Probabilistic numerics and uncertainty in computations

PubMed Central

Hennig, Philipp; Osborne, Michael A.; Girolami, Mark

2015-01-01

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations. PMID:26346321

Probabilistic numerics and uncertainty in computations.

PubMed

Hennig, Philipp; Osborne, Michael A; Girolami, Mark

2015-07-08

We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

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.

Hierarchical data-driven approach to fitting numerical relativity data for nonprecessing binary black holes with an application to final spin and radiated energy

NASA Astrophysics Data System (ADS)

Jiménez-Forteza, Xisco; Keitel, David; Husa, Sascha; Hannam, Mark; Khan, Sebastian; Pürrer, Michael

2017-03-01

Numerical relativity is an essential tool in studying the coalescence of binary black holes (BBHs). It is still computationally prohibitive to cover the BBH parameter space exhaustively, making phenomenological fitting formulas for BBH waveforms and final-state properties important for practical applications. We describe a general hierarchical bottom-up fitting methodology to design and calibrate fits to numerical relativity simulations for the three-dimensional parameter space of quasicircular nonprecessing merging BBHs, spanned by mass ratio and by the individual spin components orthogonal to the orbital plane. Particular attention is paid to incorporating the extreme-mass-ratio limit and to the subdominant unequal-spin effects. As an illustration of the method, we provide two applications, to the final spin and final mass (or equivalently: radiated energy) of the remnant black hole. Fitting to 427 numerical relativity simulations, we obtain results broadly consistent with previously published fits, but improving in overall accuracy and particularly in the approach to extremal limits and for unequal-spin configurations. We also discuss the importance of data quality studies when combining simulations from diverse sources, how detailed error budgets will be necessary for further improvements of these already highly accurate fits, and how this first detailed study of unequal-spin effects helps in choosing the most informative parameters for future numerical relativity runs.

A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.

PubMed

Ling, Hong; Luo, Ercang; Dai, Wei

2006-12-22

Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.

Final Report of the Project "From the finite element method to the virtual element method"

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

Manzini, Gianmarco; Gyrya, Vitaliy

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for themore » numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.« less

The vibroacoustic response and sound absorption performance of multilayer, microperforated rib-stiffened plates

NASA Astrophysics Data System (ADS)

Zhou, Haian; Wang, Xiaoming; Wu, Huayong; Meng, Jianbing

2017-10-01

The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed. In this structure, all plates are two-dimensional, microperforated, and periodically rib-stiffened. To investigate such a structural system, semianalytical models of one-layer and multilayer plate structures considering the vibration effects are first developed. Then approaches of the space harmonic method and Fourier transforms are applied to a one-layer plate, and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas, the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties, the equations of the sound pressures and absorption coefficients for the one-layer and multilayer stiffened plates in physical space are finally derived. Using numerical examples, the effects of the most important physical parameters—for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing—on sound absorption performance are examined. Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water. Finally, the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.

Dual-mode nested search method for categorical uncertain multi-objective optimization

NASA Astrophysics Data System (ADS)

Tang, Long; Wang, Hu

2016-10-01

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.

A third-order approximation method for three-dimensional wheel-rail contact

NASA Astrophysics Data System (ADS)

Negretti, Daniele

2012-03-01

Multibody train analysis is used increasingly by railway operators whenever a reliable and time-efficient method to evaluate the contact between wheel and rail is needed; particularly, the wheel-rail contact is one of the most important aspects that affects a reliable and time-efficient vehicle dynamics computation. The focus of the approach proposed here is to carry out such tasks by means of online wheel-rail elastic contact detection. In order to improve efficiency and save time, a main analytical approach is used for the definition of wheel and rail surfaces as well as for contact detection, then a final numerical evaluation is used to locate contact. The final numerical procedure consists in finding the zeros of a nonlinear function in a single variable. The overall method is based on the approximation of the wheel surface, which does not influence the contact location significantly, as shown in the paper.

Comment on 'Shang S. 2012. Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes 26: 3338-3343. DOI: 10.1002/hyp.8405'

NASA Technical Reports Server (NTRS)

Yatheendradas, Soni; Narapusetty, Balachandrudu; Peters-Lidard, Christa; Funk, Christopher; Verdin, James

2014-01-01

A previous study analyzed errors in the numerical calculation of actual crop evapotranspiration (ET(sub a)) under soil water stress. Assuming no irrigation or precipitation, it constructed equations for ET(sub a) over limited soil-water ranges in a root zone drying out due to evapotranspiration. It then used a single crop-soil composite to provide recommendations about the appropriate usage of numerical methods under different values of the time step and the maximum crop evapotranspiration (ET(sub c)). This comment reformulates those ET(sub a) equations for applicability over the full range of soil water values, revealing a dependence of the relative error in numerical ET(sub a) on the initial soil water that was not seen in the previous study. It is shown that the recommendations based on a single crop-soil composite can be invalid for other crop-soil composites. Finally, a consideration of the numerical error in the time-cumulative value of ET(sub a) is discussed besides the existing consideration of that error over individual time steps as done in the previous study. This cumulative ET(sub a) is more relevant to the final crop yield.

Non-nuclear methods for HMA density measurements : final report, June 2008.

DOT National Transportation Integrated Search

2008-05-01

Non-nuclear methods for the measurement of hot-mix asphalt (HMA) density offer the ability to take numerous density readings in a very short period of time, without the need for intensive licensing, training, and maintenance efforts common to nuclear...

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

NASA Astrophysics Data System (ADS)

Mamehrashi, K.; Yousefi, S. A.

2017-02-01

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

Numerical study of influence of hydrogen backflow on krypton Hall effect thruster plasma focusing

NASA Astrophysics Data System (ADS)

Yan, Shilin; Ding, Yongjie; Wei, Liqiu; Hu, Yanlin; Li, Jie; Ning, Zhongxi; Yu, Daren

2017-03-01

The influence of backflow hydrogen on plasma plume focusing of a krypton Hall effect thruster is studied via a numerical simulation method. Theoretical analysis indicates that hydrogen participates in the plasma discharge process, changes the potential and ionization distribution in the thruster discharge cavity, and finally affects the plume focusing within a vacuum vessel.

Numerical and experimental validation of a particle Galerkin method for metal grinding simulation

NASA Astrophysics Data System (ADS)

Wu, C. T.; Bui, Tinh Quoc; Wu, Youcai; Luo, Tzui-Liang; Wang, Morris; Liao, Chien-Chih; Chen, Pei-Yin; Lai, Yu-Sheng

2018-03-01

In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach.

Numerical Simulation of Particle Motion in a Curved Channel

NASA Astrophysics Data System (ADS)

Liu, Yi; Nie, Deming

2018-01-01

In this work the lattice Boltzmann method (LBM) is used to numerically study the motion of a circular particle in a curved channel at intermediate Reynolds numbers (Re). The effects of the Reynolds number and the initial particle position are taken into account. Numerical results include the streamlines, particle trajectories and final equilibrium positions. It has been found that the particle is likely to migrate to a similar equilibrium position irrespective of its initial position when Re is large.

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

New approach to canonical partition functions computation in Nf=2 lattice QCD at finite baryon density

NASA Astrophysics Data System (ADS)

Bornyakov, V. G.; Boyda, D. L.; Goy, V. A.; Molochkov, A. V.; Nakamura, Atsushi; Nikolaev, A. A.; Zakharov, V. I.

2017-05-01

We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential i μq I . Then we restore the grand canonical partition function for imaginary chemical potential using the fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using the known method of the hopping parameter expansion and compare results obtained by two methods in the deconfining as well as in the confining phases. The agreement between two methods indicates the validity of the new method. Our numerical results are obtained in two flavor lattice QCD with clover improved Wilson fermions.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Geometric versus numerical optimal control of a dissipative spin-(1/2) particle

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

Lapert, M.; Sugny, D.; Zhang, Y.

2010-12-15

We analyze the saturation of a nuclear magnetic resonance (NMR) signal using optimal magnetic fields. We consider both the problems of minimizing the duration of the control and its energy for a fixed duration. We solve the optimal control problems by using geometric methods and a purely numerical approach, the grape algorithm, the two methods being based on the application of the Pontryagin maximum principle. A very good agreement is obtained between the two results. The optimal solutions for the energy-minimization problem are finally implemented experimentally with available NMR techniques.

Advanced wave field sensing using computational shear interferometry

NASA Astrophysics Data System (ADS)

Falldorf, Claas; Agour, Mostafa; Bergmann, Ralf B.

2014-07-01

In this publication we give a brief introduction into the field of Computational Shear Interferometry (CoSI), which allows for determining arbitrary wave fields from a set of shear interferograms. We discuss limitations of the method with respect to the coherence of the underlying wave field and present various numerical methods to recover it from its sheared representations. Finally, we show experimental results on Digital Holography of objects with rough surface using a fiber coupled light emitting diode and quantitative phase contrast imaging as well as numerical refocusing in Differential Interference Contrast (DIC) microscopy.

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Numerical Simulations Of Flagellated Micro-Swimmers

NASA Astrophysics Data System (ADS)

Rorai, Cecilia; Markesteijn, Anton; Zaitstev, Mihail; Karabasov, Sergey

2017-11-01

We study flagellated microswimmers locomotion by representing the entire swimmer body. We discuss and contrast the accuracy and computational cost of different numerical approaches including the Resistive Force Theory, the Regularized Stokeslet Method and the Finite Element Method. We focus on how the accuracy of the methods in reproducing the swimming trajectories, velocities and flow field, compares to the sensitivity of these quantities to certain physical parameters, such as the body shape and the location of the center of mass. We discuss the opportunity and physical relevance of retaining inertia in our models. Finally, we present some preliminary results toward collective motion simulations. Marie Skodowska-Curie Individual Fellowship.

A new smoothing modified three-term conjugate gradient method for [Formula: see text]-norm minimization problem.

PubMed

Du, Shouqiang; Chen, Miao

2018-01-01

We consider a kind of nonsmooth optimization problems with [Formula: see text]-norm minimization, which has many applications in compressed sensing, signal reconstruction, and the related engineering problems. Using smoothing approximate techniques, this kind of nonsmooth optimization problem can be transformed into a general unconstrained optimization problem, which can be solved by the proposed smoothing modified three-term conjugate gradient method. The smoothing modified three-term conjugate gradient method is based on Polak-Ribière-Polyak conjugate gradient method. For the Polak-Ribière-Polyak conjugate gradient method has good numerical properties, the proposed method possesses the sufficient descent property without any line searches, and it is also proved to be globally convergent. Finally, the numerical experiments show the efficiency of the proposed method.

A new fictitious domain approach for Stokes equation

NASA Astrophysics Data System (ADS)

Yang, Min

2017-10-01

The purpose of this paper is to present a new fictitious domain approach based on the Nietzsche’s method combining with a penalty method for the Stokes equation. This method allows for an easy and flexible handling of the geometrical aspects. Stability and a priori error estimate are proved. Finally, a numerical experiment is provided to verify the theoretical findings.

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.

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

A Fourier-based total-field/scattered-field technique for three-dimensional broadband simulations of elastic targets near a water-sand interface.

PubMed

Shao, Yu; Wang, Shumin

2016-12-01

The numerical simulation of acoustic scattering from elastic objects near a water-sand interface is critical to underwater target identification. Frequency-domain methods are computationally expensive, especially for large-scale broadband problems. A numerical technique is proposed to enable the efficient use of finite-difference time-domain method for broadband simulations. By incorporating a total-field/scattered-field boundary, the simulation domain is restricted inside a tightly bounded region. The incident field is further synthesized by the Fourier transform for both subcritical and supercritical incidences. Finally, the scattered far field is computed using a half-space Green's function. Numerical examples are further provided to demonstrate the accuracy and efficiency of the proposed technique.

Numerical simulation study on rolling-chemical milling process of aluminum-lithium alloy skin panel

NASA Astrophysics Data System (ADS)

Huang, Z. B.; Sun, Z. G.; Sun, X. F.; Li, X. Q.

2017-09-01

Single curvature parts such as aircraft fuselage skin panels are usually manufactured by rolling-chemical milling process, which is usually faced with the problem of geometric accuracy caused by springback. In most cases, the methods of manual adjustment and multiple roll bending are used to control or eliminate the springback. However, these methods can cause the increase of product cost and cycle, and lead to material performance degradation. Therefore, it is of significance to precisely control the springback of rolling-chemical milling process. In this paper, using the method of experiment and numerical simulation on rolling-chemical milling process, the simulation model for rolling-chemical milling process of 2060-T8 aluminum-lithium alloy skin was established and testified by the comparison between numerical simulation and experiment results for the validity. Then, based on the numerical simulation model, the relative technological parameters which influence on the curvature of the skin panel were analyzed. Finally, the prediction of springback and the compensation can be realized by controlling the process parameters.

Experimental and numerical investigations of wire bending by linear winding of rectangular tooth coils

NASA Astrophysics Data System (ADS)

Komodromos, A.; Tekkaya, A. E.; Hofmann, J.; Fleischer, J.

2018-05-01

Since electric motors are gaining in importance in many fields of application, e.g. hybrid electric vehicles, optimization of the linear coil winding process greatly contributes to an increase in productivity and flexibility. For the investigation of the forming behavior of the winding wire the material behavior is characterized in different experimental setups. Numerical examinatons of the linear winding process are carried out in a case study for a rectangular bobbin in order to analyze the influence of forming parameters on the resulting properties of the wound coil. Besides the numerical investigation of the linear winding method by using the finite element method (FEM), a multi-body dynamics (MBD) simulation is carried out. The multi-body dynamics simulation is necessary to represent the movement of the bodies as well as the connection of the components during winding. The finite element method is used to represent the material behavior of the copper wire and the plastic strain distribution within the wire. It becomes clear that the MBD simulation is not sufficient for analyzing the process and the wire behavior in its entirety. Important parameters that define the final coil properties cannot be analyzed in the manner of a precise manifestation, e.g. the clearance between coil bobbin and wire as well as the wire deformation behavior in form of a diameter reduction which negatively affects the ohmic resistance. Finally, the numerical investigations are validated experimentally by linear winding tests.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates

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

Wang, Hanquan, E-mail: hanquan.wang@gmail.com; Yunnan Tongchang Scientific Computing and Data Mining Research Center, Kunming, Yunnan Province, 650221

In this paper, a projection gradient method is presented for computing ground state of spin-2 Bose–Einstein condensates (BEC). We first propose the general projection gradient method for solving energy functional minimization problem under multiple constraints, in which the energy functional takes real functions as independent variables. We next extend the method to solve a similar problem, where the energy functional now takes complex functions as independent variables. We finally employ the method into finding the ground state of spin-2 BEC. The key of our method is: by constructing continuous gradient flows (CGFs), the ground state of spin-2 BEC can bemore » computed as the steady state solution of such CGFs. We discretized the CGFs by a conservative finite difference method along with a proper way to deal with the nonlinear terms. We show that the numerical discretization is normalization and magnetization conservative and energy diminishing. Numerical results of the ground state and their energy of spin-2 BEC are reported to demonstrate the effectiveness of the numerical method.« less

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

A methodology for designing aircraft to low sonic boom constraints

NASA Technical Reports Server (NTRS)

Mack, Robert J.; Needleman, Kathy E.

1991-01-01

A method for designing conceptual supersonic cruise aircraft to meet low sonic boom requirements is outlined and described. The aircraft design is guided through a systematic evolution from initial three view drawing to a final numerical model description, while the designer using the method controls the integration of low sonic boom, high supersonic aerodynamic efficiency, adequate low speed handling, and reasonable structure and materials technologies. Some experience in preliminary aircraft design and in the use of various analytical and numerical codes is required for integrating the volume and lift requirements throughout the design process.

Pull-out fibers from composite materials at high rate of loading

NASA Technical Reports Server (NTRS)

Amijima, S.; Fujii, T.

1981-01-01

Numerical and experimental results are presented on the pullout phenomenon in composite materials at a high rate of loading. The finite element method was used, taking into account the existence of a virtual shear deformation layer as the interface between fiber and matrix. Experimental results agree well with those obtained by the finite element method. Numerical results show that the interlaminar shear stress is time dependent, in addition, it is shown to depend on the applied load time history. Under step pulse loading, the interlaminar shear stress fluctuates, finally decaying to its value under static loading.

Final Report for''Numerical Methods and Studies of High-Speed Reactive and Non-Reactive Flows''

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

Schwendeman, D W

2002-11-20

The work carried out under this subcontract involved the development and use of an adaptive numerical method for the accurate calculation of high-speed reactive flows on overlapping grids. The flow is modeled by the reactive Euler equations with an assumed equation of state and with various reaction rate models. A numerical method has been developed to solve the nonlinear hyperbolic partial differential equations in the model. The method uses an unsplit, shock-capturing scheme, and uses a Godunov-type scheme to compute fluxes and a Runge-Kutta error control scheme to compute the source term modeling the chemical reactions. An adaptive mesh refinementmore » (AMR) scheme has been implemented in order to locally increase grid resolution. The numerical method uses composite overlapping grids to handle complex flow geometries. The code is part of the ''Overture-OverBlown'' framework of object-oriented codes [1, 2], and the development has occurred in close collaboration with Bill Henshaw and David Brown, and other members of the Overture team within CASC. During the period of this subcontract, a number of tasks were accomplished, including: (1) an extension of the numerical method to handle ''ignition and grow'' reaction models and a JWL equations of state; (2) an improvement in the efficiency of the AMR scheme and the error estimator; (3) an addition of a scheme of numerical dissipation designed to suppress numerical oscillations/instabilities near expanding detonations and along grid overlaps; and (4) an exploration of the evolution to detonation in an annulus and of detonation failure in an expanding channel.« less

The development and application of CFD technology in mechanical engineering

NASA Astrophysics Data System (ADS)

Wei, Yufeng

2017-12-01

Computational Fluid Dynamics (CFD) is an analysis of the physical phenomena involved in fluid flow and heat conduction by computer numerical calculation and graphical display. The numerical method simulates the complexity of the physical problem and the precision of the numerical solution, which is directly related to the hardware speed of the computer and the hardware such as memory. With the continuous improvement of computer performance and CFD technology, it has been widely applied to the field of water conservancy engineering, environmental engineering and industrial engineering. This paper summarizes the development process of CFD, the theoretical basis, the governing equations of fluid mechanics, and introduces the various methods of numerical calculation and the related development of CFD technology. Finally, CFD technology in the mechanical engineering related applications are summarized. It is hoped that this review will help researchers in the field of mechanical engineering.

A new numerical approximation of the fractal ordinary differential equation

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Final Report DE-FG02-07ER64416

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

Seymour, Joseph D.

The document provides the Final Report for DE-FG02-07ER64416 on the use of magnetic resonance (MR) methods to quantify transport in porous media impacted by biological and chemical processes. Products resulting from the research in the form of peer reviewed publications and conference presentations are presented. The research correlated numerical simulations and MR measurements to test simulation methodology. Biofilm and uranium detection by MR was demonstrated.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

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.

Computation of rare transitions in the barotropic quasi-geostrophic equations

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bouchet, Freddy

2015-01-01

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager-Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Comparing Methods for Assessing Reliability Uncertainty Based on Pass/Fail Data Collected Over Time

DOE PAGES

Abes, Jeff I.; Hamada, Michael S.; Hills, Charles R.

2017-12-20

In this paper, we compare statistical methods for analyzing pass/fail data collected over time; some methods are traditional and one (the RADAR or Rationale for Assessing Degradation Arriving at Random) was recently developed. These methods are used to provide uncertainty bounds on reliability. We make observations about the methods' assumptions and properties. Finally, we illustrate the differences between two traditional methods, logistic regression and Weibull failure time analysis, and the RADAR method using a numerical example.

Comparing Methods for Assessing Reliability Uncertainty Based on Pass/Fail Data Collected Over Time

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

Abes, Jeff I.; Hamada, Michael S.; Hills, Charles R.

In this paper, we compare statistical methods for analyzing pass/fail data collected over time; some methods are traditional and one (the RADAR or Rationale for Assessing Degradation Arriving at Random) was recently developed. These methods are used to provide uncertainty bounds on reliability. We make observations about the methods' assumptions and properties. Finally, we illustrate the differences between two traditional methods, logistic regression and Weibull failure time analysis, and the RADAR method using a numerical example.

The 3-D numerical simulation research of vacuum injector for linear induction accelerator

NASA Astrophysics Data System (ADS)

Liu, Dagang; Xie, Mengjun; Tang, Xinbing; Liao, Shuqing

2017-01-01

Simulation method for voltage in-feed and electron injection of vacuum injector is given, and verification of the simulated voltage and current is carried out. The numerical simulation for the magnetic field of solenoid is implemented, and a comparative analysis is conducted between the simulation results and experimental results. A semi-implicit difference algorithm is adopted to suppress the numerical noise, and a parallel acceleration algorithm is used for increasing the computation speed. The RMS emittance calculation method of the beam envelope equations is analyzed. In addition, the simulated results of RMS emittance are compared with the experimental data. Finally, influences of the ferromagnetic rings on the radial and axial magnetic fields of solenoid as well as the emittance of beam are studied.

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

Methods, Software and Tools for Three Numerical Applications. Final report

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

E. R. Jessup

2000-03-01

This is a report of the results of the authors work supported by DOE contract DE-FG03-97ER25325. They proposed to study three numerical problems. They are: (1) the extension of the PMESC parallel programming library; (2) the development of algorithms and software for certain generalized eigenvalue and singular value (SVD) problems, and (3) the application of techniques of linear algebra to an information retrieval technique known as latent semantic indexing (LSI).

Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method

PubMed Central

Wu, Fengyuan; Fan, Yunyun; Liang, Li; Wang, Chao

2016-01-01

This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures. PMID:27513661

Hierarchical semi-numeric method for pairwise fuzzy group decision making.

PubMed

Marimin, M; Umano, M; Hatono, I; Tamura, H

2002-01-01

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Imaging quality analysis of computer-generated holograms using the point-based method and slice-based method

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Chen, Siqing; Zheng, Huadong; Sun, Tao; Yu, Yingjie; Gao, Hongyue; Asundi, Anand K.

2017-06-01

Computer holography has made a notably progress in recent years. The point-based method and slice-based method are chief calculation algorithms for generating holograms in holographic display. Although both two methods are validated numerically and optically, the differences of the imaging quality of these methods have not been specifically analyzed. In this paper, we analyze the imaging quality of computer-generated phase holograms generated by point-based Fresnel zone plates (PB-FZP), point-based Fresnel diffraction algorithm (PB-FDA) and slice-based Fresnel diffraction algorithm (SB-FDA). The calculation formula and hologram generation with three methods are demonstrated. In order to suppress the speckle noise, sequential phase-only holograms are generated in our work. The results of reconstructed images numerically and experimentally are also exhibited. By comparing the imaging quality, the merits and drawbacks with three methods are analyzed. Conclusions are given by us finally.

A numerical method for simulations of rigid fiber suspensions

NASA Astrophysics Data System (ADS)

Tornberg, Anna-Karin; Gustavsson, Katarina

2006-06-01

In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

2018-01-01

In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

Detection of Orbital Debris Collision Risks for the Automated Transfer Vehicle

NASA Technical Reports Server (NTRS)

Peret, L.; Legendre, P.; Delavault, S.; Martin, T.

2007-01-01

In this paper, we present a general collision risk assessment method, which has been applied through numerical simulations to the Automated Transfer Vehicle (ATV) case. During ATV ascent towards the International Space Station, close approaches between the ATV and objects of the USSTRACOM catalog will be monitored through collision rosk assessment. Usually, collision risk assessment relies on an exclusion volume or a probability threshold method. Probability methods are more effective than exclusion volumes but require accurate covariance data. In this work, we propose to use a criterion defined by an adaptive exclusion area. This criterion does not require any probability calculation but is more effective than exclusion volume methods as demonstrated by our numerical experiments. The results of these studies, when confirmed and finalized, will be used for the ATV operations.

A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations

PubMed Central

Jabbari, Mohammad Hadi; Sayehbani, Mesbah; Reisinezhad, Arsham

2013-01-01

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear finite element method in spatial discretization, an auxiliary variable is hereby introduced, and a particular numerical scheme is offered to rewrite the equations in lower-order form. Stability of the suggested numerical method is also analyzed. Subsequently, in order to display the ability of the presented model, four different test cases are considered. In these test cases, dispersive and nonlinearity effects of the periodic waves over sloping beaches and barred beaches, which are the common coastal profiles, are investigated. Outputs are compared with other existing numerical and experimental data. Finally, it is concluded that the current model can be further developed to model any morphological development of coastal profiles. PMID:23853534

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

NASA Astrophysics Data System (ADS)

Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

2009-10-01

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

Numerical analysis of laser ablation using the axisymmetric two-temperature model

NASA Astrophysics Data System (ADS)

Dziatkiewicz, Jolanta; Majchrzak, Ewa

2018-01-01

Laser ablation of the axisymmetric micro-domain is analyzed. To describe the thermal processes occurring in the micro-domain the two-temperature hyperbolic model supplemented by the boundary and initial conditions is used. This model takes into account the phase changes of material (solid-liquid and liquid-vapour) and the ablation process. At the stage of numerical computations the finite difference method with staggered grid is used. In the final part the results of computations are shown.

Neighboring extremal optimal control design including model mismatch errors

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

Kim, T.J.; Hull, D.G.

1994-11-01

The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.

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.

Further Studies of the NRL Collective Particle Accelerator VIA Numerical Modeling with the MAGIC Code.

DTIC Science & Technology

1984-08-01

COLLFCTIVF PAPTTCLE ACCELERATOR VIA NUMERICAL MODFLINC WITH THF MAGIC CODE Robert 1. Darker Auqust 19F4 Final Report for Period I April. qI84 - 30...NUMERICAL MODELING WITH THE MAGIC CODE Robert 3. Barker August 1984 Final Report for Period 1 April 1984 - 30 September 1984 Prepared for: Scientific...Collective Final Report Particle Accelerator VIA Numerical Modeling with April 1 - September-30, 1984 MAGIC Code. 6. PERFORMING ORG. REPORT NUMBER MRC/WDC-R

UOE Pipe Numerical Model: Manufacturing Process And Von Mises Residual Stresses Resulted After Each Technological Step

NASA Astrophysics Data System (ADS)

Delistoian, Dmitri; Chirchor, Mihael

2017-12-01

Fluid transportation from production areas to final customer is effectuated by pipelines. For oil and gas industry, pipeline safety and reliability represents a priority. From this reason, pipe quality guarantee directly influence pipeline designed life, but first of all protects environment. A significant number of longitudinally welded pipes, for onshore/offshore pipelines, are manufactured by UOE method. This method is based on cold forming. In present study, using finite element method is modeled UOE pipe manufacturing process and is obtained von Mises stresses for each step. Numerical simulation is performed for L415 MB (X60) steel plate with 7,9 mm thickness, length 30 mm and width 1250mm, as result it is obtained a DN 400 pipe.

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

A 1D radiative transfer benchmark with polarization via doubling and adding

NASA Astrophysics Data System (ADS)

Ganapol, B. D.

2017-11-01

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1992-01-01

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Sheykhi, Ahmad; Hashemi Asl, Doa; Dehyadegari, Amin

2018-06-01

We investigate analytically as well as numerically the properties of s-wave holographic superconductors in d-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of this kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, ρ, and disclose the effects of both nonlinear parameter b and the dimensions of spacetime, d, on the critical temperature Tc. We find that in each dimension, Tc /ρ 1 / (d - 2) decreases with increasing the nonlinear parameter b while it increases with increasing the dimension of spacetime for a fixed value of b. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the dimensionless condensation get larger with increasing the nonlinear parameter b. Besides, for a fixed value of b, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact further supports the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension.

Triangular dislocation: an analytical, artefact-free solution

NASA Astrophysics Data System (ADS)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Generalized Gilat-Raubenheimer method for density-of-states calculation in photonic crystals

NASA Astrophysics Data System (ADS)

Liu, Boyuan; Johnson, Steven G.; Joannopoulos, John D.; Lu, Ling

2018-04-01

An efficient numerical algorithm is the key for accurate evaluation of density of states (DOS) in band theory. The Gilat-Raubenheimer (GR) method proposed in 1966 is an efficient linear extrapolation method which was limited in specific lattices. Here, using an affine transformation, we provide a new generalization of the original GR method to any Bravais lattices and show that it is superior to the tetrahedron method and the adaptive Gaussian broadening method. Finally, we apply our generalized GR method to compute DOS of various gyroid photonic crystals of topological degeneracies.

A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

NASA Astrophysics Data System (ADS)

Ma, Lin

2017-11-01

This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.

New variational principles for locating periodic orbits of differential equations.

PubMed

Boghosian, Bruce M; Fazendeiro, Luis M; Lätt, Jonas; Tang, Hui; Coveney, Peter V

2011-06-13

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.

Effects of gas temperature on nozzle damping experiments on cold-flow rocket motors

NASA Astrophysics Data System (ADS)

Sun, Bing-bing; Li, Shi-peng; Su, Wan-xing; Li, Jun-wei; Wang, Ning-fei

2016-09-01

In order to explore the impact of gas temperature on the nozzle damping characteristics of solid rocket motor, numerical simulations were carried out by an experimental motor in Naval Ordnance Test Station of China Lake in California. Using the pulse decay method, different cases were numerically studied via Fluent along with UDF (User Defined Functions). Firstly, mesh sensitivity analysis and monitor position-independent analysis were carried out for the computer code validation. Then, the numerical method was further validated by comparing the calculated results and experimental data. Finally, the effects of gas temperature on the nozzle damping characteristics were studied in this paper. The results indicated that the gas temperature had cooperative effects on the nozzle damping and there had great differences between cold flow and hot fire test. By discussion and analysis, it was found that the changing of mainstream velocity and the natural acoustic frequency resulted from gas temperature were the key factors that affected the nozzle damping, while the alteration of the mean pressure had little effect. Thus, the high pressure condition could be replaced by low pressure to reduce the difficulty of the test. Finally, the relation of the coefficients "alpha" between the cold flow and hot fire was got.

First-order reactant in homogeneous turbulence before the final period of decay. [contaminant fluctuations in chemical reaction

NASA Technical Reports Server (NTRS)

Kumar, P.; Patel, S. R.

1974-01-01

A method is described for studying theoretically the concentration fluctuations of a dilute contaminate undergoing a first-order chemical reaction. The method is based on Deissler's (1958) theory for homogeneous turbulence for times before the final period, and it follows the approach used by Loeffler and Deissler (1961) to study temperature fluctuations in homogeneous turbulence. Four-point correlation equations are obtained; it is assumed that terms containing fifth-order correlation are very small in comparison with those containing fourth-order correlations, and can therefore be neglected. A spectrum equation is obtained in a form which can be solved numerically, yielding the decay law for the concentration fluctuations in homogeneous turbulence for the period much before the final period of decay.

How to Overcome Numerical Challenges to Modeling Stirling Engines

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.

2004-01-01

Nuclear thermal to electric power conversion carries the promise of longer duration missions and higher scientific data transmission rates back to Earth for a range of missions, including both Mars rovers and deep space missions. A free-piston Stirling convertor is a candidate technology that is considered an efficient and reliable power conversion device for such purposes. While already very efficient, it is believed that better Stirling engines can be developed if the losses inherent in current designs could be better understood. However, they are difficult to instrument and so efforts are underway to simulate a complete Stirling engine numerically. This has only recently been attempted and a review of the methods leading up to and including such computational analysis is presented. And finally it is proposed that the quality and depth of Stirling loss understanding may be improved by utilizing the higher fidelity and efficiency of recently developed numerical methods. One such method, the Ultra HI-FI technique is presented in detail.

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.

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

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

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

SOME CURRENT TRENDS IN NUMERICAL METHODS FOR TRANSIENT ACOUSTIC AND ELASTIC WAVES IN MULTIDIMENSIONAL INHOMOGENEOUS MEDIA. (R825225)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

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

Berti, Emanuele; Cardoso, Vitor; Gonzalez, Jose A.

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M{sub 2}/M{sub 1}=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phasemore » scales like {eta}{sup 2} and the spin of the final black hole scales like {eta}, where {eta}=q/(1+q){sup 2} is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.« less

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

A numerical study of mobility in thin films of fullerene derivatives.

PubMed

Mackenzie, Roderick C I; Frost, Jarvist M; Nelson, Jenny

2010-02-14

The effect of functional group size on the electron mobility in films of fullerene derivatives is investigated numerically. A series of four C(60) derivatives are formed by attaching saturated hydrocarbon chains to the C(60) cage via a methano bridge. For each of the derivatives investigated, molecular dynamics is used to generate a realistic material morphology. Quantum chemical methods are then used to calculate intermolecular charge transfer rates. Finally, Monte Carlo methods are used to simulate time-of-flight experiments and thus calculate the electron mobility. It is found that as the length of the aliphatic side chain increases, the configurational disorder increases and thus the mobility decreases.

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

Application of finite element method in mechanical design of automotive parts

NASA Astrophysics Data System (ADS)

Gu, Suohai

2017-09-01

As an effective numerical analysis method, finite element method (FEM) has been widely used in mechanical design and other fields. In this paper, the development of FEM is introduced firstly, then the specific steps of FEM applications are illustrated and the difficulties of FEM are summarized in detail. Finally, applications of FEM in automobile components such as automobile wheel, steel plate spring, body frame, shaft parts and so on are summarized, compared with related research experiments.

Fully coupled methods for multiphase morphodynamics

NASA Astrophysics Data System (ADS)

Michoski, C.; Dawson, C.; Mirabito, C.; Kubatko, E. J.; Wirasaet, D.; Westerink, J. J.

2013-09-01

We present numerical methods for a system of equations consisting of the two dimensional Saint-Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge-Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge-Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments.

Weighted small subdomain filtering technology

NASA Astrophysics Data System (ADS)

Tai, Zhenhua; Zhang, Fengxu; Zhang, Fengqin; Zhang, Xingzhou; Hao, Mengcheng

2017-09-01

A high-resolution method to define the horizontal edges of gravity sources is presented by improving the three-directional small subdomain filtering (TDSSF). This proposed method is the weighted small subdomain filtering (WSSF). The WSSF uses a numerical difference instead of the phase conversion in the TDSSF to reduce the computational complexity. To make the WSSF more insensitive to noise, the numerical difference is combined with the average algorithm. Unlike the TDSSF, the WSSF uses a weighted sum to integrate the numerical difference results along four directions into one contour, for making its interpretation more convenient and accurate. The locations of tightened gradient belts are used to define the edges of sources in the WSSF result. This proposed method is tested on synthetic data. The test results show that the WSSF provides the horizontal edges of sources more clearly and correctly, even if the sources are interfered with one another and the data is corrupted with random noise. Finally, the WSSF and two other known methods are applied to a real data respectively. The detected edges by the WSSF are sharper and more accurate.

