow rates ranging from 2.481μL/min to 8.269μL/min. The main effort of this measurement technique is to obtain three-dimensional velocity distribution on the cross sections of microchannel by measuring velocities of the different fluid layers along the out-of-plane direction in the microchannel, so the water flow rates can be evaluated from the discrete surface integral of velocities on the cross section. At the same time, the three-dimensional velocity fields in the measured microchannel are simulated numerically using the FLUENT software in order to verify the velocity accuracy of measurement results. The results show that the experimental values of flow rates are well consistent to the standard flow rates input by the syringe pump and the compared results between numerical simulation and experiment are consistent fundamentally. This study indicates that the micro-flow rate evaluated from three-dimensional velocity by the scanning micro-PIV technique is a promising method for the micro-flow rate research.

A Vibration-Based Strategy for Health Monitoring of Offshore Pipelines' Girth-Welds

PubMed Central

Razi, Pejman; Taheri, Farid

2014-01-01

This study presents numerical simulations and experimental verification of a vibration-based damage detection technique. Health monitoring of a submerged pipe's girth-weld against an advancing notch is attempted. Piezoelectric transducers are bonded on the pipe for sensing or actuation purposes. Vibration of the pipe is excited by two means: (i) an impulsive force; (ii) using one of the piezoelectric transducers as an actuator to propagate chirp waves into the pipe. The methodology adopts the empirical mode decomposition (EMD), which processes vibration data to establish energy-based damage indices. The results obtained from both the numerical and experimental studies confirm the integrity of the approach in identifying the existence, and progression of the advancing notch. The study also discusses and compares the performance of the two vibration excitation means in damage detection. PMID:25225877

Non-linear three dimensional spectral model of the Venusian thermosphere with super-rotation. I - Formulation and numerical technique. II - Temperature, composition and winds

NASA Technical Reports Server (NTRS)

Stevens-Rayburn, D. R.; Mengel, J. G.; Harris, I.; Mayr, H. G.

1989-01-01

A three-dimensional spectral model for the Venusion thermosphere is presented which uses spherical harmonics to represent the horizontal variations in longitude and latitude and which uses Fourier harmonics to represent the LT variations due to atmospheric rotation. A differencing scheme with tridiagonal block elimination is used to perform the height integration. Quadratic nonlinearities are taken into account. In the second part, numerical results obtained with the model are shown to reproduce the observed broad daytime maxima in CO2 and CO and the significantly larger values at dawn than at dusk. It is found that the diurnal variations in He are most sensitive to thermospheric superrotation, and that, given a globally uniform atmosphere as input, larger heating rates yield a larger temperature contrast between day and night.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order

NASA Astrophysics Data System (ADS)

Gavin, Ryan; Li, Ye; Petriello, Frank; Quackenbush, Seth

2011-11-01

We introduce an improved version of the simulation code FEWZ ( Fully Exclusive W and Z Production) for hadron collider production of lepton pairs through the Drell-Yan process at next-to-next-to-leading order (NNLO) in the strong coupling constant. The program is fully differential in the phase space of leptons and additional hadronic radiation. The new version offers users significantly more options for customization. FEWZ now bins multiple, user-selectable histograms during a single run, and produces parton distribution function (PDF) errors automatically. It also features a significantly improved integration routine, and can take advantage of multiple processor cores locally or on the Condor distributed computing system. We illustrate the new features of FEWZ by presenting numerous phenomenological results for LHC physics. We compare NNLO QCD with initial ATLAS and CMS results, and discuss in detail the effects of detector acceptance on the measurement of angular quantities associated with Z-boson production. We address the issue of technical precision in the presence of severe phase-space cuts. Program summaryProgram title: FEWZ Catalogue identifier: AEJP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJP_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.: 6 280 771 No. of bytes in distributed program, including test data, etc.: 173 027 645 Distribution format: tar.gz Programming language: Fortran 77, C++, Python Computer: Mac, PC Operating system: Mac OSX, Unix/Linux Has the code been vectorized or parallelized?: Yes. User-selectable, 1 to 219 RAM: 200 Mbytes for common parton distribution functions Classification: 11.1 External routines: CUBA numerical integration library, numerous parton distribution sets (see text); these are provided with the code. Nature of problem: Determination of the Drell-Yan Z/photon production cross section and decay into leptons, with kinematic distributions of leptons and jets including full spin correlations, at next-to-next-to-leading order in the strong coupling constant. Solution method: Virtual loop integrals are decomposed into master integrals using automated techniques. Singularities are extracted from real radiation terms via sector decomposition, which separates singularities and maps onto suitable phase space variables. Result is convoluted with parton distribution functions. Each piece is numerically integrated over phase space, which allows arbitrary cuts on the observed particles. Each sample point may be binned during numerical integration, providing histograms, and reweighted by parton distribution function error eigenvectors, which provides PDF errors. Restrictions: Output does not correspond to unweighted events, and cannot be interfaced with a shower Monte Carlo. Additional comments: !!!!! The distribution file for this program is over 170 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: One day for total cross sections with 0.1% integration errors assuming typical cuts, up to 1 week for smooth kinematic distributions with sub-percent integration errors for each bin.

An Integrative Theory of Numerical Development

ERIC Educational Resources Information Center

Siegler, Robert; Lortie-Forgues, Hugues

2014-01-01

Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…

Artificial Boundary Conditions Based on the Difference Potentials Method

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1996-01-01

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

Bone tissue engineering scaffolding: computer-aided scaffolding techniques.

PubMed

Thavornyutikarn, Boonlom; Chantarapanich, Nattapon; Sitthiseripratip, Kriskrai; Thouas, George A; Chen, Qizhi

Tissue engineering is essentially a technique for imitating nature. Natural tissues consist of three components: cells, signalling systems (e.g. growth factors) and extracellular matrix (ECM). The ECM forms a scaffold for its cells. Hence, the engineered tissue construct is an artificial scaffold populated with living cells and signalling molecules. A huge effort has been invested in bone tissue engineering, in which a highly porous scaffold plays a critical role in guiding bone and vascular tissue growth and regeneration in three dimensions. In the last two decades, numerous scaffolding techniques have been developed to fabricate highly interconnective, porous scaffolds for bone tissue engineering applications. This review provides an update on the progress of foaming technology of biomaterials, with a special attention being focused on computer-aided manufacturing (Andrade et al. 2002) techniques. This article starts with a brief introduction of tissue engineering (Bone tissue engineering and scaffolds) and scaffolding materials (Biomaterials used in bone tissue engineering). After a brief reviews on conventional scaffolding techniques (Conventional scaffolding techniques), a number of CAM techniques are reviewed in great detail. For each technique, the structure and mechanical integrity of fabricated scaffolds are discussed in detail. Finally, the advantaged and disadvantage of these techniques are compared (Comparison of scaffolding techniques) and summarised (Summary).

A fast direct solver for boundary value problems on locally perturbed geometries

NASA Astrophysics Data System (ADS)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

NASA Astrophysics Data System (ADS)

Yin, Sisi; Nishi, Tatsushi

2014-11-01

Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

On the numeric integration of dynamic attitude equations

NASA Technical Reports Server (NTRS)

Crouch, P. E.; Yan, Y.; Grossman, Robert

1992-01-01

We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows

NASA Astrophysics Data System (ADS)

Stelling, G. S.; Duinmeijer, S. P. A.

2003-12-01

This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations.

Dynamic Response of Functionally Graded Carbon Nanotube Reinforced Sandwich Plate

NASA Astrophysics Data System (ADS)

Mehar, Kulmani; Panda, Subrata Kumar

2018-03-01

In this article, the dynamic response of the carbon nanotube-reinforced functionally graded sandwich composite plate has been studied numerically with the help of finite element method. The face sheets of the sandwich composite plate are made of carbon nanotube- reinforced composite for two different grading patterns whereas the core phase is taken as isotropic material. The final properties of the structure are calculated using the rule of mixture. The geometrical model of the sandwich plate is developed and discretized suitably with the help of available shell element in ANSYS library. Subsequently, the corresponding numerical dynamic responses computed via batch input technique (parametric design language code in ANSYS) of ANSYS including Newmark’s integration scheme. The stability of the sandwich structural numerical model is established through the proper convergence study. Further, the reliability of the sandwich model is checked by comparison study between present and available results from references. As a final point, some numerical problems have been solved to examine the effect of different design constraints (carbon nanotube distribution pattern, core to face thickness ratio, volume fractions of the nanotube, length to thickness ratio, aspect ratio and constraints at edges) on the time-responses of sandwich plate.

