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Sample records for reduced order method

  1. Reduced order methods for modeling and computational reduction

    CERN Document Server

    Rozza, Gianluigi

    2014-01-01

    This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.  Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This...

  2. Time implicit high-order discontinuous galerkin method with reduced evaluation cost

    OpenAIRE

    Renac, Florent; Marmignon, Claude; Coquel, Frédéric

    2012-01-01

    International audience; Abstract: An efficient and robust time integration procedure for a high-order discontinuous Galerkin method is introduced for solving nonlinear second-order partial differential equations. The time discretization is based on an explicit formulation for the hyperbolic term and an implicit formulation for the parabolic term. The procedure uses an iterative algorithm with reduced evaluation cost. The size of the linear system to be solved is greatly reduced thanks to par...

  3. An Online Method for Interpolating Linear Parametric Reduced-Order Models

    KAUST Repository

    Amsallem, David

    2011-01-01

    A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.

  4. Method of defining rational parameters for excavator buckets vibrating devices in order to reduce soil adhesion

    Science.gov (United States)

    Zenkov, S. A.

    2017-10-01

    The article describes the method of defining rational parameters for excavator buckets vibrating devices in order to reduce soil adhesion under various operating conditions. The method includes limits formation, calculating geometric parameters of curved mold concentrator for excavator buckets with magnetostriction vibration exciters; calculating parameters of acoustic influence equipment; calculating power demand of equipment, defining adhesive forces of soil to buckets with given values of external factors; defining equipment operation mode (turn-on frequency, exposure time). Suggested method enables one to define required parameters of vibrating equipment to excavator buckets during the design phase.

  5. Koopman Mode Decomposition Methods in Dynamic Stall: Reduced Order Modeling and Control

    Science.gov (United States)

    2015-11-10

    Koopman Mode Decomposition Methods in Dynamic Stall : Reduced Order Modeling and Control During dynamic stall , large peaks in lift, pitching moment and...drag appear, and these cause an undesirable increase in the mean drag. Dynamic stall can also lead to potentially fatal structural loads due to...strong vibrations of flexible aerodynamic surfaces. Despite extensive analytical, numerical, and experimental efforts to study dynamic stall , progress is

  6. Reduced Order Podolsky Model

    Science.gov (United States)

    Thibes, Ronaldo

    2017-02-01

    We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

  7. Determining Reduced Order Models for Optimal Stochastic Reduced Order Models

    Energy Technology Data Exchange (ETDEWEB)

    Bonney, Matthew S. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Brake, Matthew R.W. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)

    2015-08-01

    The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better represent the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.

  8. Generalized Reduced Order Model Generation Project

    Data.gov (United States)

    National Aeronautics and Space Administration — M4 Engineering proposes to develop a generalized reduced order model generation method. This method will allow for creation of reduced order aeroservoelastic state...

  9. Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method.

    Science.gov (United States)

    Li, Xuanying; Li, Xiaotong; Hu, Cheng

    2017-12-01

    In this paper, without transforming the second order inertial neural networks into the first order differential systems by some variable substitutions, asymptotic stability and synchronization for a class of delayed inertial neural networks are investigated. Firstly, a new Lyapunov functional is constructed to directly propose the asymptotic stability of the inertial neural networks, and some new stability criteria are derived by means of Barbalat Lemma. Additionally, by designing a new feedback control strategy, the asymptotic synchronization of the addressed inertial networks is studied and some effective conditions are obtained. To reduce the control cost, an adaptive control scheme is designed to realize the asymptotic synchronization. It is noted that the dynamical behaviors of inertial neural networks are directly analyzed in this paper by constructing some new Lyapunov functionals, this is totally different from the traditional reduced-order variable substitution method. Finally, some numerical simulations are given to demonstrate the effectiveness of the derived theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

  10. Comparison of three preventive methods in order to reduce the incidence of ankle inversion sprains among female volleyball players

    OpenAIRE

    Stasinopoulos, D.

    2004-01-01

    Background: Ankle sprains are the most common form of acute injury in volleyball. A prevention programme consisting of technical training, proprioceptive training, and external support was previously designed to reduce the rate of ankle sprains in volleyball players.

  11. Reduced-order modelling numerical homogenization.

    Science.gov (United States)

    Abdulle, A; Bai, Y

    2014-08-06

    A general framework to combine numerical homogenization and reduced-order modelling techniques for partial differential equations (PDEs) with multiple scales is described. Numerical homogenization methods are usually efficient to approximate the effective solution of PDEs with multiple scales. However, classical numerical homogenization techniques require the numerical solution of a large number of so-called microproblems to approximate the effective data at selected grid points of the computational domain. Such computations become particularly expensive for high-dimensional, time-dependent or nonlinear problems. In this paper, we explain how numerical homogenization method can benefit from reduced-order modelling techniques that allow one to identify offline and online computational procedures. The effective data are only computed accurately at a carefully selected number of grid points (offline stage) appropriately 'interpolated' in the online stage resulting in an online cost comparable to that of a single-scale solver. The methodology is presented for a class of PDEs with multiple scales, including elliptic, parabolic, wave and nonlinear problems. Numerical examples, including wave propagation in inhomogeneous media and solute transport in unsaturated porous media, illustrate the proposed method. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  12. Optimizing Reduced-Order Transfer Functions

    Science.gov (United States)

    Spanos, John T.; Milman, Mark H.; Mingori, D. Lewis

    1992-01-01

    Transfer-function approximations made optimal in special least-squares sense. Algorithm computes reduced-order rational-fraction approximates to single-input/single-output transfer functions. Reduces amount of computation needed for such purposes as numerical simulation of dynamics and design of control subsystems.

  13. Simplified Predictive Models for CO2 Sequestration Performance Assessment: Research Topical Report on Task #4 - Reduced-Order Method (ROM) Based Models

    Energy Technology Data Exchange (ETDEWEB)

    Mishra, Srikanta; Jin, Larry; He, Jincong; Durlofsky, Louis

    2015-06-30

    Reduced-order models provide a means for greatly accelerating the detailed simulations that will be required to manage CO2 storage operations. In this work, we investigate the use of one such method, POD-TPWL, which has previously been shown to be effective in oil reservoir simulation problems. This method combines trajectory piecewise linearization (TPWL), in which the solution to a new (test) problem is represented through a linearization around the solution to a previously-simulated (training) problem, with proper orthogonal decomposition (POD), which enables solution states to be expressed in terms of a relatively small number of parameters. We describe the application of POD-TPWL for CO2-water systems simulated using a compositional procedure. Stanford’s Automatic Differentiation-based General Purpose Research Simulator (AD-GPRS) performs the full-order training simulations and provides the output (derivative matrices and system states) required by the POD-TPWL method. A new POD-TPWL capability introduced in this work is the use of horizontal injection wells that operate under rate (rather than bottom-hole pressure) control. Simulation results are presented for CO2 injection into a synthetic aquifer and into a simplified model of the Mount Simon formation. Test cases involve the use of time-varying well controls that differ from those used in training runs. Results of reasonable accuracy are consistently achieved for relevant well quantities. Runtime speedups of around a factor of 370 relative to full- order AD-GPRS simulations are achieved, though the preprocessing needed for POD-TPWL model construction corresponds to the computational requirements for about 2.3 full-order simulation runs. A preliminary treatment for POD-TPWL modeling in which test cases differ from training runs in terms of geological parameters (rather than well controls) is also presented. Results in this case involve only small differences between

  14. Order statistics & inference estimation methods

    CERN Document Server

    Balakrishnan, N

    1991-01-01

    The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A co

  15. Non-linear reduced order models for steady aerodynamics

    DEFF Research Database (Denmark)

    Zimmermann, Ralf; Goertz, Stefan

    2010-01-01

    transformation for obtaining problem-adapted global basis modes is introduced. Model order reduction is achieved by parameter space sampling, reduced solution space representation via global POD and restriction of a CFD flow solver to the reduced POD subspace. Solving the governing equations of fluid dynamics...... is replaced by solving a non-linear least-squares optimization problem. Methods for obtaining feasible starting solutions for the optimization procedure are discussed. The method is demonstrated by computing reduced-order solutions to the compressible Euler equations for the NACA 0012 airfoil based on two...