Path suppression of strongly collapsing bubbles at finite and low Reynolds numbers.

PubMed

Rechiman, Ludmila M; Dellavale, Damián; Bonetto, Fabián J

2013-06-01

We study, numerically and experimentally, three different methods to suppress the trajectories of strongly collapsing and sonoluminescent bubbles in a highly viscous sulfuric acid solution. A new numerical scheme based on the window method is proposed to account for the history force acting on a spherical bubble with variable radius. We could quantify the history force, which is not negligible in comparison with the primary Bjerknes force in this type of problem, and results are in agreement with the classical primary Bjerknes force trapping threshold analysis. Moreover, the present numerical implementation reproduces the spatial behavior associated with the positional and path instability of sonoluminescent argon bubbles in strongly gassed and highly degassed sulfuric acid solutions. Finally, the model allows us to demonstrate that spatially stationary bubbles driven by biharmonic excitation could be obtained with a different mode from the one used in previous reported experiments.

Mixed Arlequin method for multiscale poromechanics problems: Mixed Arlequin method for multiscale poromechanics problems

DOE PAGES

Sun, WaiChing; Cai, Zhijun; Choo, Jinhyun

2016-11-18

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. Here, to examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space ofmore » the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Finally, through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model.« less

Topology Optimization - Engineering Contribution to Architectural Design

NASA Astrophysics Data System (ADS)

Tajs-Zielińska, Katarzyna; Bochenek, Bogdan

2017-10-01

The idea of the topology optimization is to find within a considered design domain the distribution of material that is optimal in some sense. Material, during optimization process, is redistributed and parts that are not necessary from objective point of view are removed. The result is a solid/void structure, for which an objective function is minimized. This paper presents an application of topology optimization to multi-material structures. The design domain defined by shape of a structure is divided into sub-regions, for which different materials are assigned. During design process material is relocated, but only within selected region. The proposed idea has been inspired by architectural designs like multi-material facades of buildings. The effectiveness of topology optimization is determined by proper choice of numerical optimization algorithm. This paper utilises very efficient heuristic method called Cellular Automata. Cellular Automata are mathematical, discrete idealization of a physical systems. Engineering implementation of Cellular Automata requires decomposition of the design domain into a uniform lattice of cells. It is assumed, that the interaction between cells takes place only within the neighbouring cells. The interaction is governed by simple, local update rules, which are based on heuristics or physical laws. The numerical studies show, that this method can be attractive alternative to traditional gradient-based algorithms. The proposed approach is evaluated by selected numerical examples of multi-material bridge structures, for which various material configurations are examined. The numerical studies demonstrated a significant influence the material sub-regions location on the final topologies. The influence of assumed volume fraction on final topologies for multi-material structures is also observed and discussed. The results of numerical calculations show, that this approach produces different results as compared with classical one-material problems.

Tube wave signatures in cylindrically layered poroelastic media computed with spectral method

NASA Astrophysics Data System (ADS)

Karpfinger, Florian; Gurevich, Boris; Valero, Henri-Pierre; Bakulin, Andrey; Sinha, Bikash

2010-11-01

This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered.

Numerically evaluating the bispectrum in curved field-space— with PyTransport 2.0

NASA Astrophysics Data System (ADS)

Ronayne, John W.; Mulryne, David J.

2018-01-01

We extend the transport framework for numerically evaluating the power spectrum and bispectrum in multi-field inflation to the case of a curved field-space metric. This method naturally accounts for all sub- and super-horizon tree level effects, including those induced by the curvature of the field-space. We present an open source implementation of our equations in an extension of the publicly available PyTransport code. Finally we illustrate how our technique is applied to examples of inflationary models with a non-trivial field-space metric.

Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.

PubMed

Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

2014-01-01

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.

Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

PubMed Central

Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

2014-01-01

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed. PMID:27433525

Numerical and experimental study on buckling and postbuckling behavior of cracked cylindrical shells

NASA Astrophysics Data System (ADS)

Saemi, J.; Sedighi, M.; Shariati, M.

2015-09-01

The effect of crack on load-bearing capacity and buckling behavior of cylindrical shells is an essential consideration in their design. In this paper, experimental and numerical buckling analysis of steel cylindrical shells of various lengths and diameters with cracks have been studied using the finite element method, and the effect of crack position, crack orientation and the crack length-to-cylindrical shell perimeter ( λ = a/(2 πr)) and shell length-to-diameter ( L/ D) ratios on the buckling and post-buckling behavior of cylindrical shells has been investigated. For several specimens, buckling test was performed using an INSTRON 8802 servo hydraulic machine, and the results of experimental tests were compared to numerical results. A very good correlation was observed between numerical simulation and experimental results. Finally, based on the experimental and numerical results, sensitivity of the buckling load to the shell length, crack length and orientation has also been investigated.

On Numerical Heating

NASA Astrophysics Data System (ADS)

Liou, Meng-Sing

2013-11-01

The development of computational fluid dynamics over the last few decades has yielded enormous successes and capabilities that are being routinely employed today; however there remain some open problems to be properly resolved. One example is the so-called overheating problem, which can arise in two very different scenarios, from either colliding or receding streams. Common in both is a localized, numerically over-predicted temperature. Von Neumann reported the former, a compressive overheating, nearly 70 years ago and numerically smeared the temperature peak by introducing artificial diffusion. However, the latter is unphysical in an expansive (rarefying) situation; it still dogs every method known to the author. We will present a study aiming at resolving this overheating problem and we find that: (1) the entropy increase is one-to-one linked to the increase in the temperature rise and (2) the overheating is inevitable in the current computational fluid dynamics framework in practice. Finally we will show a simple hybrid method that fundamentally cures the overheating problem in a rarefying flow, but also retains the property of accurate shock capturing. Moreover, this remedy (enhancement of current numerical methods) can be included easily in the present Eulerian codes. This work is performed under NASA's Fundamental Aeronautics Program.

Rank-k modification methods for recursive least squares problems

NASA Astrophysics Data System (ADS)

Olszanskyj, Serge; Lebak, James; Bojanczyk, Adam

1994-09-01

In least squares problems, it is often desired to solve the same problem repeatedly but with several rows of the data either added, deleted, or both. Methods for quickly solving a problem after adding or deleting one row of data at a time are known. In this paper we introduce fundamental rank-k updating and downdating methods and show how extensions of rank-1 downdating methods based on LINPACK, Corrected Semi-Normal Equations (CSNE), and Gram-Schmidt factorizations, as well as new rank-k downdating methods, can all be derived from these fundamental results. We then analyze the cost of each new algorithm and make comparisons tok applications of the corresponding rank-1 algorithms. We provide experimental results comparing the numerical accuracy of the various algorithms, paying particular attention to the downdating methods, due to their potential numerical difficulties for ill-conditioned problems. We then discuss the computation involved for each downdating method, measured in terms of operation counts and BLAS calls. Finally, we provide serial execution timing results for these algorithms, noting preferable points for improvement and optimization. From our experiments we conclude that the Gram-Schmidt methods perform best in terms of numerical accuracy, but may be too costly for serial execution for large problems.

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

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

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

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

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

The vector radiative transfer numerical model of coupled ocean-atmosphere system using the matrix-operator method

NASA Astrophysics Data System (ADS)

Xianqiang, He; Delu, Pan; Yan, Bai; Qiankun, Zhu

2005-10-01

The numerical model of the vector radiative transfer of the coupled ocean-atmosphere system is developed based on the matrix-operator method, which is named PCOART. In PCOART, using the Fourier analysis, the vector radiative transfer equation (VRTE) splits up into a set of independent equations with zenith angle as only angular coordinate. Using the Gaussian-Quadrature method, VRTE is finally transferred into the matrix equation, which is calculated by using the adding-doubling method. According to the reflective and refractive properties of the ocean-atmosphere interface, the vector radiative transfer numerical model of ocean and atmosphere is coupled in PCOART. By comparing with the exact Rayleigh scattering look-up-table of MODIS(Moderate-resolution Imaging Spectroradiometer), it is shown that PCOART is an exact numerical calculation model, and the processing methods of the multi-scattering and polarization are correct in PCOART. Also, by validating with the standard problems of the radiative transfer in water, it is shown that PCOART could be used to calculate the underwater radiative transfer problems. Therefore, PCOART is a useful tool to exactly calculate the vector radiative transfer of the coupled ocean-atmosphere system, which can be used to study the polarization properties of the radiance in the whole ocean-atmosphere system and the remote sensing of the atmosphere and ocean.

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

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.

An inverse method using toroidal mode data

USGS Publications Warehouse

Willis, C.

1986-01-01

The author presents a numerical method for calculating the density and S-wave velocity in the upper mantle of a spherically symmetric, non-rotating Earth which consists of a perfect elastic, isotropic material. The data comes from the periods of the toroidal oscillations. She tests the method on a smoothed version of model A. The error in the reconstruction is less than 1%. The effects of perturbations in the eigenvalues are studied and she finds that the final model is sensitive to errors in the data.

A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

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

Marxen, Olaf, E-mail: olaf.marxen@vki.ac.be; Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse; Magin, Thierry E.

2013-12-15

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as wellmore » as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.« less

A Ghost Fluid/Level Set Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect

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

Rueda Villegas, Lucia; Alis, Romain; Lepilliez, Mathieu

2016-07-01

The development of numerical methods for the direct numerical simulation of two-phase flows with phase change, in the framework of interface capturing or interface tracking methods, is the main topic of this study. We propose a novel numerical method, which allows dealing with both evaporation and boiling at the interface between a liquid and a gas. Indeed, in some specific situations involving very heterogeneous thermodynamic conditions at the interface, the distinction between boiling and evaporation is not always possible. For instance, it can occur for a Leidenfrost droplet; a water drop levitating above a hot plate whose temperature is muchmore » higher than the boiling temperature. In this case, boiling occurs in the film of saturated vapor which is entrapped between the bottom of the drop and the plate, whereas the top of the water droplet evaporates in contact of ambient air. The situation can also be ambiguous for a superheated droplet or at the contact line between a liquid and a hot wall whose temperature is higher than the saturation temperature of the liquid. In these situations, the interface temperature can locally reach the saturation temperature (boiling point), for instance near a contact line, and be cooler in other places. Thus, boiling and evaporation can occur simultaneously on different regions of the same liquid interface or occur successively at different times of the history of an evaporating droplet. Standard numerical methods are not able to perform computations in these transient regimes, therefore, we propose in this paper a novel numerical method to achieve this challenging task. Finally, we present several accuracy validations against theoretical solutions and experimental results to strengthen the relevance of this new method.« less

Practical Bayesian tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Combes, Joshua; Cory, D. G.

2016-03-01

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120) and by Ferrie (2014 New J. Phys. 16 093035), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.

Review of Computational Stirling Analysis Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.

2004-01-01

Nuclear thermal to electric power conversion carries the promise of longer duration missions and higher scientific data transmission rates back to Earth for both Mars rovers and deep space missions. A free-piston Stirling convertor is a candidate technology that is considered an efficient and reliable power conversion device for such purposes. While already very efficient, it is believed that better Stirling engines can be developed if the losses inherent its current designs could be better understood. However, they are difficult to instrument and so efforts are underway to simulate a complete Stirling engine numerically. This has only recently been attempted and a review of the methods leading up to and including such computational analysis is presented. And finally it is proposed that the quality and depth of Stirling loss understanding may be improved by utilizing the higher fidelity and efficiency of recently developed numerical methods. One such method, the Ultra HI-Fl technique is presented in detail.

Bridges for Pedestrians with Random Parameters using the Stochastic Finite Elements Analysis

NASA Astrophysics Data System (ADS)

Szafran, J.; Kamiński, M.

2017-02-01

The main aim of this paper is to present a Stochastic Finite Element Method analysis with reference to principal design parameters of bridges for pedestrians: eigenfrequency and deflection of bridge span. They are considered with respect to random thickness of plates in boxed-section bridge platform, Young modulus of structural steel and static load resulting from crowd of pedestrians. The influence of the quality of the numerical model in the context of traditional FEM is shown also on the example of a simple steel shield. Steel structures with random parameters are discretized in exactly the same way as for the needs of traditional Finite Element Method. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable the determination of the structural response and, thanks to the Least Squares Method, its final probabilistic moments.

Demonstration and Research Program for Teaching Young String Players. Final Report.

ERIC Educational Resources Information Center

Yarborough, William

This report explains a system for rapidly training beginning students in the technical aspects of playing a stringed instrument. The program also affords them a well-rounded, basic knowledge of music. A "numerical" method of notation and concentrated muscular exercises greatly speeded the technical learning process. The daily coordination of ear…

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

DOE PAGES

Lu, Zhiming

2018-01-30

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Faster and More Accurate Transport Procedures for HZETRN

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Blattnig, Steve R.; Badavi, Francis F.

2010-01-01

Several aspects of code verification are examined for HZETRN. First, a detailed derivation of the numerical marching algorithms is given. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of various coding errors is also given, and the impact of these errors on exposure quantities is shown. Finally, a coupled convergence study is conducted. From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is also determined that almost all of the discretization error in HZETRN is caused by charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons are given for three applications in which HZETRN is commonly used. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

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

Lu, Zhiming

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

A numerical model for the simulation of low Mach number gas-liquid flows

NASA Astrophysics Data System (ADS)

Daru, V.; Duluc, M.-C.; Le Quéré, P.; Juric, D.

2010-03-01

This work is devoted to the numerical simulation of gas-liquid flows. The liquid phase is considered as incompressible, while the gas phase is treated as compressible in the low Mach number approach. We present a model and a numerical method aimed at the computation of such two-phase flows. The numerical model uses a lagrangian front-tracking method to deal with the interface. The model being validated with a 1-D reference solution, results in the 2-D case are presented. Two air bubbles are enclosed in a rigid cavity and surrounded with liquid water. As the initial pressure of the two bubbles is set to different values, an oscillatory motion is induced in which the bubbles undergo alternate compression and dilatation associated with alternate internal heating and cooling. This oscillatory motion can not be sustained and a damping is finally observed. It is shown in the present work that thermal conductivity of the liquid has a significant effect on both the frequency and the damping time scale of the oscillations.

Simulation of Liquid Droplet in Air and on a Solid Surface

NASA Astrophysics Data System (ADS)

Launglucknavalai, Kevin

Although multiphase gas and liquid phenomena occurs widely in engineering problems, many aspects of multiphase interaction like within droplet dynamics are still not quantified. This study aims to qualify the Lattice Boltzmann (LBM) Interparticle Potential multiphase computational method in order to build a foundation for future multiphase research. This study consists of two overall sections. The first section in Chapter 2 focuses on understanding the LBM method and Interparticle Potential model. It outlines the LBM method and how it relates to macroscopic fluid dynamics. The standard form of LBM is obtained. The perturbation solution obtaining the Navier-Stokes equations from the LBM equation is presented. Finally, the Interparticle Potential model is incorporated into the numerical LBM method. The second section in Chapter 3 presents the verification and validation cases to confirm the behavior of the single-phase and multiphase LBM models. Experimental and analytical results are used briefly to compare with numerical results when possible using Poiseuille channel flow and flow over a cylinder. While presenting the numerical results, practical considerations like converting LBM scale variables to physical scale variables are considered. Multiphase results are verified using Laplaces law and artificial behaviors of the model are explored. In this study, a better understanding of the LBM method and Interparticle Potential model is gained. This allows the numerical method to be used for comparison with experimental results in the future and provides a better understanding of multiphase physics overall.

Accurate modelling of unsteady flows in collapsible tubes.

PubMed

Marchandise, Emilie; Flaud, Patrice

2010-01-01

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

Computational Methods for Nonlinear Dynamic Problems in Solid and Structural Mechanics: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces

DTIC Science & Technology

1989-03-31

present several numerical studies designed to reveal the effect that some of the governing parameters have on the behavior of the system and, whenever...Friction and in the Control of Dynamical Systems with Frictional Forces FINAL TECHNICAL REPORT March 31, 1989 _ -- I -.7: .-.- - : AFOSR Contract F49620...SOLID AND STRUCTURAL MECHANICS: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces I I * FINAL

Design of a rapid magnetic microfluidic mixer

NASA Astrophysics Data System (ADS)

Ballard, Matthew; Owen, Drew; Mills, Zachary Grant; Hanasoge, Srinivas; Hesketh, Peter; Alexeev, Alexander

2015-11-01

Using three-dimensional simulations and experiments, we demonstrate rapid mixing of fluid streams in a microchannel using orbiting magnetic microbeads. We use a lattice Boltzmann model coupled to a Brownian dynamics model to perform numerical simulations that study in depth the effect of system parameters such as channel configuration and fluid and bead velocities. We use our findings to aid the design of an experimental micromixer. Using this experimental device, we demonstrate rapid microfluidic mixing over a compact channel length, and validate our numerical simulation results. Finally, we use numerical simulations to study the physical mechanisms leading to microfluidic mixing in our system. Our findings demonstrate a promising method of rapid microfluidic mixing over a short distance, with applications in lab-on-a-chip sample testing.

Numerical Polynomial Homotopy Continuation Method and String Vacua

DOE PAGES

Mehta, Dhagash

2011-01-01

Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

PubMed

Li, Hongwei; Guo, Yue

2017-12-01

The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Neutron Transport Models and Methods for HZETRN and Coupling to Low Energy Light Ion Transport

NASA Technical Reports Server (NTRS)

Blattnig, S.R.; Slaba, T.C.; Heinbockel, J.H.

2008-01-01

Exposure estimates inside space vehicles, surface habitats, and high altitude aircraft exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETCHEDS and FLUKA, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion (A<4) transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

The numerical study and comparison of radial basis functions in applications of the dual reciprocity boundary element method to convection-diffusion problems

NASA Astrophysics Data System (ADS)

Chanthawara, Krittidej; Kaennakham, Sayan; Toutip, Wattana

2016-02-01

The methodology of Dual Reciprocity Boundary Element Method (DRBEM) is applied to the convection-diffusion problems and investigating its performance is our first objective of the work. Seven types of Radial Basis Functions (RBF); Linear, Thin-plate Spline, Cubic, Compactly Supported, Inverse Multiquadric, Quadratic, and that proposed by [12], were closely investigated in order to numerically compare their effectiveness drawbacks etc. and this is taken as our second objective. A sufficient number of simulations were performed covering as many aspects as possible. Varidated against both exacts and other numerical works, the final results imply strongly that the Thin-Plate Spline and Linear type of RBF are superior to others in terms of both solutions' quality and CPU-time spent while the Inverse Multiquadric seems to poorly yield the results. It is also found that DRBEM can perform relatively well at moderate level of convective force and as anticipated becomes unstable when the problem becomes more convective-dominated, as normally found in all classical mesh-dependence methods.

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-12-22

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly setmore » negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.« less

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly setmore » negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.« less

Numerical Analysis of a Class of THM Coupled Model for Porous Materials

NASA Astrophysics Data System (ADS)

Liu, Tangwei; Zhou, Jingying; Lu, Hongzhi

2018-01-01

We consider the coupled models of the Thermo-hydro-mechanical (THM) problem for porous materials which arises in many engineering applications. Firstly, mathematical models of the THM coupled problem for porous materials were discussed. Secondly, for different cases, some numerical difference schemes of coupled model were constructed, respectively. Finally, aassuming that the original water vapour effect is neglectable and that the volume fraction of liquid phase and the solid phase are constants, the nonlinear equations can be reduced to linear equations. The discrete equations corresponding to the linear equations were solved by the Arnodli method.

Fluid Stochastic Petri Nets: Theory, Applications, and Solution

NASA Technical Reports Server (NTRS)

Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.

1996-01-01

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

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.

Numerical sedimentation particle-size analysis using the Discrete Element Method

NASA Astrophysics Data System (ADS)

Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.

2015-12-01

Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.

75 FR 9924 - Final Comprehensive Conservation Plan for the Red Rock Lakes National Wildlife Refuge, MT

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-04

...-time staff of five employees and various summer temporaries manage and study the refuge habitats and... majority of fishing occurring on Red Rock. In addition, the refuge is open to limited hunting of ducks..., conducting numerous studies to determine the effects and best methods of restoration, including any effects...

Three-dimensional numerical modeling of full-space transient electromagnetic responses of water in goaf

NASA Astrophysics Data System (ADS)

Chang, Jiang-Hao; Yu, Jing-Cun; Liu, Zhi-Xin

2016-09-01

The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient electromagnetic field. We used multiple transmitting loops instead of the traditional single transmitting loop to load the transmitting loop into Cartesian grids. We improved the method for calculating the z-component of the magnetic field based on the characteristics of full space. Then, we established the fullspace 3D geoelectrical model using geological data for coalmines. In addition, the transient electromagnetic responses of water-filled goaves of variable shape at different locations were simulated by using the finite-difference time-domain (FDTD) method. Moreover, we evaluated the apparent resistivity results. The numerical modeling results suggested that the resistivity differences between the coal seam and its roof and floor greatly affect the distribution of apparent resistivity, resulting in nearly circular contours with the roadway head at the center. The actual distribution of apparent resistivity for different geoelectrical models of water in goaves was consistent with the models. However, when the goaf water was located in one side, a false low-resistivity anomaly would appear on the other side owing to the full-space effect but the response was much weaker. Finally, the modeling results were subsequently confirmed by drilling, suggesting that the proposed method was effective.

Noiseless Vlasov-Poisson simulations with linearly transformed particles

DOE PAGES

Pinto, Martin C.; Sonnendrucker, Eric; Friedman, Alex; ...

2014-06-25

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development ofmore » Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Lastly, benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.« less

Taguchi Method Applied in Optimization of Shipley SJR 5740 Positive Resist Deposition

NASA Technical Reports Server (NTRS)

Hui, A.; Blosiu, J. O.; Wiberg, D. V.

1998-01-01

Taguchi Methods of Robust Design presents a way to optimize output process performance through an organized set of experiments by using orthogonal arrays. Analysis of variance and signal-to-noise ratio is used to evaluate the contribution of each of the process controllable parameters in the realization of the process optimization. In the photoresist deposition process, there are numerous controllable parameters that can affect the surface quality and thickness of the final photoresist layer.

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

NASA Astrophysics Data System (ADS)

Ma, Tiedong; Li, Teng; Cui, Bing

2018-01-01

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.

Application of an enriched FEM technique in thermo-mechanical contact problems

NASA Astrophysics Data System (ADS)

Khoei, A. R.; Bahmani, B.

2018-02-01

In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton-Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

NASA Technical Reports Server (NTRS)

Liandrat, J.; Tchamitchian, PH.

1990-01-01

The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.

An Investigation of Wave Propagations in Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

2004-01-01

Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.

Coupled Neutron Transport for HZETRN

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Blattnig, Steve R.

2009-01-01

Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light particle transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

NASA Astrophysics Data System (ADS)

Ivanov, I.; Imsland, Lars; Bogdanova, B.

2017-03-01

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Joint research effort on vibrations of twisted plates, phase 1: Final results

NASA Technical Reports Server (NTRS)

Kielb, R. E.; Leissa, A. W.; Macbain, J. C.; Carney, K. S.

1985-01-01

The complete theoretical and experimental results of the first phase of a joint government/industry/university research study on the vibration characteristics of twisted cantilever plates are given. The study is conducted to generate an experimental data base and to compare many different theoretical methods with each other and with the experimental results. Plates with aspect ratios, thickness ratios, and twist angles representative of current gas turbine engine blading are investigated. The theoretical results are generated by numerous finite element, shell, and beam analysis methods. The experimental results are obtained by precision matching a set of twisted plates and testing them at two laboratories. The second and final phase of the study will concern the effects of rotation.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

The CFS-PML in numerical simulation of ATEM

NASA Astrophysics Data System (ADS)

Zhao, Xuejiao; Ji, Yanju; Qiu, Shuo; Guan, Shanshan; Wu, Yanqi

2017-01-01

In the simulation of airborne transient electromagnetic method (ATEM) in time-domain, the truncated boundary reflection can bring a big error to the results. The complex frequency shifted perfectly matched layer (CFS-PML) absorbing boundary condition has been proved to have a better absorption of low frequency incident wave and can reduce the late reflection greatly. In this paper, we apply the CFS-PML to three-dimensional numerical simulation of ATEM in time-domain to achieve a high precision .The expression of divergence equation in CFS-PML is confirmed and its explicit iteration format based on the finite difference method and the recursive convolution technique is deduced. Finally, we use the uniformity half space model and the anomalous model to test the validity of this method. Results show that the CFS-PML can reduce the average relative error to 2.87% and increase the accuracy of the anomaly recognition.

Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

DOE PAGES

Barnard, Richard C.; Frank, Martin; Krycki, Kai

2016-02-09

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P N) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose depositionmore » depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.« less

Peelle's pertinent puzzle using the Monte Carlo technique

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

Kawano, Toshihiko; Talou, Patrick; Burr, Thomas

2009-01-01

We try to understand the long-standing problem of the Peelle's Pertinent Puzzle (PPP) using the Monte Carlo technique. We allow the probability density functions to be any kind of form to assume the impact of distribution, and obtain the least-squares solution directly from numerical simulations. We found that the standard least squares method gives the correct answer if a weighting function is properly provided. Results from numerical simulations show that the correct answer of PPP is 1.1 {+-} 0.25 if the common error is multiplicative. The thought-provoking answer of 0.88 is also correct, if the common error is additive, andmore » if the error is proportional to the measured values. The least squares method correctly gives us the most probable case, where the additive component has a negative value. Finally, the standard method fails for PPP due to a distorted (non Gaussian) joint distribution.« less

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

On making cuts for magnetic scalar potentials in multiply connected regions

NASA Astrophysics Data System (ADS)

Kotiuga, P. R.

1987-04-01

The problem of making cuts is of importance to scalar potential formulations of three-dimensional eddy current problems. Its heuristic solution has been known for a century [J. C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed. (Clarendon, Oxford, 1981), Chap. 1, Article 20] and in the last decade, with the use of finite element methods, a restricted combinatorial variant has been proposed and solved [M. L. Brown, Int. J. Numer. Methods Eng. 20, 665 (1984)]. This problem, in its full generality, has never received a rigorous mathematical formulation. This paper presents such a formulation and outlines a rigorous proof of existence. The technique used in the proof expose the incredible intricacy of the general problem and the restrictive assumptions of Brown [Int. J. Numer. Methods Eng. 20, 665 (1984)]. Finally, the results make rigorous Kotiuga's (Ph. D. Thesis, McGill University, Montreal, 1984) heuristic interpretation of cuts and duality theorems via intersection matrices.

Absorbing boundaries in numerical solutions of the time-dependent Schroedinger equation on a grid using exterior complex scaling

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

He, F.; Ruiz, C.; Becker, A.

We study the suppression of reflections in the numerical simulation of the time-dependent Schroedinger equation for strong-field problems on a grid using exterior complex scaling (ECS) as an absorbing boundary condition. It is shown that the ECS method can be applied in both the length and the velocity gauge as long as appropriate approximations are applied in the ECS transformation of the electron-field coupling. It is found that the ECS method improves the suppression of reflection as compared to the conventional masking function technique in typical simulations of atoms exposed to an intense laser pulse. Finally, we demonstrate the advantagemore » of the ECS technique to avoid unphysical artifacts in the evaluation of high harmonic spectra.« less

Penalty methods for the numerical solution of American multi-asset option problems

NASA Astrophysics Data System (ADS)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report

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

Prinja, Anil K.

The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset aremore » amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.« less

Virtual Planning, Control, and Machining for a Modular-Based Automated Factory Operation in an Augmented Reality Environment

PubMed Central

Pai, Yun Suen; Yap, Hwa Jen; Md Dawal, Siti Zawiah; Ramesh, S.; Phoon, Sin Ye

2016-01-01

This study presents a modular-based implementation of augmented reality to provide an immersive experience in learning or teaching the planning phase, control system, and machining parameters of a fully automated work cell. The architecture of the system consists of three code modules that can operate independently or combined to create a complete system that is able to guide engineers from the layout planning phase to the prototyping of the final product. The layout planning module determines the best possible arrangement in a layout for the placement of various machines, in this case a conveyor belt for transportation, a robot arm for pick-and-place operations, and a computer numerical control milling machine to generate the final prototype. The robotic arm module simulates the pick-and-place operation offline from the conveyor belt to a computer numerical control (CNC) machine utilising collision detection and inverse kinematics. Finally, the CNC module performs virtual machining based on the Uniform Space Decomposition method and axis aligned bounding box collision detection. The conducted case study revealed that given the situation, a semi-circle shaped arrangement is desirable, whereas the pick-and-place system and the final generated G-code produced the highest deviation of 3.83 mm and 5.8 mm respectively. PMID:27271840

Virtual Planning, Control, and Machining for a Modular-Based Automated Factory Operation in an Augmented Reality Environment.

PubMed

Pai, Yun Suen; Yap, Hwa Jen; Md Dawal, Siti Zawiah; Ramesh, S; Phoon, Sin Ye

2016-06-07

This study presents a modular-based implementation of augmented reality to provide an immersive experience in learning or teaching the planning phase, control system, and machining parameters of a fully automated work cell. The architecture of the system consists of three code modules that can operate independently or combined to create a complete system that is able to guide engineers from the layout planning phase to the prototyping of the final product. The layout planning module determines the best possible arrangement in a layout for the placement of various machines, in this case a conveyor belt for transportation, a robot arm for pick-and-place operations, and a computer numerical control milling machine to generate the final prototype. The robotic arm module simulates the pick-and-place operation offline from the conveyor belt to a computer numerical control (CNC) machine utilising collision detection and inverse kinematics. Finally, the CNC module performs virtual machining based on the Uniform Space Decomposition method and axis aligned bounding box collision detection. The conducted case study revealed that given the situation, a semi-circle shaped arrangement is desirable, whereas the pick-and-place system and the final generated G-code produced the highest deviation of 3.83 mm and 5.8 mm respectively.

Virtual Planning, Control, and Machining for a Modular-Based Automated Factory Operation in an Augmented Reality Environment

NASA Astrophysics Data System (ADS)

Pai, Yun Suen; Yap, Hwa Jen; Md Dawal, Siti Zawiah; Ramesh, S.; Phoon, Sin Ye

2016-06-01

This study presents a modular-based implementation of augmented reality to provide an immersive experience in learning or teaching the planning phase, control system, and machining parameters of a fully automated work cell. The architecture of the system consists of three code modules that can operate independently or combined to create a complete system that is able to guide engineers from the layout planning phase to the prototyping of the final product. The layout planning module determines the best possible arrangement in a layout for the placement of various machines, in this case a conveyor belt for transportation, a robot arm for pick-and-place operations, and a computer numerical control milling machine to generate the final prototype. The robotic arm module simulates the pick-and-place operation offline from the conveyor belt to a computer numerical control (CNC) machine utilising collision detection and inverse kinematics. Finally, the CNC module performs virtual machining based on the Uniform Space Decomposition method and axis aligned bounding box collision detection. The conducted case study revealed that given the situation, a semi-circle shaped arrangement is desirable, whereas the pick-and-place system and the final generated G-code produced the highest deviation of 3.83 mm and 5.8 mm respectively.

Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse

NASA Astrophysics Data System (ADS)

Lusso, Christelle; Ern, Alexandre; Bouchut, François; Mangeney, Anne; Farin, Maxime; Roche, Olivier

2017-03-01

This work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. We consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2D setting with a free surface. We implement a regularization method to deal with the singularity of the rheological law, using a mixed finite element approximation of the momentum and incompressibility equations, and an arbitrary Lagrangian Eulerian (ALE) formulation for the displacement of the domain. The free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. Several tests are performed to assess the efficiency of our method. The first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. On this configuration we setup rules for the choice of the numerical parameters. The second test aims to compare the results of our numerical method to those predicted by an augmented Lagrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. Finally we show the reliability of our method by comparing numerical predictions to data from experiments of granular collapse of both trapezoidal and rectangular columns over horizontal rigid or erodible granular bed made of the same material. We compare the evolution of the free surface, the velocity profiles, and the static-flowing interface. The results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed.

Study on a Multi-Frequency Homotopy Analysis Method for Period-Doubling Solutions of Nonlinear Systems

NASA Astrophysics Data System (ADS)

Fu, H. X.; Qian, Y. H.

In this paper, a modification of homotopy analysis method (HAM) is applied to study the two-degree-of-freedom coupled Duffing system. Firstly, the process of calculating the two-degree-of-freedom coupled Duffing system is presented. Secondly, the single periodic solutions and double periodic solutions are obtained by solving the constructed nonlinear algebraic equations. Finally, comparing the periodic solutions obtained by the multi-frequency homotopy analysis method (MFHAM) and the fourth-order Runge-Kutta method, it is found that the approximate solution agrees well with the numerical solution.

Spectral/ hp element methods: Recent developments, applications, and perspectives

NASA Astrophysics Data System (ADS)

Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

2018-02-01

The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

Comparison of viscous-shock-layer solutions by time-asymptotic and steady-state methods. [flow distribution around a Jupiter entry probe

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Moss, J. N.; Simmonds, A. L.

1982-01-01

Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can hamper AM resulting in severe underestimation of BME. TI turned out to be the most vulnerable, resulting in BME overestimation. Finally, we show how SS can be largely invariant to rounding errors, yielding the most accurate and computational efficient results. These research results are useful for MC simulations to estimate Bayesian model evidence.

Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

NASA Astrophysics Data System (ADS)

Carraro, F.; Valiani, A.; Caleffi, V.

2018-03-01

Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

Numerical insight into the micromechanics of jet erosion of a cohesive granular material

NASA Astrophysics Data System (ADS)

Cuéllar, Pablo; Benseghier, Zeyd; Luu, Li-Hua; Bonelli, Stéphane; Delenne, Jean-Yves; Radjaï, Farhang; Philippe, Pierre

2017-06-01

Here we investigate the physical mechanisms behind the surface erosion of a cohesive granular soil induced by an impinging jet by means of numerical simulations coupling fluid and grains at the microscale. The 2D numerical model combines the Discrete Element and Lattice Boltzmann methods (DEM-LBM) and accounts for the granular cohesion with a contact model featuring a paraboloidal yield surface. Here we review first the hydrodynamical conditions imposed by the fluid jet on a solid granular packing, turning then the attention to the impact of cohesion on the erosion kinetics. Finally, the use of an additional subcritical debonding damage model based on the work of Silvani and co-workers provides a novel insight into the internal solicitation of the cohesive granular sample by the impinging jet.

Conformal Infinity.

PubMed

Frauendiener, Jörg

2000-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related with almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved out of physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation and how it lends itself very naturally to solve radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Conformal Infinity.