Nondestructive Integrity Evaluation of PC Pile Using Wigner-Ville Distribution Method

NASA Astrophysics Data System (ADS)

Ni, Sheng-Huoo; Lo, Kuo-Feng; Huang, Yan-Hong

Nondestructive evaluation (NDE) techniques have been used for years to provide a quality control of the construction for both drilled shafts and driven concrete piles. This trace is typically made up of transient pulses reflected from structural features of the pile or changes in its surrounding environment. It is often analyzed in conjunction with the spectral response, mobility curve, arrival time, etc. The Wigner-Ville Distribution is a new numerical analysis tool for signal process technique in the time-frequency domain and it can offer assistance and enhance signal characteristics for better resolution both easily and quickly. In this study, five single pre-cast concrete piles have been tested and evaluated by both sonic echo method and Wigner-Ville distribution (WVD). Furthermore, two difficult problems in nondestructive evaluation problems are discussed and solved: the first one is with a pile with slight defect, whose necking area percentage is less than 10%, and the other is a pile with multiple defects. The results show that WVD can not only recognize the characteristics easily, but also locate the defects more clearly than the traditional pile integrity testing method.

Distributed cooperating processes in a mobile robot control system

NASA Technical Reports Server (NTRS)

Skillman, Thomas L., Jr.

1988-01-01

A mobile inspection robot has been proposed for the NASA Space Station. It will be a free flying autonomous vehicle that will leave a berthing unit to accomplish a variety of inspection tasks around the Space Station, and then return to its berth to recharge, refuel, and transfer information. The Flying Eye robot will receive voice communication to change its attitude, move at a constant velocity, and move to a predefined location along a self generated path. This mobile robot control system requires integration of traditional command and control techniques with a number of AI technologies. Speech recognition, natural language understanding, task and path planning, sensory abstraction and pattern recognition are all required for successful implementation. The interface between the traditional numeric control techniques and the symbolic processing to the AI technologies must be developed, and a distributed computing approach will be needed to meet the real time computing requirements. To study the integration of the elements of this project, a novel mobile robot control architecture and simulation based on the blackboard architecture was developed. The control system operation and structure is discussed.

Orbit determination based on meteor observations using numerical integration of equations of motion

NASA Astrophysics Data System (ADS)

Dmitriev, V.; Lupovka, V.; Gritsevich, M.

2014-07-01

We review the definitions and approaches to orbital-characteristics analysis applied to photographic or video ground-based observations of meteors. A number of camera networks dedicated to meteors registration were established all over the word, including USA, Canada, Central Europe, Australia, Spain, Finland and Poland. Many of these networks are currently operational. The meteor observations are conducted from different locations hosting the network stations. Each station is equipped with at least one camera for continuous monitoring of the firmament (except possible weather restrictions). For registered multi-station meteors, it is possible to accurately determine the direction and absolute value for the meteor velocity and thus obtain the topocentric radiant. Based on topocentric radiant one further determines the heliocentric meteor orbit. We aim to reduce total uncertainty in our orbit-determination technique, keeping it even less than the accuracy of observations. The additional corrections for the zenith attraction are widely in use and are implemented, for example, here [1]. We propose a technique for meteor-orbit determination with higher accuracy. We transform the topocentric radiant in inertial (J2000) coordinate system using the model recommended by IAU [2]. The main difference if compared to the existing orbit-determination techniques is integration of ordinary differential equations of motion instead of addition correction in visible velocity for zenith attraction. The attraction of the central body (the Sun), the perturbations by Earth, Moon and other planets of the Solar System, the Earth's flattening (important in the initial moment of integration, i.e. at the moment when a meteoroid enters the atmosphere), atmospheric drag may be optionally included in the equations. In addition, reverse integration of the same equations can be performed to analyze orbital evolution preceding to meteoroid's collision with Earth. To demonstrate the developed technique, we provide calculated orbits for several cases, including well-known meteorite-producing fireballs. A comparison of our estimates with previously published ones is also provided.

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

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.

Nanostructured plasmonic interferometers for ultrasensitive label-free biosensing

NASA Astrophysics Data System (ADS)

Gao, Yongkang

Optical biosensors that utilize surface plasmon resonance (SPR) technique to analyze the biomolecular interactions have been extensively explored in the last two decades and have become the gold standard for label-free biosensing. These powerful sensing tools allow fast, highly-sensitive monitoring of the interaction between biomolecules in real time, without the need for laborious fluorescent labeling, and have found widely ranging applications from biomedical diagnostics and drug discovery, to environmental sensing and food safety monitoring. However, the prism-coupling SPR geometry is complex and bulky, and has severely limited the integration of this technique into low-cost portable biomedical devices for point-of-care diagnostics and personal healthcare applications. Also, the complex prism-coupling scheme prevents the use of high numerical aperture (NA) optics to increase the spatial resolution for multi-channel, high-throughput detection in SPR imaging mode. This dissertation is focused on the design and fabrication of a promising new class of nanopatterned interferometric SPR sensors that integrate the strengths of miniaturized nanoplasmonic architectures with sensitive optical interferometry techniques to achieve bold advances in SPR biosensing. The nanosensor chips developed provide superior sensing performance comparable to conventional SPR systems, but employing a far simpler collinear optical transmission geometry, which largely facilitates system integration, miniaturization, and low-cost production. Moreover, the fabricated nanostructure-based SPR sensors feature a very small sensor footprint, allowing massive multiplexing on a chip for high-throughput detection. The successful transformation of SPR technique from bulky prism-coupling setup into this low-cost compact plasmonic platform would have a far-reaching impact on point-of-care diagnostic tools and also lead to advances in high-throughput sensing applications in proteomics, immunology, drug discovery, and fundamental cell biology research.

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Yao, Minwu; Walker, Kevin P.

1992-01-01

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

A technique to remove the tensile instability in weakly compressible SPH

NASA Astrophysics Data System (ADS)

Xu, Xiaoyang; Yu, Peng

2018-01-01

When smoothed particle hydrodynamics (SPH) is directly applied for the numerical simulations of transient viscoelastic free surface flows, a numerical problem called tensile instability arises. In this paper, we develop an optimized particle shifting technique to remove the tensile instability in SPH. The basic equations governing free surface flow of an Oldroyd-B fluid are considered, and approximated by an improved SPH scheme. This includes the implementations of the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation. To verify the effectiveness of the optimized particle shifting technique in removing the tensile instability, the impacting drop, the injection molding of a C-shaped cavity, and the extrudate swell, are conducted. The numerical results obtained are compared with those simulated by other numerical methods. A comparison among different numerical techniques (e.g., the artificial stress) to remove the tensile instability is further performed. All numerical results agree well with the available data.

Probability density function evolution of power systems subject to stochastic variation of renewable energy

NASA Astrophysics Data System (ADS)

Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.

2018-05-01

As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.

Development of an EMC3-EIRENE Synthetic Imaging Diagnostic

NASA Astrophysics Data System (ADS)

Meyer, William; Allen, Steve; Samuell, Cameron; Lore, Jeremy

2017-10-01

2D and 3D flow measurements are critical for validating numerical codes such as EMC3-EIRENE. Toroidal symmetry assumptions preclude tomographic reconstruction of 3D flows from single camera views. In addition, the resolution of the grids utilized in numerical code models can easily surpass the resolution of physical camera diagnostic geometries. For these reasons we have developed a Synthetic Imaging Diagnostic capability for forward projection comparisons of EMC3-EIRENE model solutions with the line integrated images from the Doppler Coherence Imaging diagnostic on DIII-D. The forward projection matrix is 2.8 Mpixel by 6.4 Mcells for the non-axisymmetric case we present. For flow comparisons, both simple line integral, and field aligned component matrices must be calculated. The calculation of these matrices is a massive embarrassingly parallel problem and performed with a custom dispatcher that allows processing platforms to join mid-problem as they become available, or drop out if resources are needed for higher priority tasks. The matrices are handled using standard sparse matrix techniques. Prepared by LLNL under Contract DE-AC52-07NA27344. This material is based upon work supported by the U.S. DOE, Office of Science, Office of Fusion Energy Sciences. LLNL-ABS-734800.