  16. Construction of reduced order models for the non-linear Navier-Stokes equations using the proper orthogonal fecomposition (POD)/Galerkin method.

    Energy Technology Data Exchange (ETDEWEB)

    Fike, Jeffrey A.

    2013-08-01

    The construction of stable reduced order models using Galerkin projection for the Euler or Navier-Stokes equations requires a suitable choice for the inner product. The standard L2 inner product is expected to produce unstable ROMs. For the non-linear Navier-Stokes equations this means the use of an energy inner product. In this report, Galerkin projection for the non-linear Navier-Stokes equations using the L2 inner product is implemented as a first step toward constructing stable ROMs for this set of physics.

  17. Morphologically accurate reduced order modeling of spiking neurons.

    Science.gov (United States)

    Kellems, Anthony R; Chaturantabut, Saifon; Sorensen, Danny C; Cox, Steven J

    2010-06-01

    Accurately simulating neurons with realistic morphological structure and synaptic inputs requires the solution of large systems of nonlinear ordinary differential equations. We apply model reduction techniques to recover the complete nonlinear voltage dynamics of a neuron using a system of much lower dimension. Using a proper orthogonal decomposition, we build a reduced-order system from salient snapshots of the full system output, thus reducing the number of state variables. A discrete empirical interpolation method is then used to reduce the complexity of the nonlinear term to be proportional to the number of reduced variables. Together these two techniques allow for up to two orders of magnitude dimension reduction without sacrificing the spatially-distributed input structure, with an associated order of magnitude speed-up in simulation time. We demonstrate that both nonlinear spiking behavior and subthreshold response of realistic cells are accurately captured by these low-dimensional models.

  18. A reduced order model for nonlinear vibroacoustic problems

    Directory of Open Access Journals (Sweden)

    Ouisse Morvan

    2012-07-01

    Full Text Available This work is related to geometrical nonlinearities applied to thin plates coupled with fluid-filled domain. Model reduction is performed to reduce the computation time. Reduced order model (ROM is issued from the uncoupled linear problem and enriched with residues to describe the nonlinear behavior and coupling effects. To show the efficiency of the proposed method, numerical simulations in the case of an elastic plate closing an acoustic cavity are presented.

  19. Reduced order modeling of fluid/structure interaction.

    Energy Technology Data Exchange (ETDEWEB)

    Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph; Brake, Matthew Robert

    2009-11-01

    This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.

  20. Reduced-Order Modeling: New Approaches for Computational Physics

    Science.gov (United States)

    Beran, Philip S.; Silva, Walter A.

    2001-01-01

    In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods ba'sed on Volterra series representations and the proper orthogonal decomposition. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models, particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two- dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of reduced-order models, thereby justifying the initial computational expense of constructing these models and inotivatim,- their use for multi-disciplinary design analysis.

  1. Accelerating transient simulation of linear reduced order models.

    Energy Technology Data Exchange (ETDEWEB)

    Thornquist, Heidi K.; Mei, Ting; Keiter, Eric Richard; Bond, Brad

    2011-10-01

    Model order reduction (MOR) techniques have been used to facilitate the analysis of dynamical systems for many years. Although existing model reduction techniques are capable of providing huge speedups in the frequency domain analysis (i.e. AC response) of linear systems, such speedups are often not obtained when performing transient analysis on the systems, particularly when coupled with other circuit components. Reduced system size, which is the ostensible goal of MOR methods, is often insufficient to improve transient simulation speed on realistic circuit problems. It can be shown that making the correct reduced order model (ROM) implementation choices is crucial to the practical application of MOR methods. In this report we investigate methods for accelerating the simulation of circuits containing ROM blocks using the circuit simulator Xyce.

  2. Reduced order modeling in topology optimization of vibroacoustic problems

    DEFF Research Database (Denmark)

    Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas

    2017-01-01

    There is an interest in introducing topology optimization techniques in the design process of structural-acoustic systems. In topology optimization, the design space must be finely meshed in order to obtain an accurate design, which results in large numbers of degrees of freedom when designing...... complex 3D parts. The optimization process can therefore become highly time consuming due to the need to solve a large system of equations at each iteration. Projection-based parametric Model Order Reduction (pMOR) methods have successfully been applied for reducing the computational cost of material...

  3. AN OVERVIEW OF REDUCED ORDER MODELING TECHNIQUES FOR SAFETY APPLICATIONS

    Energy Technology Data Exchange (ETDEWEB)

    Mandelli, D.; Alfonsi, A.; Talbot, P.; Wang, C.; Maljovec, D.; Smith, C.; Rabiti, C.; Cogliati, J.

    2016-10-01

    The RISMC project is developing new advanced simulation-based tools to perform Computational Risk Analysis (CRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermal-hydraulic behavior of the reactors primary and secondary systems, but also external event temporal evolution and component/system ageing. Thus, this is not only a multi-physics problem being addressed, but also a multi-scale problem (both spatial, µm-mm-m, and temporal, seconds-hours-years). As part of the RISMC CRA approach, a large amount of computationally-expensive simulation runs may be required. An important aspect is that even though computational power is growing, the overall computational cost of a RISMC analysis using brute-force methods may be not viable for certain cases. A solution that is being evaluated to assist the computational issue is the use of reduced order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RISMC analysis computational cost by decreasing the number of simulation runs; for this analysis improvement we used surrogate models instead of the actual simulation codes. This article focuses on the use of reduced order modeling techniques that can be applied to RISMC analyses in order to generate, analyze, and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (microseconds instead of hours/days).

  4. Using the Neumann series expansion for assembling Reduced Order Models

    Directory of Open Access Journals (Sweden)

    Nasisi S.

    2014-06-01

    Full Text Available An efficient method to remove the limitation in selecting the master degrees of freedom in a finite element model by means of a model order reduction is presented. A major difficulty of the Guyan reduction and IRS method (Improved Reduced System is represented by the need of appropriately select the master and slave degrees of freedom for the rate of convergence to be high. This study approaches the above limitation by using a particular arrangement of the rows and columns of the assembled matrices K and M and employing a combination between the IRS method and a variant of the analytical selection of masters presented in (Shah, V. N., Raymund, M., Analytical selection of masters for the reduced eigenvalue problem, International Journal for Numerical Methods in Engineering 18 (1 1982 in case first lowest frequencies had to be sought. One of the most significant characteristics of the approach is the use of the Neumann series expansion that motivates this particular arrangement of the matrices’ entries. The method shows a higher rate of convergence when compared to the standard IRS and very accurate results for the lowest reduced frequencies. To show the effectiveness of the proposed method two testing structures and the human vocal tract model employed in (Vampola, T., Horacek, J., Svec, J. G., FE modeling of human vocal tract acoustics. Part I: Prodution of Czech vowels, Acta Acustica United with Acustica 94 (3 2008 are presented.

  5. High order stiffly stable linear multistep methods

    Energy Technology Data Exchange (ETDEWEB)

    Cooper, C.N.

    1979-01-01

    Stiffly stable linear k-step methods of order k for the initial-value problem are studied. Examples for k = 1, 2, and 3 were discovered by use of Adams-type methods. A large family of stiffly stable linear 7-step methods of order 7 was also found.

  6. Reduced-order models of the coagulation cascade

    Science.gov (United States)

    Hansen, Kirk B.; Shadden, Shawn C.