PubMed

Frauendiener, Jörg

2004-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Numerical Calculation of the Spectrum of the Severe (1%) Lighting Current and Its First Derivative

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

Brown, C G; Ong, M M; Perkins, M P

2010-02-12

Recently, the direct-strike lighting environment for the stockpile-to-target sequence was updated [1]. In [1], the severe (1%) lightning current waveforms for first and subsequent return strokes are defined based on Heidler's waveform. This report presents numerical calculations of the spectra of those 1% lightning current waveforms and their first derivatives. First, the 1% lightning current models are repeated here for convenience. Then, the numerical method for calculating the spectra is presented and tested. The test uses a double-exponential waveform and its first derivative, which we fit to the previous 1% direct-strike lighting environment from [2]. Finally, the resulting spectra aremore » given and are compared with those of the double-exponential waveform and its first derivative.« less

Development of Tsunami Numerical Model Considering the Disaster Debris such as Cars, Ships and Collapsed Buildings

NASA Astrophysics Data System (ADS)

Kozono, Y.; Takahashi, T.; Sakuraba, M.; Nojima, K.

2016-12-01

A lot of debris by tsunami, such as cars, ships and collapsed buildings were generated in the 2011 Tohoku tsunami. It is useful for rescue and recovery after tsunami disaster to predict the amount and final position of disaster debris. The transport form of disaster debris varies as drifting, rolling and sliding. These transport forms need to be considered comprehensively in tsunami simulation. In this study, we focused on the following three points. Firstly, the numerical model considering various transport forms of disaster debris was developed. The proposed numerical model was compared with the hydraulic experiment by Okubo et al. (2004) in order to verify transport on the bottom surface such as rolling and sliding. Secondly, a numerical experiment considering transporting on the bottom surface and drifting was studied. Finally, the numerical model was applied for Kesennuma city where serious damage occurred by the 2011 Tohoku tsunami. In this model, the influence of disaster debris was considered as tsunami flow energy loss. The hydraulic experiments conducted in a water tank which was 10 m long by 30 cm wide. The gate confined water in a storage tank, and acted as a wave generator. A slope was set at downstream section. The initial position of a block (width: 3.2 cm, density: 1.55 g/cm3) assuming the disaster debris was placed in front of the slope. The proposed numerical model simulated well the maximum transport distance and the final stop position of the block. In the second numerical experiment, the conditions were the same as the hydraulic experiment, except for the density of the block. The density was set to various values (from 0.30 to 4.20 g/cm3). This model was able to estimate various transport forms including drifting and sliding. In the numerical simulation of the 2011 Tohoku tsunami, the condition of buildings was modeled as follows: (i)the resistance on the bottom using Manning roughness coefficient (conventional method), and (ii)structure of buildings with collapsing and washing-away due to tsunami wave pressure. In this calculation, disaster debris of collapsed buildings, cars and ships was considered. As a result, the proposed model showed that it is necessary to take the disaster debris into account in order to predict tsunami inundation accurately.

Efficient Computational Prototyping of Mixed Technology Microfluidic Components and Systems

DTIC Science & Technology

2002-08-01

AFRL-IF-RS-TR-2002-190 Final Technical Report August 2002 EFFICIENT COMPUTATIONAL PROTOTYPING OF MIXED TECHNOLOGY MICROFLUIDIC...SUBTITLE EFFICIENT COMPUTATIONAL PROTOTYPING OF MIXED TECHNOLOGY MICROFLUIDIC COMPONENTS AND SYSTEMS 6. AUTHOR(S) Narayan R. Aluru, Jacob White...Aided Design (CAD) tools for microfluidic components and systems were developed in this effort. Innovative numerical methods and algorithms for mixed

Computation of subsonic flow around airfoil systems with multiple separation

NASA Technical Reports Server (NTRS)

Jacob, K.

1982-01-01

A numerical method for computing the subsonic flow around multi-element airfoil systems was developed, allowing for flow separation at one or more elements. Besides multiple rear separation also sort bubbles on the upper surface and cove bubbles can approximately be taken into account. Also, compressibility effects for pure subsonic flow are approximately accounted for. After presentation the method is applied to several examples and improved in some details. Finally, the present limitations and desirable extensions are discussed.

Asymptotic-Preserving methods and multiscale models for plasma physics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Deluzet, Fabrice

2017-05-01

The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non-magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or diffusion equations arising in magnetized plasma simulation are reviewed.

Cluster-modified function projective synchronisation of complex networks with asymmetric coupling

NASA Astrophysics Data System (ADS)

Wang, Shuguo

2018-02-01

This paper investigates the cluster-modified function projective synchronisation (CMFPS) of a generalised linearly coupled network with asymmetric coupling and nonidentical dynamical nodes. A novel synchronisation scheme is proposed to achieve CMFPS in community networks. We use adaptive control method to derive CMFPS criteria based on Lyapunov stability theory. Each cluster of networks is synchronised with target system by state transformation with scaling function matrix. Numerical simulation results are presented finally to illustrate the effectiveness of this method.

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing; Walker, Paul D.

2017-02-01

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

Numerical form-finding method for large mesh reflectors with elastic rim trusses

NASA Astrophysics Data System (ADS)

Yang, Dongwu; Zhang, Yiqun; Li, Peng; Du, Jingli

2018-06-01

Traditional methods for designing a mesh reflector usually treat the rim truss as rigid. Due to large aperture, light weight and high accuracy requirements on spaceborne reflectors, the rim truss deformation is indeed not negligible. In order to design a cable net with asymmetric boundaries for the front and rear nets, a cable-net form-finding method is firstly introduced. Then, the form-finding method is embedded into an iterative approach for designing a mesh reflector considering the elasticity of the supporting rim truss. By iterations on form-findings of the cable-net based on the updated boundary conditions due to the rim truss deformation, a mesh reflector with a fairly uniform tension distribution in its equilibrium state could be finally designed. Applications on offset mesh reflectors with both circular and elliptical rim trusses are illustrated. The numerical results show the effectiveness of the proposed approach and that a circular rim truss is more stable than an elliptical rim truss.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Evaluation of Proteus as a Tool for the Rapid Development of Models of Hydrologic Systems

NASA Astrophysics Data System (ADS)

Weigand, T. M.; Farthing, M. W.; Kees, C. E.; Miller, C. T.

2013-12-01

Models of modern hydrologic systems can be complex and involve a variety of operators with varying character. The goal is to implement approximations of such models that are both efficient for the developer and computationally efficient, which is a set of naturally competing objectives. Proteus is a Python-based toolbox that supports prototyping of model formulations as well as a wide variety of modern numerical methods and parallel computing. We used Proteus to develop numerical approximations for three models: Richards' equation, a brine flow model derived using the Thermodynamically Constrained Averaging Theory (TCAT), and a multiphase TCAT-based tumor growth model. For Richards' equation, we investigated discontinuous Galerkin solutions with higher order time integration based on the backward difference formulas. The TCAT brine flow model was implemented using Proteus and a variety of numerical methods were compared to hand coded solutions. Finally, an existing tumor growth model was implemented in Proteus to introduce more advanced numerics and allow the code to be run in parallel. From these three example models, Proteus was found to be an attractive open-source option for rapidly developing high quality code for solving existing and evolving computational science models.

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.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1981-01-01

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

A Century of Enzyme Kinetic Analysis, 1913 to 2013

PubMed Central

Johnson, Kenneth A.

2013-01-01

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function. PMID:23850893

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.

Infrared thermography applied to the study of heated and solar pavement: from numerical modeling to small scale laboratory experiments

NASA Astrophysics Data System (ADS)

Le Touz, N.; Toullier, T.; Dumoulin, J.

2017-05-01

The present study addresses the thermal behaviour of a modified pavement structure to prevent icing at its surface in adverse winter time conditions or overheating in hot summer conditions. First a multi-physic model based on infinite elements method was built to predict the evolution of the surface temperature. In a second time, laboratory experiments on small specimen were carried out and the surface temperature was monitored by infrared thermography. Results obtained are analyzed and performances of the numerical model for real scale outdoor application are discussed. Finally conclusion and perspectives are proposed.

Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.

Bifurcations and chaos in a parametrically damped two-well Duffing oscillator subjected to symmetric periodic pulses.

PubMed

Chacón, R; Martínez García-Hoz, A

1999-06-01

We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically.

Second-order Poisson Nernst-Planck solver for ion channel transport

PubMed Central

Zheng, Qiong; Chen, Duan; Wei, Guo-Wei

2010-01-01

The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements. PMID:21552336

A statistical method to estimate low-energy hadronic cross sections

NASA Astrophysics Data System (ADS)

Balassa, Gábor; Kovács, Péter; Wolf, György

2018-02-01

In this article we propose a model based on the Statistical Bootstrap approach to estimate the cross sections of different hadronic reactions up to a few GeV in c.m.s. energy. The method is based on the idea, when two particles collide a so-called fireball is formed, which after a short time period decays statistically into a specific final state. To calculate the probabilities we use a phase space description extended with quark combinatorial factors and the possibility of more than one fireball formation. In a few simple cases the probability of a specific final state can be calculated analytically, where we show that the model is able to reproduce the ratios of the considered cross sections. We also show that the model is able to describe proton-antiproton annihilation at rest. In the latter case we used a numerical method to calculate the more complicated final state probabilities. Additionally, we examined the formation of strange and charmed mesons as well, where we used existing data to fit the relevant model parameters.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2004-03-01

We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

Extracting concrete thermal characteristics from temperature time history of RC column exposed to standard fire.

PubMed

Kim, Jung J; Youm, Kwang-Soo; Reda Taha, Mahmoud M

2014-01-01

A numerical method to identify thermal conductivity from time history of one-dimensional temperature variations in thermal unsteady-state is proposed. The numerical method considers the change of specific heat and thermal conductivity with respect to temperature. Fire test of reinforced concrete (RC) columns was conducted using a standard fire to obtain time history of temperature variations in the column section. A thermal equilibrium model in unsteady-state condition was developed. The thermal conductivity of concrete was then determined by optimizing the numerical solution of the model to meet the observed time history of temperature variations. The determined thermal conductivity with respect to temperature was then verified against standard thermal conductivity measurements of concrete bricks. It is concluded that the proposed method can be used to conservatively estimate thermal conductivity of concrete for design purpose. Finally, the thermal radiation properties of concrete for the RC column were estimated from the thermal equilibrium at the surface of the column. The radiant heat transfer ratio of concrete representing absorptivity to emissivity ratio of concrete during fire was evaluated and is suggested as a concrete criterion that can be used in fire safety assessment.

Extracting Concrete Thermal Characteristics from Temperature Time History of RC Column Exposed to Standard Fire

PubMed Central

2014-01-01

A numerical method to identify thermal conductivity from time history of one-dimensional temperature variations in thermal unsteady-state is proposed. The numerical method considers the change of specific heat and thermal conductivity with respect to temperature. Fire test of reinforced concrete (RC) columns was conducted using a standard fire to obtain time history of temperature variations in the column section. A thermal equilibrium model in unsteady-state condition was developed. The thermal conductivity of concrete was then determined by optimizing the numerical solution of the model to meet the observed time history of temperature variations. The determined thermal conductivity with respect to temperature was then verified against standard thermal conductivity measurements of concrete bricks. It is concluded that the proposed method can be used to conservatively estimate thermal conductivity of concrete for design purpose. Finally, the thermal radiation properties of concrete for the RC column were estimated from the thermal equilibrium at the surface of the column. The radiant heat transfer ratio of concrete representing absorptivity to emissivity ratio of concrete during fire was evaluated and is suggested as a concrete criterion that can be used in fire safety assessment. PMID:25180197

Study of motion of optimal bodies in the soil of grid method

NASA Astrophysics Data System (ADS)

Kotov, V. L.; Linnik, E. Yu

2016-11-01

The paper presents a method of calculating the optimum forms in axisymmetric numerical method based on the Godunov and models elastoplastic soil vedium Grigoryan. Solved two problems in a certain definition of generetrix rotation of the body of a given length and radius of the base, having a minimum impedance and maximum penetration depth. Numerical calculations are carried out by a modified method of local variations, which allows to significantly reduce the number of operations at different representations of generetrix. Significantly simplify the process of searching for optimal body allows the use of a quadratic model of local interaction for preliminary assessments. It is noted the qualitative similarity of the process of convergence of numerical calculations for solving the optimization problem based on local interaction model and within the of continuum mechanics. A comparison of the optimal bodies with absolutely optimal bodies possessing the minimum resistance of penetration below which is impossible to achieve under given constraints on the geometry. It is shown that the conical striker with a variable vertex angle, which equal to the angle of the solution is absolutely optimal body of minimum resistance of penetration for each value of the velocity of implementation will have a final depth of penetration is only 12% more than the traditional body absolutely optimal maximum depth penetration.

New Developments in Magnetostatic Cleanliness Modeling

NASA Astrophysics Data System (ADS)

Mehlem, K.; Wiegand, A.; Weickert, S.

2012-05-01

The paper describes improvements and extensions of the multiple magnetic dipole modeling method (MDM) for cleanliness verification which had been introduced by the author1 in 1977 and then applied during 3 decades to numerous international projects. The solutions of specific modeling problems which had been left unsolved so far, are described in the present paper. Special attention is given to the ambiguities of MDM solutions caused by the limited data coverage available. Constraint handling by the constraint-free NLP solver, optimal MDM sizing and multiple-point far-field compensation techniques are presented. The recent extension of the MDM method to field gradient data is formulated and demonstrated by an example. Finally, a complex MDM application (Ulysses) is presented. Finally, a short description of the MDM software GAMAG, recently introduced by the author1, is given.

A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Zhang, Guoyu; Huang, Chengming; Li, Meng

2018-04-01

We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.

Mean-Field Description of Ionic Size Effects with Non-Uniform Ionic Sizes: A Numerical Approach

PubMed Central

Zhou, Shenggao; Wang, Zhongming; Li, Bo

2013-01-01

Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, i.e., there is no explicit, Boltzmann type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such non-uniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with non-uniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson–Boltzmann theory, or the generalized Poisson–Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed. PMID:21929014

International Workshop on Discrete Time Domain Modelling of Electromagnetic Fields and Networks (2nd) Held in Berlin, Germany on October 28-29, 1993

DTIC Science & Technology

1993-10-29

natural logarithm of the ratio of two maxima a period apart. Both methods are based on the results from the numerical integration. The details of this...check and okay member funtions are for sofware handshaking between the client and sever pracrss. Finally, the Forward function is used to initiate a

Transition to turbulence in plane channel flows

NASA Technical Reports Server (NTRS)

Biringen, S.

1984-01-01

Results obtained from a numerical simulation of the final stages of transition to turbulence in plane channel flow are described. Three dimensional, incompressible Navier-Stokes equations are numerically integrated to obtain the time evolution of two and three dimensional finite amplitude disturbances. Computations are performed on CYBER-203 vector processor for a 32x51x32 grid. Results are presented for no-slip boundary conditions at the solid walls as well as for periodic suction blowing to simulate active control of transition by mass transfer. Solutions indicate that the method is capable of simulating the complex character of vorticity dynamics during the various stages of transition and final breakdown. In particular, evidence points to the formation of a lambda-shape vortex and the subsequent system of horseshoe vortices inclined to the main flow direction as the main elements of transition. Calculations involving periodic suction-blowing indicate that interference with a wave of suitable phase and amplitude reduces the disturbance growth rates.

FE-simulation of hot forging with an integrated heat treatment with the objective of residual stress prediction

NASA Astrophysics Data System (ADS)

Behrens, Bernd-Arno; Chugreeva, Anna; Chugreev, Alexander

2018-05-01

Hot forming as a coupled thermo-mechanical process comprises numerous material phenomena with a corresponding impact on the material behavior during and after the forming process as well as on the final component performance. In this context, a realistic FE-simulation requires reliable mathematical models as well as detailed thermo-mechanical material data. This paper presents experimental and numerical results focused on the FE-based simulation of a hot forging process with a subsequent heat treatment step aiming at the prediction of the final mechanical properties and residual stress state in the forged component made of low alloy CrMo-steel DIN 42CrMo4. For this purpose, hot forging experiments of connecting rod geometry with a corresponding metallographic analysis and x-ray residual stress measurements have been carried out. For the coupled thermo-mechanical-metallurgical FE-simulations, a special user-defined material model based on the additive strain decomposition method and implemented in Simufact Forming via MSC.Marc solver features has been used.

Research on efficiency evaluation model of integrated energy system based on hybrid multi-attribute decision-making.

PubMed

Li, Yan

2017-05-25

The efficiency evaluation model of integrated energy system, involving many influencing factors, and the attribute values are heterogeneous and non-deterministic, usually cannot give specific numerical or accurate probability distribution characteristics, making the final evaluation result deviation. According to the characteristics of the integrated energy system, a hybrid multi-attribute decision-making model is constructed. The evaluation model considers the decision maker's risk preference. In the evaluation of the efficiency of the integrated energy system, the evaluation value of some evaluation indexes is linguistic value, or the evaluation value of the evaluation experts is not consistent. These reasons lead to ambiguity in the decision information, usually in the form of uncertain linguistic values and numerical interval values. In this paper, the risk preference of decision maker is considered when constructing the evaluation model. Interval-valued multiple-attribute decision-making method and fuzzy linguistic multiple-attribute decision-making model are proposed. Finally, the mathematical model of efficiency evaluation of integrated energy system is constructed.

An axisymmetric PFEM formulation for bottle forming simulation

NASA Astrophysics Data System (ADS)

Ryzhakov, Pavel B.

2017-01-01

A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.

A discontinuous Galerkin method for two-dimensional PDE models of Asian options

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.; Cvejnová, D.

2016-06-01

In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

A semi-implicit finite element method for viscous lipid membranes

NASA Astrophysics Data System (ADS)

Rodrigues, Diego S.; Ausas, Roberto F.; Mut, Fernando; Buscaglia, Gustavo C.

2015-10-01

A finite element formulation to approximate the behavior of lipid membranes is proposed. The mathematical model incorporates tangential viscous stresses and bending elastic forces, together with the inextensibility constraint and the enclosed volume constraint. The membrane is discretized by a surface mesh made up of planar triangles, over which a mixed formulation (velocity-curvature) is built based on the viscous bilinear form (Boussinesq-Scriven operator) and the Laplace-Beltrami identity relating position and curvature. A semi-implicit approach is then used to discretize in time, with piecewise linear interpolants for all variables. Two stabilization terms are needed: The first one stabilizes the inextensibility constraint by a pressure-gradient-projection scheme (Codina and Blasco (1997) [33]), the second couples curvature and velocity to improve temporal stability, as proposed by Bänsch (2001) [36]. The volume constraint is handled by a Lagrange multiplier (which turns out to be the internal pressure), and an analogous strategy is used to filter out rigid-body motions. The nodal positions are updated in a Lagrangian manner according to the velocity solution at each time step. An automatic remeshing strategy maintains suitable refinement and mesh quality throughout the simulation. Numerical experiments show the convergent and robust behavior of the proposed method. Stability limits are obtained from numerous relaxation tests, and convergence with mesh refinement is confirmed both in the relaxation transient and in the final equilibrium shape. Virtual tweezing experiments are also reported, computing the dependence of the deformed membrane shape with the tweezing velocity (a purely dynamical effect). For sufficiently high velocities, a tether develops which shows good agreement, both in its final radius and in its transient behavior, with available analytical solutions. Finally, simulation results of a membrane subject to the simultaneous action of six tweezers illustrate the robustness of the method.

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.

Role of short-range correlation in facilitation of wave propagation in a long-range ladder chain

NASA Astrophysics Data System (ADS)

Farzadian, O.; Niry, M. D.

2018-09-01

We extend a new method for generating a random chain, which has a kind of short-range correlation induced by a repeated sequence while retaining long-range correlation. Three distinct methods are considered to study the localization-delocalization transition of mechanical waves in one-dimensional disordered media with simultaneous existence of short and long-range correlation. First, a transfer-matrix method was used to calculate numerically the localization length of a wave in a binary chain. We found that the existence of short-range correlation in a long-range correlated chain can increase the localization length at the resonance frequency Ωc. Then, we carried out an analytical study of the delocalization properties of the waves in correlated disordered media around Ωc. Finally, we apply a dynamical method based on the direct numerical simulation of the wave equation to study the propagation of waves in the correlated chain. Imposing short-range correlation on the long-range background will lead the propagation to super-diffusive transport. The results obtained with all three methods are in agreement with each other.

Behaviors of printed circuit boards due to microwave supported curing process of coating materials.

PubMed

Bremerkamp, Felix; Nowottnick, Mathias; Seehase, Dirk; Bui, Trinh Dung

2012-01-01

The Application of a microwave supported curing process for coatings in the field of electronic industry poses a challenge. Here the implementation of this technology is represented. Within the scope of the investigation special PCB Test Layouts were designed and the polymer curing process examined by the method of dielectric analysis. Furthermore the coupling of microwave radiation with conductive PCB structures was analyzed experimentally by means of special test boards. The formation of standing waves and regular heating distribution along the conductive wires on the PCB could be observed. The experimental results were compared with numerical simulation. In this context the numerical analysis of microwave PCB interaction led to important findings concerning wave propagation on wired PCB. The final valuation demonstrated a substantial similarity between numerical simulations and experimental results.

An accelerated proximal augmented Lagrangian method and its application in compressive sensing.

PubMed

Sun, Min; Liu, Jing

2017-01-01

As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case [Formula: see text] convergence rate of PALM-IPR in a non-ergodic sense. Finally, numerical results show that our new method is feasible and efficient for solving compressive sensing.

Numerical study on response time of a parallel plate capacitive polyimide humidity sensor based on microhole upper electrode

NASA Astrophysics Data System (ADS)

Zhou, Wenhe; He, Xuan; Wu, Jianyun; Wang, Liangbi; Wang, Liangcheng

2017-07-01

The parallel plate capacitive humidity sensor based on the grid upper electrode is considered to be a promising one in some fields which require a humidity sensor with better dynamic characteristics. To strengthen the structure and balance the electric charge of the grid upper electrode, a strip is needed. However, it is the strip that keeps the dynamic characteristics of the sensor from being further improved. The numerical method is time- and cost-saving, but the numerical study on the response time of the sensor is just of bits and pieces. The numerical models presented by these studies did not consider the porosity effect of the polymer film on the dynamic characteristics. To overcome the defect of the grid upper electrode, a new structure of the upper electrode is provided by this paper first, and then a model considering the porosity effects of the polymer film on the dynamic characteristics is presented and validated. Finally, with the help of software FLUENT, parameter effects on the response time of the humidity sensor based on the microhole upper electrode are studied by the numerical method. The numerical results show that the response time of the microhole upper electrode sensor is 86% better than that of the grid upper electrode sensor, the response time of humidity sensor can be improved by reducing the hole spacing, increasing the aperture, reducing film thickness, and reasonably enlarging the porosity of the film.

Two-Relaxation-Time Lattice Boltzmann Method for Advective-Diffusive-Reactive Transport

NASA Astrophysics Data System (ADS)

Yan, Z.; Hilpert, M.

2016-12-01

The lattice Boltzmann method (LBM) has been applied to study a wide range of reactive transport in porous and fractured media. The single-relaxation-time (SRT) LBM, employing single relaxation time, is the most popular LBM due to its simplicity of understanding and implementation. Nevertheless, the SRT LBM may suffer from numerical instability for small value of the relaxation time. By contrast, the multiple-relaxation-time (MRT) LBM, employing multiple relaxation times, can improve the numerical stability through tuning the multiple relaxation times, but the complexity of implementing this method restricts its applications. The two-relaxation-time (TRT) LBM, which employs two relaxation times, combines the advantages of SRT and MRT LBMs. The TRT LBM can produce simulations with better accuracy and stability than the SRT one, and is easier to implement than the MRT one. This work evaluated the numerical accuracy and stability of the TRT method by comparing the simulation results with analytical solutions of Gaussian hill transport and Taylor dispersion under different advective velocities. The accuracy generally increased with the tunable relaxation time τ, and the stability first increased and then decreased as τ increased, showing an optimal TRT method emerging the best numerical stability. The free selection of τ enabled the TRT LBM to simulate the Gaussian hill transport and Taylor dispersion under relatively high advective velocity, under which the SRT LBM suffered from numerical instability. Finally, the TRT method was applied to study the contaminant degradation by chemotactic microorganisms in porous media, which acted as a reprehensive of reactive transport in this study, and well predicted the evolution of microorganisms and degradation of contaminants for different transport scenarios. To sum up, the TRT LBM produced simulation results with good accuracy and stability for various advective-diffusive-reactive transport through tuning the relaxation time τ, illustrating its potential to study various biogeochemical behaviors in the subsurface environment.

MUSTA fluxes for systems of conservation laws

NASA Astrophysics Data System (ADS)

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

2006-08-01

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporate GFORCE in the framework of the MUSTA approach [E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003], resulting in a version that we call GMUSTA. For non-linear systems this gives results that are comparable to those of the Godunov method in conjunction with the exact Riemann solver or complete approximate Riemann solvers, noting however that in our approach, the solution of the Riemann problem in the conventional sense is avoided. Both the GFORCE and GMUSTA fluxes are extended to multi-dimensional non-linear systems in a straightforward unsplit manner, resulting in linearly stable schemes that have the same stability regions as the straightforward multi-dimensional extension of Godunov's method. The methods are applicable to general meshes. The schemes of this paper share with the family of centred methods the common properties of being simple and applicable to a large class of hyperbolic systems, but the schemes of this paper are distinctly more accurate. Finally, we proceed to the practical implementation of our numerical fluxes in the framework of high-order finite volume WENO methods for multi-dimensional non-linear hyperbolic systems. Numerical results are presented for the Euler equations and for the equations of magnetohydrodynamics.

Numerical wind-tunnel simulation for Spar platform

NASA Astrophysics Data System (ADS)

Shen, Wenjun

2017-05-01

ANSYS Fluent software is used in the simulation analysis of numerical wind tunnel model for the upper Spar platform module. Design Modeler (DM), Meshing, FLUENT and CFD-POST are chosen in the numerical calculation. And DM is used to deal with and repair the geometric model, and Meshing is used to mesh the model, Fluent is used to set up and solve the calculation condition, finally CFD-POST is used for post-processing of the results. The wind loads are obtained under different direction and incidence angles. Finally, comparison is made between numerical results and empirical formula.

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

DOE PAGES

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2016-10-21

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an Eulerian framework and evolution equations are developed for the marginal PDFs. Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.« less

A new digitized reverse correction method for hypoid gears based on a one-dimensional probe

NASA Astrophysics Data System (ADS)

Li, Tianxing; Li, Jubo; Deng, Xiaozhong; Yang, Jianjun; Li, Genggeng; Ma, Wensuo

2017-12-01

In order to improve the tooth surface geometric accuracy and transmission quality of hypoid gears, a new digitized reverse correction method is proposed based on the measurement data from a one-dimensional probe. The minimization of tooth surface geometrical deviations is realized from the perspective of mathematical analysis and reverse engineering. Combining the analysis of complex tooth surface generation principles and the measurement mechanism of one-dimensional probes, the mathematical relationship between the theoretical designed tooth surface, the actual machined tooth surface and the deviation tooth surface is established, the mapping relation between machine-tool settings and tooth surface deviations is derived, and the essential connection between the accurate calculation of tooth surface deviations and the reverse correction method of machine-tool settings is revealed. Furthermore, a reverse correction model of machine-tool settings is built, a reverse correction strategy is planned, and the minimization of tooth surface deviations is achieved by means of the method of numerical iterative reverse solution. On this basis, a digitized reverse correction system for hypoid gears is developed by the organic combination of numerical control generation, accurate measurement, computer numerical processing, and digitized correction. Finally, the correctness and practicability of the digitized reverse correction method are proved through a reverse correction experiment. The experimental results show that the tooth surface geometric deviations meet the engineering requirements after two trial cuts and one correction.

Adaptive numerical algorithms to simulate the dynamical Casimir effect in a closed cavity with different boundary conditions

NASA Astrophysics Data System (ADS)

Villar, Paula I.; Soba, Alejandro

2017-07-01

We present an alternative numerical approach to compute the number of particles created inside a cavity due to time-dependent boundary conditions. The physical model consists of a rectangular cavity, where a wall always remains still while the other wall of the cavity presents a smooth movement in one direction. The method relies on the setting of the boundary conditions (Dirichlet and Neumann) and the following resolution of the corresponding equations of modes. By a further comparison between the ground state before and after the movement of the cavity wall, we finally compute the number of particles created. To demonstrate the method, we investigate the creation of particle production in vibrating cavities, confirming previously known results in the appropriate limits. Within this approach, the dynamical Casimir effect can be investigated, making it possible to study a variety of scenarios where no analytical results are known. Of special interest is, of course, the realistic case of the electromagnetic field in a three-dimensional cavity, with transverse electric (TE)-mode and transverse magnetic (TM)-mode photon production. Furthermore, with our approach we are able to calculate numerically the particle creation in a tuneable resonant superconducting cavity by the use of the generalized Robin boundary condition. We compare the numerical results with analytical predictions as well as a different numerical approach. Its extension to three dimensions is also straightforward.

Backward-stochastic-differential-equation approach to modeling of gene expression

NASA Astrophysics Data System (ADS)

Shamarova, Evelina; Chertovskih, Roman; Ramos, Alexandre F.; Aguiar, Paulo

2017-03-01

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

Backward-stochastic-differential-equation approach to modeling of gene expression.

PubMed

Shamarova, Evelina; Chertovskih, Roman; Ramos, Alexandre F; Aguiar, Paulo

2017-03-01

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

Energy analysis in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-07-01

The gravity assist or flyby is investigated by analysing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. First, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighbourhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the Solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

NASA Astrophysics Data System (ADS)

Khait, A.; Shemer, L.

2018-05-01

The evolution of unidirectional wave trains containing a wave that gradually becomes steep is evaluated experimentally and numerically using the Boundary Element Method (BEM). The boundary conditions for the nonlinear numerical simulations corresponded to the actual movements of the wavemaker paddle as recorded in the physical experiments, allowing direct comparison between the measured in experiments' characteristics of the wave train and the numerical predictions. The high level of qualitative and quantitative agreement between the measurements and simulations validated the kinematic criterion for the inception of breaking and the location of the spilling breaker, on the basis of the BEM computations and associated experiments. The breaking inception is associated with the fluid particle at the crest of the steep wave that has been accelerated to match and surpass the crest velocity. The previously observed significant slow-down of the crest while approaching breaking is verified numerically; both narrow-/broad-banded wave trains are considered. Finally, the relative importance of linear and nonlinear contributions is analyzed.

Energy Analysis in the Elliptic Restricted Three-body Problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-05-01

The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics.

PubMed

Brocchini, Maurizio

2013-12-08

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

PubMed Central

Brocchini, Maurizio

2013-01-01

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention. PMID:24353475

Numerical modeling of time-lapse monitoring of CO2 sequestration in a layered basalt reservoir

USGS Publications Warehouse

Khatiwada, M.; Van Wijk, K.; Clement, W.P.; Haney, M.

2008-01-01

As part of preparations in plans by The Big Sky Carbon Sequestration Partnership (BSCSP) to inject CO2 in layered basalt, we numerically investigate seismic methods as a noninvasive monitoring technique. Basalt seems to have geochemical advantages as a reservoir for CO2 storage (CO2 mineralizes quite rapidly while exposed to basalt), but poses a considerable challenge in term of seismic monitoring: strong scattering from the layering of the basalt complicates surface seismic imaging. We perform numerical tests using the Spectral Element Method (SEM) to identify possibilities and limitations of seismic monitoring of CO2 sequestration in a basalt reservoir. While surface seismic is unlikely to detect small physical changes in the reservoir due to the injection of CO2, the results from Vertical Seismic Profiling (VSP) simulations are encouraging. As a perturbation, we make a 5%; change in wave velocity, which produces significant changes in VSP images of pre-injection and post-injection conditions. Finally, we perform an analysis using Coda Wave Interferometry (CWI), to quantify these changes in the reservoir properties due to CO2 injection.

Full wave two-dimensional modeling of scattering and inverse scattering for layered rough surfaces with buried objects

NASA Astrophysics Data System (ADS)

Kuo, Chih-Hao

Efficient and accurate modeling of electromagnetic scattering from layered rough surfaces with buried objects finds applications ranging from detection of landmines to remote sensing of subsurface soil moisture. The formulation of a hybrid numerical/analytical solution to electromagnetic scattering from layered rough surfaces is first presented in this dissertation. The solution to scattering from each rough interface is sought independently based on the extended boundary condition method (EBCM), where the scattered fields of each rough interface are expressed as a summation of plane waves and then cast into reflection/transmission matrices. To account for interactions between multiple rough boundaries, the scattering matrix method (SMM) is applied to recursively cascade reflection and transmission matrices of each rough interface and obtain the composite reflection matrix from the overall scattering medium. The validation of this method against the Method of Moments (MoM) and Small Perturbation Method (SPM) is addressed and the numerical results which investigate the potential of low frequency radar systems in estimating deep soil moisture are presented. Computational efficiency of the proposed method is also discussed. In order to demonstrate the capability of this method in modeling coherent multiple scattering phenomena, the proposed method has been employed to analyze backscattering enhancement and satellite peaks due to surface plasmon waves from layered rough surfaces. Numerical results which show the appearance of enhanced backscattered peaks and satellite peaks are presented. Following the development of the EBCM/SMM technique, a technique which incorporates a buried object in layered rough surfaces by employing the T-matrix method and the cylindrical-to-spatial harmonics transformation is proposed. Validation and numerical results are provided. Finally, a multi-frequency polarimetric inversion algorithm for the retrieval of subsurface soil properties using VHF/UHF band radar measurements is devised. The top soil dielectric constant is first determined using an L-band inversion algorithm. For the retrieval of subsurface properties, a time-domain inversion technique is employed together with a parameter optimization for the pulse shape of time delay echoes from VHF/UHF band radar observations. Numerical studies to investigate the accuracy of the proposed inversion technique in presence of errors are addressed.

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

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

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.

Fractal analysis of GPS time series for early detection of disastrous seismic events

NASA Astrophysics Data System (ADS)

Filatov, Denis M.; Lyubushin, Alexey A.