Axicons, prisms and integrators: searching for simple laser beam shaping solutions

NASA Astrophysics Data System (ADS)

Lizotte, Todd

2010-08-01

Over the last thirty five years there have been many papers presented at numerous conferences and published within a host of optical journals. What is presented in many cases is either too exotic or technically challenging in practical application terms and it could be said both are testaments to the imagination of engineers and researchers. For many brute force laser processing applications such as paint stripping, large area ablation or general skiving of flex circuits, the opportunity to use a beam shaper that is inexpensive is a welcomed tool. Shaping the laser beam for less demanding applications, provides for a more uniform removal rate and increases the overall quality of the part being processed. It is a well known fact customers like their parts to look good. Many times, complex optical beam shaping techniques are considered because no one is aware of the historical solutions that have been lost to the ages. These complex solutions can range in price from 10,000 to 60,000 and require many months to design and fabricate. This paper will provide an overview of various beam shaping techniques that are both elegant and simple in concept and design. Optical techniques using axicons, prisms and reflective integrators will be discussed in an overview format.

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

Graphical programming interface: A development environment for MRI methods.

PubMed

Zwart, Nicholas R; Pipe, James G

2015-11-01

To introduce a multiplatform, Python language-based, development environment called graphical programming interface for prototyping MRI techniques. The interface allows developers to interact with their scientific algorithm prototypes visually in an event-driven environment making tasks such as parameterization, algorithm testing, data manipulation, and visualization an integrated part of the work-flow. Algorithm developers extend the built-in functionality through simple code interfaces designed to facilitate rapid implementation. This article shows several examples of algorithms developed in graphical programming interface including the non-Cartesian MR reconstruction algorithms for PROPELLER and spiral as well as spin simulation and trajectory visualization of a FLORET example. The graphical programming interface framework is shown to be a versatile prototyping environment for developing numeric algorithms used in the latest MR techniques. © 2014 Wiley Periodicals, Inc.

Visualization of Global Sensitivity Analysis Results Based on a Combination of Linearly Dependent and Independent Directions

NASA Technical Reports Server (NTRS)

Davies, Misty D.; Gundy-Burlet, Karen

2010-01-01

A useful technique for the validation and verification of complex flight systems is Monte Carlo Filtering -- a global sensitivity analysis that tries to find the inputs and ranges that are most likely to lead to a subset of the outputs. A thorough exploration of the parameter space for complex integrated systems may require thousands of experiments and hundreds of controlled and measured variables. Tools for analyzing this space often have limitations caused by the numerical problems associated with high dimensionality and caused by the assumption of independence of all of the dimensions. To combat both of these limitations, we propose a technique that uses a combination of the original variables with the derived variables obtained during a principal component analysis.

Physiologically based pharmacokinetic modeling using microsoft excel and visual basic for applications.

PubMed

Marino, Dale J

2005-01-01

Abstract Physiologically based pharmacokinetic (PBPK) models are mathematical descriptions depicting the relationship between external exposure and internal dose. These models have found great utility for interspecies extrapolation. However, specialized computer software packages, which are not widely distributed, have typically been used for model development and utilization. A few physiological models have been reported using more widely available software packages (e.g., Microsoft Excel), but these tend to include less complex processes and dose metrics. To ascertain the capability of Microsoft Excel and Visual Basis for Applications (VBA) for PBPK modeling, models for styrene, vinyl chloride, and methylene chloride were coded in Advanced Continuous Simulation Language (ACSL), Excel, and VBA, and simulation results were compared. For styrene, differences between ACSL and Excel or VBA compartment concentrations and rates of change were less than +/-7.5E-10 using the same numerical integration technique and time step. Differences using VBA fixed step or ACSL Gear's methods were generally <1.00E-03, although larger differences involving very small values were noted after exposure transitions. For vinyl chloride and methylene chloride, Excel and VBA PBPK model dose metrics differed by no more than -0.013% or -0.23%, respectively, from ACSL results. These differences are likely attributable to different step sizes rather than different numerical integration techniques. These results indicate that Microsoft Excel and VBA can be useful tools for utilizing PBPK models, and given the availability of these software programs, it is hoped that this effort will help facilitate the use and investigation of PBPK modeling.

Evaluation of radiation loading on finite cylindrical shells using the fast Fourier transform: A comparison with direct numerical integration.

PubMed

Liu, S X; Zou, M S

2018-03-01

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration.

Method for the numerical integration of equations of perturbed satellite motion in problems of space geodesy

NASA Astrophysics Data System (ADS)

Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.

A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.

A Numerical Study of Hypersonic Forebody/Inlet Integration Problem

NASA Technical Reports Server (NTRS)

Kumar, Ajay

1991-01-01

A numerical study of hypersonic forebody/inlet integration problem is presented in the form of the view-graphs. The following topics are covered: physical/chemical modeling; solution procedure; flow conditions; mass flow rate at inlet face; heating and skin friction loads; 3-D forebogy/inlet integration model; and sensitivity studies.

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

Hierarchical modeling for reliability analysis using Markov models. B.S./M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Fagundo, Arturo

1994-01-01

Markov models represent an extremely attractive tool for the reliability analysis of many systems. However, Markov model state space grows exponentially with the number of components in a given system. Thus, for very large systems Markov modeling techniques alone become intractable in both memory and CPU time. Often a particular subsystem can be found within some larger system where the dependence of the larger system on the subsystem is of a particularly simple form. This simple dependence can be used to decompose such a system into one or more subsystems. A hierarchical technique is presented which can be used to evaluate these subsystems in such a way that their reliabilities can be combined to obtain the reliability for the full system. This hierarchical approach is unique in that it allows the subsystem model to pass multiple aggregate state information to the higher level model, allowing more general systems to be evaluated. Guidelines are developed to assist in the system decomposition. An appropriate method for determining subsystem reliability is also developed. This method gives rise to some interesting numerical issues. Numerical error due to roundoff and integration are discussed at length. Once a decomposition is chosen, the remaining analysis is straightforward but tedious. However, an approach is developed for simplifying the recombination of subsystem reliabilities. Finally, a real world system is used to illustrate the use of this technique in a more practical context.

A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

NASA Technical Reports Server (NTRS)

Berger, B. S.; Duangudom, S.

1973-01-01

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

Quasi-integrability in the modified defocusing non-linear Schrödinger model and dark solitons

NASA Astrophysics Data System (ADS)

Blas, H.; Zambrano, M.

2016-03-01

The concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schrödinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of deformations of the sine-Gordon, Bullough-Dodd and focusing NLS models, holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potential V=η {I}^2-in /6{I}^3 and the saturable type potential satisfying [InlineEquation not available: see fulltext.], with a deformation parameter ɛ ∈ [InlineMediaObject not available: see fulltext.] and I = | ψ|2. The issue of the renormalization of the charges and anomalies, and their (quasi)conservation laws are properly addressed. The saturable NLS supports elastic scattering of two soliton solutions for a wide range of values of { η, ɛ, q}. Our results may find potential applications in several areas of non-linear science, such as the Bose-Einstein condensation.

Temporal abstraction and inductive logic programming for arrhythmia recognition from electrocardiograms.