    2015-11-01

    Previous models of flow-mediated thrombogenesis have generally included the transport and reaction of dozens of biochemical species involved in the coagulation cascade. Researchers have shown, however, that thrombin generation curves can be accurately reproduced by a significantly smaller system of reactions. These reduced-order models are based on the system of ordinary differential equations representative of a well-mixed system, however, not the system of advection-diffusion-reaction equations required to model the flow-mediated case. Additionally, they focus solely on reproducing the thrombin generation curve, although accurate representation of certain intermediate species may be required to model additional aspects of clot formation, e.g. interactions with activated and non-activated platelets. In this work, we develop a method to reduce the order of a coagulation model through optimization techniques. The results of this reduced-order model are then compared to those of the full system in several representative cardiovascular flows. This work was supported by NSF grant 1354541, the NSF GRFP, and NIH grant HL108272.

  7. Advanced Fluid Reduced Order Models for Compressible Flow.

    Energy Technology Data Exchange (ETDEWEB)

    Tezaur, Irina Kalashnikova [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Fike, Jeffrey A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Carlberg, Kevin Thomas [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Barone, Matthew F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Maddix, Danielle [Stanford Univ., CA (United States); Mussoni, Erin E. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Balajewicz, Maciej [Univ. of Illinois, Urbana-Champaign, IL (United States)

    2017-09-01

    This report summarizes fiscal year (FY) 2017 progress towards developing and implementing within the SPARC in-house finite volume flow solver advanced fluid reduced order models (ROMs) for compressible captive-carriage flow problems of interest to Sandia National Laboratories for the design and qualification of nuclear weapons components. The proposed projection-based model order reduction (MOR) approach, known as the Proper Orthogonal Decomposition (POD)/Least- Squares Petrov-Galerkin (LSPG) method, can substantially reduce the CPU-time requirement for these simulations, thereby enabling advanced analyses such as uncertainty quantification and de- sign optimization. Following a description of the project objectives and FY17 targets, we overview briefly the POD/LSPG approach to model reduction implemented within SPARC . We then study the viability of these ROMs for long-time predictive simulations in the context of a two-dimensional viscous laminar cavity problem, and describe some FY17 enhancements to the proposed model reduction methodology that led to ROMs with improved predictive capabilities. Also described in this report are some FY17 efforts pursued in parallel to the primary objective of determining whether the ROMs in SPARC are viable for the targeted application. These include the implemen- tation and verification of some higher-order finite volume discretization methods within SPARC (towards using the code to study the viability of ROMs on three-dimensional cavity problems) and a novel structure-preserving constrained POD/LSPG formulation that can improve the accuracy of projection-based reduced order models. We conclude the report by summarizing the key takeaways from our FY17 findings, and providing some perspectives for future work.

  8. Reduced-Order Modeling of a Heaving Airfoil

    Science.gov (United States)

    Haj-Hariri, H.; Murphy, P. C.; Lewin, G. C.

    2005-01-01

    A reduced-order model of a flapping airfoil is developed using Proper Orthogonal Decomposition (POD). The proper basis functions, developed from snapshots of full Navier-Stokes simulations, are used for a Galerkin projection of the governing equations. The resulting coupled, nonlinear ordinary di.erential equations have a low dimension because the first few basis members capture most of the energy of the flow. The reduced-order model is used to simulate heaving motions that are both similar to and different from the motion(s) used to generate the basis functions, and the errors in the model are quantified. Several methods are used to generate mode sets that can be used over a range of heaving parameters, including snapshots from one, two, and multiple Navier-Stokes simulations. As snapshots from additional simulations are added to the decomposition, the mode sets become richer and can simulate a wider range of parameter space, at some computational cost. Whereas the POD method is fully applicable in three dimensions, the simulation technique based on a body-fixed and body-fitted grid suffers large overhead when extended to three dimensions. To reduce the overhead, an embedding technique is discussed which embeds the solid wing into a fixed Cartesian grid. The wing, which can now have multiple pieces and also be flexible, is represented by a distribution of body forces. This distribution is determined to give exactly the flow around a flapping wing.

  9. Reduced Order Modeling Methods for Turbomachinery Design

    Science.gov (United States)

    2009-03-01

    fnp (x) ] (3.15...matrix becomes f =       F0 · · · 0 ... . . . 0 Fnp       (3.24) 102 F0 =       1 x11 · · · ... ... ... 1 x1nt · · · xnk1 ... xnknt...F1 =       0 1 0 ... ... ... 0 1 0 · · · ... · · · 0 ... 0       , Fnp =       0 · · · 0 ... ... ... 0 · · · 0 1 ...

  10. Parametric Methods for Order Tracking Analysis

    DEFF Research Database (Denmark)

    Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm

    2017-01-01

    Order tracking analysis is often used to find the critical speeds at which structural resonances are excited by a rotating machine. Typically, order tracking analysis is performed via non-parametric methods. In this report, however, we demonstrate some of the advantages of using a parametric method...

  11. Towards a Wind Turbine Wake Reduced-Order Model

    Science.gov (United States)

    Hamilton, Nicholas; Viggiano, Bianca; Calaf, Marc; Tutkun, Murat; Cal, Raúl Bayoán

    2017-11-01

    A reduced-order model for a wind turbine wake is sought for prediction and control. Basis functions from the proper orthogonal decomposition (POD) represent the spatially coherent turbulence structures in the wake; eigenvalues delineate the turbulence kinetic energy associated with each mode. Back-projecting the POD modes onto the velocity snapshots produces coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each mode coefficient. Tikhonov regularization is employed to recalibrate the dynamical system, reducing error in the modeled mode coefficients and adding stability to the system. The wakeROM is periodically reinitialized by relating the incoming turbulent velocity to the POD mode coefficients. A high-level view of the wakeROM provides as a platform to discuss promising research direction, alternate processes that will enhance stability, and portability to control methods. NSF- ECCS-1032647, NSF-CBET-1034581, Research Council of Norway Project Number 231491.

  12. Optical method of atomic ordering estimation

    Energy Technology Data Exchange (ETDEWEB)

    Prutskij, T. [Instituto de Ciencias, BUAP, Privada 17 Norte, No 3417, col. San Miguel Huyeotlipan, Puebla, Pue. (Mexico); Attolini, G. [IMEM/CNR, Parco Area delle Scienze 37/A - 43010, Parma (Italy); Lantratov, V.; Kalyuzhnyy, N. [Ioffe Physico-Technical Institute, 26 Polytekhnicheskaya, St Petersburg 194021, Russian Federation (Russian Federation)

    2013-12-04

    It is well known that within metal-organic vapor-phase epitaxy (MOVPE) grown semiconductor III-V ternary alloys atomically ordered regions are spontaneously formed during the epitaxial growth. This ordering leads to bandgap reduction and to valence bands splitting, and therefore to anisotropy of the photoluminescence (PL) emission polarization. The same phenomenon occurs within quaternary semiconductor alloys. While the ordering in ternary alloys is widely studied, for quaternaries there have been only a few detailed experimental studies of it, probably because of the absence of appropriate methods of its detection. Here we propose an optical method to reveal atomic ordering within quaternary alloys by measuring the PL emission polarization.

  13. Reduced-Order Kalman Filtering for Processing Relative Measurements

    Science.gov (United States)

    Bayard, David S.

    2008-01-01

    A study in Kalman-filter theory has led to a method of processing relative measurements to estimate the current state of a physical system, using less computation than has previously been thought necessary. As used here, relative measurements signifies measurements that yield information on the relationship between a later and an earlier state of the system. An important example of relative measurements arises in computer vision: Information on relative motion is extracted by comparing images taken at two different times. Relative measurements do not directly fit into standard Kalman filter theory, in which measurements are restricted to those indicative of only the current state of the system. One approach heretofore followed in utilizing relative measurements in Kalman filtering, denoted state augmentation, involves augmenting the state of the system at the earlier of two time instants and then propagating the state to the later time instant.While state augmentation is conceptually simple, it can also be computationally prohibitive because it doubles the number of states in the Kalman filter. When processing a relative measurement, if one were to follow the state-augmentation approach as practiced heretofore, one would find it necessary to propagate the full augmented state Kalman filter from the earlier time to the later time and then select out the reduced-order components. The main result of the study reported here is proof of a property called reduced-order equivalence (ROE). The main consequence of ROE is that it is not necessary to augment with the full state, but, rather, only the portion of the state that is explicitly used in the partial relative measurement. In other words, it suffices to select the reduced-order components first and then propagate the partial augmented state Kalman filter from the earlier time to the later time; the amount of computation needed to do this can be substantially less than that needed for propagating the full augmented

  14. High-Order Adaptive Galerkin Methods

    NARCIS (Netherlands)

    Canuto, C.; Nochetto, R.H.; Stevenson, R.; Verani, M.; Kirby, R.M.; Berzins, M.; Hesthaven, J.S.