2017-03-01

A new method of fractal analysis of time series for estimating the chaoticity of behaviour of open stochastic dynamical systems is developed. The method is a modification of the conventional detrended fluctuation analysis (DFA) technique. We start from analysing both methods from the physical point of view and demonstrate the difference between them which results in a higher accuracy of the new method compared to the conventional DFA. Then, applying the developed method to estimate the measure of chaoticity of a real dynamical system - the Earth's crust, we reveal that the latter exhibits two distinct mechanisms of transition to a critical state: while the first mechanism has already been known due to numerous studies of other dynamical systems, the second one is new and has not previously been described. Using GPS time series, we demonstrate efficiency of the developed method in identification of critical states of the Earth's crust. Finally we employ the method to solve a practically important task: we show how the developed measure of chaoticity can be used for early detection of disastrous seismic events and provide a detailed discussion of the numerical results, which are shown to be consistent with outcomes of other researches on the topic.

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Distributed synchronization of networked drive-response systems: A nonlinear fixed-time protocol.

PubMed

Zhao, Wen; Liu, Gang; Ma, Xi; He, Bing; Dong, Yunfeng

2017-11-01

The distributed synchronization of networked drive-response systems is investigated in this paper. A novel nonlinear protocol is proposed to ensure that the tracking errors converge to zeros in a fixed-time. By comparison with previous synchronization methods, the present method considers more practical conditions and the synchronization time is not dependent of arbitrary initial conditions but can be offline pre-assign according to the task assignment. Finally, the feasibility and validity of the presented protocol have been illustrated by a numerical simulation. Copyright © 2017. Published by Elsevier Ltd.

A stage structure pest management model with impulsive state feedback control

NASA Astrophysics Data System (ADS)

Pang, Guoping; Chen, Lansun; Xu, Weijian; Fu, Gang

2015-06-01

A stage structure pest management model with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

Electronic response to nuclear breathing mode

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

Ludwig, Hendrik; Ruffini, Remo; ICRANet, University of Nice-Sophia Antipolis, 28 Av. de Valrose, 06103 Nice Cedex 2

2015-12-17

Based on our previous work on stationary oscillation modes of electrons around giant nuclei, we show how to treat a general driving force on the electron gas, such as the one generated by the breathing mode of the nucleus, by means of the spectral method. As an example we demonstrate this method for a system with Z = 10{sup 4} in β-equilibrium with the electrons compressed up to the nuclear radius. In this case the stationary modes can be obtained analytically, which allows for a very speedy numerical calculation of the final result.

Research on the Rural Express Alliance based on ANP improved profit Allocation

NASA Astrophysics Data System (ADS)

Zhuang, Yufeng; Zhang, Bin

2018-01-01

Online shopping platform in rural distribution difficulties, leading to rural online shopping market and logistics market development is slow. At present, China Post and other private courier companies are not possible to do. So we need to build distribution alliances. Reasonable profit allocation mechanism is the key to the stable development of this distribution alliance. So we proposed the Shapley Value Method and the ANP Improved Model to allocate profits. Finally, the rationality of the method is proved by numerical analysis before and after using the corrected Shapley Value.

Successes and surprises with computer-extended series

NASA Astrophysics Data System (ADS)

van Dyke, M.

An alternative to purely numerical solution of flow problems showing promise is the seminumerical technique that involves extending a perturbation series to high order by delegating the mounting arithmetic to a computer. It is noted, however, that since the method is still under development, several erroneous conclusions have been published. First, three clear successes of this method are described. It is then shown how a failure to carefully assess results has in two cases led to false conclusions. Finally, two problems are discussed that yield surprising results not yet accepted by all other investigators.

A class of renormalised meshless Laplacians for boundary value problems

NASA Astrophysics Data System (ADS)

Basic, Josip; Degiuli, Nastia; Ban, Dario

2018-02-01

A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.

SENS-5D trajectory and wind-sensitivity calculations for unguided rockets

NASA Technical Reports Server (NTRS)

Singh, R. P.; Huang, L. C. P.; Cook, R. A.

1975-01-01

A computational procedure is described which numerically integrates the equations of motion of an unguided rocket. Three translational and two angular (roll discarded) degrees of freedom are integrated through the final burnout; and then, through impact, only three translational motions are considered. Input to the routine is: initial time, altitude and velocity, vehicle characteristics, and other defined options. Input format has a wide range of flexibility for special calculations. Output is geared mainly to the wind-weighting procedure, and includes summary of trajectory at burnout, apogee and impact, summary of spent-stage trajectories, detailed position and vehicle data, unit-wind effects for head, tail and cross winds, coriolis deflections, range derivative, and the sensitivity curves (the so called F(Z) and DF(Z) curves). The numerical integration procedure is a fourth-order, modified Adams-Bashforth Predictor-Corrector method. This method is supplemented by a fourth-order Runge-Kutta method to start the integration at t=0 and whenever error criteria demand a change in step size.

Concurrent topological design of composite structures and materials containing multiple phases of distinct Poisson's ratios

NASA Astrophysics Data System (ADS)

Long, Kai; Yuan, Philip F.; Xu, Shanqing; Xie, Yi Min

2018-04-01

Most studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson's ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson's ratios. The proposed method aims to minimize the mean compliance of the macrostructure with a given mass of base materials. In contrast to the traditional interpolation of the stiffness matrix through numerical results, an interpolation scheme of the Young's modulus and Poisson's ratio using different parameters is adopted. The numerical results demonstrate that the Poisson effect plays a key role in reducing the mean compliance of the final design. An important contribution of the present study is that the proposed concurrent optimization method can automatically distribute base materials with distinct Poisson's ratios between the macrostructural and microstructural levels under a single constraint of the total mass.

The generation of symmetric and asymmetric lump solitons by a bottom topography

NASA Astrophysics Data System (ADS)

Lu, Zhiming

2016-11-01

A group of Lump solutions to the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation is obtained analytically by making use of Hirota bilinear transform method. Then the generation of symmetric and asymmetric lump solitons by an obliquely-placed three-dimensional bottom topography is numerically investigated using the forced Kadomtsev-Petviashvili-I (fKP-I) equation. The numerical method is based on the third order Runge-Kutta method and the Crank-Nicolson scheme. The main result is the asymmetric generation of asymmetric lump-type solitons downstream of the obstacle.The lump soliton with a smaller amplitude is generated with a longer period and moves in a larger angle with respect to the positive x-axis than the one with a larger amplitude. The amplitude of the lump solitons strongly depend on the volume of the obstacle rather than the shape. Finally the effects of the detuning parameter on the generation of lump solitons is also studied. Project supported by NSFC with No. 11272196.

Wavefront-aberration measurement and systematic-error analysis of a high numerical-aperture objective

NASA Astrophysics Data System (ADS)

Liu, Zhixiang; Xing, Tingwen; Jiang, Yadong; Lv, Baobin

2018-02-01

A two-dimensional (2-D) shearing interferometer based on an amplitude chessboard grating was designed to measure the wavefront aberration of a high numerical-aperture (NA) objective. Chessboard gratings offer better diffraction efficiencies and fewer disturbing diffraction orders than traditional cross gratings. The wavefront aberration of the tested objective was retrieved from the shearing interferogram using the Fourier transform and differential Zernike polynomial-fitting methods. Grating manufacturing errors, including the duty-cycle and pattern-deviation errors, were analyzed with the Fourier transform method. Then, according to the relation between the spherical pupil and planar detector coordinates, the influence of the distortion of the pupil coordinates was simulated. Finally, the systematic error attributable to grating alignment errors was deduced through the geometrical ray-tracing method. Experimental results indicate that the measuring repeatability (3σ) of the wavefront aberration of an objective with NA 0.4 was 3.4 mλ. The systematic-error results were consistent with previous analyses. Thus, the correct wavefront aberration can be obtained after calibration.

H∞ memory feedback control with input limitation minimization for offshore jacket platform stabilization

NASA Astrophysics Data System (ADS)

Yang, Jia Sheng

2018-06-01

In this paper, we investigate a H∞ memory controller with input limitation minimization (HMCIM) for offshore jacket platforms stabilization. The main objective of this study is to reduce the control consumption as well as protect the actuator when satisfying the requirement of the system performance. First, we introduce a dynamic model of offshore platform with low order main modes based on mode reduction method in numerical analysis. Then, based on H∞ control theory and matrix inequality techniques, we develop a novel H∞ memory controller with input limitation. Furthermore, a non-convex optimization model to minimize input energy consumption is proposed. Since it is difficult to solve this non-convex optimization model by optimization algorithm, we use a relaxation method with matrix operations to transform this non-convex optimization model to be a convex optimization model. Thus, it could be solved by a standard convex optimization solver in MATLAB or CPLEX. Finally, several numerical examples are given to validate the proposed models and methods.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Swimming in a two-dimensional Brinkman fluid: Computational modeling and regularized solutions

NASA Astrophysics Data System (ADS)

Leiderman, Karin; Olson, Sarah D.

2016-02-01

The incompressible Brinkman equation represents the homogenized fluid flow past obstacles that comprise a small volume fraction. In nondimensional form, the Brinkman equation can be characterized by a single parameter that represents the friction or resistance due to the obstacles. In this work, we derive an exact fundamental solution for 2D Brinkman flow driven by a regularized point force and describe the numerical method to use it in practice. To test our solution and method, we compare numerical results with an analytic solution of a stationary cylinder in a uniform Brinkman flow. Our method is also compared to asymptotic theory; for an infinite-length, undulating sheet of small amplitude, we recover an increasing swimming speed as the resistance is increased. With this computational framework, we study a model swimmer of finite length and observe an enhancement in propulsion and efficiency for small to moderate resistance. Finally, we study the interaction of two swimmers where attraction does not occur when the initial separation distance is larger than the screening length.

Study on energy saving of subway station based on orthogonal experimental method

NASA Astrophysics Data System (ADS)

Guo, Lei

2017-05-01

With the characteristics of quick, efficient and large amount transport, the subway has become an important way to solve urban traffic congestion. As the subway environment will follow the change of external environment factors such as temperature and load of personnel changes, three-dimensional numerical simulations study is conducted by using CFD software for air distribution of subway platform. The influence of different loads (the supply air temperature and velocity of air condition, personnel load, heat flux of the wall) on the subway platform flow field are also analysed. The orthogonal experiment method is applied to the numerical simulation analysis for human comfort under different parameters. Based on those results, the functional relationship between human comfort and the boundary conditions of the platform is produced by multiple linear regression fitting method, the order of major boundary conditions which affect human comfort is obtained. The above study provides a theoretical basis for the final energy-saving strategies.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

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

Wang, Q.; Sprague, M. A.; Jonkman, J.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less

A Modified Isotropic-Kinematic Hardening Model to Predict the Defects in Tube Hydroforming Process

NASA Astrophysics Data System (ADS)

Jin, Kai; Guo, Qun; Tao, Jie; Guo, Xun-zhong

2017-11-01

Numerical simulations of tube hydroforming process of hollow crankshafts were conducted by using finite element analysis method. Moreover, the modified model involving the integration of isotropic-kinematic hardening model with ductile criteria model was used to more accurately optimize the process parameters such as internal pressure, feed distance and friction coefficient. Subsequently, hydroforming experiments were performed based on the simulation results. The comparison between experimental and simulation results indicated that the prediction of tube deformation, crack and wrinkle was quite accurate for the tube hydroforming process. Finally, hollow crankshafts with high thickness uniformity were obtained and the thickness distribution between numerical and experimental results was well consistent.

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.

One-Dimensional Modelling of Internal Ballistics

NASA Astrophysics Data System (ADS)

Monreal-González, G.; Otón-Martínez, R. A.; Velasco, F. J. S.; García-Cascáles, J. R.; Ramírez-Fernández, F. J.

2017-10-01

A one-dimensional model is introduced in this paper for problems of internal ballistics involving solid propellant combustion. First, the work presents the physical approach and equations adopted. Closure relationships accounting for the physical phenomena taking place during combustion (interfacial friction, interfacial heat transfer, combustion) are deeply discussed. Secondly, the numerical method proposed is presented. Finally, numerical results provided by this code (UXGun) are compared with results of experimental tests and with the outcome from a well-known zero-dimensional code. The model provides successful results in firing tests of artillery guns, predicting with good accuracy the maximum pressure in the chamber and muzzle velocity what highlights its capabilities as prediction/design tool for internal ballistics.

Hybrid control of the Neimark-Sacker bifurcation in a delayed Nicholson's blowflies equation.

PubMed

Wang, Yuanyuan; Wang, Lisha

In this article, for delayed Nicholson's blowflies equation, we propose a hybrid control nonstandard finite-difference (NSFD) scheme in which state feedback and parameter perturbation are used to control the Neimark-Sacker bifurcation. Firstly, the local stability of the positive equilibria for hybrid control delay differential equation is discussed according to Hopf bifurcation theory. Then, for any step-size, a hybrid control numerical algorithm is introduced to generate the Neimark-Sacker bifurcation at a desired point. Finally, numerical simulation results confirm that the control strategy is efficient in controlling the Neimark-Sacker bifurcation. At the same time, the results show that the NSFD control scheme is better than the Euler control method.

Study of rainfall-induced landslide: a review

NASA Astrophysics Data System (ADS)

Tohari, A.

2018-02-01

Rainfall-induced landslides pose a substantial risk to people and infrastructure. For this reason, there have been numerous studies to understand the landslide mechanism. Most of them were performed on the numerical analysis and laboratory experiment. This paper presents a review of existing research on field hydrological condition of soil slopes leading to the initiation of rainfall-induced landslide. Existing methods to study field hydrological response of slopes are first reviewed, emphasizing their limitations and suitability of application. The typical hydrological response profiles in the slope are then discussed. Subsequently, some significant findings on hydrological condition leading to rainfall-induced landslides are summarized and discussed. Finally, several research topics are recommended for future study.

Optical ablation/temperature gage (COTA)

NASA Astrophysics Data System (ADS)

Cassaing, J.; Balageas, D.

ONERA has ground and flight tested for heat-shield recession a novel technique, different from current radiation and acoustic measurement methods. It uses a combined ablation/temperature gage that views the radiation optically from a cavity embedded within the heat shield. Flight measurements, both of temperature and of passage of the ablation front, are compared with data generated by a predictive numerical code. The ablation and heat diffusion into the instrumented ablator can be simulated numerically to evaluate accurately the errors due to the presence of the gage. This technology was established in 1978 and finally adopted after ground tests in arc heater facilities. After four years of flight evaluations, it is possible to evaluate and criticize the sensor reliability.

Evaluation of Neutron-induced Cross Sections and their Related Covariances with Physical Constraints

NASA Astrophysics Data System (ADS)

De Saint Jean, C.; Archier, P.; Privas, E.; Noguère, G.; Habert, B.; Tamagno, P.

2018-02-01

Nuclear data, along with numerical methods and the associated calculation schemes, continue to play a key role in reactor design, reactor core operating parameters calculations, fuel cycle management and criticality safety calculations. Due to the intensive use of Monte-Carlo calculations reducing numerical biases, the final accuracy of neutronic calculations increasingly depends on the quality of nuclear data used. This paper gives a broad picture of all ingredients treated by nuclear data evaluators during their analyses. After giving an introduction to nuclear data evaluation, we present implications of using the Bayesian inference to obtain evaluated cross sections and related uncertainties. In particular, a focus is made on systematic uncertainties appearing in the analysis of differential measurements as well as advantages and drawbacks one may encounter by analyzing integral experiments. The evaluation work is in general done independently in the resonance and in the continuum energy ranges giving rise to inconsistencies in evaluated files. For future evaluations on the whole energy range, we call attention to two innovative methods used to analyze several nuclear reaction models and impose constraints. Finally, we discuss suggestions for possible improvements in the evaluation process to master the quantification of uncertainties. These are associated with experiments (microscopic and integral), nuclear reaction theories and the Bayesian inference.

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.

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games.

PubMed

Liu, Jiacai; Zhao, Wenjian

2016-11-08

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

Green's functions in equilibrium and nonequilibrium from real-time bold-line Monte Carlo

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David R.; Millis, Andrew J.

2014-03-01

Green's functions for the Anderson impurity model are obtained within a numerically exact formalism. We investigate the limits of analytical continuation for equilibrium systems, and show that with real time methods even sharp high-energy features can be reliably resolved. Continuing to an Anderson impurity in a junction, we evaluate two-time correlation functions, spectral properties, and transport properties, showing how the correspondence between the spectral function and the differential conductance breaks down when nonequilibrium effects are taken into account. Finally, a long-standing dispute regarding this model has involved the voltage splitting of the Kondo peak, an effect which was predicted over a decade ago by approximate analytical methods but never successfully confirmed by numerics. We settle the issue by demonstrating in an unbiased manner that this splitting indeed occurs. Yad Hanadiv-Rothschild Foundation, TG-DMR120085, TG-DMR130036, NSF CHE-1213247, NSF DMR 1006282, DOE ER 46932.

Building of fuzzy decision trees using ID3 algorithm

NASA Astrophysics Data System (ADS)

Begenova, S. B.; Avdeenko, T. V.

2018-05-01

Decision trees are widely used in the field of machine learning and artificial intelligence. Such popularity is due to the fact that with the help of decision trees graphic models, text rules can be built and they are easily understood by the final user. Because of the inaccuracy of observations, uncertainties, the data, collected in the environment, often take an unclear form. Therefore, fuzzy decision trees becoming popular in the field of machine learning. This article presents a method that includes the features of the two above-mentioned approaches: a graphical representation of the rules system in the form of a tree and a fuzzy representation of the data. The approach uses such advantages as high comprehensibility of decision trees and the ability to cope with inaccurate and uncertain information in fuzzy representation. The received learning method is suitable for classifying problems with both numerical and symbolic features. In the article, solution illustrations and numerical results are given.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Numerical weather prediction model tuning via ensemble prediction system

NASA Astrophysics Data System (ADS)

Jarvinen, H.; Laine, M.; Ollinaho, P.; Solonen, A.; Haario, H.

2011-12-01

This paper discusses a novel approach to tune predictive skill of numerical weather prediction (NWP) models. NWP models contain tunable parameters which appear in parameterizations schemes of sub-grid scale physical processes. Currently, numerical values of these parameters are specified manually. In a recent dual manuscript (QJRMS, revised) we developed a new concept and method for on-line estimation of the NWP model parameters. The EPPES ("Ensemble prediction and parameter estimation system") method requires only minimal changes to the existing operational ensemble prediction infra-structure and it seems very cost-effective because practically no new computations are introduced. The approach provides an algorithmic decision making tool for model parameter optimization in operational NWP. In EPPES, statistical inference about the NWP model tunable parameters is made by (i) generating each member of the ensemble of predictions using different model parameter values, drawn from a proposal distribution, and (ii) feeding-back the relative merits of the parameter values to the proposal distribution, based on evaluation of a suitable likelihood function against verifying observations. In the presentation, the method is first illustrated in low-order numerical tests using a stochastic version of the Lorenz-95 model which effectively emulates the principal features of ensemble prediction systems. The EPPES method correctly detects the unknown and wrongly specified parameters values, and leads to an improved forecast skill. Second, results with an atmospheric general circulation model based ensemble prediction system show that the NWP model tuning capacity of EPPES scales up to realistic models and ensemble prediction systems. Finally, a global top-end NWP model tuning exercise with preliminary results is published.

Precise and Fast Computation of the Gravitational Field of a General Finite Body and Its Application to the Gravitational Study of Asteroid Eros

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

Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp

In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitationalmore » acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.« less

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Equivalent orthotropic elastic moduli identification method for laminated electrical steel sheets

NASA Astrophysics Data System (ADS)

Saito, Akira; Nishikawa, Yasunari; Yamasaki, Shintaro; Fujita, Kikuo; Kawamoto, Atsushi; Kuroishi, Masakatsu; Nakai, Hideo

2016-05-01

In this paper, a combined numerical-experimental methodology for the identification of elastic moduli of orthotropic media is presented. Special attention is given to the laminated electrical steel sheets, which are modeled as orthotropic media with nine independent engineering elastic moduli. The elastic moduli are determined specifically for use with finite element vibration analyses. We propose a three-step methodology based on a conventional nonlinear least squares fit between measured and computed natural frequencies. The methodology consists of: (1) successive augmentations of the objective function by increasing the number of modes, (2) initial condition updates, and (3) appropriate selection of the natural frequencies based on their sensitivities on the elastic moduli. Using the results of numerical experiments, it is shown that the proposed method achieves more accurate converged solution than a conventional approach. Finally, the proposed method is applied to measured natural frequencies and mode shapes of the laminated electrical steel sheets. It is shown that the method can successfully identify the orthotropic elastic moduli that can reproduce the measured natural frequencies and frequency response functions by using finite element analyses with a reasonable accuracy.

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

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Extension of a coarse grained particle method to simulate heat transfer in fluidized beds

DOE PAGES

Lu, Liqiang; Morris, Aaron; Li, Tingwen; ...

2017-04-18

The heat transfer in a gas-solids fluidized bed is simulated with computational fluid dynamic-discrete element method (CFD-DEM) and coarse grained particle method (CGPM). In CGPM fewer numerical particles and their collisions are tracked by lumping several real particles into a computational parcel. Here, the assumption is that the real particles inside a coarse grained particle (CGP) are made from same species and share identical physical properties including density, diameter and temperature. The parcel-fluid convection term in CGPM is calculated using the same method as in DEM. For all other heat transfer mechanisms, we derive in this study mathematical expressions thatmore » relate the new heat transfer terms for CGPM to those traditionally derived in DEM. This newly derived CGPM model is verified and validated by comparing the results with CFD-DEM simulation results and experiment data. The numerical results compare well with experimental data for both hydrodynamics and temperature profiles. Finally, the proposed CGPM model can be used for fast and accurate simulations of heat transfer in large scale gas-solids fluidized beds.« less

Extension of a coarse grained particle method to simulate heat transfer in fluidized beds

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

Lu, Liqiang; Morris, Aaron; Li, Tingwen

The heat transfer in a gas-solids fluidized bed is simulated with computational fluid dynamic-discrete element method (CFD-DEM) and coarse grained particle method (CGPM). In CGPM fewer numerical particles and their collisions are tracked by lumping several real particles into a computational parcel. Here, the assumption is that the real particles inside a coarse grained particle (CGP) are made from same species and share identical physical properties including density, diameter and temperature. The parcel-fluid convection term in CGPM is calculated using the same method as in DEM. For all other heat transfer mechanisms, we derive in this study mathematical expressions thatmore » relate the new heat transfer terms for CGPM to those traditionally derived in DEM. This newly derived CGPM model is verified and validated by comparing the results with CFD-DEM simulation results and experiment data. The numerical results compare well with experimental data for both hydrodynamics and temperature profiles. Finally, the proposed CGPM model can be used for fast and accurate simulations of heat transfer in large scale gas-solids fluidized beds.« less

Visualization and analysis of flow structures in an open cavity

NASA Astrophysics Data System (ADS)

Liu, Jun; Cai, Jinsheng; Yang, Dangguo; Wu, Junqiang; Wang, Xiansheng

2018-05-01

A numerical study is performed on the supersonic flow over an open cavity at Mach number of 1.5. A newly developed visualization method is employed to visualize the complicated flow structures, which provide an insight into major flow physics. Four types of shock/compressive waves which existed in experimental schlieren are observed in numerical visualization results. Furthermore, other flow structures such as multi-scale vortices are also obtained in the numerical results. And a new type of shocklet which is beneath large vortices is found. The shocklet beneath the vortex originates from leading edge, then, is strengthened by successive interactions between feedback compressive waves and its attached vortex. Finally, it collides against the trailing surface and generates a large number of feedback compressive waves and intensive pressure fluctuations. It is suggested that the shocklets beneath vortex play an important role of cavity self-sustained oscillation.

Numerical determination of lateral loss coefficients for subchannel analysis in nuclear fuel bundles

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

Sin Kim; Goon-Cherl Park

1995-09-01

An accurate prediction of cross-flow based on detailed knowledge of the velocity field in subchannels of a nuclear fuel assembly is of importance in nuclear fuel performance analysis. In this study, the low-Reynolds number {kappa}-{epsilon} turbulence model has been adopted in two adjacent subchannels with cross-flow. The secondary flow is estimated accurately by the anisotropic algebraic Reynolds stress model. This model was numerically calculated by the finite element method and has been verified successfully through comparison with existing experimental data. Finally, with the numerical analysis of the velocity field in such subchannel domain, an analytical correlation of the lateral lossmore » coefficient is obtained to predict the cross-flow rate in subchannel analysis codes. The correlation is expressed as a function of the ratio of the lateral flow velocity to the donor subchannel axial velocity, recipient channel Reynolds number and pitch-to-diameter.« less

Satellite Sounder Data Assimilation for Improving Alaska Region Weather Forecast

NASA Technical Reports Server (NTRS)

Zhu, Jiang; Stevens, E.; Zavodsky, B. T.; Zhang, X.; Heinrichs, T.; Broderson, D.

2014-01-01

Data assimilation has been demonstrated very useful in improving both global and regional numerical weather prediction. Alaska has very coarser surface observation sites. On the other hand, it gets much more satellite overpass than lower 48 states. How to utilize satellite data to improve numerical prediction is one of hot topics among weather forecast community in Alaska. The Geographic Information Network of Alaska (GINA) at University of Alaska is conducting study on satellite data assimilation for WRF model. AIRS/CRIS sounder profile data are used to assimilate the initial condition for the customized regional WRF model (GINA-WRF model). Normalized standard deviation, RMSE, and correlation statistic analysis methods are applied to analyze one case of 48 hours forecasts and one month of 24-hour forecasts in order to evaluate the improvement of regional numerical model from Data assimilation. The final goal of the research is to provide improved real-time short-time forecast for Alaska regions.

Numerical analysis of the beam position monitor pickup for the Iranian light source facility

NASA Astrophysics Data System (ADS)

Shafiee, M.; Feghhi, S. A. H.; Rahighi, J.

2017-03-01

In this paper, we describe the design of a button type Beam Position Monitor (BPM) for the low emittance storage ring of the Iranian Light Source Facility (ILSF). First, we calculate sensitivities, induced power and intrinsic resolution based on solving Laplace equation numerically by finite element method (FEM), in order to find the potential at each point of BPM's electrode surface. After the optimization of the designed BPM, trapped high order modes (HOM), wakefield and thermal loss effects are calculated. Finally, after fabrication of BPM, it is experimentally tested by using a test-stand. The results depict that the designed BPM has a linear response in the area of 2×4 mm2 inside the beam pipe and the sensitivity of 0.080 and 0.087 mm-1 in horizontal and vertical directions. Experimental results also depict that they are in a good agreement with numerical analysis.

Numerical simulation of one-dimensional heat transfer in composite bodies with phase change. M.S. Thesis, 1980 Final Report; [wing deicing pads

NASA Technical Reports Server (NTRS)

Dewitt, K. J.; Baliga, G.

1982-01-01

A numerical simulation was developed to investigate the one dimensional heat transfer occurring in a system composed of a layered aircraft blade having an ice deposit on its surface. The finite difference representation of the heat conduction equations was done using the Crank-Nicolson implicit finite difference formulation. The simulation considers uniform or time dependent heat sources, from heaters which can be either point sources or of finite thickness. For the ice water phase change, a numerical method which approximates the latent heat effect by a large heat capacity over a small temperature interval was applied. The simulation describes the temperature profiles within the various layers of the de-icer pad, as well as the movement of the ice water interface. The simulation could also be used to predict the one dimensional temperature profiles in any composite slab having different boundary conditions.

Numerical simulation of turbulent jet noise, part 2

NASA Technical Reports Server (NTRS)

Metcalfe, R. W.; Orszag, S. A.

1976-01-01

Results on the numerical simulation of jet flow fields were used to study the radiated sound field, and in addition, to extend and test the capabilities of the turbulent jet simulation codes. The principal result of the investigation was the computation of the radiated sound field from a turbulent jet. In addition, the computer codes were extended to account for the effects of compressibility and eddy viscosity, and the treatment of the nonlinear terms of the Navier-Stokes equations was modified so that they can be computed in a semi-implicit way. A summary of the flow model and a description of the numerical methods used for its solution are presented. Calculations of the radiated sound field are reported. In addition, the extensions that were made to the fundamental dynamical codes are described. Finally, the current state-of-the-art for computer simulation of turbulent jet noise is summarized.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Laser wavelength effect on charge transfer and excitation processes in laser-assisted collisions of Li+ + H

NASA Astrophysics Data System (ADS)

Domínguez-Gutiérrez, F. Javier; Cabrera-Trujillo, R.

2014-05-01

Total, n = 2 , and 3 charge transfer and n = 2 target excitation probabilities for collision of Li+ with ground state atomic hydrogen are calculated numerically, in the impact energy collision range 0.25-5 keV. The total wave function at the end of the dynamics of the collision is obtained by solving the time-dependent Schrödinger equation by means the finite-difference method. We use a pseudo-potential method to model the electronic structure of the Li+ ion. The n = 2 , and 3 charge transfer and n = 2 target excitation probabilities are obtained by projecting the stationary states of Lithium and Hydrogen neutral atoms to the total wave function of the collision, respectively; the stationary states of Li and H are obtained numerically. To assess the validity of our method, our numerical results have been compared with those obtained experimentally and by other theoretical methods found in the literature. We study the laser-assited collision by using a short (3 fs at FWHM) and intense (3.15 ×12 W/cm2) Gaussian laser pulse. We consider a wavelength range between 400 - 1000 nm in steps of 100 nm. Finally, we analyze the laser assisted collision by a qualitatively way with a two level approach. We acknowledge support from grant PAPIIT IN 110-714 and CONACyT (Ph.D. scholarship).

The Artificial Neural Networks Based on Scalarization Method for a Class of Bilevel Biobjective Programming Problem

PubMed Central

Chen, Zhong; Liu, June; Li, Xiong

2017-01-01

A two-stage artificial neural network (ANN) based on scalarization method is proposed for bilevel biobjective programming problem (BLBOP). The induced set of the BLBOP is firstly expressed as the set of minimal solutions of a biobjective optimization problem by using scalar approach, and then the whole efficient set of the BLBOP is derived by the proposed two-stage ANN for exploring the induced set. In order to illustrate the proposed method, seven numerical examples are tested and compared with results in the classical literature. Finally, a practical problem is solved by the proposed algorithm. PMID:29312446

A generalization of random matrix theory and its application to statistical physics.

PubMed

Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H

2017-02-01

To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.

Time Hierarchies and Model Reduction in Canonical Non-linear Models

PubMed Central

Löwe, Hannes; Kremling, Andreas; Marin-Sanguino, Alberto

2016-01-01

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems. PMID:27708665

Passive quantum error correction of linear optics networks through error averaging

NASA Astrophysics Data System (ADS)

Marshman, Ryan J.; Lund, Austin P.; Rohde, Peter P.; Ralph, Timothy C.

2018-02-01

We propose and investigate a method of error detection and noise correction for bosonic linear networks using a method of unitary averaging. The proposed error averaging does not rely on ancillary photons or control and feedforward correction circuits, remaining entirely passive in its operation. We construct a general mathematical framework for this technique and then give a series of proof of principle examples including numerical analysis. Two methods for the construction of averaging are then compared to determine the most effective manner of implementation and probe the related error thresholds. Finally we discuss some of the potential uses of this scheme.

Pseudospectral method for gravitational wave collapse

NASA Astrophysics Data System (ADS)

Hilditch, David; Weyhausen, Andreas; Brügmann, Bernd

2016-03-01

We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first-order generalized harmonic gauge formulation. The relevant theory is reviewed, and the numerical method is critically examined and specialized for the task at hand. In particular, we investigate formulation parameters—gauge- and constraint-preserving boundary conditions well suited to nonvanishing gauge source functions. Different types of axisymmetric twist-free moment-of-time-symmetry gravitational wave initial data are discussed. A treatment of the axisymmetric apparent horizon condition is presented with careful attention to regularity on axis. Our apparent horizon finder is then evaluated in a number of test cases. Moving on to evolutions, we investigate modifications to the generalized harmonic gauge constraint damping scheme to improve conservation in the strong-field regime. We demonstrate strong-scaling of our pseudospectral penalty code. We employ the Cartoon method to efficiently evolve axisymmetric data in our 3 +1 -dimensional code. We perform test evolutions of the Schwarzschild spacetime perturbed by gravitational waves and by gauge pulses, both to demonstrate the use of our black-hole excision scheme and for comparison with earlier results. Finally, numerical evolutions of supercritical Brill waves are presented to demonstrate durability of the excision scheme for the dynamical formation of a black hole.

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Survey of Natural Language Processing Techniques in Bioinformatics.

PubMed

Zeng, Zhiqiang; Shi, Hua; Wu, Yun; Hong, Zhiling

2015-01-01

Informatics methods, such as text mining and natural language processing, are always involved in bioinformatics research. In this study, we discuss text mining and natural language processing methods in bioinformatics from two perspectives. First, we aim to search for knowledge on biology, retrieve references using text mining methods, and reconstruct databases. For example, protein-protein interactions and gene-disease relationship can be mined from PubMed. Then, we analyze the applications of text mining and natural language processing techniques in bioinformatics, including predicting protein structure and function, detecting noncoding RNA. Finally, numerous methods and applications, as well as their contributions to bioinformatics, are discussed for future use by text mining and natural language processing researchers.

On the analytic and numeric optimisation of airplane trajectories under real atmospheric conditions

NASA Astrophysics Data System (ADS)

Gonzalo, J.; Domínguez, D.; López, D.

2014-12-01

From the beginning of aviation era, economic constraints have forced operators to continuously improve the planning of the flights. The revenue is proportional to the cost per flight and the airspace occupancy. Many methods, the first started in the middle of last century, have explore analytical, numerical and artificial intelligence resources to reach the optimal flight planning. In parallel, advances in meteorology and communications allow an almost real-time knowledge of the atmospheric conditions and a reliable, error-bounded forecast for the near future. Thus, apart from weather risks to be avoided, airplanes can dynamically adapt their trajectories to minimise their costs. International regulators are aware about these capabilities, so it is reasonable to envisage some changes to allow this dynamic planning negotiation to soon become operational. Moreover, current unmanned airplanes, very popular and often small, suffer the impact of winds and other weather conditions in form of dramatic changes in their performance. The present paper reviews analytic and numeric solutions for typical trajectory planning problems. Analytic methods are those trying to solve the problem using the Pontryagin principle, where influence parameters are added to state variables to form a split condition differential equation problem. The system can be solved numerically -indirect optimisation- or using parameterised functions -direct optimisation-. On the other hand, numerical methods are based on Bellman's dynamic programming (or Dijkstra algorithms), where the fact that two optimal trajectories can be concatenated to form a new optimal one if the joint point is demonstrated to belong to the final optimal solution. There is no a-priori conditions for the best method. Traditionally, analytic has been more employed for continuous problems whereas numeric for discrete ones. In the current problem, airplane behaviour is defined by continuous equations, while wind fields are given in a discrete grid at certain time intervals. The research demonstrates advantages and disadvantages of each method as well as performance figures of the solutions found for typical flight conditions under static and dynamic atmospheres. This provides significant parameters to be used in the selection of solvers for optimal trajectories.