PubMed

Carrault, G; Cordier, M-O; Quiniou, R; Wang, F

2003-07-01

This paper proposes a novel approach to cardiac arrhythmia recognition from electrocardiograms (ECGs). ECGs record the electrical activity of the heart and are used to diagnose many heart disorders. The numerical ECG is first temporally abstracted into series of time-stamped events. Temporal abstraction makes use of artificial neural networks to extract interesting waves and their features from the input signals. A temporal reasoner called a chronicle recogniser processes such series in order to discover temporal patterns called chronicles which can be related to cardiac arrhythmias. Generally, it is difficult to elicit an accurate set of chronicles from a doctor. Thus, we propose to learn automatically from symbolic ECG examples the chronicles discriminating the arrhythmias belonging to some specific subset. Since temporal relationships are of major importance, inductive logic programming (ILP) is the tool of choice as it enables first-order relational learning. The approach has been evaluated on real ECGs taken from the MIT-BIH database. The performance of the different modules as well as the efficiency of the whole system is presented. The results are rather good and demonstrate that integrating numerical techniques for low level perception and symbolic techniques for high level classification is very valuable.

Merits and limitations of optimality criteria method for structural optimization

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Guptill, James D.; Berke, Laszlo

1993-01-01

The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. Salient features of the code include multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analyzers, and analytical and numerical sensitivities. The performance of the OC method, on the basis of the examples solved, was found to be satisfactory for problems with few active constraints or with small numbers of design variables. For problems with large numbers of behavior constraints and design variables, the OC method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

PROPOSED SIAM PROBLEM

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

BAILEY, DAVID H.; BORWEIN, JONATHAN M.

A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form {integral}{sub 0}{sup {infinity}} t{sup m}f{sup n}(t) dt, where the function f(t) is one of the classical Bessel functions. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers. In several instances, while we were able to numerically discover what appears to be a solid analytic identity, based on extremely high-precision numerical computations, wemore » were unable to find a rigorous proof. Thus we present here a brief list of some of these unproven but numerically confirmed identities.« less

Calculating corner singularities by boundary integral equations.

PubMed

Shi, Hualiang; Lu, Ya Yan; Du, Qiang

2017-06-01

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes. The numerically found singularity exponents agree well with the exact values in all the test cases presented here, indicating that the numerical solutions are accurate.

The Cenozoic fold-and-thrust belt of Eastern Sardinia: Evidences from the integration of field data with numerically balanced geological cross section

NASA Astrophysics Data System (ADS)

Arragoni, S.; Maggi, M.; Cianfarra, P.; Salvini, F.

2016-06-01

Newly collected structural data in Eastern Sardinia (Italy) integrated with numerical techniques led to the reconstruction of a 2-D admissible and balanced model revealing the presence of a widespread Cenozoic fold-and-thrust belt. The model was achieved with the FORC software, obtaining a 3-D (2-D + time) numerical reconstruction of the continuous evolution of the structure through time. The Mesozoic carbonate units of Eastern Sardinia and their basement present a fold-and-thrust tectonic setting, with a westward direction of tectonic transport (referred to the present-day coordinates). The tectonic style of the upper levels is thin skinned, with flat sectors prevailing over ramps and younger-on-older thrusts. Three regional tectonic units are present, bounded by two regional thrusts. Strike-slip faults overprint the fold-and-thrust belt and developed during the Sardinia-Corsica Block rotation along the strike of the preexisting fault ramps, not affecting the numerical section balancing. This fold-and-thrust belt represents the southward prosecution of the Alpine Corsica collisional chain and the missing link between the Alpine Chain and the Calabria-Peloritani Block. Relative ages relate its evolution to the meso-Alpine event (Eocene-Oligocene times), prior to the opening of the Tyrrhenian Sea (Tortonian). Results fill a gap of information about the geodynamic evolution of the European margin in Central Mediterranean, between Corsica and the Calabria-Peloritani Block, and imply the presence of remnants of this double-verging belt, missing in the Southern Tyrrhenian basin, within the Southern Apennine chain. The used methodology proved effective for constraining balanced cross sections also for areas lacking exposures of the large-scale structures, as the case of Eastern Sardinia.

A Full-Featured User Friendly CO 2-EOR and Sequestration Planning Software

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

Savage, Bill

A Full-Featured, User Friendly CO 2-EOR and Sequestration Planning Software This project addressed the development of an integrated software solution that includes a graphical user interface, numerical simulation, visualization tools and optimization processes for reservoir simulation modeling of CO 2-EOR. The objective was to assist the industry in the development of domestic energy resources by expanding the application of CO 2-EOR technologies, and ultimately to maximize the CO 2} sequestration capacity of the U.S. The software resulted in a field-ready application for the industry to address the current CO 2-EOR technologies. The software has been made available to the publicmore » without restrictions and with user friendly operating documentation and tutorials. The software (executable only) can be downloaded from NITEC’s website at www.nitecllc.com. This integrated solution enables the design, optimization and operation of CO 2-EOR processes for small and mid-sized operators, who currently cannot afford the expensive, time intensive solutions that the major oil companies enjoy. Based on one estimate, small oil fields comprise 30% of the of total economic resource potential for the application of CO 2-EOR processes in the U.S. This corresponds to 21.7 billion barrels of incremental, technically recoverable oil using the current “best practices”, and 31.9 billion barrels using “next-generation” CO 2-EOR techniques. The project included a Case Study of a prospective CO 2-EOR candidate field in Wyoming by a small independent, Linc Energy Petroleum Wyoming, Inc. NITEC LLC has an established track record of developing innovative and user friendly software. The Principle Investigator is an experienced manager and engineer with expertise in software development, numerical techniques, and GUI applications. Unique, presently-proprietary NITEC technologies have been integrated into this application to further its ease of use and technical functionality.« less

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Spike-train spectra and network response functions for non-linear integrate-and-fire neurons.

PubMed

Richardson, Magnus J E

2008-11-01

Reduced models have long been used as a tool for the analysis of the complex activity taking place in neurons and their coupled networks. Recent advances in experimental and theoretical techniques have further demonstrated the usefulness of this approach. Despite the often gross simplification of the underlying biophysical properties, reduced models can still present significant difficulties in their analysis, with the majority of exact and perturbative results available only for the leaky integrate-and-fire model. Here an elementary numerical scheme is demonstrated which can be used to calculate a number of biologically important properties of the general class of non-linear integrate-and-fire models. Exact results for the first-passage-time density and spike-train spectrum are derived, as well as the linear response properties and emergent states of recurrent networks. Given that the exponential integrate-fire model has recently been shown to agree closely with the experimentally measured response of pyramidal cells, the methodology presented here promises to provide a convenient tool to facilitate the analysis of cortical-network dynamics.

An Integrated Solution for Performing Thermo-fluid Conjugate Analysis

NASA Technical Reports Server (NTRS)

Kornberg, Oren

2009-01-01

A method has been developed which integrates a fluid flow analyzer and a thermal analyzer to produce both steady state and transient results of 1-D, 2-D, and 3-D analysis models. The Generalized Fluid System Simulation Program (GFSSP) is a one dimensional, general purpose fluid analysis code which computes pressures and flow distributions in complex fluid networks. The MSC Systems Improved Numerical Differencing Analyzer (MSC.SINDA) is a one dimensional general purpose thermal analyzer that solves network representations of thermal systems. Both GFSSP and MSC.SINDA have graphical user interfaces which are used to build the respective model and prepare it for analysis. The SINDA/GFSSP Conjugate Integrator (SGCI) is a formbase graphical integration program used to set input parameters for the conjugate analyses and run the models. The contents of this paper describes SGCI and its thermo-fluids conjugate analysis techniques and capabilities by presenting results from some example models including the cryogenic chill down of a copper pipe, a bar between two walls in a fluid stream, and a solid plate creating a phase change in a flowing fluid.

Optical fringe-reflection deflectometry with sparse representation

NASA Astrophysics Data System (ADS)

Xiao, Yong-Liang; Li, Sikun; Zhang, Qican; Zhong, Jianxin; Su, Xianyu; You, Zhisheng

2018-05-01

Optical fringe-reflection deflectometry is a surprisingly attractive scratch detection technique for specular surfaces owing to its unparalleled local sensibility. Full-field surface topography is obtained from a measured normal field using gradient integration. However, there may not be an ideal measured gradient field for deflectometry reconstruction in practice. Both the non-integrability condition and various kinds of image noise distributions, which are present in the indirect measured gradient field, may lead to ambiguity about the scratches on specular surfaces. In order to reduce misjudgment of scratches, sparse representation is introduced into the Southwell curl equation for deflectometry. The curl can be represented as a linear combination of the given redundant dictionary for curl and the sparsest solution for gradient refinement. The non-integrability condition and noise permutation can be overcome with sparse representation for gradient refinement. Numerical simulations demonstrate that the accuracy rate of judgment of scratches can be enhanced with sparse representation compared to the standard least-squares integration. Preliminary experiments are performed with the application of practical measured deflectometric data to verify the validity of the algorithm.