    2015-01-01

    We design adaptive high-order Galerkin methods for the solution of linear elliptic problems and study their performance. We first consider adaptive Fourier-Galerkin methods and Legendre-Galerkin methods, which offer unlimited approximation power only restricted by solution and data regularity. Their

  15. Sixth order stable central difference method for self-adjoint ...

    African Journals Online (AJOL)

    A numerical method based on finite difference scheme with uniform mesh is presented for solving self-adjoint singularly perturbed two-point boundary value problems. First, the original problem is reduced to its conventional form and then, the reduced problem is solved by using sixth order stable central difference method.

  16. Empirical Reduced-Order Modeling for Boundary Feedback Flow Control

    Directory of Open Access Journals (Sweden)

    Seddik M. Djouadi

    2008-01-01

    Full Text Available This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation- (PDE- based models in general. Specifically, the proper orthogonal decomposition (POD of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the Galerkin model. The rationale for doing so is that linear subspace approximations to exact submanifolds associated with nonlinear controllability and observability require only standard matrix manipulations utilizing simulation/experimental data. The proposed method uses a chirp signal as input to produce the output in the eigensystem realization algorithm (ERA. This method estimates the system's Markov parameters that accurately reproduce the output. Balanced truncation is used to show that model reduction is still effective on ERA produced approximated systems. The method is applied to a prototype convective flow on obstacle geometry. An H∞ feedback flow controller is designed based on the reduced model to achieve tracking and then applied to the full-order model with excellent performance.

  17. Microbial methods of reducing technetium

    Science.gov (United States)

    Wildung, Raymond E [Richland, WA; Garland, Thomas R [Greybull, WY; Gorby, Yuri A [Richland, WA; Hess, Nancy J [Benton City, WA; Li, Shu-Mei W [Richland, WA; Plymale, Andrew E [Richland, WA

    2001-01-01

    The present invention is directed toward a method for microbial reduction of a technetium compound to form other compounds of value in medical imaging. The technetium compound is combined in a mixture with non-growing microbial cells which contain a technetium-reducing enzyme system, a stabilizing agent and an electron donor in a saline solution under anaerobic conditions. The mixture is substantially free of an inorganic technetium reducing agent and its reduction products. The resulting product is Tc of lower oxidation states, the form of which can be partially controlled by the stabilizing agent. It has been discovered that the microorganisms Shewanella alga, strain Bry and Shewanelia putrifacians, strain CN-32 contain the necessary enzyme systems for technetium reduction and can form both mono nuclear and polynuclear reduced Tc species depending on the stabilizing agent.

  18. Improved Multilevel Fast Multipole Method for Higher-Order discretizations

    DEFF Research Database (Denmark)

    Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

    2014-01-01

    The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion...... being that going above 2nd order is not worthwhile. In this paper, we challenge this conclusion, providing results that demonstrate the potential performance gains with Higher-Order MLFMM and showing some modifications to the traditional MLFMM that can benefit both Higher-Order and standard...

  19. Control of fluid flows using multivariate spline reduced order models

    NARCIS (Netherlands)

    Tol, H.J.; de Visser, C.C.; Kotsonis, M.

    2016-01-01

    This paper presents a study on control of fluid flows using multivariate spline reduced order models. A new approach is presented for model reduction of the incompressible Navier-Stokes equations using multivariate splines defined on triangulations. State space descriptions are derived that can be

  20. Model predictive control based on reduced order models applied to belt conveyor system.

    Science.gov (United States)

    Chen, Wei; Li, Xin

    2016-11-01

    In the paper, a model predictive controller based on reduced order model is proposed to control belt conveyor system, which is an electro-mechanics complex system with long visco-elastic body. Firstly, in order to design low-degree controller, the balanced truncation method is used for belt conveyor model reduction. Secondly, MPC algorithm based on reduced order model for belt conveyor system is presented. Because of the error bound between the full-order model and reduced order model, two Kalman state estimators are applied in the control scheme to achieve better system performance. Finally, the simulation experiments are shown that balanced truncation method can significantly reduce the model order with high-accuracy and model predictive control based on reduced-model performs well in controlling the belt conveyor system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  1. Accelerated gravitational-wave parameter estimation with reduced order modeling

    CERN Document Server

    Canizares, Priscilla; Gair, Jonathan; Raymond, Vivien; Smith, Rory; Tiglio, Manuel

    2014-01-01

    Inferring the astrophysical parameters of coalescing compact binaries is a key science goal of the upcoming advanced LIGO-Virgo gravitational-wave detector network and, more generally, gravitational-wave astronomy. However, current parameter estimation approaches for such scenarios can lead to computationally intractable problems in practice. Therefore there is a pressing need for new, fast and accurate Bayesian inference techniques. In this letter we demonstrate that a reduced order modeling approach enables rapid parameter estimation studies. By implementing a reduced order quadrature scheme within the LIGO Algorithm Library, we show that Bayesian inference on the 9-dimensional parameter space of non-spinning binary neutron star inspirals can be sped up by a factor of 30 for the early advanced detectors' configurations. This speed-up will increase to about $150$ as the detectors improve their low-frequency limit to 10Hz, reducing to hours analyses which would otherwise take months to complete. Although thes...

  2. Reduced-order anti-synchronization of the projections of the fractional order hyperchaotic and chaotic systems

    Science.gov (United States)

    Srivastava, Mayank; Agrawal, Saurabh; Das, Subir

    2013-10-01

    The article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization.

  3. Bilinear reduced order approximate model of parabolic distributed solar collectors

    KAUST Repository

    Elmetennani, Shahrazed

    2015-07-01

    This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the gaussian interpolation has been studied.

  4. Vortex network community based reduced-order force model

    Science.gov (United States)

    Gopalakrishnan Meena, Muralikrishnan; Nair, Aditya; Taira, Kunihiko

    2017-11-01

    We characterize the vortical wake interactions by utilizing network theory and cluster-based approaches, and develop a data-inspired unsteady force model. In the present work, the vortical interaction network is defined by nodes representing vortical elements and the edges quantified by induced velocity measures amongst the vortices. The full vorticity field is reduced to a finite number of vortical clusters based on network community detection algorithm, which serves as a basis for a skeleton network that captures the essence of the wake dynamics. We use this reduced representation of the wake to develop a data-inspired reduced-order force model that can predict unsteady fluid forces on the body. The overall formulation is demonstrated for laminar flows around canonical bluff body wake and stalled flow over an airfoil. We also show the robustness of the present network-based model against noisy data, which motivates applications towards turbulent flows and experimental measurements. Supported by the National Science Foundation (Grant 1632003).

  5. Design of reduced-order state estimators for linear time-varying multivariable systems

    Science.gov (United States)

    Nguyen, Charles C.

    1987-01-01

    The design of reduced-order state estimators for linear time-varying multivariable systems is considered. Employing the concepts of matrix operators and the method of canonical transformations, this paper shows that there exists a reduced-order state estimator for linear time-varying systems that are 'lexicography-fixedly observable'. In addition, the eigenvalues of the estimator can be arbitrarily assigned. A simple algorithm is proposed for the design of the state estimator.