Surrogate models for sheet metal stamping problem based on the combination of proper orthogonal decomposition and radial basis function

NASA Astrophysics Data System (ADS)

Dang, Van Tuan; Lafon, Pascal; Labergere, Carl

2017-10-01

In this work, a combination of Proper Orthogonal Decomposition (POD) and Radial Basis Function (RBF) is proposed to build a surrogate model based on the Benchmark Springback 3D bending from the Numisheet2011 congress. The influence of the two design parameters, the geometrical parameter of the die radius and the process parameter of the blank holder force, on the springback of the sheet after a stamping operation is analyzed. The classical Design of Experience (DoE) uses Full Factorial to design the parameter space with sample points as input data for finite element method (FEM) numerical simulation of the sheet metal stamping process. The basic idea is to consider the design parameters as additional dimensions for the solution of the displacement fields. The order of the resultant high-fidelity model is reduced through the use of POD method which performs model space reduction and results in the basis functions of the low order model. Specifically, the snapshot method is used in our work, in which the basis functions is derived from snapshot deviation of the matrix of the final displacements fields of the FEM numerical simulation. The obtained basis functions are then used to determine the POD coefficients and RBF is used for the interpolation of these POD coefficients over the parameter space. Finally, the presented POD-RBF approach which is used for shape optimization can be performed with high accuracy.

From three-dimensional long-term tectonic numerical models to synthetic structural data: semi-automatic extraction of instantaneous & finite strain quantities

NASA Astrophysics Data System (ADS)

Duclaux, Guillaume; May, Dave

2017-04-01

Over the past three decades thermo-mechanical numerical modelling has transformed the way we look at deformation in the lithosphere. More than just generating aesthetically pleasing pictures, the output from a numerical models contains a rich source of quantitative information that can be used to measure deformation quantities in plan view or three-dimensions. Adding value to any numerical experiment requires a thorough post-processing of the modelling results. Such work aims to produce visual information that will resonate to seasoned structural geologists and assist with comparing experimental and observational data. Here we introduce two methods to generate synthetic structural data from numerical model outputs. We first present an image processing and shape recognition workflow developed to extract the active faults orientation from surface velocity gradients. In order to measure the active faults lengths and directions along with their distribution at the surface of the model we implemented an automated sequential mapping technique based on the second invariant of the strain rate tensor and using a suite a python functions. Active fault direction measurements are achieved using a probabilistic method for extracting linear features orientation from any surface. This method has the undeniable advantage to avoid interpretation bias. Strike measurements for individual segments are weighted according to their length and orientation distribution data are presented in an equal-area moving average rose diagrams produced using a weighted method. Finally, we discuss a method for mapping finite strain in three-dimensions. A high-resolution Lagrangian regular grid which advects during the numerical experiment is used to track the progressive deformation within the model. Thanks to this data we can measure the finite strain ellipsoids for any region of interest in the model. This method assumes that the finite strain is homogenous within one unit cell of the grid. We can compute individual ellipsoid's parameters (orientation, shape, etc.) and represent the finite deformation for any region of interest in a Flinn diagram. In addition, we can use the finite strain ellipsoids to estimate the prevailing foliation and/or lineation directions anywhere in the model. These two methods are applied to measure the instantaneous and finite deformation patterns within an oblique rift zone ongoing constant extension in the absence of surface processes.

Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition

NASA Astrophysics Data System (ADS)

Hu, Yong; Han, Liguo; Xu, Zhuo; Zhang, Fengjiao; Zeng, Jingwen

2017-04-01

Full Waveform Inversion (FWI) can be used to build high resolution velocity models, but there are still many challenges in seismic field data processing. The most difficult problem is about how to recover long-wavelength components of subsurface velocity models when seismic data is lacking of low frequency information and without long-offsets. To solve this problem, we propose to use Waveform Mode Decomposition (WMD) method to reconstruct low frequency information for FWI to obtain a smooth model, so that the initial model dependence of FWI can be reduced. In this paper, we use adjoint-state method to calculate the gradient for Waveform Mode Decomposition Full Waveform Inversion (WMDFWI). Through the illustrative numerical examples, we proved that the low frequency which is reconstructed by WMD method is very reliable. WMDFWI in combination with the adaptive multi-step inversion strategy can obtain more faithful and accurate final inversion results. Numerical examples show that even if the initial velocity model is far from the true model and lacking of low frequency information, we still can obtain good inversion results with WMD method. From numerical examples of anti-noise test, we see that the adaptive multi-step inversion strategy for WMDFWI has strong ability to resist Gaussian noise. WMD method is promising to be able to implement for the land seismic FWI, because it can reconstruct the low frequency information, lower the dominant frequency in the adjoint source, and has a strong ability to resist noise.

Theory and computation of optimal low- and medium-thrust transfers

NASA Technical Reports Server (NTRS)

Chuang, C.-H.

1993-01-01

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.

Nonlinear multivariate and time series analysis by neural network methods

NASA Astrophysics Data System (ADS)

Hsieh, William W.

2004-03-01

Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño-Southern Oscillation and the stratospheric quasi-biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real-world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm.

A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1982-01-01

A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres.

Magnetic Field Applications in Semiconductor Crystal Growth and Metallurgy

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Ramachandran, Narayanan; Grugel, Richard; Curreri, Peter A. (Technical Monitor)

2002-01-01

The Traveling Magnetic Field (TMF) technique, recently proposed to control meridional flow in electrically conducting melts, is reviewed. In particular, the natural convection damping capability of this technique has been numerically demonstrated with the implication of significantly improving crystal quality. Advantages of the traveling magnetic field, in comparison to the more mature rotating magnetic field method, are discussed. Finally, results of experiments with mixing metallic alloys in long ampoules using TMF is presented

Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria

NASA Astrophysics Data System (ADS)

Sun, Zhigang; Wang, Changxi; Niu, Xuming; Song, Yingdong

2017-08-01

In this paper, a Reliability-Sensitivity Based Design Optimization (RSBDO) methodology for the design of the ceramic matrix composites (CMCs) components has been proposed. A practical and efficient method for reliability analysis and sensitivity analysis of complex components with arbitrary distribution parameters are investigated by using the perturbation method, the respond surface method, the Edgeworth series and the sensitivity analysis approach. The RSBDO methodology is then established by incorporating sensitivity calculation model into RBDO methodology. Finally, the proposed RSBDO methodology is applied to the design of the CMCs components. By comparing with Monte Carlo simulation, the numerical results demonstrate that the proposed methodology provides an accurate, convergent and computationally efficient method for reliability-analysis based finite element modeling engineering practice.

A century of enzyme kinetic analysis, 1913 to 2013.

PubMed

Johnson, Kenneth A

2013-09-02

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Predict the fatigue life of crack based on extended finite element method and SVR

NASA Astrophysics Data System (ADS)

Song, Weizhen; Jiang, Zhansi; Jiang, Hui

2018-05-01

Using extended finite element method (XFEM) and support vector regression (SVR) to predict the fatigue life of plate crack. Firstly, the XFEM is employed to calculate the stress intensity factors (SIFs) with given crack sizes. Then predicetion model can be built based on the function relationship of the SIFs with the fatigue life or crack length. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Because of the accuracy of the forward Euler method only ensured by the small step size, a new prediction method is presented to resolve the issue. The numerical examples were studied to demonstrate the proposed method allow a larger step size and have a high accuracy.

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

2018-03-20

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

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

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Enthalpy-based multiple-relaxation-time lattice Boltzmann method for solid-liquid phase-change heat transfer in metal foams.

PubMed

Liu, Qing; He, Ya-Ling; Li, Qing

2017-08-01

In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.

Enthalpy-based multiple-relaxation-time lattice Boltzmann method for solid-liquid phase-change heat transfer in metal foams

NASA Astrophysics Data System (ADS)

Liu, Qing; He, Ya-Ling; Li, Qing

2017-08-01

In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.

Preformulation considerations for controlled release dosage forms. Part III. Candidate form selection using numerical weighting and scoring.

PubMed

Chrzanowski, Frank

2008-01-01

Two numerical methods, Decision Analysis (DA) and Potential Problem Analysis (PPA) are presented as alternative selection methods to the logical method presented in Part I. In DA properties are weighted and outcomes are scored. The weighted scores for each candidate are totaled and final selection is based on the totals. Higher scores indicate better candidates. In PPA potential problems are assigned a seriousness factor and test outcomes are used to define the probability of occurrence. The seriousness-probability products are totaled and forms with minimal scores are preferred. DA and PPA have never been compared to the logical-elimination method. Additional data were available for two forms of McN-5707 to provide complete preformulation data for five candidate forms. Weight and seriousness factors (independent variables) were obtained from a survey of experienced formulators. Scores and probabilities (dependent variables) were provided independently by Preformulation. The rankings of the five candidate forms, best to worst, were similar for all three methods. These results validate the applicability of DA and PPA for candidate form selection. DA and PPA are particularly applicable in cases where there are many candidate forms and where each form has some degree of unfavorable properties.

A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A new weak Galerkin finite element method for elliptic interface problems

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

Mu, Lin; Wang, Junping; Ye, Xiu

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Tiger LDRD final report

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

Steich, D J; Brugger, S T; Kallman, J S

2000-02-01

This final report describes our efforts on the Three-Dimensional Massively Parallel CEM Technologies LDRD project (97-ERD-009). Significant need exists for more advanced time domain computational electromagnetics modeling. Bookkeeping details and modifying inflexible software constitute a vast majority of the effort required to address such needs. The required effort escalates rapidly as problem complexity increases. For example, hybrid meshes requiring hybrid numerics on massively parallel platforms (MPPs). This project attempts to alleviate the above limitations by investigating flexible abstractions for these numerical algorithms on MPPs using object-oriented methods, providing a programming environment insulating physics from bookkeeping. The three major design iterationsmore » during the project, known as TIGER-I to TIGER-III, are discussed. Each version of TIGER is briefly discussed along with lessons learned during the development and implementation. An Application Programming Interface (API) of the object-oriented interface for Tiger-III is included in three appendices. The three appendices contain the Utilities, Entity-Attribute, and Mesh libraries developed during the project. The API libraries represent a snapshot of our latest attempt at insulated the physics from the bookkeeping.« less

Microbial diversity and their roles in the vinegar fermentation process.

PubMed

Li, Sha; Li, Pan; Feng, Feng; Luo, Li-Xin

2015-06-01

Vinegar is one of the oldest acetic acid-diluted solution products in the world. It is produced from any fermentable sugary substrate by various fermentation methods. The final vinegar products possess unique functions, which are endowed with many kinds of compounds formed in the fermentation process. The quality of vinegar is determined by many factors, especially by the raw materials and microbial diversity involved in vinegar fermentation. Given that metabolic products from the fermenting strains are directly related to the quality of the final products of vinegar, the microbial diversity and features of the dominant strains involved in different fermentation stages should be analyzed to improve the strains and stabilize fermentation. Moreover, although numerous microbiological studies have been conducted to examine the process of vinegar fermentation, knowledge about microbial diversity and their roles involved in fermentation is still fragmentary and not systematic enough. Therefore, in this review, the dominant microorganism species involved in the stages of alcoholic fermentation and acetic acid fermentation of dissimilar vinegars were summarized. We also summarized various physicochemical properties and crucial compounds in disparate types of vinegar. Furthermore, the merits and drawbacks of vital fermentation methods were generalized. Finally, we described in detail the relationships among microbial diversity, raw materials, fermentation methods, physicochemical properties, compounds, functionality, and final quality of vinegar. The integration of this information can provide us a detailed map about the microbial diversity and function involved in vinegar fermentation.

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

NASA Technical Reports Server (NTRS)

Chuang, C.-H.; Goodson, Troy D.; Ledsinger, Laura A.

1995-01-01

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Total decay and transition rates from LQCD

NASA Astrophysics Data System (ADS)

Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel

2018-03-01

We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. In addition, we discuss possible extensions of our approach and, as an example application, prospects for applying the formalism to study the onset of deep-inelastic scattering. More details are given in the published version of this work, Ref. [1].

Numerical investigation of mixing characterstics of chevron nozzle by passive controls method

NASA Astrophysics Data System (ADS)

Devipriya, J.; Kanimozhi, Dr.

2017-05-01

This paper deals with the Reduction of noise in the aircraft exhaust is done by installing Chevrons with particular parameters in the Nozzle section. Numerical investigations have been carried out on chevron Nozzles to evaluate the importance of Chevron parameters by adding number of Chevrons and the mixing characteristics of jet. After assessing the Chevron parameters we vary the Chevron shapes at the exit by installing the triangular wedge in order to regulate maximum noise reduction along with a negligible thrust loss. Finally the results is compared with free jet Nozzle with Chevron and Chevron with wedge has been analysed using CFX CFD software and the results of potential core decay of these Nozzles has been measured from the analysis.

Polarization-independent beam focusing by high-contrast grating reflectors

NASA Astrophysics Data System (ADS)

Su, Wei; Zheng, Gaige; Jiang, Liyong; Li, Xiangyin

2014-08-01

A kind of high-contrast grating (HCG) reflector for beam focusing has been proposed. We design a planar grating structure with a parabolic surface and numerical simulations using a finite different time domain (FDTD) method to verify that the structure has the capability of focusing both transverse-magnetic (TM) and transverse-electric (TE) polarized lights. Finally, we expand the design structure into a three-dimensional (3D) case. Numerical results demonstrate that the power intensities at the focal point are all greater than 8.5 dB compared with incident intensity, which means the structure has a better focusing effect. Further analysis of incident wavelength sensitivity (1.55, 1.79 and 2 μm) reveals that the proposed structure has a wide range of working wavelength.

Modeling and simulation of dynamics of a planar-motion rigid body with friction and surface contact

NASA Astrophysics Data System (ADS)

Wang, Xiaojun; Lv, Jing

2017-07-01

The modeling and numerical method for the dynamics of a planar-motion rigid body with frictional contact between plane surfaces were presented based on the theory of contact mechanics and the algorithm of linear complementarity problem (LCP). The Coulomb’s dry friction model is adopted as the friction law, and the normal contact forces are expressed as functions of the local deformations and their speeds in contact bodies. The dynamic equations of the rigid body are obtained by the Lagrange equation. The transition problem of stick-slip motions between contact surfaces is formulated and solved as LCP through establishing the complementary conditions of the friction law. Finally, a numerical example is presented as an example to show the application.

A computer program for predicting nonlinear uniaxial material responses using viscoplastic models

NASA Technical Reports Server (NTRS)

Chang, T. Y.; Thompson, R. L.

1984-01-01

A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.

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.

On the Hosoya index of a family of deterministic recursive trees

NASA Astrophysics Data System (ADS)

Chen, Xufeng; Zhang, Jingyuan; Sun, Weigang

2017-01-01

In this paper, we calculate the Hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule. We then obtain a recursive solution of the Hosoya index based on the operations of a determinant. The computational complexity of our proposed algorithm is O(log2 n) with n being the network size, which is lower than that of the existing numerical methods. Finally, we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the Hosoya index.

LQR Control of Shell Vibrations Via Piezoceramic Actuators

NASA Technical Reports Server (NTRS)

delRosario, R. C. H.; Smith, R. C.

1997-01-01

A model-based Linear Quadratic Regulator (LQR) method for controlling vibrations in cylindrical shells is presented. Surface-mounted piezo-ceramic patches are employed as actuators which leads to unbounded control input operators. Modified Donnell-Mushtari shell equations incorporating strong or Kelvin-Voigt damping are used to model the system. The model is then abstractly formulated in terms of sesquilinear forms. This provides a framework amenable for proving model well-posedness and convergence of LQR gains using analytic semigroup results combined with LQR theory for unbounded input operators. Finally, numerical examples demonstrating the effectiveness of the method are presented.

Exploring the spectrum of planar AdS4 /CFT3 at finite coupling

NASA Astrophysics Data System (ADS)

Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto

2018-04-01

The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

Numerical study of droplet evaporation in an acoustic levitator

NASA Astrophysics Data System (ADS)

Bänsch, Eberhard; Götz, Michael

2018-03-01

We present a finite element method for the simulation of all relevant processes of the evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical model and the numerical implementation take into account heat and mass transfer across the interface between the liquid and gaseous phase and the influence of acoustic streaming on this process, as well as the displacement and deformation of the droplet due to acoustic radiation pressure. We apply this numerical method to several theoretical and experimental examples and compare our results with the well-known d2-law for the evaporation of spherical droplets and with theoretical predictions for the acoustic streaming velocity. We study the influence of acoustic streaming on the distribution of water vapor and temperature in the levitation device, with special attention to the vapor distribution in the emerging toroidal vortices. We also compare the evaporation rate of a droplet with and without acoustic streaming, as well as the evaporation rates in dependence of different temperatures and sound pressure levels. Finally, a simple model of protein inactivation due to heat damage is considered and studied for different evaporation settings and their respective influence on protein damage.

Modeling of Powder Bed Manufacturing Defects

NASA Astrophysics Data System (ADS)

Mindt, H.-W.; Desmaison, O.; Megahed, M.; Peralta, A.; Neumann, J.

2018-01-01

Powder bed additive manufacturing offers unmatched capabilities. The deposition resolution achieved is extremely high enabling the production of innovative functional products and materials. Achieving the desired final quality is, however, hampered by many potential defects that have to be managed in due course of the manufacturing process. Defects observed in products manufactured via powder bed fusion have been studied experimentally. In this effort we have relied on experiments reported in the literature and—when experimental data were not sufficient—we have performed additional experiments providing an extended foundation for defect analysis. There is large interest in reducing the effort and cost of additive manufacturing process qualification and certification using integrated computational material engineering. A prerequisite is, however, that numerical methods can indeed capture defects. A multiscale multiphysics platform is developed and applied to predict and explain the origin of several defects that have been observed experimentally during laser-based powder bed fusion processes. The models utilized are briefly introduced. The ability of the models to capture the observed defects is verified. The root cause of the defects is explained by analyzing the numerical results thus confirming the ability of numerical methods to provide a foundation for rapid process qualification.

Symmetry, stability, and computation of degenerate lasing modes

NASA Astrophysics Data System (ADS)

Liu, David; Zhen, Bo; Ge, Li; Hernandez, Felipe; Pick, Adi; Burkhardt, Stephan; Liertzer, Matthias; Rotter, Stefan; Johnson, Steven G.

2017-02-01

We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

Numerical comparisons of ground motion predictions with kinematic rupture modeling

NASA Astrophysics Data System (ADS)

Yuan, Y. O.; Zurek, B.; Liu, F.; deMartin, B.; Lacasse, M. D.

2017-12-01

Recent advances in large-scale wave simulators allow for the computation of seismograms at unprecedented levels of detail and for areas sufficiently large to be relevant to small regional studies. In some instances, detailed information of the mechanical properties of the subsurface has been obtained from seismic exploration surveys, well data, and core analysis. Using kinematic rupture modeling, this information can be used with a wave propagation simulator to predict the ground motion that would result from an assumed fault rupture. The purpose of this work is to explore the limits of wave propagation simulators for modeling ground motion in different settings, and in particular, to explore the numerical accuracy of different methods in the presence of features that are challenging to simulate such as topography, low-velocity surface layers, and shallow sources. In the main part of this work, we use a variety of synthetic three-dimensional models and compare the relative costs and benefits of different numerical discretization methods in computing the seismograms of realistic-size models. The finite-difference method, the discontinuous-Galerkin method, and the spectral-element method are compared for a range of synthetic models having different levels of complexity such as topography, large subsurface features, low-velocity surface layers, and the location and characteristics of fault ruptures represented as an array of seismic sources. While some previous studies have already demonstrated that unstructured-mesh methods can sometimes tackle complex problems (Moczo et al.), we investigate the trade-off between unstructured-mesh methods and regular-grid methods for a broad range of models and source configurations. Finally, for comparison, our direct simulation results are briefly contrasted with those predicted by a few phenomenological ground-motion prediction equations, and a workflow for accurately predicting ground motion is proposed.

Numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources

NASA Astrophysics Data System (ADS)

Crochet, M. W.; Gonthier, K. A.

2013-12-01

Systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures. These equations often contain sources, referred to as nozzling terms, that cannot be posed in divergence form, and have proven to be particularly challenging in the development of finite-volume methods. Upwind schemes have recently shown promise in properly resolving the steady wave solution of the associated multiphase Riemann problem. However, these methods require a full characteristic decomposition of the system eigenstructure, which may be either unavailable or computationally expensive. Central schemes, such as the Kurganov-Tadmor (KT) family of methods, require minimal characteristic information, which makes them easily applicable to systems with an arbitrary number of phases. However, the proper implementation of nozzling terms in these schemes has been mathematically ambiguous. The primary objectives of this work are twofold: first, an extension of the KT family of schemes is proposed that formally accounts for the nonconservative nozzling sources. This modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense. Second, this modified method is applied to multiple, but equivalent, forms of the multiphase equations to perform a numerical study by solving several one-dimensional test problems. Both ideal and Mie-Grüneisen equations of state are used, with the results compared to an analytical solution. This study demonstrates that the magnitudes of the resulting numerical errors are sensitive to the form of the equations considered, and suggests an optimal form to minimize these errors. Finally, a separate modification of the wave propagation speeds used in the KT family is also suggested that can reduce the extent of numerical diffusion in multiphase flows.

On the Unreasonable Effectiveness of post-Newtonian Theory in Gravitational-Wave Physics

ScienceCinema

Will, Clifford M.

2017-12-22

The first indirect detection of gravitational waves involved a binary system of neutron stars.  In the future, the first direct detection may also involve binary systems -- inspiralling and merging binary neutron stars or black holes. This means that it is essential to understand in full detail the two-body system in general relativity, a notoriously difficult problem with a long history. Post-Newtonian approximation methods are thought to work only under slow motion and weak field conditions, while numerical solutions of Einstein's equations are thought to be limited to the final merger phase.  Recent results have shown that post-Newtonian approximations seem to remain unreasonably valid well into the relativistic regime, while advances in numerical relativity now permit solutions for numerous orbits before merger.  It is now possible to envision linking post-Newtonian theory and numerical relativity to obtain a complete "solution" of the general relativistic two-body problem.  These solutions will play a central role in detecting and understanding gravitational wave signals received by interferometric observatories on Earth and in space.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

A comprehensive fluvial geomorphology study of riverbank erosion on the Red River in Winnipeg, Manitoba, Canada

NASA Astrophysics Data System (ADS)

Kimiaghalam, Navid; Goharrokhi, Masoud; Clark, Shawn P.; Ahmari, Habib

2015-10-01

Riverbank erosion on the Red River in Winnipeg, Manitoba has raised concerns over the last 20 years and more. Although several recent studies have shown that fluvial erosion can reduce riverbank stability and promote geotechnical slope failure, there are too few that have focused on this phenomenon. The present study includes field measurements, experimental testing, and numerical modelling to quantify fluvial erosion through a 10 km reach of the Red River. Results have shown that seasonal freeze-thaw processes can dramatically reduce the critical shear stress and increase erodibility of the riverbanks. Moreover, a simple method has been employed using hydrodynamic numerical models to define the applied shear stresses on the river banks based on the river water level, which will be useful for further research and design purposes. The TEMP/W numerical model was used to define seasonal frost depth to estimate freeze-thaw effects. Finally all field measurements, experimental and numerical models results were used to predict annual fluvial erosion through this reach of the river.

Dual-band plasmonic resonator based on Jerusalem cross-shaped nanoapertures

NASA Astrophysics Data System (ADS)

Cetin, Arif E.; Kaya, Sabri; Mertiri, Alket; Aslan, Ekin; Erramilli, Shyamsunder; Altug, Hatice; Turkmen, Mustafa

2015-06-01

In this paper, we both experimentally and numerically introduce a dual-resonant metamaterial based on subwavelength Jerusalem cross-shaped apertures. We numerically investigate the physical origin of the dual-resonant behavior, originating from the constituting aperture elements, through finite difference time domain calculations. Our numerical calculations show that at the dual-resonances, the aperture system supports large and easily accessible local electromagnetic fields. In order to experimentally realize the aperture system, we utilize a high-precision and lift-off free fabrication method based on electron-beam lithography. We also introduce a fine-tuning mechanism for controlling the dual-resonant spectral response through geometrical device parameters. Finally, we show the aperture system's highly advantageous far- and near-field characteristics through numerical calculations on refractive index sensitivity. The quantitative analyses on the availability of the local fields supported by the aperture system are employed to explain the grounds behind the sensitivity of each spectral feature within the dual-resonant behavior. Possessing dual-resonances with large and accessible electromagnetic fields, Jerusalem cross-shaped apertures can be highly advantageous for wide range of applications demanding multiple spectral features with strong nearfield characteristics.

Binary Black Holes, Gravitational Waves, and Numerical Relativity

NASA Technical Reports Server (NTRS)

Centrella, Joan

2007-01-01

This viewgraph presentation reviews the massive black hole (MBH) binaries that are found at the center of most galaxies, "astronomical messenger", gravitational waves (GW), and the use of numerical relativity understand the features of these phenomena. The final merger of two black holes releases a tremendous amount of energy and is one of the brightest sources in the gravitational wave sky. Observing these sources with gravitational wave detectors requires that we know the radiation waveforms they emit. Since these mergers take place in regions of very strong gravitational fields, we need to solve Einstein's equations of general relativity on a computer in order to calculate these waveforms. For more than 30 years, scientists have tried to compute these waveforms using the methods of numerical relativity.. This talk will take you on this quest for the holy grail of numerical relativity, showing how a spacetime is constructed on a computer to build a simulation laboratory for binary black hole mergers. We will focus on the recent advances that are revealing these waveforms, and the dramatic new potential for discoveries that arises when these sources will be observed by LIGO and LISA.

Faster and more accurate transport procedures for HZETRN

NASA Astrophysics Data System (ADS)

Slaba, T. C.; Blattnig, S. R.; Badavi, F. F.

2010-12-01

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle ( A ⩽ 4) and heavy ion ( A > 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete description of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms to 100 g/cm 2 in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100 g/cm 2 of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Faster and more accurate transport procedures for HZETRN

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

Slaba, T.C., E-mail: Tony.C.Slaba@nasa.go; Blattnig, S.R., E-mail: Steve.R.Blattnig@nasa.go; Badavi, F.F., E-mail: Francis.F.Badavi@nasa.go

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle (A {<=} 4) and heavy ion (A > 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete descriptionmore » of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms to 100 g/cm{sup 2} in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100 g/cm{sup 2} of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.« less

Chaotification of complex networks with impulsive control.

PubMed

Guan, Zhi-Hong; Liu, Feng; Li, Juan; Wang, Yan-Wu

2012-06-01

This paper investigates the chaotification problem of complex dynamical networks (CDN) with impulsive control. Both the discrete and continuous cases are studied. The method is presented to drive all states of every node in CDN to chaos. The proposed impulsive control strategy is effective for both the originally stable and unstable CDN. The upper bound of the impulse intervals for originally stable networks is derived. Finally, the effectiveness of the theoretical results is verified by numerical examples.

Magnetization of InAs parabolic quantum dot: An exact diagonalization approach

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

Aswathy, K. M., E-mail: aswathykm20@gmail.com; Sanjeev Kumar, D.

2016-04-13

The magnetization of two electron InAs quantum dot has been studied as a function of magnetic field. The electron-electron interaction has been taken into account by using exact diagonalization method numerically. The magnetization at zero external magnetic field is zero and increases in the negative direction. There is also a paramagnetic peak where the energy levels cross from singlet state to triplet state. Finally, the magnetization falls again to even negative values and saturates.

A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM

NASA Astrophysics Data System (ADS)

Joseph, G. Arul; Balamuralitharan, S.

2018-04-01

In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population. Smoking is the main cause to spread Asthma in the environment. Numerical simulation is also discussed. Finally by using Liao’s Homotopy analysis Method (LHAM), we found that the approximate analytical solution of Asthmatic disease in the environmental.

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

Mixed-method tutoring support improves learning outcomes of veterinary students in basic subjects.

PubMed

García-Iglesias, María J; Pérez-Martínez, Claudia; Gutiérrez-Martín, César B; Díez-Laiz, Raquel; Sahagún-Prieto, Ana M

2018-02-01

Tutoring is a useful tool in the university teaching-learning binomial, although its development is impaired in large classes. Recent improvements in information and communication technologies have made tutoring possible via the Internet. The aim of this study was to evaluate the efficacy of mixed-method academic tutoring in two basic subjects in Veterinary Science studies at the University of León (Spain) to optimize the usefulness of tutoring support in the college environment. This quasi-experimental study was firstly carried out as a pilot study in a small group of tutored students of "Cytology and Histology" (CH) (47/186; 25.3%) and "Veterinary Pharmacology" (VP) (33/141; 23.4%) subjects, and was implemented in a large class of CH the next academic year (150 students) while comparing the results with those obtained in a previous tutorless course (162 students). Tutored students were given access to online questionnaires with electronic feedback on each subject. In addition to traditional tutoring carried out in both tutored and tutorless students, the pilot study included three sessions of face-to-face tutoring in order to monitor the progress of students. Its efficacy was assessed by monitoring students' examination scores and attendance as well as a satisfaction survey. Although the examination attendance rate in the pilot study was not significantly different between tutored and tutorless groups in both subjects, an increase for numerical scores in tutored groups was observed, with a significant higher final score in VP (p = 0.001) and in the CH practice exams (first term, p = 0.009; final, p = 0.023). Good and merit scores were also better in tutored students with significant differences in VP (p = 0.005). Students felt comfortable with the tutoring service (100% in CH; 91.7% in VP). Implementation of this additional support in CH also resulted in a significant increase of attendance at the final exam in tutored courses (87.3% versus 77.2%; p = 0.026), scaled (p = 0.001) and numerical scores (final score, p = 0.001). Online tutoring support, together with conventional teaching methods, may be a useful method to incorporate student-centered learning in basic subjects in Veterinary Science.

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

solveME: fast and reliable solution of nonlinear ME models.

PubMed

Yang, Laurence; Ma, Ding; Ebrahim, Ali; Lloyd, Colton J; Saunders, Michael A; Palsson, Bernhard O

2016-09-22

Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints. Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints. Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.

Interpolating seismic data via the POCS method based on shearlet transform

NASA Astrophysics Data System (ADS)

Jicheng, Liu; Yongxin, Chou; Jianjiang, Zhu

2018-06-01

A method based on shearlet transform and the projection onto convex sets with L0-norm constraint is proposed to interpolate irregularly sampled 2D and 3D seismic data. The 2D directional filter of shearlet transform is constructed by modulating a low-pass diamond filter pair to minimize the effect of additional edges introduced by the missing traces. In order to abate the spatial aliasing and control the maximal gap between missing traces for a 3D data cube, a 2D separable jittered sampling strategy is discussed. Finally, numerical experiments on 2D and 3D synthetic and real data with different under-sampling rates prove the validity of the proposed method.

The method of fundamental solutions for computing acoustic interior transmission eigenvalues

NASA Astrophysics Data System (ADS)

Kleefeld, Andreas; Pieronek, Lukas

2018-03-01

We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.

Study on bending behaviour of nickel–titanium rotary endodontic instruments by analytical and numerical analyses

PubMed Central

Tsao, C C; Liou, J U; Wen, P H; Peng, C C; Liu, T S

2013-01-01

Aim To develop analytical models and analyse the stress distribution and flexibility of nickel–titanium (NiTi) instruments subject to bending forces. Methodology The analytical method was used to analyse the behaviours of NiTi instruments under bending forces. Two NiTi instruments (RaCe and Mani NRT) with different cross-sections and geometries were considered. Analytical results were derived using Euler–Bernoulli nonlinear differential equations that took into account the screw pitch variation of these NiTi instruments. In addition, the nonlinear deformation analysis based on the analytical model and the finite element nonlinear analysis was carried out. Numerical results are obtained by carrying out a finite element method. Results According to analytical results, the maximum curvature of the instrument occurs near the instrument tip. Results of the finite element analysis revealed that the position of maximum von Mises stress was near the instrument tip. Therefore, the proposed analytical model can be used to predict the position of maximum curvature in the instrument where fracture may occur. Finally, results of analytical and numerical models were compatible. Conclusion The proposed analytical model was validated by numerical results in analysing bending deformation of NiTi instruments. The analytical model is useful in the design and analysis of instruments. The proposed theoretical model is effective in studying the flexibility of NiTi instruments. Compared with the finite element method, the analytical model can deal conveniently and effectively with the subject of bending behaviour of rotary NiTi endodontic instruments. PMID:23173762

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

Rotorcraft acoustic radiation prediction based on a refined blade-vortex interaction model

NASA Astrophysics Data System (ADS)

Rule, John Allen

1997-08-01

The analysis of rotorcraft aerodynamics and acoustics is a challenging problem, primarily due to the fact that a rotorcraft continually flies through its own wake. The generation mechanism for a rotorcraft wake, which is dominated by strong, concentrated blade-tip trailing vortices, is similar to that in fixed wing aerodynamics. However, following blades encounter shed vortices from previous blades before they are swept downstream, resulting in sharp, impulsive loading on the blades. The blade/wake encounter, known as Blade-Vortex Interaction, or BVI, is responsible for a significant amount of vibratory loading and the characteristic rotorcraft acoustic signature in certain flight regimes. The present work addressed three different aspects of this interaction at a fundamental level. First, an analytical model for the prediction of trailing vortex structure is discussed. The model as presented is the culmination of a lengthy research effort to isolate the key physical mechanisms which govern vortex sheet rollup. Based on the Betz model, properties of the flow such as mass flux, axial momentum flux, and axial flux of angular momentum are conserved on either a differential or integral basis during the rollup process. The formation of a viscous central core was facilitated by the assumption of a turbulent mixing process with final vortex velocity profiles chosen to be consistent with a rotational flow mixing model and experimental observation. A general derivation of the method is outlined, followed by a comparison of model predictions with experimental vortex measurements, and finally a viscous blade drag model to account for additional effects of aerodynamic drag on vortex structure. The second phase of this program involved the development of a new formulation of lifting surface theory with the ultimate goal of an accurate, reduced order hybrid analytical/numerical model for fast rotorcraft load calculations. Currently, accurate rotorcraft airload analyses are limited by the massive computational power required to capture the small time scale events associated with BVI. This problem has two primary facets: accurate knowledge of the wake geometry, and accurate resolution of the impulsive loading imposed by a tip vortex on a blade. The present work addressed the second facet, providing a mathematical framework for solving the impulsive loading problem analytically, then asymptotically matching this solution to a low-resolution numerical calculation. A method was developed which uses continuous sheets of integrated boundary elements to model the lifting surface and wake. Special elements were developed to capture local behavior in high-gradient regions of the flow, thereby reducing the burden placed on the surrounding numerical method. Unsteady calculations for several classical cases were made in both frequency and time domain to demonstrate the performance of the method. Finally, a new unsteady, compressible boundary element method was applied to the problem of BVI acoustic radiation prediction. This numerical method, combined with the viscous core trailing vortex model, was used to duplicate the geometry and flight configuration of a detailed experimental BVI study carried out at NASA Ames Research Center. Blade surface pressure and near- and far-field acoustic radiation calculations were made. All calculations were shown to compare favorably with experimentally measured values. The linear boundary element method with non-linear corrections proved sufficient over most of the rotor azimuth, and particular in the region of the blade vortex interaction, suggesting that full non-linear CFD schemes are not necessary for rotorcraft noise prediction.