Computer program ETC improves computation of elastic transfer matrices of Legendre polynomials P/0/ and P/1/

NASA Technical Reports Server (NTRS)

Gibson, G.; Miller, M.

1967-01-01

Computer program ETC improves computation of elastic transfer matrices of Legendre polynomials P/0/ and P/1/. Rather than carrying out a double integration numerically, one of the integrations is accomplished analytically and the numerical integration need only be carried out over one variable.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

NASA Astrophysics Data System (ADS)

M. Salem, A.; Galal, Ismail; Rania, Fathy

2014-04-01

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems.

PubMed

Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

2015-11-11

Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.

Numerical and Experimental study of secondary flows in a rotating two-phase flow: the tea leaf paradox

NASA Astrophysics Data System (ADS)

Calderer, Antoni; Neal, Douglas; Prevost, Richard; Mayrhofer, Arno; Lawrenz, Alan; Foss, John; Sotiropoulos, Fotis

2015-11-01

Secondary flows in a rotating flow in a cylinder, resulting in the so called ``tea leaf paradox'', are fundamental for understanding atmospheric pressure systems, developing techniques for separating red blood cells from the plasma, and even separating coagulated trub in the beer brewing process. We seek to gain deeper insights in this phenomenon by integrating numerical simulations and experiments. We employ the Curvilinear Immersed boundary method (CURVIB) of Calderer et al. (J. Comp. Physics 2014), which is a two-phase flow solver based on the level set method, to simulate rotating free-surface flow in a cylinder partially filled with water as in the tea leave paradox flow. We first demonstrate the validity of the numerical model by simulating a cylinder with a rotating base filled with a single fluid, obtaining results in excellent agreement with available experimental data. Then, we present results for the cylinder case with free surface, investigate the complex formation of secondary flow patterns, and show comparisons with new experimental data for this flow obtained by Lavision. Computational resources were provided by the Minnesota Supercomputing Institute.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

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

Rodriguez, Alejandro; Ibanescu, Mihai; Joannopoulos, J. D.

2007-09-15

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustratemore » our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.« less

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

NASA Technical Reports Server (NTRS)

Gallardo, V. C.; Storace, A. S.; Gaffney, E. F.; Bach, L. J.; Stallone, M. J.

1981-01-01

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.

Back-Analyses of Landfill Instability Induced by High Water Level: Case Study of Shenzhen Landfill

PubMed Central

Peng, Ren; Hou, Yujing; Zhan, Liangtong; Yao, Yangping

2016-01-01

In June 2008, the Shenzhen landfill slope failed. This case is used as an example to study the deformation characteristics and failure mode of a slope induced by high water levels. An integrated monitoring system, including water level gauges, electronic total stations, and inclinometers, was used to monitor the slope failure process. The field measurements suggest that the landfill landslide was caused by a deep slip along the weak interface of the composite liner system at the base of the landfill. The high water level is considered to be the main factor that caused this failure. To calculate the relative interface shear displacements in the geosynthetic multilayer liner system, a series of numerical direct shear tests were carried out. Based on the numerical results, the composite lining system simplified and the centrifuge modeling technique was used to quantitatively evaluate the effect of water levels on landfill instability. PMID:26771627

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

Development of an Intelligent Monitoring and Control System for a Heterogeneous Numerical Propulsion System Simulation

NASA Technical Reports Server (NTRS)

Reed, John A.; Afjeh, Abdollah A.; Lewandowski, Henry; Homer, Patrick T.; Schlichting, Richard D.

1996-01-01

The NASA Numerical Propulsion System Simulation (NPSS) project is exploring the use of computer simulation to facilitate the design of new jet engines. Several key issues raised in this research are being examined in an NPSS-related research project: zooming, monitoring and control, and support for heterogeneity. The design of a simulation executive that addresses each of these issues is described. In this work, the strategy of zooming, which allows codes that model at different levels of fidelity to be integrated within a single simulation, is applied to the fan component of a turbofan propulsion system. A prototype monitoring and control system has been designed for this simulation to support experimentation with expert system techniques for active control of the simulation. An interconnection system provides a transparent means of connecting the heterogeneous systems that comprise the prototype.

Meteorological and air pollution modeling for an urban airport

NASA Technical Reports Server (NTRS)

Swan, P. R.; Lee, I. Y.

1980-01-01

Results are presented of numerical experiments modeling meteorology, multiple pollutant sources, and nonlinear photochemical reactions for the case of an airport in a large urban area with complex terrain. A planetary boundary-layer model which predicts the mixing depth and generates wind, moisture, and temperature fields was used; it utilizes only surface and synoptic boundary conditions as input data. A version of the Hecht-Seinfeld-Dodge chemical kinetics model is integrated with a new, rapid numerical technique; both the San Francisco Bay Area Air Quality Management District source inventory and the San Jose Airport aircraft inventory are utilized. The air quality model results are presented in contour plots; the combined results illustrate that the highly nonlinear interactions which are present require that the chemistry and meteorology be considered simultaneously to make a valid assessment of the effects of individual sources on regional air quality.

Microwave (SSM/I) Estimates of the Precipitation Rate to Improve Numerical Atmospheric Model Forecasts

NASA Technical Reports Server (NTRS)

Raymond, William H.; Olson, William S.

1990-01-01

Delay in the spin-up of precipitation early in numerical atmospheric forecasts is a deficiency correctable by diabatic initialization combined with diabatic forcing. For either to be effective requires some knowledge of the magnitude and vertical placement of the latent heating fields. Until recently the best source of cloud and rain water data was the remotely sensed vertical integrated precipitation rate or liquid water content. Vertical placement of the condensation remains unknown. Some information about the vertical distribution of the heating rates and precipitating liquid water and ice can be obtained from retrieval techniques that use a physical model of precipitating clouds to refine and improve the interpretation of the remotely sensed data. A description of this procedure and an examination of its 3-D liquid water products, along with improved modeling methods that enhance or speed-up storm development is discussed.

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

Integrating spatial and numerical structure in mathematical patterning

NASA Astrophysics Data System (ADS)

Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.

2018-03-01

This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

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

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Simulation results of Pulse Shape Discrimination (PSD) for background reduction in INTEGRAL Spectrometer (SPI) germanium detectors

NASA Technical Reports Server (NTRS)

Slassi-Sennou, S. A.; Boggs, S. E.; Feffer, P. T.; Lin, R. P.

1997-01-01

Pulse Shape Discrimination (PSD) for background reduction will be used in the INTErnational Gamma Ray Astrophysics Laboratory (INTEGRAL) imaging spectrometer (SPI) to improve the sensitivity from 200 keV to 2 MeV. The observation of significant astrophysical gamma ray lines in this energy range is expected, where the dominant component of the background is the beta(sup -) decay in the Ge detectors due to the activation of Ge nuclei by cosmic rays. The sensitivity of the SPI will be improved by rejecting beta(sup -) decay events while retaining photon events. The PSD technique will distinguish between single and multiple site events. Simulation results of PSD for INTEGRAL-type Ge detectors using a numerical model for pulse shape generation are presented. The model was shown to agree with the experimental results for a narrow inner bore closed end cylindrical detector. Using PSD, a sensitivity improvement factor of the order of 2.4 at 0.8 MeV is expected.

Large memory capacity in chaotic artificial neural networks: a view of the anti-integrable limit.

PubMed

Lin, Wei; Chen, Guanrong

2009-08-01

In the literature, it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns, better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions. This paper, from the viewpoint of the anti-integrable limit, elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions. Particularly, by virtue of the anti-integrable limit technique, this paper shows that any finite-dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model's memory capacity and pattern-retrieval ability. To some extent, this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern-retrieval ability of the artificial neural network models.