  6. Construction of energy-stable Galerkin reduced order models.

    Energy Technology Data Exchange (ETDEWEB)

    Kalashnikova, Irina; Barone, Matthew Franklin; Arunajatesan, Srinivasan; van Bloemen Waanders, Bart Gustaaf

    2013-05-01

    This report aims to unify several approaches for building stable projection-based reduced order models (ROMs). Attention is focused on linear time-invariant (LTI) systems. The model reduction procedure consists of two steps: the computation of a reduced basis, and the projection of the governing partial differential equations (PDEs) onto this reduced basis. Two kinds of reduced bases are considered: the proper orthogonal decomposition (POD) basis and the balanced truncation basis. The projection step of the model reduction can be done in two ways: via continuous projection or via discrete projection. First, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of PDEs using continuous projection is proposed. The idea is to apply to the set of PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The resulting ROM will be energy-stable for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special weighted L2 inner product, termed the %E2%80%9Csymmetry inner product%E2%80%9D. Attention is then turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, a weighted L2 inner product termed the %E2%80%9CLyapunov inner product%E2%80%9D, is derived. The weighting matrix that defines the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system arising from the discretization of a system of PDEs in space. It is shown that a ROM constructed via discrete projection using the Lyapunov inner product will be energy-stable for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. Comparisons are also made between the symmetry inner product and the Lyapunov inner product. The performance of ROMs constructed

  7. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    KAUST Repository

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  8. Sparsity enabled cluster reduced-order models for control

    Science.gov (United States)

    Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

    2018-01-01

    Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

  9. A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

    Energy Technology Data Exchange (ETDEWEB)

    Paul Cizmas; Brian Richardson; Thomas Brenner; Raymond Fontenot

    2009-09-30

    A reduced-order model based on proper orthogonal decomposition (POD) has been developed to simulate transient two- and three-dimensional isothermal and non-isothermal flows in a fluidized bed. Reduced-order models of void fraction, gas and solids temperatures, granular energy, and z-direction gas and solids velocity have been added to the previous version of the code. These algorithms are presented and their implementation is discussed. Verification studies are presented for each algorithm. A number of methods to accelerate the computations performed by the reduced-order model are presented. The errors associated with each acceleration method are computed and discussed. Using a combination of acceleration methods, a two-dimensional isothermal simulation using the reduced-order model is shown to be 114 times faster than using the full-order model. In the pursue of achieving the objectives of the project and completing the tasks planned for this program, several unplanned and unforeseen results, methods and studies have been generated. These additional accomplishments are also presented and they include: (1) a study of the effect of snapshot sampling time on the computation of the POD basis functions, (2) an investigation of different strategies for generating the autocorrelation matrix used to find the POD basis functions, (3) the development and implementation of a bubble detection and tracking algorithm based on mathematical morphology, (4) a method for augmenting the proper orthogonal decomposition to better capture flows with discontinuities, such as bubbles, and (5) a mixed reduced-order/full-order model, called point-mode proper orthogonal decomposition, designed to avoid unphysical due to approximation errors. The limitations of the proper orthogonal decomposition method in simulating transient flows with moving discontinuities, such as bubbling flows, are discussed and several methods are proposed to adapt the method for future use.

  10. An improved method using factor division algorithm for reducing the ...

    Indian Academy of Sciences (India)

    An improved method is proposed to determine the reduced order model of large scale linear time invariant system. The dominant poles of the low order system are calculated by clustering method. The selection of pole to the cluster point is based on the contributions of each pole in redefining time moment and ...

  11. [Discussion on twirling reinforcing-reducing method].

    Science.gov (United States)

    Shen, Te-Li

    2014-01-01

    The essence of twirling reinforcing-reducing method is discussed to provide theoretical guidance for clinical application of reinforcing-reducing method. Through retrospection on historical literature of twirling reinforcing-reducing method, records and explanatory notes are thoroughly explored. Several existing opinions are analyzed and explained for instance twirling method has connection with circulation direction of channels; twirling method is subdivided into right and left, male and female, hand and foot; twriling method is related to quantity of stimulus and operation time; twriling method belongs to spiral motion and so on. As a result, it is found that the key of twirling reinforcing-reducing method is the posture of needle-holding hand that defines three-dimensional motion. If twirling method is subdivided into right and left, male and female, hand and foot and so on, steric effects of lifting-thrusting movement that come along with twirling method could be ignored at the same time. It is that the essence of twirling reinforcing-reducing method is close to the principle of lifting-thrusting reinforcing-reducing method, enriching effect with slow insertion and fast withdrawal of needle while reducing effect with fast insertion and slow withdrawal, which is recorded in Miraculous Pivot: Nine needle and Twelve Yuan. With this principle as guide, manipulation could be avoided to become a mere formality and illusory metaphysics during clinical application of twirling reinforcing-reducing method.

  12. Efficiency of High Order Spectral Element Methods on Petascale Architectures

    KAUST Repository

    Hutchinson, Maxwell

    2016-06-14

    High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.

  13. Reliable design of H-2 optimal reduced-order controllers via a homotopy algorithm

    Science.gov (United States)

    Collins, Emmanuel G.; Richter, Stephen; Davis, Larry D.

    1992-01-01

    Due to control processor limitations, the design of reduced-order controllers is an active area of research. Suboptimal methods based on truncating the order of the corresponding linear-quadratic-Gaussian (LQG) compensator tend to fail if the requested controller dimension is sufficiently small and/or the requested controller authority is sufficiently high. Also, traditional parameter optimization approaches have only local convergence properties. This paper discusses a homotopy algorithm for optimal reduced-order control that has global convergence properties. The exposition is for discrete-time systems. The algorithm has been implemented in MATLAB and is applied to a benchmark problem.

  14. Improving the Accuracy of High-Order Nodal Transport Methods

    Energy Technology Data Exchange (ETDEWEB)

    Azmy, Y.Y.; Buscaglia, G.C.; Zamonsky, O.M.

    1999-09-27

    This paper outlines some recent advances towards improving the accuracy of neutron calculations using the Arbitrarily High Order Transport-Nodal (AHOT-N) Method. These transport advances consist of several contributions: (a) A formula for the spatial weights that allows for the polynomial order to be raised arbitrarily high without suffering from pollution from round-off, error; (b) A reconstruction technique for the angular flux, based upon a recursive formula, that reduces the pointwise error by one order; (c) An a posterior error indicator that estimates the true error and its distribution throughout the domain, so that it can be used for adaptively reftig the approximation. Present results are mainly for ID, extension to 2D-3D is in progress.

  15. A Perturbed Fourth Order Runge-Kutta Method for First Order ...

    African Journals Online (AJOL)

    In this paper a perturbed fourth order Runge-Kutta (PRK) method for solving firstorder ordinary differential equations (ODEs) is proposed. The scheme is an improvement over well-known fourth order Runge-kutta (RK) method and the most recent fifth order Runge-Kutta Fehlberg (RKF) method [2]. It has error constants much ...

  16. Reduced order modelling techniques for mesh movement strategies as applied to fluid structure interactions

    CSIR Research Space (South Africa)

    Bogaers, Alfred EJ

    2010-01-01

    Full Text Available In this paper, we implement the method of Proper Orthogonal Decomposition (POD) to generate a reduced order model (ROM) of an optimization based mesh movement technique. In the study it is shown that POD can be used effectively to generate a ROM...

  17. The fractional - order controllers: Methods for their synthesis and application

    OpenAIRE

    Petras, I.

    2000-01-01

    This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractional-order controllers. In the next section we describe how to apply the fractional controller on control systems.

  18. First Order Reliability Application and Verification Methods for Semistatic Structures

    Science.gov (United States)

    Verderaime, Vincent

    1994-01-01

    Escalating risks of aerostructures stimulated by increasing size, complexity, and cost should no longer be ignored by conventional deterministic safety design methods. The deterministic pass-fail concept is incompatible with probability and risk assessments, its stress audits are shown to be arbitrary and incomplete, and it compromises high strength materials performance. A reliability method is proposed which combines first order reliability principles with deterministic design variables and conventional test technique to surmount current deterministic stress design and audit deficiencies. Accumulative and propagation design uncertainty errors are defined and appropriately implemented into the classical safety index expression. The application is reduced to solving for a factor that satisfies the specified reliability and compensates for uncertainty errors, and then using this factor as, and instead of, the conventional safety factor in stress analyses. The resulting method is consistent with current analytical skills and verification practices, the culture of most designers, and with the pace of semistatic structural designs.