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

Sidler, Rolf, E-mail: rsidler@gmail.com; Carcione, José M.; Holliger, Klaus

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in themore » radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.« less

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

PubMed Central

Wang, Jinfeng; Li, Hong; Fang, Zhichao

2014-01-01

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L 2-norm for the scalar unknown u and a priori error estimates in (L 2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H 1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. PMID:24701153

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

NASA Technical Reports Server (NTRS)

Vanel, Florence O.

1995-01-01

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

New method for initial density reconstruction

NASA Astrophysics Data System (ADS)

Shi, Yanlong; Cautun, Marius; Li, Baojiu

2018-01-01

A theoretically interesting and practically important question in cosmology is the reconstruction of the initial density distribution provided a late-time density field. This is a long-standing question with a revived interest recently, especially in the context of optimally extracting the baryonic acoustic oscillation (BAO) signals from observed galaxy distributions. We present a new efficient method to carry out this reconstruction, which is based on numerical solutions to the nonlinear partial differential equation that governs the mapping between the initial Lagrangian and final Eulerian coordinates of particles in evolved density fields. This is motivated by numerical simulations of the quartic Galileon gravity model, which has similar equations that can be solved effectively by multigrid Gauss-Seidel relaxation. The method is based on mass conservation, and does not assume any specific cosmological model. Our test shows that it has a performance comparable to that of state-of-the-art algorithms that were very recently put forward in the literature, with the reconstructed density field over ˜80 % (50%) correlated with the initial condition at k ≲0.6 h /Mpc (1.0 h /Mpc ). With an example, we demonstrate that this method can significantly improve the accuracy of BAO reconstruction.

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Dumbser, Michael; Siviglia, Annunziato; Toro, Eleuterio F.

2010-03-01

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space-time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.

Measuring global monopole velocities, one by one

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

Lopez-Eiguren, Asier; Urrestilla, Jon; Achúcarro, Ana, E-mail: asier.lopez@ehu.eus, E-mail: jon.urrestilla@ehu.eus, E-mail: achucar@lorentz.leidenuniv.nl

We present an estimation of the average velocity of a network of global monopoles in a cosmological setting using large numerical simulations. In order to obtain the value of the velocity, we improve some already known methods, and present a new one. This new method estimates individual global monopole velocities in a network, by means of detecting each monopole position in the lattice and following the path described by each one of them. Using our new estimate we can settle an open question previously posed in the literature: velocity-dependent one-scale (VOS) models for global monopoles predict two branches of scalingmore » solutions, one with monopoles moving at subluminal speeds and one with monopoles moving at luminal speeds. Previous attempts to estimate monopole velocities had large uncertainties and were not able to settle that question. Our simulations find no evidence of a luminal branch. We also estimate the values of the parameters of the VOS model. With our new method we can also study the microphysics of the complicated dynamics of individual monopoles. Finally we use our large simulation volume to compare the results from the different estimator methods, as well as to asses the validity of the numerical approximations made.« less

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

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

Morales, Jorge A.; Leroy, Matthieu; Bos, Wouter J.T.

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analyticalmore » solutions. The test cases considered are two-dimensional Taylor–Couette flow, the z-pinch configuration, three dimensional Orszag–Tang flow, Ohmic-decay in a periodic cylinder, three-dimensional Taylor–Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field. Finally, we present a magnetohydrodynamic flow simulation in toroidal geometry with non-symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method.« less

A numerical model of a red blood cell infected by Plasmodium falciparum malaria: coupling cell mechanics with ligand-receptor interactions

NASA Astrophysics Data System (ADS)

Ishida, Shunichi; Imai, Yohsuke; Ichikawa, Yuki; Nix, Stephanie; Matsunaga, Daiki; Omori, Toshihiro; Ishikawa, Takuji

2016-01-01

We developed a numerical model of the behavior of a red blood cell infected by Plasmodium falciparum malaria on a wall in shear flow. The fluid and solid mechanics of an infected red blood cell (Pf-IRBC) were coupled with the biochemical interaction of ligand-receptor bindings. We used the boundary element method for fluid mechanics, the finite element method for membrane mechanics, and the Monte Carlo method for ligand-receptor interactions. We simulated the behavior of a Pf-IRBC in shear flow, focusing on the effects of bond type. For slip bonds, the Pf-IRBC exhibited firm adhesion, tumbling motion, and tank-treading motion, depending on the applied shear rate. The behavior of catch bonds resembled that of slip bonds, except for a 'catch' state at high shear stress. When the reactive compliance decreased to a value in the order of ? nm, both the slip and catch bonds behaved like an ideal bond. Such bonds do not respond to the force applied to the bond, and the velocity is stabilized at a high shear rate. Finally, we compared the numerical results with previous experiments for A4- and ItG-infected cells. We found that the interaction between PfEMP1 and ICAM-1 could be a nearly ideal bond, with a dissociation rate ranging from ? to ?.

Soil hydraulic properties estimate based on numerical analysis of disc infiltrometer three-dimensional infiltration curve

NASA Astrophysics Data System (ADS)

Latorre, Borja; Peña-Sancho, Carolina; Angulo-Jaramillo, Rafaël; Moret-Fernández, David

2015-04-01

Measurement of soil hydraulic properties is of paramount importance in fields such as agronomy, hydrology or soil science. Fundamented on the analysis of the Haverkamp et al. (1994) model, the aim of this paper is to explain a technique to estimate the soil hydraulic properties (sorptivity, S, and hydraulic conductivity, K) from the full-time cumulative infiltration curves. The method (NSH) was validated by means of 12 synthetic infiltration curves generated with HYDRUS-3D from known soil hydraulic properties. The K values used to simulate the synthetic curves were compared to those estimated with the proposed method. A procedure to identify and remove the effect of the contact sand layer on the cumulative infiltration curve was also developed. A sensitivity analysis was performed using the water level measurement as uncertainty source. Finally, the procedure was evaluated using different infiltration times and data noise. Since a good correlation between the K used in HYDRUS-3D to model the infiltration curves and those estimated by the NSH method was obtained, (R2 =0.98), it can be concluded that this technique is robust enough to estimate the soil hydraulic conductivity from complete infiltration curves. The numerical procedure to detect and remove the influence of the contact sand layer on the K and S estimates seemed to be robust and efficient. An effect of the curve infiltration noise on the K estimate was observed, which uncertainty increased with increasing noise. Finally, the results showed that infiltration time was an important factor to estimate K. Lower values of K or smaller uncertainty needed longer infiltration times.

Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

NASA Astrophysics Data System (ADS)

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2018-03-01

We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.

Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays.

PubMed

Senan, Sibel; Syed Ali, M; Vadivel, R; Arik, Sabri

2017-02-01

In this study, we present an approach for the decentralized event-triggered synchronization of Markovian jumping neutral-type neural networks with mixed delays. We present a method for designing decentralized event-triggered synchronization, which only utilizes locally available information, in order to determine the time instants for transmission from sensors to a central controller. By applying a novel Lyapunov-Krasovskii functional, as well as using the reciprocal convex combination method and some inequality techniques such as Jensen's inequality, we obtain several sufficient conditions in terms of a set of linear matrix inequalities (LMIs) under which the delayed neural networks are stochastically stable in terms of the error systems. Finally, we conclude that the drive systems synchronize stochastically with the response systems. We show that the proposed stability criteria can be verified easily using the numerically efficient Matlab LMI toolbox. The effectiveness and feasibility of the results obtained are verified by numerical examples. Copyright © 2016 Elsevier Ltd. All rights reserved.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Aerodynamic influence coefficient method using singularity splines

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1974-01-01

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Research on soundproof properties of cylindrical shells of generalized phononic crystals

NASA Astrophysics Data System (ADS)

Liu, Ru; Shu, Haisheng; Wang, Xingguo

2017-04-01

Based on the previous studies, the concept of generalized phononic crystals (GPCs) is further introduced into the cylindrical shell structures in this paper. And a type of cylindrical shells of generalized phononic crystals (CS-GPCs) is constructed, the structural field and acoustic-structural coupled field of the composite cylindrical shells are examined respectively. For the structural field, the transfer matrix method of mechanical state vector is adopted to build the transfer matrix of radial waves propagating from inside to outside. For the acoustic-structural coupled field, the expressions of the acoustic transmission/reflection coefficients and the sound insulation of acoustic waves with the excitation of center line sound source are set up. And the acoustic transmission coefficient and the frequency response of sound insulation in this mode were numerical calculated. Furthermore, the theoretical analysis results are verified by using the method of combining the numerical calculation and finite element simulation. Finally, the effects of inner and outer fluid parameters on the transmission/reflection coefficients of CS-GPCs are analyzed in detail.

Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations

NASA Astrophysics Data System (ADS)

Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.

2018-05-01

The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

A theoretical study of concentration of profiles of primary cytochemical-enzyme reaction products in membrane-bound cell organelles and its application to lysosomal acid phosphatase.

PubMed

Cornelisse, C J; Hermens, W T; Joe, M T; Duijndam, W A; van Duijn, P

1976-11-01

A numerical method was developed for computing the steady-state concentration gradient of a diffusible enzyme reaction product in a membrane-limited compartment of a simplified theoretical cell model. In cytochemical enzyme reactions proceeding according to the metal-capture principle, the local concentration of the primary reaction product is an important factor in the onset of the precipitation process and in the distribution of the final reaction product. The following variables were incorporated into the model: enzyme activity, substrate concentration, Km, diffusion coefficient of substrate and product, particle radius and cell radius. The method was applied to lysosomal acid phosphatase. Numerical values for the variables were estimated from experimental data in the literature. The results show that the calculated phosphate concentrations inside lysosomes are several orders of magnitude lower than the critical concentrations for efficient phosphate capture found in a previous experimental model study. Reasons for this apparent discrepancy are discussed.

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games

PubMed Central

Liu, Jiacai; Zhao, Wenjian

2016-01-01

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method. PMID:27834830

Estimating linear effects in ANOVA designs: the easy way.

PubMed

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

2012-09-01

Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

NASA Astrophysics Data System (ADS)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

The evolution of human mobility based on the public goods game

NASA Astrophysics Data System (ADS)

Yan, Shiqing

2017-07-01

We explore the evolution of human mobility behavior based on public goods game. By using mean field method, the population distribution in different regions is theoretical calculated. Numerical simulation results show that the correlation between the region's degree and its final population is not significant under a larger human migration rate. Human mobility could effectively promote cooperative behavior and the population balance of different regions. Therefore, encouraging individuals to migrate may increase the total benefits of the whole society. Moreover, increasing the cooperation cost could reduce the number of cooperators, and that would happen to the correlation between the region's degree and its final population. The results indicate the total population could not dramatically rise with the region's degree under an unfair society.

Phase segregation in multiphase turbulent channel flow

NASA Astrophysics Data System (ADS)

Bianco, Federico; Soldati, Alfredo

2014-11-01

The phase segregation of a rapidly quenched mixture (namely spinodal decomposition) is numerically investigated. A phase field approach is considered. Direct numerical simulation of the coupled Navier-Stokes and Cahn-Hilliard equations is performed with spectral accuracy and focus has been put on domain growth scaling laws, in a wide range of regimes. The numerical method has been first validated against well known results of literature, then spinodal decomposition in a turbulent bounded flow (channel flow) has been considered. As for homogeneous isotropic case, turbulent fluctuations suppress the segregation process when surface tension at the interfaces is relatively low (namely low Weber number regimes). For these regimes, segregated domains size reaches a statistically steady state due to mixing and break-up phenomena. In contrast with homogenous and isotropic turbulence, the presence of mean shear, leads to a typical domain size that show a wall-distance dependence. Finally, preliminary results on the effects to the drag forces at the wall, due to phase segregation, have been discussed. Regione FVG, program PAR-FSC.

FAST Model Calibration and Validation of the OC5-DeepCwind Floating Offshore Wind System Against Wave Tank Test Data

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

Wendt, Fabian F; Robertson, Amy N; Jonkman, Jason

During the course of the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project, which focused on the validation of numerical methods through comparison against tank test data, the authors created a numerical FAST model of the 1:50-scale DeepCwind semisubmersible system that was tested at the Maritime Research Institute Netherlands ocean basin in 2013. This paper discusses several model calibration studies that were conducted to identify model adjustments that improve the agreement between the numerical simulations and the experimental test data. These calibration studies cover wind-field-specific parameters (coherence, turbulence), hydrodynamic and aerodynamic modeling approaches, as well as rotor model (blade-pitchmore » and blade-mass imbalances) and tower model (structural tower damping coefficient) adjustments. These calibration studies were conducted based on relatively simple calibration load cases (wave only/wind only). The agreement between the final FAST model and experimental measurements is then assessed based on more-complex combined wind and wave validation cases.« less

Cylindrical and spherical Akhmediev breather and freak waves in ultracold neutral plasmas

NASA Astrophysics Data System (ADS)

El-Tantawy, S. A.; El-Awady, E. I.

2018-01-01

The properties of cylindrical and spherical ion-acoustic breathers Akhmediev breather and freak waves in strongly coupled ultracold neutral plasmas (UNPs), whose constituents are inertial strongly coupled ions and weakly coupled Maxwellian electrons, are investigated numerically. Using the derivative expansion method, the basic set of fluid equations is reduced to a nonplanar (cylindrical and spherical)/modified nonlinear Schrödinger equation (mNLSE). The analytical solutions of the mNLSE were not possible until now, so their numerical solutions are obtained using the finite difference scheme with the help of the Dirichlet boundary conditions. Moreover, the criteria for the existence and propagation of breathers are discussed in detail. The geometrical effects due to the cylindrical and spherical geometries on the breather profile are studied numerically. It is found that the propagation of the ion-acoustic breathers in one-dimensional planar and nonplanar geometries is very different. Finally, our results may help to manipulate matter breathers experimentally in UNPs.

Experimental and numerical analysis of the influence of tyres' properties on the straight running stability of a sport-touring motorcycle

NASA Astrophysics Data System (ADS)

Cossalter, Vittore; Doria, Alberto; Formentini, Matteo; Peretto, Martino

2012-03-01

The behaviour of a motorcycle on the road is largely governed by tyre properties. This paper presents experimental and numerical analyses dealing with the influence of tyre properties on the stability of weave and wobble in straight running. The final goal is to find optimal sets of tyre properties that improve the stability of a motorcycle. The investigation is based on road tests carried out on a sport-touring motorcycle equipped with sensors. Three sets of tyres are tested at different speeds in the presence of weave and wobble. The analysis of telemetry data highlights significant differences in the trends of frequency and damping of weave and wobble against speed. The experimental analysis is integrated by a parametric numerical analysis. Tyre properties are varied according to the design of experiments method, in order to highlight the single effects on stability of lateral and cornering coefficient of front and rear tyres.

Experimental and numerical study on transverse piezoelectricity of xBiInO3-(1 - x)PbTiO3 films by multilayer cantilevers

NASA Astrophysics Data System (ADS)

Sun, Ke-xue; Zhang, Shu-yi; Shui, Xiu-ji; Wasa, Kiyotaka

2018-02-01

The effective transverse piezoelectric coefficient of the piezoelectric films xBiInO3-(1 - x)PbTiO3 (x = 0,0.10,0.15,0.20) were studied experimentally and numerically by multilayer cantilevers. The xBiInO3-(1 - x)PbTiO3 thin films were deposited on (101)SrRuO3/(100)Pt/(100)MgO substrates and then covered with Pt electrode by RF-magnetron sputtering method. In experiments, the tip vibration amplitudes of the cantilevers for different x of the films were measured, in which the optimized compositions for maximizing the tip vibration can be found. Meanwhile, based on the bending model of multilayer piezoelectric cantilevers, the tip-deflection and transverse piezoelectricity of the cantilevers were simulated by COMSOL software. By comparing the experimental and numerical results, both are in agreement very well, and the mechanism of the optimized transverse piezoelectricity of the cantilevers was proposed finally.

Numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation

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

Braumann, Andreas; Kraft, Markus, E-mail: mk306@cam.ac.u; Wagner, Wolfgang

2010-10-01

This paper is concerned with computational aspects of a multidimensional population balance model of a wet granulation process. Wet granulation is a manufacturing method to form composite particles, granules, from small particles and binders. A detailed numerical study of a stochastic particle algorithm for the solution of a five-dimensional population balance model for wet granulation is presented. Each particle consists of two types of solids (containing pores) and of external and internal liquid (located in the pores). Several transformations of particles are considered, including coalescence, compaction and breakage. A convergence study is performed with respect to the parameter that determinesmore » the number of numerical particles. Averaged properties of the system are computed. In addition, the ensemble is subdivided into practically relevant size classes and analysed with respect to the amount of mass and the particle porosity in each class. These results illustrate the importance of the multidimensional approach. Finally, the kinetic equation corresponding to the stochastic model is discussed.« less

Analysis of artery blood flow before and after angioplasty

NASA Astrophysics Data System (ADS)

Tomaszewski, Michał; Baranowski, Paweł; Małachowski, Jerzy; Damaziak, Krzysztof; Bukała, Jakub

2018-01-01

The study presents a comparison of results obtained from numerical simulations of blood flow in two different arteries. One of them was considered to be narrowed in order to simulate an arteriosclerosis obstructing the blood flow in the vessel, whereas the second simulates the vessel after angioplasty treatment. During the treatment, a biodegradable stent is inserted into the artery, which prevents the vessel walls from collapsing. The treatment was simulated through the use of numerical simulation using the finite element method. The final mesh geometry obtained from the analysis was exported to the dedicated software in order to create geometry in which a flow domain inside the artery with the stent was created. The flow analysis was conducted in ANSYS Fluent software with non-deformable vessel walls.

Numerical simulation of an electrothermal deicer pad. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Marano, J. J.

1983-01-01

A numerical simulation is developed to investigate the removal of ice from composite aircraft blades by means of electrothermal deicing. The model considers one dimensional, unsteady state heat transfer in the composite blade-ice body. The heat conduction equations are approximated by using the Crank-Nicolson finite difference scheme, and the phase change in the ice layer is handled using the Enthalpy method. To solve the system of equations which result, Gauss-Seidel iteration is used. The simulation computes the temperature profile in the composite blade-ice body, as well as the movement of the ice-water interface, as a function of time. This information can be used to evaluate deicer performance. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

The Final Merger of Black-Hole Binaries

NASA Technical Reports Server (NTRS)

Kelly, Bernard J.; Centrealla, Joan; Baker, John G.; Kelly, Bernard J.; vanMeter, James R.

2010-01-01

Recent breakthroughs in the field of numerical relativity have led to dramatic progress in understanding the predictions of General Relativity for the dynamical interactions of two black holes in the regime of very strong gravitational fields. Such black-hole binaries are important astrophysical systems and are a key target of current and developing gravitational-wave detectors. The waveform signature of strong gravitational radiation emitted as the black holes fall together and merge provides a clear observable record of the process. After decades of slow progress / these mergers and the gravitational-wave signals they generate can now be routinely calculated using the methods of numerical relativity. We review recent advances in understanding the predicted physics of events and the consequent radiation, and discuss some of the impacts this new knowledge is having in various areas of astrophysics

The advanced role of computational mechanics and visualization in science and technology: analysis of the Germanwings Flight 9525 crash

NASA Astrophysics Data System (ADS)

Chen, Goong; Wang, Yi-Ching; Perronnet, Alain; Gu, Cong; Yao, Pengfei; Bin-Mohsin, Bandar; Hajaiej, Hichem; Scully, Marlan O.

2017-03-01

Computational mathematics, physics and engineering form a major constituent of modern computational science, which now stands on an equal footing with the established branches of theoretical and experimental sciences. Computational mechanics solves problems in science and engineering based upon mathematical modeling and computing, bypassing the need for expensive and time-consuming laboratory setups and experimental measurements. Furthermore, it allows the numerical simulations of large scale systems, such as the formation of galaxies that could not be done in any earth bound laboratories. This article is written as part of the 21st Century Frontiers Series to illustrate some state-of-the-art computational science. We emphasize how to do numerical modeling and visualization in the study of a contemporary event, the pulverizing crash of the Germanwings Flight 9525 on March 24, 2015, as a showcase. Such numerical modeling and the ensuing simulation of aircraft crashes into land or mountain are complex tasks as they involve both theoretical study and supercomputing of a complex physical system. The most tragic type of crash involves ‘pulverization’ such as the one suffered by this Germanwings flight. Here, we show pulverizing airliner crashes by visualization through video animations from supercomputer applications of the numerical modeling tool LS-DYNA. A sound validation process is challenging but essential for any sophisticated calculations. We achieve this by validation against the experimental data from a crash test done in 1993 of an F4 Phantom II fighter jet into a wall. We have developed a method by hybridizing two primary methods: finite element analysis and smoothed particle hydrodynamics. This hybrid method also enhances visualization by showing a ‘debris cloud’. Based on our supercomputer simulations and the visualization, we point out that prior works on this topic based on ‘hollow interior’ modeling can be quite problematic and, thus, not likely to be correct. We discuss the effects of terrain on pulverization using the information from the recovered flight-data-recorder and show our forensics and assessments of what may have happened during the final moments of the crash. Finally, we point out that our study has potential for being made into real-time flight crash simulators to help the study of crashworthiness and survivability for future aviation safety. Some forward-looking statements are also made.

Modeling and simulation of flow field in giant magnetostrictive pump

NASA Astrophysics Data System (ADS)

Zhao, Yapeng; Ren, Shiyong; Lu, Quanguo

2017-09-01

Recent years, there has been significant research in the design and analysis of giant magnetostrictive pump. In this paper, the flow field model of giant magnetostrictive pump was established and the relationship between pressure loss and working frequency of piston was studied by numerical simulation method. Then, the influence of different pump chamber height on pressure loss in giant magnetostrictive pump was studied by means of flow field simulation. Finally, the fluid pressure and velocity vector distribution in giant magnetostrictive pump chamber were simulated.

Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators

NASA Astrophysics Data System (ADS)

Koca, Ilknur

2018-03-01

The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.

Numerical Wake Prediction Methods for Submerged Appended Bodies, A Literature Survey.

DTIC Science & Technology

1983-02-01

Flement 62543N, Task Area 421-252, Work Unit number 1-1506-202-11. INTRODUCTION In order to design a propeller for a submerged vehicle, it is essential to...know the velocity field (i.e. wake) in the propeller plane. One of the goals of the application of computational fluid dynamics to ship design is to...tests for the purpose of obtaining wake data will be either unnecessary or would be needed only at the final stage of design . Before such a goal can

Optimal impulsive manoeuvres and aerodynamic braking

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1985-01-01

A method developed for obtaining solutions to the aerodynamic braking problem, using impulses in the exoatmospheric phases is discussed. The solution combines primer vector theory and the results of a suboptimal atmospheric guidance program. For a specified initial and final orbit, the solution determines: (1) the minimum impulsive cost using a maximum of four impulses, (2) the optimal atmospheric entry and exit-state vectors subject to equality and inequality constraints, and (3) the optimal coast times. Numerical solutions which illustrate the characteristics of the solution are presented.

Skin mechanical properties and modeling: A review.

PubMed

Joodaki, Hamed; Panzer, Matthew B

2018-04-01

The mechanical properties of the skin are important for various applications. Numerous tests have been conducted to characterize the mechanical behavior of this tissue, and this article presents a review on different experimental methods used. A discussion on the general mechanical behavior of the skin, including nonlinearity, viscoelasticity, anisotropy, loading history dependency, failure properties, and aging effects, is presented. Finally, commonly used constitutive models for simulating the mechanical response of skin are discussed in the context of representing the empirically observed behavior.

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

Doering, C.; Bier, M.; Christodoulou, K.

This is the final report of a one-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Polymers, composites, and synthetic modern materials are replacing traditional materials in many older scientific, engineering, commercial, and military applications. This project sought to focus on the new polymeric materials, deriving and analyzing models that predict their seemingly mysterious transport properties. It sought to identify the dominant physical mechanisms and the pertinent dimensionless parameters, produce viable theoretical models, and devise asymptotic and numerical methods for use in specific problems.

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: A two scale nonlinear fractal sea surface model in a one dimensional deep sea

NASA Astrophysics Data System (ADS)

Xie, Tao; Zou, Guang-Hui; William, Perrie; Kuang, Hai-Lan; Chen, Wei

2010-05-01

Using the theory of nonlinear interactions between long and short waves, a nonlinear fractal sea surface model is presented for a one dimensional deep sea. Numerical simulation results show that spectra intensity changes at different locations (in both the wave number domain and temporal-frequency domain), and the system obeys the energy conservation principle. Finally, a method to limit the fractal parameters is also presented to ensure that the model system does not become ill-posed.

Numerical Relativity, Black Hole Mergers, and Gravitational Waves: Part III

NASA Technical Reports Server (NTRS)

Centrella, Joan

2012-01-01

This series of 3 lectures will present recent developments in numerical relativity, and their applications to simulating black hole mergers and computing the resulting gravitational waveforms. In this third and final lecture, we present applications of the results of numerical relativity simulations to gravitational wave detection and astrophysics.

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ormiston, R. A.

1975-01-01

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

Multimodal electromechanical model of piezoelectric transformers by Hamilton's principle.

PubMed

Nadal, Clement; Pigache, Francois

2009-11-01

This work deals with a general energetic approach to establish an accurate electromechanical model of a piezoelectric transformer (PT). Hamilton's principle is used to obtain the equations of motion for free vibrations. The modal characteristics (mass, stiffness, primary and secondary electromechanical conversion factors) are also deduced. Then, to illustrate this general electromechanical method, the variational principle is applied to both homogeneous and nonhomogeneous Rosen-type PT models. A comparison of modal parameters, mechanical displacements, and electrical potentials are presented for both models. Finally, the validity of the electrodynamical model of nonhomogeneous Rosen-type PT is confirmed by a numerical comparison based on a finite elements method and an experimental identification.

Data association approaches in bearings-only multi-target tracking

NASA Astrophysics Data System (ADS)

Xu, Benlian; Wang, Zhiquan

2008-03-01

According to requirements of time computation complexity and correctness of data association of the multi-target tracking, two algorithms are suggested in this paper. The proposed Algorithm 1 is developed from the modified version of dual Simplex method, and it has the advantage of direct and explicit form of the optimal solution. The Algorithm 2 is based on the idea of Algorithm 1 and rotational sort method, it combines not only advantages of Algorithm 1, but also reduces the computational burden, whose complexity is only 1/ N times that of Algorithm 1. Finally, numerical analyses are carried out to evaluate the performance of the two data association algorithms.

Transportation optimization with fuzzy trapezoidal numbers based on possibility theory.

PubMed

He, Dayi; Li, Ran; Huang, Qi; Lei, Ping

2014-01-01

In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.

The elastic field induced by a hemispherical inclusion in the half-space

NASA Astrophysics Data System (ADS)

Wu, Linzhi

2003-06-01

The elastic field induced by a hekispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Green's function method and series expansion technique. The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment. Finally, numerical results are given for the displacement and stress fields along the axis of symmetry ( x 3-axis).

Minimum constitutive relation error based static identification of beams using force method

NASA Astrophysics Data System (ADS)

Guo, Jia; Takewaki, Izuru

2017-05-01

A new static identification approach based on the minimum constitutive relation error (CRE) principle for beam structures is introduced. The exact stiffness and the exact bending moment are shown to make the CRE minimal for given displacements to beam damages. A two-step substitution algorithm—a force-method step for the bending moment and a constitutive-relation step for the stiffness—is developed and its convergence is rigorously derived. Identifiability is further discussed and the stiffness in the undeformed region is found to be unidentifiable. An extra set of static measurements is complemented to remedy the drawback. Convergence and robustness are finally verified through numerical examples.

C deg continuity elements by Hybrid Stress method. M.S. Thesis, 1982 Final Report

NASA Technical Reports Server (NTRS)

Kang, David Sung-Soo

1991-01-01

An intensive study of the assumed variable distribution necessary for the Assumed Displacement Formulation, the Hellinger-Reissner Formulation, and the Hu-Washizu Formulation is made in a unified manner. With emphasis on physical explanation, a systematic method for the Hybrid Stress element construction is outlined. The numerical examples use four and eight node plane stress elements and eight and twenty node solid elements. Computation cost study indicates that the hybrid stress element derived using recently developed Uncoupled Stress Formulation is comparable in CPU time to the Assumed Displacement element. Overall, main emphasis is placed on providing a broader understanding of the Hybrid Stress Formulation.

A recurrent neural network for solving bilevel linear programming problem.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian

2014-04-01

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

NASA Astrophysics Data System (ADS)

Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

NASA Technical Reports Server (NTRS)

Hou, Gene

2000-01-01

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

Adaptive target binarization method based on a dual-camera system

NASA Astrophysics Data System (ADS)

Lei, Jing; Zhang, Ping; Xu, Jiangtao; Gao, Zhiyuan; Gao, Jing

2018-01-01

An adaptive target binarization method based on a dual-camera system that contains two dynamic vision sensors was proposed. First, a preprocessing procedure of denoising is introduced to remove the noise events generated by the sensors. Then, the complete edge of the target is retrieved and represented by events based on an event mosaicking method. Third, the region of the target is confirmed by an event-to-event method. Finally, a postprocessing procedure of image open and close operations of morphology methods is adopted to remove the artifacts caused by event-to-event mismatching. The proposed binarization method has been extensively tested on numerous degraded images with nonuniform illumination, low contrast, noise, or light spots and successfully compared with other well-known binarization methods. The experimental results, which are based on visual and misclassification error criteria, show that the proposed method performs well and has better robustness on the binarization of degraded images.

Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation.

PubMed

Nakatsui, M; Horimoto, K; Lemaire, F; Ürgüplü, A; Sedoglavic, A; Boulier, F

2011-09-01

Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.

An Approximate Model for the Performance and Acoustic Predictions of Counterrotating Propeller Configurations. M.S. Thesis

NASA Technical Reports Server (NTRS)

Denner, Brett William

1989-01-01

An approximate method was developed to analyze and predict the acoustics of a counterrotating propeller configuration. The method employs the analytical techniques of Lock and Theodorsen as described by Davidson to predict the steady performance of a counterrotating configuration. Then, a modification of the method of Lesieutre is used to predict the unsteady forces on the blades. Finally, the steady and unsteady loads are used in the numerical method of Succi to predict the unsteady acoustics of the propeller. The numerical results are compared with experimental acoustic measurements of a counterrotating propeller configuration by Gazzaniga operating under several combinations of advance ratio, blade pitch, and number of blades. In addition, a constant-speed commuter-class propeller configuration was designed with the Davidson method and the acoustics analyzed at three advance ratios. Noise levels and frequency spectra were calculated at a number of locations around the configuration. The directivity patterns of the harmonics in both the horizontal and vertical planes were examined, with the conclusion that the noise levels of the even harmonics are relatively independent of direction whereas the noise levels of the odd harmonics are extremely dependent on azimuthal direction in the horizontal plane. The equations of Succi are examined to explain this behavior.

A comparison of methods to estimate seismic phase delays--Numerical examples for coda wave interferometry

USGS Publications Warehouse

Mikesell, T. Dylan; Malcolm, Alison E.; Yang, Di; Haney, Matthew M.

2015-01-01

Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here, we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We illustrate the differences of all three methods compared to one another using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has better time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements. DTW is a new tool that may find new applications in seismology and other geophysical methods (e.g., as a waveform inversion misfit function).

Modeling the source of GW150914 with targeted numerical-relativity simulations

NASA Astrophysics Data System (ADS)

Lovelace, Geoffrey; Lousto, Carlos O.; Healy, James; Scheel, Mark A.; Garcia, Alyssa; O'Shaughnessy, Richard; Boyle, Michael; Campanelli, Manuela; Hemberger, Daniel A.; Kidder, Lawrence E.; Pfeiffer, Harald P.; Szilágyi, Béla; Teukolsky, Saul A.; Zlochower, Yosef

2016-12-01

In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes (Abbott et al Virgo, LIGO Scientific 2016 Phys. Rev. Lett. 116 061102). In the final 0.2 s (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO’s measurement (Abbott et al LIGO Scientific Collaboration, Virgo Collaboration 2016 Phys. Rev. Lett. 116 241102). In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations.

Stability of streamwise vortices

NASA Technical Reports Server (NTRS)

Khorrami, M. K.; Grosch, C. E.; Ash, R. L.

1987-01-01

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Study on validation method for femur finite element model under multiple loading conditions

NASA Astrophysics Data System (ADS)

Guan, Fengjiao; Zhang, Guanjun; Liu, Jie; Wang, Shujing; Luo, Xu

2018-03-01

Acquisition of accurate and reliable constitutive parameters related to bio-tissue materials was beneficial to improve biological fidelity of a Finite Element (FE) model and predict impact damages more effectively. In this paper, a femur FE model was established under multiple loading conditions with diverse impact positions. Then, based on sequential response surface method and genetic algorithms, the material parameters identification was transformed to a multi-response optimization problem. Finally, the simulation results successfully coincided with force-displacement curves obtained by numerous experiments. Thus, computational accuracy and efficiency of the entire inverse calculation process were enhanced. This method was able to effectively reduce the computation time in the inverse process of material parameters. Meanwhile, the material parameters obtained by the proposed method achieved higher accuracy.

Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation

NASA Astrophysics Data System (ADS)

Yarmohammadi, M.; Javadi, S.; Babolian, E.

2018-04-01

In this study a new spectral iterative method (SIM) based on fractional interpolation is presented for solving nonlinear fractional differential equations (FDEs) involving Caputo derivative. This method is equipped with a pre-algorithm to find the singularity index of solution of the problem. This pre-algorithm gives us a real parameter as the index of the fractional interpolation basis, for which the SIM achieves the highest order of convergence. In comparison with some recent results about the error estimates for fractional approximations, a more accurate convergence rate has been attained. We have also proposed the order of convergence for fractional interpolation error under the L2-norm. Finally, general error analysis of SIM has been considered. The numerical results clearly demonstrate the capability of the proposed method.