Computer prediction of large reflector antenna radiation properties

NASA Technical Reports Server (NTRS)

Botula, A.

1980-01-01

A FORTRAN program for calculating reflector antenna radiation patterns was rewritten and extended to include reflectors composed of a number of panels. These individual panels must be analytic surfaces. The theoretical foundation for the program is as follows: Geometrical optics techniques are used to trace rays from a feed antenna to the reflector surface and back to a mathematical plane just in front of the reflector. The resulting tangential electric field distribution, assumed to be the only source of forward radiation, is integrated numerically to calculate the radiation pattern for a desired set of angles. When the reflector is composed of more than one panel, each panel is treated as a separated antenna, the ray-tracing procedure and integration being repeated for each panel. The results of the individual aperture plane integrations are stored and summed to yield the relative electric field strength over the angles of interest. An example and several test cases are included to demonstrate the use of the program and verify the new method of computation.

Monolithic integration of InGaAs/InP multiple quantum wells on SOI substrates for photonic devices

NASA Astrophysics Data System (ADS)

Li, Zhibo; Wang, Mengqi; Fang, Xin; Li, Yajie; Zhou, Xuliang; Yu, Hongyan; Wang, Pengfei; Wang, Wei; Pan, Jiaoqing

2018-02-01

A direct epitaxy of III-V nanowires with InGaAs/InP multiple quantum wells on v-shaped trenches patterned silicon on insulator (SOI) substrates was realized by combining the standard semiconductor fabrication process with the aspect ratio trapping growth technique. Silicon thickness as well as the width and gap of each nanowire were carefully designed to accommodate essential optical properties and appropriate growth conditions. The III-V element ingredient, crystalline quality, and surface topography of the grown nanowires were characterized by X-ray diffraction spectroscopy, photoluminescence, and scanning electron microscope. Geometrical details and chemical information of multiple quantum wells were revealed by transmission electron microscopy and energy dispersive spectroscopy. Numerical simulations confirmed that the optical guided mode supported by one single nanowire was able to propagate 50 μm with ˜30% optical loss. This proposed integration scheme opens up an alternative pathway for future photonic integrations of III-V devices on the SOI platform at nanoscale.

A Numerical Method for Integrating Orbits

NASA Astrophysics Data System (ADS)

Sahakyan, Karen P.; Melkonyan, Anahit A.; Hayrapetyan, S. R.

2007-08-01

A numerical method based of trigonometric polynomials for integrating of ordinary differential equations of first and second order is suggested. This method is a trigonometric analogue of Everhart's method and can be especially useful for periodical trajectories.

An optimal modeling of multidimensional wave digital filtering network for free vibration analysis of symmetrically laminated composite FSDT plates

NASA Astrophysics Data System (ADS)

Tseng, Chien-Hsun

2015-02-01

The technique of multidimensional wave digital filtering (MDWDF) that builds on traveling wave formulation of lumped electrical elements, is successfully implemented on the study of dynamic responses of symmetrically laminated composite plate based on the first order shear deformation theory. The philosophy applied for the first time in this laminate mechanics relies on integration of certain principles involving modeling and simulation, circuit theory, and MD digital signal processing to provide a great variety of outstanding features. Especially benefited by the conservation of passivity gives rise to a nonlinear programming problem (NLP) for the issue of numerical stability of a MD discrete system. Adopting the augmented Lagrangian genetic algorithm, an effective optimization technique for rapidly achieving solution spaces of NLP models, numerical stability of the MDWDF network is well received at all time by the satisfaction of the Courant-Friedrichs-Levy stability criterion with the least restriction. In particular, optimum of the NLP has led to the optimality of the network in terms of effectively and accurately predicting the desired fundamental frequency, and thus to give an insight into the robustness of the network by looking at the distribution of system energies. To further explore the application of the optimum network, more numerical examples are engaged in efforts to achieve a qualitative understanding of the behavior of the laminar system. These are carried out by investigating various effects based on different stacking sequences, stiffness and span-to-thickness ratios, mode shapes and boundary conditions. Results are scrupulously validated by cross referencing with early published works, which show that the present method is in excellent agreement with other numerical and analytical methods.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

New Langevin and gradient thermostats for rigid body dynamics.

PubMed

Davidchack, R L; Ouldridge, T E; Tretyakov, M V

2015-04-14

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.

Aerodynamic influence coefficient method using singularity splines.

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1973-01-01

A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.

Review of Bioassays for Monitoring Fate and Transport ofEstrogenic Endocrine Disrupting Compounds in Water

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

CGCampbell@lbl.gov

Endocrine disrupting compounds (EDCs) are recognizedcontaminants threatening water quality. Despite efforts in sourceidentification, few strategies exist for characterization or treatment ofthis environmental pollution. Given that there are numerous EDCs that cannegatively affect humans and wildlife, general screening techniques likebioassays and biosensors provide an essential rapid and intensiveanalysis capacity. Commonly applied bioassays include the ELISA and YESassays, but promising technologies include ER-CALUXa, ELRA, Endotecta,RIANA, and IR-bioamplification. Two biosensors, Endotecta and RIANA, arefield portable using non-cellular biological detection strategies.Environmental management of EDCs in water requires integration ofbiosensors and bioassays for monitoring and assessment.

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

The modeling of an automotive electronic control system and the application of optimizing methods

NASA Astrophysics Data System (ADS)

Zhang, Yansheng; Yang, Zhigang; Zhang, Xiang

2005-12-01

Now, MATLAB/SIMULINK software is popularly used by automotive electronic control designers to develop automotive electronic control systems and perform numerical simulations. But they will face problems, such as value initialization in the "integrator" block, conversion among different data types, selection of "if" block and "switch" block, realization of the "if-clause" under multiple options and the auto-switching control, etc. Taking as an example the designing of an Automated Mechanical Transmission (AMT) system, this paper discusses some techniques and methods for modeling the automotive electronic control system with MATLAB/SIMULINK, offering designers some successful examples.

Artificial Intelligence in Autonomous Telescopes

NASA Astrophysics Data System (ADS)

Mahoney, William; Thanjavur, Karun

2011-03-01

Artificial Intelligence (AI) is key to the natural evolution of today's automated telescopes to fully autonomous systems. Based on its rapid development over the past five decades, AI offers numerous, well-tested techniques for knowledge based decision making essential for real-time telescope monitoring and control, with minimal - and eventually no - human intervention. We present three applications of AI developed at CFHT for monitoring instantaneous sky conditions, assessing quality of imaging data, and a prototype for scheduling observations in real-time. Closely complementing the current remote operations at CFHT, we foresee further development of these methods and full integration in the near future.

Stabilization of computational procedures for constrained dynamical systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.

1988-01-01

A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Solution methods for one-dimensional viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, John M.; Simitses, George J.

1987-01-01

A recently developed differential methodology for solution of one-dimensional nonlinear viscoelastic problems is presented. Using the example of an eccentrically loaded cantilever beam-column, the results from the differential formulation are compared to results generated using a previously published integral solution technique. It is shown that the results obtained from these distinct methodologies exhibit a surprisingly high degree of correlation with one another. A discussion of the various factors affecting the numerical accuracy and rate of convergence of these two procedures is also included. Finally, the influences of some 'higher order' effects, such as straining along the centroidal axis are discussed.