  19. Improving the Accuracy of High-Order Nodal Transport Methods

    Energy Technology Data Exchange (ETDEWEB)

    Azmy, Y.Y.; Buscaglia, G.C.; Zamonsky, O.M.

    1999-09-27

    This paper outlines some recent advances towards improving the accuracy of neutron transport calculations using the Arbitrarily High Order Transport-Nodal (AHOT-N) Method. These advances consist of several contributions: (a) A formula for the spatial weights that allows for the polynomial order to be raised arbitrarily high without suffering adverse effects from round-off error; (b) A reconstruction technique for the angular flux, based upon a recursive formula, that reduces the pointwise error by one ordeq (c) An a posterior error indicator that estimates the true error and its distribution throughout the domain, so that it can be used for adaptively refining the approximation. Present results are mainly for ID, extension to 2D-3D is in progress.

  20. A Reduced-Order Controller Considering High-Order Modal Information of High-Rise Buildings for AMD Control System with Time-Delay

    Directory of Open Access Journals (Sweden)

    Zuo-Hua Li

    2017-01-01

    Full Text Available Time-delays of control force calculation, data acquisition, and actuator response will degrade the performance of Active Mass Damper (AMD control systems. To reduce the influence, model reduction method is used to deal with the original controlled structure. However, during the procedure, the related hierarchy information of small eigenvalues will be directly discorded. As a result, the reduced-order model ignores the information of high-order mode, which will reduce the design accuracy of an AMD control system. In this paper, a new reduced-order controller based on the improved Balanced Truncation (BT method is designed to reduce the calculation time and to retain the abandoned high-order modal information. It includes high-order natural frequency, damping ratio, and vibration modal information of the original structure. Then, a control gain design method based on Guaranteed Cost Control (GCC algorithm is presented to eliminate the adverse effects of data acquisition and actuator response time-delays in the design process of the reduced-order controller. To verify its effectiveness, the proposed methodology is applied to a numerical example of a ten-storey frame and an experiment of a single-span four-storey steel frame. Both numerical and experimental results demonstrate that the reduced-order controller with GCC algorithm has an excellent control effect; meanwhile it can compensate time-delays effectively.

  1. The Use Of Alternative Methods In Reducing Menopausal ...

    African Journals Online (AJOL)

    Results: 37.4% of women were determined to use alternative methods to reduce their menopausal symptoms. In the consequence of statistical analysis, a significant relation was found between the menopausal complaints such as hot flashes, night sweats and sleeping problem and the use of alternative methods in order to ...

  2. The Matrix Element Method at Next-to-Leading Order

    OpenAIRE

    Campbell, John M.; Giele, Walter T.; Williams, Ciaran

    2012-01-01

    This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...

  3. Optimized first-order methods for smooth convex minimization.

    Science.gov (United States)

    Kim, Donghwan; Fessler, Jeffrey A

    2016-09-01

    We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle [5] recently described a numerical method for computing the N-iteration optimal step coefficients in a class of first-order algorithms that includes gradient methods, heavy-ball methods [15], and Nesterov's fast gradient methods [10,12]. However, the numerical method in [5] is computationally expensive for large N, and the corresponding numerically optimized first-order algorithm in [5] requires impractical memory and computation for large-scale optimization problems. In this paper, we propose optimized first-order algorithms that achieve a convergence bound that is two times smaller than for Nesterov's fast gradient methods; our bound is found analytically and refines the numerical bound in [5]. Furthermore, the proposed optimized first-order methods have efficient forms that are remarkably similar to Nesterov's fast gradient methods.

  4. Assessment of gene order computing methods for Alzheimer's disease

    Directory of Open Access Journals (Sweden)

    Hu Benqiong

    2013-01-01

    Full Text Available Abstract Background Computational genomics of Alzheimer disease (AD, the most common form of senile dementia, is a nascent field in AD research. The field includes AD gene clustering by computing gene order which generates higher quality gene clustering patterns than most other clustering methods. However, there are few available gene order computing methods such as Genetic Algorithm (GA and Ant Colony Optimization (ACO. Further, their performance in gene order computation using AD microarray data is not known. We thus set forth to evaluate the performances of current gene order computing methods with different distance formulas, and to identify additional features associated with gene order computation. Methods Using different distance formulas- Pearson distance and Euclidean distance, the squared Euclidean distance, and other conditions, gene orders were calculated by ACO and GA (including standard GA and improved GA methods, respectively. The qualities of the gene orders were compared, and new features from the calculated gene orders were identified. Results Compared to the GA methods tested in this study, ACO fits the AD microarray data the best when calculating gene order. In addition, the following features were revealed: different distance formulas generated a different quality of gene order, and the commonly used Pearson distance was not the best distance formula when used with both GA and ACO methods for AD microarray data. Conclusion Compared with Pearson distance and Euclidean distance, the squared Euclidean distance generated the best quality gene order computed by GA and ACO methods.

  5. The matrix element method at next-to-leading order

    Science.gov (United States)

    Campbell, John M.; Giele, Walter T.; Williams, Ciaran

    2012-11-01

    This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory, for electro-weak final states. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of unweighted next-to-leading order events. As examples of the application of our next-to-leading order matrix element method we consider the measurement of the mass of the Z boson and also the search for the Higgs boson in the four lepton channel.

  6. A Reduced Order, One Dimensional Model of Joint Response

    Energy Technology Data Exchange (ETDEWEB)

    DOHNER,JEFFREY L.

    2000-11-06

    As a joint is loaded, the tangent stiffness of the joint reduces due to slip at interfaces. This stiffness reduction continues until the direction of the applied load is reversed or the total interface slips. Total interface slippage in joints is called macro-slip. For joints not undergoing macro-slip, when load reversal occurs the tangent stiffness immediately rebounds to its maximum value. This occurs due to stiction effects at the interface. Thus, for periodic loads, a softening and rebound hardening cycle is produced which defines a hysteretic, energy absorbing trajectory. For many jointed sub-structures, this hysteretic trajectory can be approximated using simple polynomial representations. This allows for complex joint substructures to be represented using simple non-linear models. In this paper a simple one dimensional model is discussed.

  7. Methods Reduce Cost, Enhance Quality of Nanotubes

    Science.gov (United States)

    2009-01-01

    For all the challenges posed by the microgravity conditions of space, weight is actually one of the more significant problems NASA faces in the development of the next generation of U.S. space vehicles. For the Agency s Constellation Program, engineers at NASA centers are designing and testing new vessels as safe, practical, and cost-effective means of space travel following the eventual retirement of the space shuttle. Program components like the Orion Crew Exploration Vehicle, intended to carry astronauts to the International Space Station and the Moon, must be designed to specific weight requirements to manage fuel consumption and match launch rocket capabilities; Orion s gross liftoff weight target is about 63,789 pounds. Future space vehicles will require even greater attention to lightweight construction to help conserve fuel for long-range missions to Mars and beyond. In order to reduce spacecraft weight without sacrificing structural integrity, NASA is pursuing the development of materials that promise to revolutionize not only spacecraft construction, but also a host of potential applications on Earth. Single-walled carbon nanotubes are one material of particular interest. These tubular, single-layer carbon molecules - 100,000 of them braided together would be no thicker than a human hair - display a range of remarkable characteristics. Possessing greater tensile strength than steel at a fraction of the weight, the nanotubes are efficient heat conductors with metallic or semiconductor electrical properties depending on their diameter and chirality (the pattern of each nanotube s hexagonal lattice structure). All of these properties make the nanotubes an appealing material for spacecraft construction, with the potential for nanotube composites to reduce spacecraft weight by 50 percent or more. The nanotubes may also feature in a number of other space exploration applications, including life support, energy storage, and sensor technologies. NASA s various

  8. Block variable order step size method for solving higher order orbital problems

    Science.gov (United States)

    Rasedee, Ahmad Fadly Nurullah; Ijam, Hazizah Mohd; Sathar, Mohammad Hasan Abdul; Ishak, Norizarina; Nazri, Muhamad Azrin; Kamarudin, Nur Shuhada; Ramli, Nur Ainna

    2017-11-01

    Previous numerical methods for solving systems of higher order ordinary differential equations (ODEs) directly require calculating the integration coefficients at every step. This research provides a block multi step method for solving orbital problems with periodic solutions in the form of higher order ODEs directly. The advantage of the proposed method is, it requires calculating the integration coefficients only once at the beginning of the integration is presented. The derived formulae is then validated by running simulations with known higher order orbital equations. To provide further efficiency, a relationship between integration coefficients of various order is obtained.