Modeling multiscale evolution of numerous voids in shocked brittle material.

PubMed

Yu, Yin; Wang, Wenqiang; He, Hongliang; Lu, Tiecheng

2014-04-01

The influence of the evolution of numerous voids on macroscopic properties of materials is a multiscale problem that challenges computational research. A shock-wave compression model for brittle material, which can obtain both microscopic evolution and macroscopic shock properties, was developed using discrete element methods (lattice model). Using a model interaction-parameter-mapping procedure, qualitative features, as well as trends in the calculated shock-wave profiles, are shown to agree with experimental results. The shock wave splits into an elastic wave and a deformation wave in porous brittle materials, indicating significant shock plasticity. Void collapses in the deformation wave were the natural reason for volume shrinkage and deformation. However, media slippage and rotation deformations indicated by complex vortex patterns composed of relative velocity vectors were also confirmed as an important source of shock plasticity. With increasing pressure, the contribution from slippage deformation to the final plastic strain increased. Porosity was found to determine the amplitude of the elastic wave; porosity and shock stress together determine propagation speed of the deformation wave, as well as stress and strain on the final equilibrium state. Thus, shock behaviors of porous brittle material can be systematically designed for specific applications.

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

Rigorous simulations of a helical core fiber by the use of transformation optics formalism.

PubMed

Napiorkowski, Maciej; Urbanczyk, Waclaw

2014-09-22

We report for the first time on rigorous numerical simulations of a helical-core fiber by using a full vectorial method based on the transformation optics formalism. We modeled the dependence of circular birefringence of the fundamental mode on the helix pitch and analyzed the effect of a birefringence increase caused by the mode displacement induced by a core twist. Furthermore, we analyzed the complex field evolution versus the helix pitch in the first order modes, including polarization and intensity distribution. Finally, we show that the use of the rigorous vectorial method allows to better predict the confinement loss of the guided modes compared to approximate methods based on equivalent in-plane bending models.

Faithful replication of grating patterns in polymer through electrohydrodynamic instabilities

NASA Astrophysics Data System (ADS)

Li, H.; Yu, W.; Wang, T.; Zhang, H.; Cao, Y.; Abraham, E.; Desmulliez, M. P. Y.

2014-07-01

Electrohydrodynamic instability patterning (EHDIP) as an alternative patterning method has attracted a great deal of attention over the past decade. This article demonstrates the faithful transfer of patterns with a high aspect ratio onto a polymer film via electrohydrodynamic instabilities for a given patterned grating mask. We perform a simple mathematical analysis to determine the influence of process parameters on the pressure difference ▵P. Through numerical simulation, it is demonstrated that thick films subject to large electric fields are essential to realize this faithful replication. In particular, the influence of the material properties of the polymer on pattern replication is discussed in detail. It is found that, to achieve the smaller periodic patterns with a higher resolution, film with a larger value of the dielectric constant and smaller value of the surface tension should be chosen. In addition, an ideal replication of the mask pattern with a short evolution time is possible by reducing the viscosity of the polymer liquid. Finally, the experiments of the pattern replication with and without defects are demonstrated to compare with the numerical simulation results. It is found that experiments are in good agreement with the simulation results and prove that the numerical simulation method provides an effective way to predict faithful replication.

Characteristics of steady vibration in a rotating hub-beam system

NASA Astrophysics Data System (ADS)

Zhao, Zhen; Liu, Caishan; Ma, Wei

2016-02-01

A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

Analytical representation of dynamical quantities in G W from a matrix resolvent

NASA Astrophysics Data System (ADS)

Gesenhues, J.; Nabok, D.; Rohlfing, M.; Draxl, C.

2017-12-01

The power of the G W formalism is, to a large extent, based on the explicit treatment of dynamical correlations in the self-energy. This dynamics is taken into account by calculating the energy dependence of the screened Coulomb interaction W , followed by a convolution with the Green's function G . In order to obtain the energy dependence of W the prevalent methods are plasmon-pole models and numerical integration techniques. In this paper, we discuss an alternative approach, in which the energy-dependent screening is calculated by determining the resolvent, which is set up from a matrix representation of the dielectric function. On the one hand, this refrains from a numerical energy convolution and allows one to actually write down the energy dependence of W explicitly (like in the plasmon-pole models). On the other hand, the method is at least as accurate as the numerical approaches due to its multipole nature. We discuss the theoretical setup in some detail, give insight into the computational aspects, and present results for Si, C, GaAs, and LiF. Finally, we argue that the analytic representability is not only useful for educational purposes but may also be of avail for the development of theory that goes beyond G W .

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

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

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

New convergence results for the scaled gradient projection method

NASA Astrophysics Data System (ADS)

Bonettini, S.; Prato, M.

2015-09-01

The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a variable scaling matrix multiplying the gradient, which may change at each iteration. In the last few years, extensive numerical experimentation showed that SGP equipped with a suitable choice of the scaling matrix is a very effective tool for solving large scale variational problems arising in image and signal processing. In spite of the very reliable numerical results observed, only a weak convergence theorem is provided establishing that any limit point of the sequence generated by SGP is stationary. Here, under the only assumption that the objective function is convex and that a solution exists, we prove that the sequence generated by SGP converges to a minimum point, if the scaling matrices sequence satisfies a simple and implementable condition. Moreover, assuming that the gradient of the objective function is Lipschitz continuous, we are also able to prove the {O}(1/k) convergence rate with respect to the objective function values. Finally, we present the results of a numerical experience on some relevant image restoration problems, showing that the proposed scaling matrix selection rule performs well also from the computational point of view.

Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation

NASA Astrophysics Data System (ADS)

Gasmi, Hatem; Hamdi, Essaïeb; Bouden Romdhane, Nejla

2014-07-01

Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young's modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young's modulus of equivalent medium for wave propagation analysis.

Numerical study of the influence of geometrical characteristics of a vertical helical coil on a bubbly flow

NASA Astrophysics Data System (ADS)

Saffari, H.; Moosavi, R.

2014-11-01

In this article, turbulent single-phase and two-phase (air-water) bubbly fluid flows in a vertical helical coil are analyzed by using computational fluid dynamics (CFD). The effects of the pipe diameter, coil diameter, coil pitch, Reynolds number, and void fraction on the pressure loss, friction coefficient, and flow characteristics are investigated. The Eulerian-Eulerian model is used in this work to simulate the two-phase fluid flow. Three-dimensional governing equations of continuity, momentum, and energy are solved by using the finite volume method. The k- ɛ turbulence model is used to calculate turbulence fluctuations. The SIMPLE algorithm is employed to solve the velocity and pressure fields. Due to the effect of a secondary force in helical pipes, the friction coefficient is found to be higher in helical pipes than in straight pipes. The friction coefficient increases with an increase in the curvature, pipe diameter, and coil pitch and decreases with an increase in the coil diameter and void fraction. The close correlation between the numerical results obtained in this study and the numerical and empirical results of other researchers confirm the accuracy of the applied method. For void fractions up to 0.1, the numerical results indicate that the friction coefficient increases with increasing the pipe diameter and keeping the coil pitch and diameter constant and decreases with increasing the coil diameter. Finally, with an increase in the Reynolds number, the friction coefficient decreases, while the void fraction increases.

Application of numerical grid generation for improved CFD analysis of multiphase screw machines

NASA Astrophysics Data System (ADS)

Rane, S.; Kovačević, A.

2017-08-01

Algebraic grid generation is widely used for discretization of the working domain of twin screw machines. Algebraic grid generation is fast and has good control over the placement of grid nodes. However, the desired qualities of grid which should be able to handle multiphase flows such as oil injection, may be difficult to achieve at times. In order to obtain fast solution of multiphase screw machines, it is important to further improve the quality and robustness of the computational grid. In this paper, a deforming grid of a twin screw machine is generated using algebraic transfinite interpolation to produce initial mesh upon which an elliptic partial differential equations (PDE) of the Poisson’s form is solved numerically to produce smooth final computational mesh. The quality of numerical cells and their distribution obtained by the differential method is greatly improved. In addition, a similar procedure was introduced to fully smoothen the transition of the partitioning rack curve between the rotors thus improving continuous movement of grid nodes and in turn improve robustness and speed of the Computational Fluid Dynamic (CFD) solver. Analysis of an oil injected twin screw compressor is presented to compare the improvements in grid quality factors in the regions of importance such as interlobe space, radial tip and the core of the rotor. The proposed method that combines algebraic and differential grid generation offer significant improvement in grid quality and robustness of numerical solution.

Dynamical friction for supersonic motion in a homogeneous gaseous medium

NASA Astrophysics Data System (ADS)

Thun, Daniel; Kuiper, Rolf; Schmidt, Franziska; Kley, Wilhelm

2016-05-01

Context. The supersonic motion of gravitating objects through a gaseous ambient medium constitutes a classical problem in theoretical astrophysics. Its application covers a broad range of objects and scales from planetesimals, planets, and all kind of stars up to galaxies and black holes. In particular, the dynamical friction caused by the wake that forms behind the object plays an important role for the dynamics of the system. To calculate the dynamical friction for a particular system, standard formulae based on linear theory are often used. Aims: It is our goal to check the general validity of these formulae and provide suitable expressions for the dynamical friction acting on the moving object, based on the basic physical parameters of the problem: first, the mass, radius, and velocity of the perturber; second, the gas mass density, soundspeed, and adiabatic index of the gaseous medium; and finally, the size of the forming wake. Methods: We perform dedicated sequences of high-resolution numerical studies of rigid bodies moving supersonically through a homogeneous ambient medium and calculate the total drag acting on the object, which is the sum of gravitational and hydrodynamical drag. We study cases without gravity with purely hydrodynamical drag, as well as gravitating objects. In various numerical experiments, we determine the drag force acting on the moving body and its dependence on the basic physical parameters of the problem, as given above. From the final equilibrium state of the simulations, for gravitating objects we compute the dynamical friction by direct numerical integration of the gravitational pull acting on the embedded object. Results: The numerical experiments confirm the known scaling laws for the dependence of the dynamical friction on the basic physical parameters as derived in earlier semi-analytical studies. As a new important result we find that the shock's stand-off distance is revealed as the minimum spatial interaction scale of dynamical friction. Below this radius, the gas settles into a hydrostatic state, which - owing to its spherical symmetry - causes no net gravitational pull onto the moving body. Finally, we derive an analytic estimate for the stand-off distance that can easily be used when calculating the dynamical friction force.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

NASA Astrophysics Data System (ADS)

Leclaire, Sébastien; Parmigiani, Andrea; Malaspinas, Orestis; Chopard, Bastien; Latt, Jonas

2017-03-01

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

A review of spatial downscaling of satellite remotely sensed soil moisture

NASA Astrophysics Data System (ADS)

Peng, Jian; Loew, Alexander; Merlin, Olivier; Verhoest, Niko E. C.

2017-06-01

Satellite remote sensing technology has been widely used to estimate surface soil moisture. Numerous efforts have been devoted to develop global soil moisture products. However, these global soil moisture products, normally retrieved from microwave remote sensing data, are typically not suitable for regional hydrological and agricultural applications such as irrigation management and flood predictions, due to their coarse spatial resolution. Therefore, various downscaling methods have been proposed to improve the coarse resolution soil moisture products. The purpose of this paper is to review existing methods for downscaling satellite remotely sensed soil moisture. These methods are assessed and compared in terms of their advantages and limitations. This review also provides the accuracy level of these methods based on published validation studies. In the final part, problems and future trends associated with these methods are analyzed.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Experimental characterization and numerical modeling of tissue electrical conductivity during pulsed electric fields for irreversible electroporation treatment planning.

PubMed

Neal, Robert E; Garcia, Paulo A; Robertson, John L; Davalos, Rafael V

2012-04-01

Irreversible electroporation is a new technique to kill cells in targeted tissue, such as tumors, through a nonthermal mechanism using electric pulses to irrecoverably disrupt the cell membrane. Treatment effects relate to the tissue electric field distribution, which can be predicted with numerical modeling for therapy planning. Pulse effects will change the cell and tissue properties through thermal and electroporation (EP)-based processes. This investigation characterizes these changes by measuring the electrical conductivity and temperature of ex vivo renal porcine tissue within a single pulse and for a 200 pulse protocol. These changes are incorporated into an equivalent circuit model for cells and tissue with a variable EP-based resistance, providing a potential method to estimate conductivity as a function of electric field and pulse length for other tissues. Finally, a numerical model using a human kidney volumetric mesh evaluated how treatment predictions vary when EP- and temperature-based electrical conductivity changes are incorporated. We conclude that significant changes in predicted outcomes will occur when the experimental results are applied to the numerical model, where the direction and degree of change varies with the electric field considered.

Modeling ventilation time in forage tower silos.

PubMed

Bahloul, A; Chavez, M; Reggio, M; Roberge, B; Goyer, N

2012-10-01

The fermentation process in forage tower silos produces a significant amount of gases, which can easily reach dangerous concentrations and constitute a hazard for silo operators. To maintain a non-toxic environment, silo ventilation is applied. Literature reviews show that the fermentation gases reach high concentrations in the headspace of a silo and flow down the silo from the chute door to the feed room. In this article, a detailed parametric analysis of forced ventilation scenarios built via numerical simulation was performed. The methodology is based on the solution of the Navier-Stokes equations, coupled with transport equations for the gas concentrations. Validation was achieved by comparing the numerical results with experimental data obtained from a scale model silo using the tracer gas testing method for O2 and CO2 concentrations. Good agreement was found between the experimental and numerical results. The set of numerical simulations made it possible to establish a simple analytical model to predict the minimum time required to ventilate a silo to make it safe to enter. This ventilation time takes into account the headspace above the forage, the airflow rate, and the initial concentrations of O2 and CO2. The final analytical model was validated with available results from the literature.

Traco Final Exam and Course Evaluation | Center for Cancer Research

Cancer.gov

Numerous students have requested a certificate upon completion of TRACO.  To obtain a certificate you MUST answer 17 of the 26 final examination questions correctly. In the final examination, 1 question is derived from each of the 1-hour lectures.

Multistage degradation modeling for BLDC motor based on Wiener process

NASA Astrophysics Data System (ADS)

Yuan, Qingyang; Li, Xiaogang; Gao, Yuankai

2018-05-01

Brushless DC motors are widely used, and their working temperatures, regarding as degradation processes, are nonlinear and multistage. It is necessary to establish a nonlinear degradation model. In this research, our study was based on accelerated degradation data of motors, which are their working temperatures. A multistage Wiener model was established by using the transition function to modify linear model. The normal weighted average filter (Gauss filter) was used to improve the results of estimation for the model parameters. Then, to maximize likelihood function for parameter estimation, we used numerical optimization method- the simplex method for cycle calculation. Finally, the modeling results show that the degradation mechanism changes during the degradation of the motor with high speed. The effectiveness and rationality of model are verified by comparison of the life distribution with widely used nonlinear Wiener model, as well as a comparison of QQ plots for residual. Finally, predictions for motor life are gained by life distributions in different times calculated by multistage model.

Quantum theory of multiscale coarse-graining.

PubMed

Han, Yining; Jin, Jaehyeok; Wagner, Jacob W; Voth, Gregory A

2018-03-14

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Image analysis method for the measurement of water saturation in a two-dimensional experimental flow tank

NASA Astrophysics Data System (ADS)

Belfort, Benjamin; Weill, Sylvain; Lehmann, François

2017-07-01

A novel, non-invasive imaging technique is proposed that determines 2D maps of water content in unsaturated porous media. This method directly relates digitally measured intensities to the water content of the porous medium. This method requires the classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The main advantages of this approach are that no calibration experiment is needed, because calibration curve relating water content and reflected light intensities is established during the main monitoring phase of each experiment and that no tracer or dye is injected into the flow tank. The procedure enables effective processing of a large number of photographs and thus produces 2D water content maps at high temporal resolution. A drainage/imbibition experiment in a 2D flow tank with inner dimensions of 40 cm × 14 cm × 6 cm (L × W × D) is carried out to validate the methodology. The accuracy of the proposed approach is assessed using a statistical framework to perform an error analysis and numerical simulations with a state-of-the-art computational code that solves the Richards' equation. Comparison of the cumulative mass leaving and entering the flow tank and water content maps produced by the photographic measurement technique and the numerical simulations demonstrate the efficiency and high accuracy of the proposed method for investigating vadose zone flow processes. Finally, the photometric procedure has been developed expressly for its extension to heterogeneous media. Other processes may be investigated through different laboratory experiments which will serve as benchmark for numerical codes validation.

Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems

NASA Astrophysics Data System (ADS)

Mei, Lijie; Wu, Xinyuan

2017-06-01

Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.

Detection of a sudden change of the field time series based on the Lorenz system.

PubMed

Da, ChaoJiu; Li, Fang; Shen, BingLu; Yan, PengCheng; Song, Jian; Ma, DeShan

2017-01-01

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series.

Fractional-order TV-L2 model for image denoising

NASA Astrophysics Data System (ADS)

Chen, Dali; Sun, Shenshen; Zhang, Congrong; Chen, YangQuan; Xue, Dingyu

2013-10-01

This paper proposes a new fractional order total variation (TV) denoising method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, regularization parameter selection and blocky effect. Two fractional order TV-L2 models are constructed for image denoising. The majorization-minimization (MM) algorithm is used to decompose these two complex fractional TV optimization problems into a set of linear optimization problems which can be solved by the conjugate gradient algorithm. The final adaptive numerical procedure is given. Finally, we report experimental results which show that the proposed methodology avoids the blocky effect and achieves state-of-the-art performance. In addition, two medical image processing experiments are presented to demonstrate the validity of the proposed methodology.

BOOK REVIEW Analytical and Numerical Approaches to Mathematical Relativity

NASA Astrophysics Data System (ADS)

Stewart, John M.

2007-08-01

The 319th Wilhelm-and-Else-Heraeus Seminar 'Mathematical Relativity: New Ideas and Developments' took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume, preceded by a foreword by Roger Penrose. The first group consists of four papers on 'differential geometry and differential topology'. Paul Ehrlich opens with a very witty review of global Lorentzian geometry, which caused this reviewer to think more carefully about how he uses the adjective 'generic'. Robert Low addresses the issue of causality with a description of the 'space of null geodesics' and a tentative proposal for a new definition of causal boundary. The underlying review of global Lorentzian geometry is continued by Antonio Masiello, looking at variational approaches (actually valid for more general semi-Riemannian manifolds). This group concludes with a very clear review of pp-wave spacetimes from José Flores and Miguel Sánchez. (This reviewer was delighted to see a reproduction of Roger Penrose's seminal (1965) picture of null geodesics in plane wave spacetimes which attracted him into the subject.) Robert Beig opens the second group 'analytic methods and differential equations' with a brief but careful discussion of symmetric (regular) hyperbolicity for first (second) order systems, respectively, of partial differential equations. His description is peppered with examples, many specific to relativstic continuum mechanics. There follows a succinct review of linear elliptic boundary value problems with applications to general relativity from Sergio Dain. The numerous examples he provides are thought-provoking. The 'standard cosmological model' has been well understood for three quarters of a century. However recent observations suggest that the expansion in our Universe may be accelerating. Alan Rendall provides a careful discussion of the changes, both mathematical and physical, to the standard model which might be needed. This reviewer found the exposition much clearer than much of the phenomenological literature. Finally László Szabados gives a very systematic spacetime discussion of the group theoretical analysis of general relativity by Beig and Ó Murchadha, addressing the Poincaré structure and the centre-of-mass of asymptotically flat spacetimes. The third and final group is entitled 'numerical methods'. Beverly Berger summarizes her 'Living Review' on numerical approaches to spacetime singularities and includes more recent analytical results emphasizing the synergy between mathematical and numerical approaches. For numerical evolutions on a domain of compact spatial support boundary conditions will be needed and, as pointed out by this reviewer, for unconstrained evolutions it is essential that the boundary conditions ensure constraint conservation. This aspect is discussed in a clear elementary way by Simonetta Frittelli and Roberto Gómez. Dave Neilsen, Luis Lehner, Olivier Sarbach and Manuel Tiglio review algorithms adopted recently by the Louisiana group, particularly summation by parts and constraint monitoring with applications to bubble and black hole spacetimes. Finally Maria Babiuc, Béla Szilágyi and Jeffrey Winicour discuss the Pittsburgh group's approach with particular reference to harmonic gauge conditions. It is perhaps unfortunate for the editors of this work that published proceedings of more recent numerical relativity meetings exist already. However, as this reviewer has tried to indicate, this slim (but not inexpensive) volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institution's library purchases a copy!

A nominally second-order cell-centered Lagrangian scheme for simulating elastic–plastic flows on two-dimensional unstructured grids

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

Maire, Pierre-Henri, E-mail: maire@celia.u-bordeaux1.fr; Abgrall, Rémi, E-mail: remi.abgrall@math.u-bordeau1.fr; Breil, Jérôme, E-mail: breil@celia.u-bordeaux1.fr

2013-02-15

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic–plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs themore » von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.« less

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

A Formal Approach to Requirements-Based Programming

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2005-01-01

No significant general-purpose method is currently available to mechanically transform system requirements into a provably equivalent model. The widespread use of such a method represents a necessary step toward high-dependability system engineering for numerous application domains. Current tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The "gap" unfilled by such tools and methods is that the formal models cannot be proven to be equivalent to the requirements. We offer a method for mechanically transforming requirements into a provably equivalent formal model that can be used as the basis for code generation and other transformations. This method is unique in offering full mathematical tractability while using notations and techniques that are well known and well trusted. Finally, we describe further application areas we are investigating for use of the approach.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

Kondo effect in the seven-orbital Anderson model hybridized with Γ8 conduction electrons

NASA Astrophysics Data System (ADS)

Hotta, Takashi

2018-05-01

We clarify the two-channel Kondo effect in the seven-orbital Anderson model hybridized with Γ8 conduction electrons by employing a numerical renormalization group method. From the numerical analysis for the case with two local f electrons, corresponding to Pr3+ or U4+ ion, we confirm that a residual entropy of 0.5 log 2 , a characteristic of two-channel Kondo phenomena, appears for the local Γ3 non-Kramers doublet state. For further understanding on the Γ3 state, the effective model is constructed on the basis of a j-j coupling scheme. Then, we rediscover the two-channel s-d model concerning quadrupole degrees of freedom. Finally, we briefly introduce our recent result on the two-channel Kondo effect for the case with three local f electrons.

Fluctuating hydrodynamics of multispecies nonreactive mixtures

DOE PAGES

Balakrishnan, Kaushik; Garcia, Alejandro L.; Donev, Aleksandar; ...

2014-01-22

In this study we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of nonequilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well asmore » reverse diffusion in a ternary mixture. Finally, good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multispecies fluids.« less

Inferring physical properties of galaxies from their emission-line spectra

NASA Astrophysics Data System (ADS)

Ucci, G.; Ferrara, A.; Gallerani, S.; Pallottini, A.

2017-02-01

We present a new approach based on Supervised Machine Learning algorithms to infer key physical properties of galaxies (density, metallicity, column density and ionization parameter) from their emission-line spectra. We introduce a numerical code (called GAME, GAlaxy Machine learning for Emission lines) implementing this method and test it extensively. GAME delivers excellent predictive performances, especially for estimates of metallicity and column densities. We compare GAME with the most widely used diagnostics (e.g. R23, [N II] λ6584/Hα indicators) showing that it provides much better accuracy and wider applicability range. GAME is particularly suitable for use in combination with Integral Field Unit spectroscopy, both for rest-frame optical/UV nebular lines and far-infrared/sub-millimeter lines arising from photodissociation regions. Finally, GAME can also be applied to the analysis of synthetic galaxy maps built from numerical simulations.

Lattice Wigner equation.

PubMed

Solórzano, S; Mendoza, M; Succi, S; Herrmann, H J

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Nonlinear mechanics of composite materials with periodic microstructure

NASA Technical Reports Server (NTRS)

Jordan, E. H.; Walker, K. P.

1991-01-01

This report summarizes the result of research done under NASA NAG3-882 Nonlinear Mechanics of Composites with Periodic Microstructure. The effort involved the development of non-finite element methods to calculate local stresses around fibers in composite materials. The theory was developed and some promising numerical results were obtained. It is expected that when this approach is fully developed, it will provide an important tool for calculating local stresses and averaged constitutive behavior in composites. NASA currently has a major contractual effort (NAS3-24691) to bring the approach developed under this grant to application readiness. The report has three sections. One, the general theory that appeared as a NASA TM, a second section that gives greater details about the theory connecting Greens functions and Fourier series approaches, and a final section shows numerical results.

Lattice Wigner equation

NASA Astrophysics Data System (ADS)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

A Unit-Cell Model for Predicting the Elastic Constants of 3D Four Directional Cylindrical Braided Composite Shafts

NASA Astrophysics Data System (ADS)

Hao, Wenfeng; Liu, Ye; Huang, Xinrong; Liu, Yinghua; Zhu, Jianguo

2018-06-01

In this work, the elastic constants of 3D four directional cylindrical braided composite shafts were predicted using analytical and numerical methods. First, the motion rule of yarn carrier of 3D four directional cylindrical braided composite shafts was analyzed, and the horizontal projection of yarn motion trajectory was obtained. Then, the geometry models of unit-cells with different braiding angles and fiber volume contents were built up, and the meso-scale models of 3D cylindrical braided composite shafts were obtained. Finally, the effects of braiding angles and fiber volume contents on the elastic constants of 3D braided composite shafts were analyzed theoretically and numerically. These results play a crucial role in investigating the mechanical properties of 3D 4-directional braided composites shafts.

Fast angular synchronization for phase retrieval via incomplete information

NASA Astrophysics Data System (ADS)

Viswanathan, Aditya; Iwen, Mark

2015-08-01

We consider the problem of recovering the phase of an unknown vector, x ∈ ℂd, given (normalized) phase difference measurements of the form xjxk*/|xjxk*|, j,k ∈ {1,...,d}, and where xj* denotes the complex conjugate of xj. This problem is sometimes referred to as the angular synchronization problem. This paper analyzes a linear-time-in-d eigenvector-based angular synchronization algorithm and studies its theoretical and numerical performance when applied to a particular class of highly incomplete and possibly noisy phase difference measurements. Theoretical results are provided for perfect (noiseless) measurements, while numerical simulations demonstrate the robustness of the method to measurement noise. Finally, we show that this angular synchronization problem and the specific form of incomplete phase difference measurements considered arise in the phase retrieval problem - where we recover an unknown complex vector from phaseless (or magnitude) measurements.

User's Manual for LINER: FORTRAN Code for the Numerical Simulation of Plane Wave Propagation in a Lined Two-Dimensional Channel

NASA Technical Reports Server (NTRS)

Reichert, R, S.; Biringen, S.; Howard, J. E.

1999-01-01

LINER is a system of Fortran 77 codes which performs a 2D analysis of acoustic wave propagation and noise suppression in a rectangular channel with a continuous liner at the top wall. This new implementation is designed to streamline the usage of the several codes making up LINER, resulting in a useful design tool. Major input parameters are placed in two main data files, input.inc and nurn.prm. Output data appear in the form of ASCII files as well as a choice of GNUPLOT graphs. Section 2 briefly describes the physical model. Section 3 discusses the numerical methods; Section 4 gives a detailed account of program usage, including input formats and graphical options. A sample run is also provided. Finally, Section 5 briefly describes the individual program files.

Wave-filter-based approach for generation of a quiet space in a rectangular cavity

NASA Astrophysics Data System (ADS)

Iwamoto, Hiroyuki; Tanaka, Nobuo; Sanada, Akira

2018-02-01

This paper is concerned with the generation of a quiet space in a rectangular cavity using active wave control methodology. It is the purpose of this paper to present the wave filtering method for a rectangular cavity using multiple microphones and its application to an adaptive feedforward control system. Firstly, the transfer matrix method is introduced for describing the wave dynamics of the sound field, and then feedforward control laws for eliminating transmitted waves is derived. Furthermore, some numerical simulations are conducted that show the best possible result of active wave control. This is followed by the derivation of the wave filtering equations that indicates the structure of the wave filter. It is clarified that the wave filter consists of three portions; modal group filter, rearrangement filter and wave decomposition filter. Next, from a numerical point of view, the accuracy of the wave decomposition filter which is expressed as a function of frequency is investigated using condition numbers. Finally, an experiment on the adaptive feedforward control system using the wave filter is carried out, demonstrating that a quiet space is generated in the target space by the proposed method.

Systematic screening and characterization of flavonoid glycosides in Carthamus tinctorius L. by liquid chromatography/UV diode-array detection/electrospray ionization tandem mass spectrometry.

PubMed

Jin, Yu; Xiao, Yuan-sheng; Zhang, Fei-fang; Xue, Xing-ya; Xu, Qing; Liang, Xin-miao

2008-02-13

The traditional Chinese medicine (TCM) is a complex system, which always consists of numerous compounds with significant difference in the content and physical and chemical properties. In this paper, a screening method based on target molecular weights was developed to characterize the flavonoid glycosides in the flower of Carthamus tinctorius L. The screening tables of aglycone and glycan were designed, respectively, in order to select and combine freely. The multiple reaction monitoring (MRM) scan mode with higher sensitivity and selectivity was adopted in the screening, which benefit the characterization for the minor components. Seventy-seven flavonoid glycosides were screened out finally, and their structures were characterized by tandem mass spectrometric method in both positive and negative ion modes. The glycosylation mode, aglycone, sequence and/or the interglycosidic linkages of the glycan portion and glycosylation position were elucidated by the fragmentation rule in the MS. Numerous compounds screened out with this method showed the structure variety in secondary plant metabolites, and the purposeful screening systemically and subsequent structure characterization offered more information about the chemical constitutions of TCM.

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

NASA Technical Reports Server (NTRS)

Debussche, A.; Dubois, T.; Temam, R.

1993-01-01

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Finite element modeling of borehole heat exchanger systems. Part 1. Fundamentals

NASA Astrophysics Data System (ADS)

Diersch, H.-J. G.; Bauer, D.; Heidemann, W.; Rühaak, W.; Schätzl, P.

2011-08-01

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. The first part of the paper derives the fundamental equations for BHE systems and their finite element representations, where the thermal exchange between the borehole components is modeled via thermal transfer relations. For this purpose improved relationships for thermal resistances and capacities of BHE are introduced. Pipe-to-grout thermal transfer possesses multiple grout points for double U-shape and single U-shape BHE to attain a more accurate modeling. The numerical solution of the final 3D problems is performed via a widely non-sequential (essentially non-iterative) coupling strategy for the BHE and porous medium discretization. Four types of vertical BHE are supported: double U-shape (2U) pipe, single U-shape (1U) pipe, coaxial pipe with annular (CXA) and centred (CXC) inlet. Two computational strategies are used: (1) The analytical BHE method based on Eskilson and Claesson's (1988) solution, (2) numerical BHE method based on Al-Khoury et al.'s (2005) solution. The second part of the paper focusses on BHE meshing aspects, the validation of BHE solutions and practical applications for borehole thermal energy store systems.

Time Domain Strain/Stress Reconstruction Based on Empirical Mode Decomposition: Numerical Study and Experimental Validation.

PubMed

He, Jingjing; Zhou, Yibin; Guan, Xuefei; Zhang, Wei; Zhang, Weifang; Liu, Yongming

2016-08-16

Structural health monitoring has been studied by a number of researchers as well as various industries to keep up with the increasing demand for preventive maintenance routines. This work presents a novel method for reconstruct prompt, informed strain/stress responses at the hot spots of the structures based on strain measurements at remote locations. The structural responses measured from usage monitoring system at available locations are decomposed into modal responses using empirical mode decomposition. Transformation equations based on finite element modeling are derived to extrapolate the modal responses from the measured locations to critical locations where direct sensor measurements are not available. Then, two numerical examples (a two-span beam and a 19956-degree of freedom simplified airfoil) are used to demonstrate the overall reconstruction method. Finally, the present work investigates the effectiveness and accuracy of the method through a set of experiments conducted on an aluminium alloy cantilever beam commonly used in air vehicle and spacecraft. The experiments collect the vibration strain signals of the beam via optical fiber sensors. Reconstruction results are compared with theoretical solutions and a detailed error analysis is also provided.

Modeling Anisotropic Elastic Wave Propagation in Jointed Rock Masses

NASA Astrophysics Data System (ADS)

Hurley, R.; Vorobiev, O.; Ezzedine, S. M.; Antoun, T.

2016-12-01

We present a numerical approach for determining the anisotropic stiffness of materials with nonlinearly-compliant joints capable of sliding. The proposed method extends existing ones for upscaling the behavior of a medium with open cracks and inclusions to cases relevant to natural fractured and jointed rocks, where nonlinearly-compliant joints can undergo plastic slip. The method deviates from existing techniques by incorporating the friction and closure states of the joints, and recovers an anisotropic elastic form in the small-strain limit when joints are not sliding. We present the mathematical formulation of our method and use Representative Volume Element (RVE) simulations to evaluate its accuracy for joint sets with varying complexity. We then apply the formulation to determine anisotropic elastic constants of jointed granite found at the Nevada Nuclear Security Site (NNSS) where the Source Physics Experiments (SPE), a campaign of underground chemical explosions, are performed. Finally, we discuss the implementation of our numerical approach in a massively parallel Lagrangian code Geodyn-L and its use for studying wave propagation from underground explosions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Optimal rotated staggered-grid finite-difference schemes for elastic wave modeling in TTI media

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2015-11-01

The rotated staggered-grid finite-difference (RSFD) is an effective approach for numerical modeling to study the wavefield characteristics in tilted transversely isotropic (TTI) media. But it surfaces from serious numerical dispersion, which directly affects the modeling accuracy. In this paper, we propose two different optimal RSFD schemes based on the sampling approximation (SA) method and the least-squares (LS) method respectively to overcome this problem. We first briefly introduce the RSFD theory, based on which we respectively derive the SA-based RSFD scheme and the LS-based RSFD scheme. Then different forms of analysis are used to compare the SA-based RSFD scheme and the LS-based RSFD scheme with the conventional RSFD scheme, which is based on the Taylor-series expansion (TE) method. The contrast in numerical accuracy analysis verifies the greater accuracy of the two proposed optimal schemes, and indicates that these schemes can effectively widen the wavenumber range with great accuracy compared with the TE-based RSFD scheme. Further comparisons between these two optimal schemes show that at small wavenumbers, the SA-based RSFD scheme performs better, while at large wavenumbers, the LS-based RSFD scheme leads to a smaller error. Finally, the modeling results demonstrate that for the same operator length, the SA-based RSFD scheme and the LS-based RSFD scheme can achieve greater accuracy than the TE-based RSFD scheme, while for the same accuracy, the optimal schemes can adopt shorter difference operators to save computing time.