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

NASA Technical Reports Server (NTRS)

Radhadrishnan, Krishnan

1993-01-01

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Enviro-HIRLAM/ HARMONIE Studies in ECMWF HPC EnviroAerosols Project

NASA Astrophysics Data System (ADS)

Hansen Sass, Bent; Mahura, Alexander; Nuterman, Roman; Baklanov, Alexander; Palamarchuk, Julia; Ivanov, Serguei; Pagh Nielsen, Kristian; Penenko, Alexey; Edvardsson, Nellie; Stysiak, Aleksander Andrzej; Bostanbekov, Kairat; Amstrup, Bjarne; Yang, Xiaohua; Ruban, Igor; Bergen Jensen, Marina; Penenko, Vladimir; Nurseitov, Daniyar; Zakarin, Edige

2017-04-01

The EnviroAerosols on ECMWF HPC project (2015-2017) "Enviro-HIRLAM/ HARMONIE model research and development for online integrated meteorology-chemistry-aerosols feedbacks and interactions in weather and atmospheric composition forecasting" is aimed at analysis of importance of the meteorology-chemistry/aerosols interactions and to provide a way for development of efficient techniques for on-line coupling of numerical weather prediction and atmospheric chemical transport via process-oriented parameterizations and feedback algorithms, which will improve both the numerical weather prediction and atmospheric composition forecasts. Two main application areas of the on-line integrated modelling are considered: (i) improved numerical weather prediction with short-term feedbacks of aerosols and chemistry on formation and development of meteorological variables, and (ii) improved atmospheric composition forecasting with on-line integrated meteorological forecast and two-way feedbacks between aerosols/chemistry and meteorology. During 2015-2016 several research projects were realized. At first, the study on "On-line Meteorology-Chemistry/Aerosols Modelling and Integration for Risk Assessment: Case Studies" focused on assessment of scenarios with accidental and continuous emissions of sulphur dioxide for case studies for Atyrau (Kazakhstan) near the northern part of the Caspian Sea and metallurgical enterprises on the Kola Peninsula (Russia), with GIS integration of modelling results into the RANDOM (Risk Assessment of Nature Detriment due to Oil spill Migration) system. At second, the studies on "The sensitivity of precipitation simulations to the soot aerosol presence" & "The precipitation forecast sensitivity to data assimilation on a very high resolution domain" focused on sensitivity and changes in precipitation life-cycle under black carbon polluted conditions over Scandinavia. At third, studies on "Aerosol effects over China investigated with a high resolution convection permitting weather model" & "Meteorological and chemical urban scale modelling for Shanghai metropolitan area" with focus on aerosol effects and influence of urban areas in China at regional-subregional-urban scales. At fourth, study on "Direct variational data assimilation algorithm for atmospheric chemistry data with transport and transformation model" with focus on testing chemical data assimilation algorithm of in situ concentration measurements on real data scenario. At firth, study on "Aerosol influence on High Resolution NWP HARMONIE Operational Forecasts" with focus on impact of sea salt aerosols on numerical weather prediction during low precipitation events. And finally, study on "Impact of regional afforestation on climatic conditions in metropolitan areas: case study of Copenhagen" with focus on impact of forest and land-cover change on formation and development of temperature regimes in the Copenhagen metropolitan area of Denmark. Selected results and findings will be presented and discussed.

Numerical evaluation of electromagnetic fields due to dipole antennas in the presence of stratified media

NASA Technical Reports Server (NTRS)

Tsang, L.; Brown, R.; Kong, J. A.; Simmons, G.

1974-01-01

Two numerical methods are used to evaluate the integrals that express the em fields due to dipole antennas radiating in the presence of a stratified medium. The first method is a direct integration by means of Simpson's rule. The second method is indirect and approximates the kernel of the integral by means of the fast Fourier transform. In contrast to previous analytical methods that applied only to two-layer cases the numerical methods can be used for any arbitrary number of layers with general properties.

The three-body problem with short-range interactions

NASA Astrophysics Data System (ADS)

Nielsen, E.; Fedorov, D. V.; Jensen, A. S.; Garrido, E.

2001-06-01

The quantum mechanical three-body problem is studied for general short-range interactions. We work in coordinate space to facilitate accurate computations of weakly bound and spatially extended systems. Hyperspherical coordinates are used in both the interpretation and as an integral part of the numerical method. Universal properties and model independence are discussed throughout the report. We present an overview of the hyperspherical adiabatic Faddeev equations. The wave function is expanded on hyperspherical angular eigenfunctions which in turn are found numerically using the Faddeev equations. We generalize the formalism to any dimension of space d greater or equal to two. We present two numerical techniques for solving the Faddeev equations on the hypersphere. These techniques are effective for short and intermediate/large distances including use for hard core repulsive potentials. We study the asymptotic limit of large hyperradius and derive the analytic behaviour of the angular eigenvalues and eigenfunctions. We discuss four applications of the general method. We first analyze the Efimov and Thomas effects for arbitrary angular momenta and for arbitrary dimensions d. Second we apply the method to extract the general behaviour of weakly bound three-body systems in two dimensions. Third we illustrate the method in three dimensions by structure computations of Borromean halo nuclei, the hypertriton and helium molecules. Fourth we investigate in three dimensions three-body continuum properties of Borromean halo nuclei and recombination reactions of helium atoms as an example of direct relevance for the stability of Bose-Einstein condensates.

Intrinsic modulation of pulse-coupled integrate-and-fire neurons

NASA Astrophysics Data System (ADS)

Coombes, S.; Lord, G. J.

1997-11-01

Intrinsic neuromodulation is observed in sensory and neuromuscular circuits and in biological central pattern generators. We model a simple neuronal circuit with a system of two pulse-coupled integrate-and-fire neurons and explore the parameter regimes for periodic firing behavior. The inclusion of biologically realistic features shows that the speed and onset of neuronal response plays a crucial role in determining the firing phase for periodic rhythms. We explore the neurophysiological function of distributed delays arising from both the synaptic transmission process and dendritic structure as well as discrete delays associated with axonal communication delays. Bifurcation and stability diagrams are constructed with a mixture of simple analysis, numerical continuation and the Kuramoto phase-reduction technique. Moreover, we show that, for asynchronous behavior, the strength of electrical synapses can control the firing rate of the system.

A rapid boundary integral equation technique for protein electrostatics

NASA Astrophysics Data System (ADS)

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

2007-06-01

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

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2018-01-01

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe nonequilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations.

Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

NASA Astrophysics Data System (ADS)

Meng, Xiang-guo; Goan, Hsi-Sheng; Wang, Ji-suo; Zhang, Ran

2018-03-01

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V , d) , but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.

Maintenance Audit through Value Analysis Technique: A Case Study

NASA Astrophysics Data System (ADS)

Carnero, M. C.; Delgado, S.

2008-11-01

The increase in competitiveness, technological changes and the increase in the requirements of quality and service have forced a change in the design and application of maintenance, as well as the way in which it is considered within the managerial strategy. There are numerous maintenance activities that must be developed in a service company. As a result the maintenance functions as a whole have to be outsourced. Nevertheless, delegating this subject to specialized personnel does not exempt the company from responsibilities, but rather leads to the need for control of each maintenance activity. In order to achieve this control and to evaluate the efficiency and effectiveness of the company it is essential to carry out an audit that diagnoses the problems that could develop. In this paper a maintenance audit applied to a service company is developed. The methodology applied is based on the expert systems. The expert system by means of rules uses the weighting technique SMART and value analysis to obtain the weighting between the decision functions and between the alternatives. The expert system applies numerous rules and relations between different variables associated with the specific maintenance functions, to obtain the maintenance state by sections and the general maintenance state of the enterprise. The contributions of this paper are related to the development of a maintenance audit in a service enterprise, in which maintenance is not generally considered a strategic subject and to the integration of decision-making tools such as the weighting technique SMART with value analysis techniques, typical in the design of new products, in the area of the rule-based expert systems.

Fluid{Structure Interaction Modeling of Modified-Porosity Parachutes and Parachute Clusters

NASA Astrophysics Data System (ADS)

Boben, Joseph J.

To increase aerodynamic performance, the geometric porosity of a ringsail spacecraft parachute canopy is sometimes increased, beyond the "rings" and "sails" with hundreds of "ring gaps" and "sail slits." This creates extra computational challenges for fluid-structure interaction (FSI) modeling of clusters of such parachutes, beyond those created by the lightness of the canopy structure, geometric complexities of hundreds of gaps and slits, and the contact between the parachutes of the cluster. In FSI computation of parachutes with such "modified geometric porosity," the ow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the Homogenized Modeling of Geometric Porosity (HMGP), which was introduced to deal with the hundreds of gaps and slits. The ow needs to be actually resolved. All these computational challenges need to be addressed simultaneously in FSI modeling of clusters of spacecraft parachutes with modified geometric porosity. The core numerical technology is the Stabilized Space-Time FSI (SSTFSI) technique, and the contact between the parachutes is handled with the Surface-Edge-Node Contact Tracking (SENCT) technique. In the computations reported here, in addition to the SSTFSI and SENCT techniques and HMGP, we use the special techniques we have developed for removing the numerical spinning component of the parachute motion and for restoring the mesh integrity without a remesh. We present results for 2- and 3-parachute clusters with two different payload models. We also present the FSI computations we carried out for a single, subscale modified-porosity parachute.