  9. A 5-step maximal order method for direct solution of second order ...

    African Journals Online (AJOL)

    In this work, we propose a direct solution of second order ordinary differential equations without reduction to systems of first order equations. The method is based on collocating the differential system arising from a polynomial basis function at selected grid points xn+i, i = 0(1)5, which yields a five-step continuous method.

  10. A Generalized Runge-Kutta Method of order three

    DEFF Research Database (Denmark)

    Thomsen, Per Grove

    2002-01-01

    The report presents a numerical method for the solution of stiff systems of ODE's and index one DAE's. The type of method is a 4- stage Generalized Linear Method that is reformulated in a special Semi Implicit Runge Kutta Method of SDIRK type. Error estimation is by imbedding a method of order 4...... based on the same stages as the method and the coefficients are selected for ease of implementation. The method has 4 stages and the stage-order is 2. For purposes of generating dense output and for initializing the iteration in the internal stages a continuous extension is derived. The method is A......-stable and we present the region of absolute stability and the order star of the order 3 method that is used for computing the solution....

  11. Approaches for Reduced Order Modeling of Electrically Actuated von Karman Microplates

    KAUST Repository

    Saghir, Shahid

    2016-07-25

    This article presents and compares different approaches to develop reduced order models for the nonlinear von Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches are made for this case. Keywords: electrically actuated microplates, static analysis, dynamics of microplates, diaphragm vibration, large amplitude vibrations, nonlinear dynamics

  12. Exploration of POD-Galerkin Techniques for Developing Reduced Order Models of Reaction-Advection Equations

    Science.gov (United States)

    2014-04-01

    Distribution A: Approved for Public Release; Distribution Unlimited 13. SUPPLEMENTARY NOTES Technical paper presented at 44th AIAA Fluid Dynamics...order models”, J. Fluid Mech., Vol. 641, pp. 1-50, 2009. 4. Haaskonk, B., and Ohlberger, M., “Reduced Basis Method for Finite Volume Approximations...Physics, 2009. 6. Bouhoubeiny, E., Druault, P., and Mecanique , C.R., “Note on the POD-based time interpolation from successive PIV images”, Academie des

  13. Investigation of the Stability of POD-Galerkin Techniques for Reduced Order Model Development

    Science.gov (United States)

    2016-01-09

    Technical Paper 3. DATES COVERED (From - To) 24 November 2015 – 09 January 2016 4. TITLE AND SUBTITLE Investigation of the Stability of POD -Galerkin...CA (04-09 January 2016) PA Clearance Number 15704; Clearance Date 12/15/2015 14. ABSTRACT Detailed investigations are performed to analyze and...equations. The ROM is obtained by employing Galerkin’s method to reduce the high-order PDEs to a lower-order ODE system by means of POD eigen-bases

  14. Singular perturbations introduction to system order reduction methods with applications

    CERN Document Server

    Shchepakina, Elena; Mortell, Michael P

    2014-01-01

    These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...

  15. Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    F. Soleymani

    2011-01-01

    Full Text Available This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach. Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative. The analytical study of the main theorem is presented in detail to show the fourth order of convergence. Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class. Finally, numerical examples are taken into account to manifest the accuracy of the derived methods.

  16. A new sixth order method for nonlinear equations in R.

    Science.gov (United States)

    Singh, Sukhjit; Gupta, D K

    2014-01-01

    A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x 0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton's method and other sixth order methods considered.

  17. Higher-Order Integral Equation Methods in Computational Electromagnetics

    DEFF Research Database (Denmark)

    Jørgensen, Erik; Meincke, Peter

    Higher-order integral equation methods have been investigated. The study has focused on improving the accuracy and efficiency of the Method of Moments (MoM) applied to electromagnetic problems. A new set of hierarchical Legendre basis functions of arbitrary order is developed. The new basis...

  18. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Mohammad Maleki

    2012-01-01

    Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

  19. Reduced basis method for source mask optimization

    CERN Document Server

    Pomplun, J; Burger, S; Schmidt, F; Tyminski, J; Flagello, D; Toshiharu, N; 10.1117/12.866101

    2010-01-01

    Image modeling and simulation are critical to extending the limits of leading edge lithography technologies used for IC making. Simultaneous source mask optimization (SMO) has become an important objective in the field of computational lithography. SMO is considered essential to extending immersion lithography beyond the 45nm node. However, SMO is computationally extremely challenging and time-consuming. The key challenges are due to run time vs. accuracy tradeoffs of the imaging models used for the computational lithography. We present a new technique to be incorporated in the SMO flow. This new approach is based on the reduced basis method (RBM) applied to the simulation of light transmission through the lithography masks. It provides a rigorous approximation to the exact lithographical problem, based on fully vectorial Maxwell's equations. Using the reduced basis method, the optimization process is divided into an offline and an online steps. In the offline step, a RBM model with variable geometrical param...

  20. Air Vehicle Integration and Technology Research (AVIATR). Delivery Order 0013: Nonlinear, Low-Order/Reduced-Order Modeling Applications and Demonstration

    Science.gov (United States)

    2011-12-01

    Approved for public release; distribution unlimited 7.4 CEAC Measured Thermal Strains In high temperature testing, piezoelectric -type response...Instrumentation The vibration response will be measured with a combination of accelerometers (AC), strain gauges (SG) and laser doppler vibrometer (LDV), Figure A...method will use scanning laser vibrometer with shaker excitation. Data obtained from the survey shall include resonant frequencies, mode shapes

  1. Wall Shear Stress Distribution in a Patient-Specific Cerebral Aneurysm Model using Reduced Order Modeling

    Science.gov (United States)

    Han, Suyue; Chang, Gary Han; Schirmer, Clemens; Modarres-Sadeghi, Yahya

    2016-11-01

    We construct a reduced-order model (ROM) to study the Wall Shear Stress (WSS) distributions in image-based patient-specific aneurysms models. The magnitude of WSS has been shown to be a critical factor in growth and rupture of human aneurysms. We start the process by running a training case using Computational Fluid Dynamics (CFD) simulation with time-varying flow parameters, such that these parameters cover the range of parameters of interest. The method of snapshot Proper Orthogonal Decomposition (POD) is utilized to construct the reduced-order bases using the training CFD simulation. The resulting ROM enables us to study the flow patterns and the WSS distributions over a range of system parameters computationally very efficiently with a relatively small number of modes. This enables comprehensive analysis of the model system across a range of physiological conditions without the need to re-compute the simulation for small changes in the system parameters.

  2. Recursive regularization step for high-order lattice Boltzmann methods

    Science.gov (United States)

    Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

    2017-09-01

    A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

  3. Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

    Science.gov (United States)

    Yao, Weigang; Liou, Meng-Sing

    2012-01-01

    The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis

  4. Reduced order models for thermal analysis : final report : LDRD Project No. 137807.

    Energy Technology Data Exchange (ETDEWEB)

    Hogan, Roy E., Jr.; Gartling, David K.