Training driving ability in a traumatic brain-injured individual using a driving simulator: a case report

PubMed Central

Imhoff, Sarah; Lavallière, Martin; Germain-Robitaille, Mathieu; Teasdale, Normand; Fait, Philippe

2017-01-01

Background Traumatic brain injury (TBI) causes functional deficits that may significantly interfere with numerous activities of daily living such as driving. We report the case of a 20-year-old woman having lost her driver’s license after sustaining a moderate TBI. Objective We aimed to evaluate the effectiveness of an in-simulator training program with automated feedback on driving performance in a TBI individual. Methods The participant underwent an initial and a final in-simulator driving assessment and 11 in-simulator training sessions with driving-specific automated feedbacks. Driving performance (simulation duration, speed regulation and lateral positioning) was measured in the driving simulator. Results Speeding duration decreased during training sessions from 1.50 ± 0.80 min (4.16 ± 2.22%) to 0.45 ± 0.15 min (0.44 ± 0.42%) but returned to initial duration after removal of feedbacks for the final assessment. Proper lateral positioning improved with training and was maintained at the final assessment. Time spent in an incorrect lateral position decreased from 18.85 min (53.61%) in the initial assessment to 1.51 min (4.64%) on the final assessment. Conclusion Driving simulators represent an interesting therapeutic avenue. Considerable research efforts are needed to confirm the effectiveness of this method for driving rehabilitation of individuals who have sustained a TBI. PMID:28243152

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy; Saini, Subhash (Technical Monitor)

1999-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

Projection-free approximate balanced truncation of large unstable systems

NASA Astrophysics Data System (ADS)

Flinois, Thibault L. B.; Morgans, Aimee S.; Schmid, Peter J.

2015-08-01

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition algorithm theoretically yields a converged transformation that balances the Gramians (including the unstable subspace). We then apply the method to a spatially developing unstable system and show that it results in reduced-order models of similar quality to the ones obtained with existing methods. Due to the unbounded growth of unstable modes, a practical restriction on the final impulse response simulation time appears, which can be adjusted depending on the desired order of the reduced-order model. Recommendations are given to further reduce the cost of the method if the system is large and to improve the performance of the method if it does not yield acceptable results in its unmodified form. Finally, the method is applied to the linearized flow around a cylinder at Re = 100 to show that it actually is able to accurately reproduce impulse responses for more realistic unstable large-scale systems in practice. The well-established approximate balanced truncation numerical framework therefore can be safely applied to unstable systems without any modifications. Additionally, balanced reduced-order models can readily be obtained even for large systems, where the computational cost of existing methods is prohibitive.

A new art code for tomographic interferometry

NASA Technical Reports Server (NTRS)

Tan, H.; Modarress, D.

1987-01-01

A new algebraic reconstruction technique (ART) code based on the iterative refinement method of least squares solution for tomographic reconstruction is presented. Accuracy and the convergence of the technique is evaluated through the application of numerically generated interferometric data. It was found that, in general, the accuracy of the results was superior to other reported techniques. The iterative method unconditionally converged to a solution for which the residual was minimum. The effects of increased data were studied. The inversion error was found to be a function of the input data error only. The convergence rate, on the other hand, was affected by all three parameters. Finally, the technique was applied to experimental data, and the results are reported.

A boundary element method for Stokes flows with interfaces

NASA Astrophysics Data System (ADS)

Alinovi, Edoardo; Bottaro, Alessandro

2018-03-01

The boundary element method is a widely used and powerful technique to numerically describe multiphase flows with interfaces, satisfying Stokes' approximation. However, low viscosity ratios between immiscible fluids in contact at an interface and large surface tensions may lead to consistency issues as far as mass conservation is concerned. A simple and effective approach is described to ensure mass conservation at all viscosity ratios and capillary numbers within a standard boundary element framework. Benchmark cases are initially considered demonstrating the efficacy of the proposed technique in satisfying mass conservation, comparing with approaches and other solutions present in the literature. The methodology developed is finally applied to the problem of slippage over superhydrophobic surfaces.

Pinning synchronization of memristor-based neural networks with time-varying delays.

PubMed

Yang, Zhanyu; Luo, Biao; Liu, Derong; Li, Yueheng

2017-09-01

In this paper, the synchronization of memristor-based neural networks with time-varying delays via pinning control is investigated. A novel pinning method is introduced to synchronize two memristor-based neural networks which denote drive system and response system, respectively. The dynamics are studied by theories of differential inclusions and nonsmooth analysis. In addition, some sufficient conditions are derived to guarantee asymptotic synchronization and exponential synchronization of memristor-based neural networks via the presented pinning control. Furthermore, some improvements about the proposed control method are also discussed in this paper. Finally, the effectiveness of the obtained results is demonstrated by numerical simulations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Design and numerical simulation of novel giant magnetostrictive ultrasonic transducer

NASA Astrophysics Data System (ADS)

Li, Pengyang; Liu, Qiang; Li, Shujuan; Wang, Quandai; Zhang, Dongya; Li, Yan

This paper provides a design method of a novel giant magnetostrictive ultrasonic transducer utilized in incremental sheet metal forming. The frequency equations of the ultrasonic vibrator were deduced and the corresponding correctness verified by the modal and harmonic response characteristic through the finite element method (FEM) and ANSYS software. In addition, the magnetic field of the vibrator system was designed and verified by the ANSYS. Finally, the frequency tests based on the impedance response analysis and the amplitude measurements based on the laser displacement sensor were performed on the prototype. The results confirmed the appropriate design of this transducer, setting the foundation for a low mechanical quality factor and satisfying amplitude.

Multistability and instability analysis of recurrent neural networks with time-varying delays.

PubMed

Zhang, Fanghai; Zeng, Zhigang

2018-01-01

This paper provides new theoretical results on the multistability and instability analysis of recurrent neural networks with time-varying delays. It is shown that such n-neuronal recurrent neural networks have exactly [Formula: see text] equilibria, [Formula: see text] of which are locally exponentially stable and the others are unstable, where k 0 is a nonnegative integer such that k 0 ≤n. By using the combination method of two different divisions, recurrent neural networks can possess more dynamic properties. This method improves and extends the existing results in the literature. Finally, one numerical example is provided to show the superiority and effectiveness of the presented results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Studies in nonlinear problems of energy. Final report

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

Matkowsky, B.J.

1998-12-01

The author completed a successful research program on Nonlinear Problems of Energy, with emphasis on combustion and flame propagation. A total of 183 papers associated with the grant has appeared in the literature, and the efforts have twice been recognized by DOE`s Basic Science Division for Top Accomplishment. In the research program the author concentrated on modeling, analysis and computation of combustion phenomena, with particular emphasis on the transition from laminar to turbulent combustion. Thus he investigated the nonlinear dynamics and pattern formation in the successive stages of transition. He described the stability of combustion waves, and transitions to wavesmore » exhibiting progressively higher degrees of spatio-temporal complexity. Combustion waves are characterized by large activation energies, so that chemical reactions are significant only in thin layers, termed reaction zones. In the limit of infinite activation energy, the zones shrink to moving surfaces, termed fronts, which must be found during the course of the analysis, so that the problems are moving free boundary problems. The analytical studies were carried out for the limiting case with fronts, while the numerical studies were carried out for the case of finite, though large, activation energy. Accurate resolution of the solution in the reaction zone(s) is essential, otherwise false predictions of dynamical behavior are possible. Since the reaction zones move, and their location is not known a-priori, the author has developed adaptive pseudo-spectral methods, which have proven to be very useful for the accurate, efficient computation of solutions of combustion, and other, problems. The approach is based on a combination of analytical and numerical methods. The numerical computations built on and extended the information obtained analytically. Furthermore, the solutions obtained analytically served as benchmarks for testing the accuracy of the solutions determined computationally. Finally, the computational results suggested new analysis to be considered. A cumulative list of publications citing the grant make up the contents of this report.« less

Numeracy Skills in Patients With Degenerative Disorders and Focal Brain Lesions

PubMed Central

Cappelletti, Marinella; Butterworth, Brian; Kopelman, Michael

2012-01-01

Objective: To characterize the numerical profile of patients with acquired brain disorders. Method: We investigated numeracy skills in 76 participants—40 healthy controls and 36 patients with neurodegenerative disorders (Alzheimer dementia, frontotemporal dementia, semantic dementia, progressive aphasia) and with focal brain lesions affecting parietal, frontal, and temporal areas as in herpes simplex encephalitis (HSE). All patients were tested with the same comprehensive battery of paper-and-pencil and computerized tasks assessing numerical abilities and calculation. Degenerative and HSE patients also performed nonnumerical semantic tasks. Results: Our results, based on nonparametric group statistics as well as on the analysis of individual patients, and all highly significant, show that: (a) all patients, including those with parietal lesions—a key brain area for numeracy processing—had intact processing of number quantity; (b) patients with impaired semantic knowledge had much better preserved numerical knowledge; and (c) most patients showed impaired calculation skills, with the exception of most semantic dementia and HSE patients. Conclusion: Our results allow us, for the first time, to characterize the numeracy skills in patients with a variety of neurological conditions and to suggest that the pattern of numerical performance can vary considerably across different neurological populations. Moreover, the selective sparing of calculation skills in most semantic dementia and HSE suggest that numerical abilities are an independent component of the semantic system. Finally, our data suggest that, besides the parietal areas, other brain regions might be critical to the understanding and processing of numerical concepts. PMID:22122516

Unsteady Fast Random Particle Mesh method for efficient prediction of tonal and broadband noises of a centrifugal fan unit

NASA Astrophysics Data System (ADS)

Heo, Seung; Cheong, Cheolung; Kim, Taehoon

2015-09-01

In this study, efficient numerical method is proposed for predicting tonal and broadband noises of a centrifugal fan unit. The proposed method is based on Hybrid Computational Aero-Acoustic (H-CAA) techniques combined with Unsteady Fast Random Particle Mesh (U-FRPM) method. The U-FRPM method is developed by extending the FRPM method proposed by Ewert et al. and is utilized to synthesize turbulence flow field from unsteady RANS solutions. The H-CAA technique combined with U-FRPM method is applied to predict broadband as well as tonal noises of a centrifugal fan unit in a household refrigerator. Firstly, unsteady flow field driven by a rotating fan is computed by solving the RANS equations with Computational Fluid Dynamic (CFD) techniques. Main source regions around the rotating fan are identified by examining the computed flow fields. Then, turbulence flow fields in the main source regions are synthesized by applying the U-FRPM method. The acoustic analogy is applied to model acoustic sources in the main source regions. Finally, the centrifugal fan noise is predicted by feeding the modeled acoustic sources into an acoustic solver based on the Boundary Element Method (BEM). The sound spectral levels predicted using the current numerical method show good agreements with the measured spectra at the Blade Pass Frequencies (BPFs) as well as in the high frequency range. On the more, the present method enables quantitative assessment of relative contributions of identified source regions to the sound field by comparing predicted sound pressure spectrum due to modeled sources.

New results for global exponential synchronization in neural networks via functional differential inclusions.

PubMed

Wang, Dongshu; Huang, Lihong; Tang, Longkun

2015-08-01

This paper is concerned with the synchronization dynamical behaviors for a class of delayed neural networks with discontinuous neuron activations. Continuous and discontinuous state feedback controller are designed such that the neural networks model can realize exponential complete synchronization in view of functional differential inclusions theory, Lyapunov functional method and inequality technique. The new proposed results here are very easy to verify and also applicable to neural networks with continuous activations. Finally, some numerical examples show the applicability and effectiveness of our main results.

Tailoring dye-sensitized upconversion nanoparticle excitation bands towards excitation wavelength selective imaging

DOE PAGES

Wu, Xiang; Lee, Hyungseok; Bilsel, Osman; ...

2015-01-01

One of the key roadblocks in UCNP development is its extremely limited choices of excitation wavelengths. We report a generic design to program UCNPs to possess highly tunable dye characteristic excitation bands. Using such distinctive properties, we were able to develop a new excitation wavelength selective security imaging. Finally, this work unleashed the greater freedom of the excitation wavelengths of the upconversion nanoparticles and we believe it is a game-changer in the field and this method will enable numerous applications that are currently limited by existing UCNPs.

Cavity design for high-frequency axion dark matter detectors

DOE PAGES

Stern, I.; Chisholm, A. A.; Hoskins, J.; ...

2015-12-30

In this paper, in an effort to extend the usefulness of microwave cavity detectors to higher axion masses, above ~8 μeV (~2 GHz), a numerical trade study of cavities was conducted to investigate the merit of using variable periodic post arrays and regulating vane designs for higher-frequency searches. The results show that both designs could be used to develop resonant cavities for high-mass axion searches. Finally, multiple configurations of both methods obtained the scanning sensitivity equivalent to approximately 4 coherently coupled cavities with a single tuning rod.

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

Dulat, Falko; Lionetti, Simone; Mistlberger, Bernhard

We present an analytic computation of the Higgs production cross section in the gluon fusion channel, which is differential in the components of the Higgs momentum and inclusive in the associated partonic radiation through NNLO in perturbative QCD. Our computation includes the necessary higher order terms in the dimensional regulator beyond the finite part that are required for renormalisation and collinear factorisation at N 3LO. We outline in detail the computational methods which we employ. We present numerical predictions for realistic final state observables, specifically distributions for the decay products of the Higgs boson in the γγ decay channel.

A dynamic unilateral contact problem with adhesion and friction in viscoelasticity

NASA Astrophysics Data System (ADS)

Cocou, Marius; Schryve, Mathieu; Raous, Michel

2010-08-01

The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between two viscoelastic bodies of Kelvin-Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples are presented.

Recent advances in hypersonic technology

NASA Technical Reports Server (NTRS)

Dwoyer, Douglas L.

1990-01-01

This paper will focus on recent advances in hypersonic aerodynamic prediction techniques. Current capabilities of existing numerical methods for predicting high Mach number flows will be discussed and shortcomings will be identified. Physical models available for inclusion into modern codes for predicting the effects of transition and turbulence will also be outlined and their limitations identified. Chemical reaction models appropriate to high-speed flows will be addressed, and the impact of their inclusion in computational fluid dynamics codes will be discussed. Finally, the problem of validating predictive techniques for high Mach number flows will be addressed.

Output regulation control for switched stochastic delay systems with dissipative property under error-dependent switching

NASA Astrophysics Data System (ADS)

Li, L. L.; Jin, C. L.; Ge, X.

2018-01-01

In this paper, the output regulation problem with dissipative property for a class of switched stochastic delay systems is investigated, based on an error-dependent switching law. Under the assumption that none subsystem is solvable for the problem, a sufficient condition is derived by structuring multiple Lyapunov-Krasovskii functionals with respect to multiple supply rates, via designing error feedback regulators. The condition is also established when dissipative property reduces to passive property. Finally, two numerical examples are given to demonstrate the feasibility and efficiency of the present method.

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

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.

Numerical Researches on Dynamical Systems with Relativistic Spin

NASA Astrophysics Data System (ADS)

Han, W. B.

2010-04-01

It is well known that spinning compact binaries are one of the most important research objects in the universe. Especially, EMRIs (extreme mass ratio inspirals) involving stellar compact objects which orbit massive black holes, are considered to be primary sources of gravitational radiation (GW) which could be detected by the space-based interferometer LISA. GW signals from EMRIs can be used to test general relativity, measure the masses and spins of central black holes and study essential physics near horizons. Compared with the situation without spin, the complexity of extreme objects, most of which rotate very fast, is much higher. So the dynamics of EMRI systems are numerically and analytically studied. We focus on how the spin effects on the dynamics of these systems and the produced GW radiations. Firstly, an ideal model of spinning test particles around Kerr black hole is considered. For equatorial orbits, we present the correct expression of effective potential and analyze the stability of circular orbits. Especially, the gravitational binding energy and frame-dragging effect of extreme Kerr black hole are much bigger than those without spin. For general orbits, spin can monotonically enlarge orbital inclination and destroy the symmetry of orbits about equatorial plane. It is the most important that extreme spin can produce orbital chaos. By carefully investigating the relations between chaos and orbital parameters, we point out that chaos usually appears for orbits with small pericenter, big eccentricity and orbital inclination. It is emphasized that Poincaré section method is invalid to detect the chaos of spinning particles, and the way of systems toward chaos is the period-doubling bifurcation. Furthermore, we study how spins effect on GW radiations from spinning test particles orbiting Kerr black holes. It is found that spins can increase orbit eccentricity and then make h+ component be detected more easily. But for h× component, because spins change orbital inclination in a complicated way, it is more difficult to build GW signal templates. Secondly, based on the scalar gravity theory, a numerical relativistic model of EMRIs is constructed to consider the self-gravity and radiation reaction of low-mass objects. Finally, we develop a new method with multiple steps for Hamilton systems to meet the needs of numerical researches. This method can effectively maintain each conserved quantity of the separable Hamilton system. In addition, for constrained system with a few first integrals, we present a new numerical stabilization method named as adjustment-stabilization method, which can maintain all known conserved quantities in a given dynamical system and greatly improve the numerical accuracy. Our new method is the most complete stabilization method up to now.

Numerical conversion of transient to harmonic response functions for linear viscoelastic materials.

PubMed

Buschmann, M D

1997-02-01

Viscoelastic material behavior is often characterized using one of the three measurements: creep, stress-relaxation or dynamic sinusoidal tests. A two-stage numerical method was developed to allow representation of data from creep and stress-relaxation tests on the Fourier axis in the Laplace domain. The method assumes linear behavior and is theoretically applicable to any transient test which attains an equilibrium state. The first stage numerically resolves the Laplace integral to convert temporal stress and strain data, from creep or stress-relaxation, to the stiffness function, G(s), evaluated on the positive real axis in the Laplace domain. This numerical integration alone allows the direct comparison of data from transient experiments which attain a final equilibrium state, such as creep and stress relaxation, and allows such data to be fitted to models expressed in the Laplace domain. The second stage of this numerical procedure maps the stiffness function, G(s), from the positive real axis to the positive imaginary axis to reveal the harmonic response function, or dynamic stiffness, G(j omega). The mapping for each angular frequency, s, is accomplished by fitting a polynomial to a subset of G(s) centered around a particular value of s, substituting js for s and thereby evaluating G(j omega). This two-stage transformation circumvents previous numerical difficulties associated with obtaining Fourier transforms of the stress and strain time domain signals. The accuracy of these transforms is verified using model functions from poroelasticity, corresponding to uniaxial confined compression of an isotropic material and uniaxial unconfined compression of a transversely isotropic material. The addition of noise to the model data does not significantly deteriorate the transformed results and data points need not be equally spaced in time. To exemplify its potential utility, this two-stage transform is applied to experimental stress relaxation data to obtain the dynamic stiffness which is then compared to direct measurements of dynamic stiffness using steady-state sinusoidal tests of the same cartilage disk in confined compression. In addition to allowing calculation of the dynamic stiffness from transient tests and the direct comparison of experimental data from different tests, these numerical methods should aid in the experimental analysis of linear and nonlinear material behavior, and increase the speed of curve-fitting routines by fitting creep or stress relaxation data to models expressed in the Laplace domain.

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

DOE PAGES

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; ...

2017-09-05

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments.more » These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. Finally, the TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.« less

Final Report - Subcontract B623760

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

Bank, R.

2017-11-17

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent ofmore » the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.« less

Time-dependent flow model of a generalized Burgers' fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

NASA Astrophysics Data System (ADS)

Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood

2018-06-01

Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.

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

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

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

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments.more » These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. Finally, the TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.« less

Simulation of meso-damage of refractory based on cohesion model and molecular dynamics method

NASA Astrophysics Data System (ADS)

Zhao, Jiuling; Shang, Hehao; Zhu, Zhaojun; Zhang, Guoxing; Duan, Leiguang; Sun, Xinya

2018-06-01

In order to describe the meso-damage of the refractories more accurately, and to study of the relationship between the mesostructured of the refractories and the macro-mechanics, this paper takes the magnesia-carbon refractories as the research object and uses the molecular dynamics method to instead the traditional sequential algorithm to establish the meso-particles filling model including small and large particles. Finally, the finite element software-ABAQUS is used to conducts numerical simulation on the meso-damage evolution process of refractory materials. From the results, the process of initiation and propagation of microscopic interface cracks can be observed intuitively, and the macroscopic stress-strain curve of the refractory material is obtained. The results show that the combination of molecular dynamics modeling and the use of Python in the interface to insert the cohesive element numerical simulation, obtaining of more accurate interface parameters through parameter inversion, can be more accurate to observe the interface of the meso-damage evolution process and effective to consider the effect of the mesostructured of the refractory material on its macroscopic mechanical properties.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Predicting the Thermal Conductivity of AlSi/Polyester Abradable Coatings: Effects of the Numerical Method

NASA Astrophysics Data System (ADS)

Bolot, Rodolphe; Seichepine, Jean-Louis; Qiao, Jiang Hao; Coddet, Christian

2011-01-01

The final target of this study is to achieve a better understanding of the behavior of thermally sprayed abradable seals such as AlSi/polyester composites. These coatings are used as seals between the static and the rotating parts in aero-engines. The machinability of the composite coatings during the friction of the blades depends on their mechanical and thermal effective properties. In order to predict these properties from micrographs, numerical studies were performed with different software packages such as OOF developed by NIST and TS2C developed at the UTBM. In 2008, differences were reported concerning predictions of effective thermal conductivities obtained with the two codes. In this article, a particular attention was paid to the mathematical formulation of the problem. In particular, results obtained with a finite difference method using a cell-centered approach or a nodal formulation allow explaining the discrepancies previously noticed. A comparison of the predictions of the computed effective thermal conductivities is thus proposed. This study is part of the NEWAC project, funded by the European Commission within the 6th RTD Framework programm (FP6).

Towards inverse modeling of turbidity currents: The inverse lock-exchange problem

NASA Astrophysics Data System (ADS)

Lesshafft, Lutz; Meiburg, Eckart; Kneller, Ben; Marsden, Alison

2011-04-01

A new approach is introduced for turbidite modeling, leveraging the potential of computational fluid dynamics methods to simulate the flow processes that led to turbidite formation. The practical use of numerical flow simulation for the purpose of turbidite modeling so far is hindered by the need to specify parameters and initial flow conditions that are a priori unknown. The present study proposes a method to determine optimal simulation parameters via an automated optimization process. An iterative procedure matches deposit predictions from successive flow simulations against available localized reference data, as in practice may be obtained from well logs, and aims at convergence towards the best-fit scenario. The final result is a prediction of the entire deposit thickness and local grain size distribution. The optimization strategy is based on a derivative-free, surrogate-based technique. Direct numerical simulations are performed to compute the flow dynamics. A proof of concept is successfully conducted for the simple test case of a two-dimensional lock-exchange turbidity current. The optimization approach is demonstrated to accurately retrieve the initial conditions used in a reference calculation.

Numerical predictions and experiments for optimizing hidden corrosion detection in aircraft structures using Lamb modes.

PubMed

Terrien, N; Royer, D; Lepoutre, F; Déom, A

2007-06-01

To increase the sensitivity of Lamb waves to hidden corrosion in aircraft structures, a preliminary step is to understand the phenomena governing this interaction. A hybrid model combining a finite element approach and a modal decomposition method is used to investigate the interaction of Lamb modes with corrosion pits. The finite element mesh is used to describe the region surrounding the corrosion pits while the modal decomposition method permits to determine the waves reflected and transmitted by the damaged area. Simulations make easier the interpretation of some parts of the measured waveform corresponding to superposition of waves diffracted by the corroded area. Numerical results permit to extract significant information from the transmitted waveform and thus to optimize the signal processing for the detection of corrosion at an early stage. Now, we are able to detect corrosion pits down to 80-mum depth distributed randomly on a square centimeter of an aluminum plate. Moreover, thickness variations present on aircraft structures can be discriminated from a slightly corroded area. Finally, using this experimental setup, aircraft structures have been tested.

Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning

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

Ponce, Colin; Vassilevski, Panayot S.

2016-02-18

We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. Wemore » present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.« less

A layered modulation method for pixel matching in online phase measuring profilometry

NASA Astrophysics Data System (ADS)

Li, Hongru; Feng, Guoying; Bourgade, Thomas; Yang, Peng; Zhou, Shouhuan; Asundi, Anand

2016-10-01

An online phase measuring profilometry with new layered modulation method for pixel matching is presented. In this method and in contrast with previous modulation matching methods, the captured images are enhanced by Retinex theory for better modulation distribution, and all different layer modulation masks are fully used to determine the displacement of a rectilinear moving object. High, medium and low modulation masks are obtained by performing binary segmentation with iterative Otsu method. The final shifting pixels are calculated based on centroid concept, and after that the aligned fringe patterns can be extracted from each frame. After performing Stoilov algorithm and a series of subsequent operations, the object profile on a translation stage is reconstructed. All procedures are carried out automatically, without setting specific parameters in advance. Numerical simulations are detailed and experimental results verify the validity and feasibility of the proposed approach.

Technology of focus detection for 193nm projection lithographic tool

NASA Astrophysics Data System (ADS)

Di, Chengliang; Yan, Wei; Hu, Song; Xu, Feng; Li, Jinglong

2012-10-01

With the shortening printing wavelength and increasing numerical aperture of lithographic tool, the depth of focus(DOF) sees a rapidly drop down trend, reach a scale of several hundred nanometers while the repeatable accuracy of focusing and leveling must be one-tenth of DOF, approximately several dozen nanometers. For this feature, this article first introduces several focusing technology, Obtained the advantages and disadvantages of various methods by comparing. Then get the accuracy of dual-grating focusing method through theoretical calculation. And the dual-grating focusing method based on photoelastic modulation is divided into coarse focusing and precise focusing method to analyze, establishing image processing model of coarse focusing and photoelastic modulation model of accurate focusing. Finally, focusing algorithm is simulated with MATLAB. In conclusion dual-grating focusing method shows high precision, high efficiency and non-contact measurement of the focal plane, meeting the demands of focusing in 193nm projection lithography.

Probabilistic Structural Analysis Theory Development

NASA Technical Reports Server (NTRS)

Burnside, O. H.

1985-01-01

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Experimental and numerical study of a 10MW TLP wind turbine in waves and wind

NASA Astrophysics Data System (ADS)

Pegalajar-Jurado, Antonio; Hansen, Anders M.; Laugesen, Robert; Mikkelsen, Robert F.; Borg, Michael; Kim, Taeseong; Heilskov, Nicolai F.; Bredmose, Henrik

2016-09-01

This paper presents tests on a 1:60 version of the DTU 10MW wind turbine mounted on a tension leg platform and their numerical reproduction. Both the experimental setup and the numerical model are Froude-scaled, and the dynamic response of the floating wind turbine to wind and waves is compared in terms of motion in the six degrees of freedom, nacelle acceleration and mooring line tension. The numerical model is implemented in the aero-elastic code Flex5, featuring the unsteady BEM method and the Morison equation for the modelling of aerodynamics and hydrodynamics, respectively. It was calibrated with the tests by matching key system features, namely the steady thrust curve and the decay tests in water. The calibrated model is used to reproduce the wind-wave climates in the laboratory, including regular and irregular waves, with and without wind. The model predictions are compared to the measured data, and a good agreement is found for surge and heave, while some discrepancies are observed for pitch, nacelle acceleration and line tension. The addition of wind generally improves the agreement with test results. The aerodynamic damping is identified in both tests and simulations. Finally, the sources of the discrepancies are discussed and some improvements in the numerical model are suggested in order to obtain a better agreement with the experiments.

Spectral editing of weakly coupled spins using variable flip angles in PRESS constant echo time difference spectroscopy: Application to GABA

NASA Astrophysics Data System (ADS)

Snyder, Jeff; Hanstock, Chris C.; Wilman, Alan H.

2009-10-01

A general in vivo magnetic resonance spectroscopy editing technique is presented to detect weakly coupled spin systems through subtraction, while preserving singlets through addition, and is applied to the specific brain metabolite γ-aminobutyric acid (GABA) at 4.7 T. The new method uses double spin echo localization (PRESS) and is based on a constant echo time difference spectroscopy approach employing subtraction of two asymmetric echo timings, which is normally only applicable to strongly coupled spin systems. By utilizing flip angle reduction of one of the two refocusing pulses in the PRESS sequence, we demonstrate that this difference method may be extended to weakly coupled systems, thereby providing a very simple yet effective editing process. The difference method is first illustrated analytically using a simple two spin weakly coupled spin system. The technique was then demonstrated for the 3.01 ppm resonance of GABA, which is obscured by the strong singlet peak of creatine in vivo. Full numerical simulations, as well as phantom and in vivo experiments were performed. The difference method used two asymmetric PRESS timings with a constant total echo time of 131 ms and a reduced 120° final pulse, providing 25% GABA yield upon subtraction compared to two short echo standard PRESS experiments. Phantom and in vivo results from human brain demonstrate efficacy of this method in agreement with numerical simulations.

A Fast, Open EEG Classification Framework Based on Feature Compression and Channel Ranking

PubMed Central

Han, Jiuqi; Zhao, Yuwei; Sun, Hongji; Chen, Jiayun; Ke, Ang; Xu, Gesen; Zhang, Hualiang; Zhou, Jin; Wang, Changyong

2018-01-01

Superior feature extraction, channel selection and classification methods are essential for designing electroencephalography (EEG) classification frameworks. However, the performance of most frameworks is limited by their improper channel selection methods and too specifical design, leading to high computational complexity, non-convergent procedure and narrow expansibility. In this paper, to remedy these drawbacks, we propose a fast, open EEG classification framework centralized by EEG feature compression, low-dimensional representation, and convergent iterative channel ranking. First, to reduce the complexity, we use data clustering to compress the EEG features channel-wise, packing the high-dimensional EEG signal, and endowing them with numerical signatures. Second, to provide easy access to alternative superior methods, we structurally represent each EEG trial in a feature vector with its corresponding numerical signature. Thus, the recorded signals of many trials shrink to a low-dimensional structural matrix compatible with most pattern recognition methods. Third, a series of effective iterative feature selection approaches with theoretical convergence is introduced to rank the EEG channels and remove redundant ones, further accelerating the EEG classification process and ensuring its stability. Finally, a classical linear discriminant analysis (LDA) model is employed to classify a single EEG trial with selected channels. Experimental results on two real world brain-computer interface (BCI) competition datasets demonstrate the promising performance of the proposed framework over state-of-the-art methods. PMID:29713262

A synthetic method for atmospheric diffusion simulation and environmental impact assessment of accidental pollution in the chemical industry in a WEBGIS context.

PubMed

Ni, Haochen; Rui, Yikang; Wang, Jiechen; Cheng, Liang

2014-09-05

The chemical industry poses a potential security risk to factory personnel and neighboring residents. In order to mitigate prospective damage, a synthetic method must be developed for an emergency response. With the development of environmental numeric simulation models, model integration methods, and modern information technology, many Decision Support Systems (DSSs) have been established. However, existing systems still have limitations, in terms of synthetic simulation and network interoperation. In order to resolve these limitations, the matured simulation model for chemical accidents was integrated into the WEB Geographic Information System (WEBGIS) platform. The complete workflow of the emergency response, including raw data (meteorology information, and accident information) management, numeric simulation of different kinds of accidents, environmental impact assessments, and representation of the simulation results were achieved. This allowed comprehensive and real-time simulation of acute accidents in the chemical industry. The main contribution of this paper is that an organizational mechanism of the model set, based on the accident type and pollutant substance; a scheduling mechanism for the parallel processing of multi-accident-type, multi-accident-substance, and multi-simulation-model; and finally a presentation method for scalar and vector data on the web browser on the integration of a WEB Geographic Information System (WEBGIS) platform. The outcomes demonstrated that this method could provide effective support for deciding emergency responses of acute chemical accidents.

A simple iterative independent component analysis algorithm for vibration source signal identification of complex structures

NASA Astrophysics Data System (ADS)

Lee, Dong-Sup; Cho, Dae-Seung; Kim, Kookhyun; Jeon, Jae-Jin; Jung, Woo-Jin; Kang, Myeng-Hwan; Kim, Jae-Ho

2015-01-01

Independent Component Analysis (ICA), one of the blind source separation methods, can be applied for extracting unknown source signals only from received signals. This is accomplished by finding statistical independence of signal mixtures and has been successfully applied to myriad fields such as medical science, image processing, and numerous others. Nevertheless, there are inherent problems that have been reported when using this technique: instability and invalid ordering of separated signals, particularly when using a conventional ICA technique in vibratory source signal identification of complex structures. In this study, a simple iterative algorithm of the conventional ICA has been proposed to mitigate these problems. The proposed method to extract more stable source signals having valid order includes an iterative and reordering process of extracted mixing matrix to reconstruct finally converged source signals, referring to the magnitudes of correlation coefficients between the intermediately separated signals and the signals measured on or nearby sources. In order to review the problems of the conventional ICA technique and to validate the proposed method, numerical analyses have been carried out for a virtual response model and a 30 m class submarine model. Moreover, in order to investigate applicability of the proposed method to real problem of complex structure, an experiment has been carried out for a scaled submarine mockup. The results show that the proposed method could resolve the inherent problems of a conventional ICA technique.

A Synthetic Method for Atmospheric Diffusion Simulation and Environmental Impact Assessment of Accidental Pollution in the Chemical Industry in a WEBGIS Context

PubMed Central

Ni, Haochen; Rui, Yikang; Wang, Jiechen; Cheng, Liang

2014-01-01

The chemical industry poses a potential security risk to factory personnel and neighboring residents. In order to mitigate prospective damage, a synthetic method must be developed for an emergency response. With the development of environmental numeric simulation models, model integration methods, and modern information technology, many Decision Support Systems (DSSs) have been established. However, existing systems still have limitations, in terms of synthetic simulation and network interoperation. In order to resolve these limitations, the matured simulation model for chemical accidents was integrated into the WEB Geographic Information System (WEBGIS) platform. The complete workflow of the emergency response, including raw data (meteorology information, and accident information) management, numeric simulation of different kinds of accidents, environmental impact assessments, and representation of the simulation results were achieved. This allowed comprehensive and real-time simulation of acute accidents in the chemical industry. The main contribution of this paper is that an organizational mechanism of the model set, based on the accident type and pollutant substance; a scheduling mechanism for the parallel processing of multi-accident-type, multi-accident-substance, and multi-simulation-model; and finally a presentation method for scalar and vector data on the web browser on the integration of a WEB Geographic Information System (WEBGIS) platform. The outcomes demonstrated that this method could provide effective support for deciding emergency responses of acute chemical accidents. PMID:25198686

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.