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

On the use of the line integral in the numerical treatment of conservative problems

NASA Astrophysics Data System (ADS)

Brugnano, Luigi; Iavernaro, Felice

2016-06-01

We sketch out the use of the line integral as a tool to devise numerical methods suitable for conservative and, in particular, Hamiltonian problems. The monograph [3] presents the fundamental theory on line integral methods and this short note aims at exploring some aspects and results emerging from their study.

Andean Mountain Building: An Integrated Topographic, GPS, Seismological and Numerical Study

NASA Technical Reports Server (NTRS)

Liu, Mian; Stein, Seth

2003-01-01

The main objective of this project was to better understand the geodynamics controlling the mountain building and topographic evolution in the central Andes using an integrated approach that combines GPS, seismological, and numerical studies.

Liquid biopsy genotyping in lung cancer: ready for clinical utility?

PubMed

Huang, Wei-Lun; Chen, Yi-Lin; Yang, Szu-Chun; Ho, Chung-Liang; Wei, Fang; Wong, David T; Su, Wu-Chou; Lin, Chien-Chung

2017-03-14

Liquid biopsy is a blood test that detects evidence of cancer cells or tumor DNA in the circulation. Despite complicated collection methods and the requirement for technique-dependent platforms, it has generated substantial interest due, in part, to its potential to detect driver oncogenes such as epidermal growth factor receptor (EGFR) mutants in lung cancer. This technology is advancing rapidly and is being incorporated into numerous EGFR tyrosine kinase inhibitor (EGFR-TKI) development programs. It appears ready for integration into clinical care. Recent studies have demonstrated that biological fluids such as saliva and urine can also be used for detecting EGFR mutant DNA through application other user-friendly techniques. This review focuses on the clinical application of liquid biopsies to lung cancer genotyping, including EGFR and other targets of genotype-directed therapy and compares multiple platforms used for liquid biopsy.

Point-of-care ultrasound (POCUS): unnecessary gadgetry or evidence-based medicine?

PubMed

Smallwood, Nicholas; Dachsel, Martin

2018-06-01

Over the last decade there has been increasing interest and enthusiasm in point-of-care ultrasound (POCUS) as an aide to traditional examination techniques in assessing acutely unwell adult patients. However, it currently remains the domain of a relatively small handful of physicians within the UK. There are numerous reasons for this, notably a lack of training pathways and supervisors but also a lack of understanding of the evidence base behind this imaging modality. This review article aims to explore some of the evidence base behind POCUS for a number of medical pathologies, and where possible compare it to evidenced traditional examination techniques. We discuss the issues around training in bedside ultrasound and recommend a push to integrate POCUS training into internal medicine curricula and support trainers to comprehensively deliver this. © Royal College of Physicians 2018. All rights reserved.

Antenna theory: Analysis and design

NASA Astrophysics Data System (ADS)

Balanis, C. A.

The book's main objective is to introduce the fundamental principles of antenna theory and to apply them to the analysis, design, and measurements of antennas. In a description of antennas, the radiation mechanism is discussed along with the current distribution on a thin wire. Fundamental parameters of antennas are examined, taking into account the radiation pattern, radiation power density, radiation intensity, directivity, numerical techniques, gain, antenna efficiency, half-power beamwidth, beam efficiency, bandwidth, polarization, input impedance, and antenna temperature. Attention is given to radiation integrals and auxiliary potential functions, linear wire antennas, loop antennas, linear and circular arrays, self- and mutual impedances of linear elements and arrays, broadband dipoles and matching techniques, traveling wave and broadband antennas, frequency independent antennas and antenna miniaturization, the geometrical theory of diffraction, horns, reflectors and lens antennas, antenna synthesis and continuous sources, and antenna measurements.

Using remote sensing and GIS techniques to estimate discharge and recharge. fluxes for the Death Valley regional groundwater flow system, USA

USGS Publications Warehouse

D'Agnese, F. A.; Faunt, C.C.; Keith, Turner A.

1996-01-01

The recharge and discharge components of the Death Valley regional groundwater flow system were defined by remote sensing and GIS techniques that integrated disparate data types to develop a spatially complex representation of near-surface hydrological processes. Image classification methods were applied to multispectral satellite data to produce a vegetation map. This map provided a basis for subsequent evapotranspiration and infiltration estimations. The vegetation map was combined with ancillary data in a GIS to delineate different types of wetlands, phreatophytes and wet playa areas. Existing evapotranspiration-rate estimates were then used to calculate discharge volumes for these areas. A previously used empirical method of groundwater recharge estimation was modified by GIS methods to incorporate data describing soil-moisture conditions, and a recharge potential map was produced. These discharge and recharge maps were readily converted to data arrays for numerical modelling codes. Inverse parameter estimation techniques also used these data to evaluate the reliability and sensitivity of estimated values.

Agent independent task planning

NASA Technical Reports Server (NTRS)

Davis, William S.

1990-01-01

Agent-Independent Planning is a technique that allows the construction of activity plans without regard to the agent that will perform them. Once generated, a plan is then validated and translated into instructions for a particular agent, whether a robot, crewmember, or software-based control system. Because Space Station Freedom (SSF) is planned for orbital operations for approximately thirty years, it will almost certainly experience numerous enhancements and upgrades, including upgrades in robotic manipulators. Agent-Independent Planning provides the capability to construct plans for SSF operations, independent of specific robotic systems, by combining techniques of object oriented modeling, nonlinear planning and temporal logic. Since a plan is validated using the physical and functional models of a particular agent, new robotic systems can be developed and integrated with existing operations in a robust manner. This technique also provides the capability to generate plans for crewmembers with varying skill levels, and later apply these same plans to more sophisticated robotic manipulators made available by evolutions in technology.

Feasibility study of solid surface subreflector production techniques

NASA Technical Reports Server (NTRS)

1982-01-01

The principal effort was to study technical feasibility and cost aspects of the production technique of spin forming a subreflector reflective surface to a desired surface of revolution, back the surface with fiberglass to stabilize it sufficiently so that it may be machined to the target surface tolerance of .008 inches Root Mean Square (RMS) with a goal of .003 inches RMS. To verify this production technique, analyses was performed to define the production procedure. A price estimate for a 150 inch diameter subreflector for a 34 meter cassegrain antenna. During this feasibility study, numerous production processes were evaluated theoretically as production approaches for single surface, non-welded subreflectors. The first successful was the principal process of spin forming the reflective surface, backing with fiberglass and machining to a final contour. The second successful process was spin forming or bump forming a thicker reflective surface, with an integral (welded in) structure as a backing and machining the mounting pads and reflector to a final configuration.

A reference web architecture and patterns for real-time visual analytics on large streaming data

NASA Astrophysics Data System (ADS)

Kandogan, Eser; Soroker, Danny; Rohall, Steven; Bak, Peter; van Ham, Frank; Lu, Jie; Ship, Harold-Jeffrey; Wang, Chun-Fu; Lai, Jennifer

2013-12-01

Monitoring and analysis of streaming data, such as social media, sensors, and news feeds, has become increasingly important for business and government. The volume and velocity of incoming data are key challenges. To effectively support monitoring and analysis, statistical and visual analytics techniques need to be seamlessly integrated; analytic techniques for a variety of data types (e.g., text, numerical) and scope (e.g., incremental, rolling-window, global) must be properly accommodated; interaction, collaboration, and coordination among several visualizations must be supported in an efficient manner; and the system should support the use of different analytics techniques in a pluggable manner. Especially in web-based environments, these requirements pose restrictions on the basic visual analytics architecture for streaming data. In this paper we report on our experience of building a reference web architecture for real-time visual analytics of streaming data, identify and discuss architectural patterns that address these challenges, and report on applying the reference architecture for real-time Twitter monitoring and analysis.