    2010-09-01

    This LDRD Senior's Council Project is focused on the development, implementation and evaluation of Reduced Order Models (ROM) for application in the thermal analysis of complex engineering problems. Two basic approaches to developing a ROM for combined thermal conduction and enclosure radiation problems are considered. As a prerequisite to a ROM a fully coupled solution method for conduction/radiation models is required; a parallel implementation is explored for this class of problems. High-fidelity models of large, complex systems are now used routinely to verify design and performance. However, there are applications where the high-fidelity model is too large to be used repetitively in a design mode. One such application is the design of a control system that oversees the functioning of the complex, high-fidelity model. Examples include control systems for manufacturing processes such as brazing and annealing furnaces as well as control systems for the thermal management of optical systems. A reduced order model (ROM) seeks to reduce the number of degrees of freedom needed to represent the overall behavior of the large system without a significant loss in accuracy. The reduction in the number of degrees of freedom of the ROM leads to immediate increases in computational efficiency and allows many design parameters and perturbations to be quickly and effectively evaluated. Reduced order models are routinely used in solid mechanics where techniques such as modal analysis have reached a high state of refinement. Similar techniques have recently been applied in standard thermal conduction problems e.g. though the general use of ROM for heat transfer is not yet widespread. One major difficulty with the development of ROM for general thermal analysis is the need to include the very nonlinear effects of enclosure radiation in many applications. Many ROM methods have considered only linear or mildly nonlinear problems. In the present study a reduced order model is

  5. Method to render second order beam optics programs symplectic

    Energy Technology Data Exchange (ETDEWEB)

    Douglas, D.; Servranckx, R.V.

    1984-10-01

    We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs.

  6. Stable reduced-order models of generalized dynamical systems using coordinate-transformed Arnoldi algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Silveira, L.M.; Kamon, M.; Elfadel, I.; White, J. [Massachusetts Inst. of Technology, Cambridge, MA (United States)

    1996-12-31

    Model order reduction based on Krylov subspace iterative methods has recently emerged as a major tool for compressing the number of states in linear models used for simulating very large physical systems (VLSI circuits, electromagnetic interactions). There are currently two main methods for accomplishing such a compression: one is based on the nonsymmetric look-ahead Lanczos algorithm that gives a numerically stable procedure for finding Pade approximations, while the other is based on a less well characterized Arnoldi algorithm. In this paper, we show that for certain classes of generalized state-space systems, the reduced-order models produced by a coordinate-transformed Arnoldi algorithm inherit the stability of the original system. Complete Proofs of our results will be given in the final paper.

  7. Traveling wave solution by differential transformation method and reduced differential transformation method

    Directory of Open Access Journals (Sweden)

    Hamed Faghanpour Ganji

    2016-09-01

    Full Text Available The present study further examines two recent semi-analytic methods, a reduced order of nonlinear differential transformation method (also called RDTM and differential transformation method along with Pade approximation to discuss Jaulent–Miodek and coupled Whitham–Broer–Kaup equations. The basic ideas of these methods are briefly introduced and performance of the proposed methods for above mentioned equations is evaluated via comparing with exact solution. The results illustrate that the so-called DTM method, unlike RDTM, due to the presence of secular terms (similar to perturbation method, cannot be found practical for nonlinear partial differential equations (particularly in Acoustic and Wave propagation problems even through utilizing Pade approximation; meanwhile, RDTM method, despite its simplicity and rapid convergence, assured a significant accuracy and great agreement, and thus it is fair to say that nonlinear problems together with Acoustic application which cannot be solved via Analytical methods, can be studied with reduced order of nonlinear differential transformation method.

  8. An accurate scheme by block method for third order ordinary ...

    African Journals Online (AJOL)

    A block linear multistep method for solving special third order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to special third order initial value ...

  9. Comparative study of synchronization methods of fractional order chaotic systems

    Science.gov (United States)

    Singh, Ajit K.; Yadav, Vijay K.; Das, S.

    2016-09-01

    In this article, the active control method and the backstepping method are used during the synchronization of fractional order chaotic systems. The salient feature of the article is the analysis of time of synchronization between fractional order Chen and Qi systems using both the methods. Numerical simulation and graphical results clearly exhibit that backstepping approach is better than active control method for synchronization of the considered pair of systems, as it takes less time to synchronize while using the first one compare to second one.

  10. A survey of theory and methods of invariant item ordering.

    Science.gov (United States)

    Sijtsma, K; Junker, B W

    1996-05-01

    In many testing situations, ordering the items by difficulty is helpful in analysing the testing data; examples include intelligence testing, analysis of differential item functioning, person-fit analysis, and exploring hypotheses about the order in which cognitive operations are acquired by children. In each situation, interpretation and analysis are made easier if the items are ordered by difficulty in the same way for every individual taking the test, i.e. the item response functions do not cross. This is an invariant item ordering. In this paper we review a class of non-parametric unidimensional item response models in which the ordinal properties of items (and persons) can be studied, and survey both old and new methods for the investigation of invariant item ordering in empirical data sets. Our model formulation derives in particular from the work of Holland & Rosenbaum (1986), Junker (1993) and Mokken (1971). We survey methods based on the work of Mokken (1971), Rosenbaum (1987a, b), and Sijtsma & Meijer (1992), and we also discuss some new proposals for checking invariant item ordering. When violations are detected, these methods allow a rough assessment of where on the latent scale the item response functions cross. We also study similarities and differences between these various methods and provide guidelines for their use. Finally, the methods are illustrated with data from a developmental psychology experiment in which the ability to draw inferences about transitive relations is explored.

  11. A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring.

    Energy Technology Data Exchange (ETDEWEB)

    Roettgen, Dan; Seegar, Ben; Tai, Wei Che; Baek, Seunghun; Dossogne, Tilan; Allen, Matthew; Kuether, Robert J.; Brake, Matthew Robert; Mayes, Randall L.

    2015-10-01

    Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.

  12. A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring [PowerPoint

    Energy Technology Data Exchange (ETDEWEB)

    Roettgen, Dan [Wisc; Seeger, Benjamin [Stuttgart; Tai, Wei Che [Washington; Baek, Seunghun [Michigan; Dossogne, Tilan [Liege; Allen, Matthew S [Wisc; Kuether, Robert J.; Brake, Matthew Robert; Mayes, Randall L.

    2016-01-01

    Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.

  13. Numerical methods of higher order of accuracy for incompressible flows

    Czech Academy of Sciences Publication Activity Database

    Kozel, K.; Louda, Petr; Příhoda, Jaromír

    2010-01-01

    Roč. 80, č. 8 (2010), s. 1734-1745 ISSN 0378-4754 Institutional research plan: CEZ:AV0Z20760514 Keywords : higher order methods * upwind methods * backward-facing step Subject RIV: BK - Fluid Dynamics Impact factor: 0.812, year: 2010

  14. A fourth order exponentially-fitted multiderivative method for Stiff ...

    African Journals Online (AJOL)

    A fourth order exponentially-fitted multiderivative method for Stiff initial value problems. ... Journal of the Nigerian Association of Mathematical Physics ... implemented and preliminary numerical results indicate that the approach compares favourably with other existing methods that have solved the same set of stiff problems.

  15. Continuous implicit method for the solution of general second order ...

    African Journals Online (AJOL)

    Methods of collocation and interpolation were adopted to generate a continuous implicit scheme for the solution of second order ordinary differential equation. Newton polynomial approximation method was used to generate the unknown parameter in the corrector. This enables us to solve both initial and boundary value ...

  16. How can we strengthen students’ social relations in order to reduce school dropout?

    DEFF Research Database (Denmark)

    Ingholt, Liselotte; Sørensen, Betina Bang; Andersen, Susan

    2015-01-01

    was performed to investigate the specific relationships between the social environment within the schools and the institutional structures in order to analyse reasons for school dropout and their relation to well-being, cigarette smoking and substance use. METHODS: The development study was based......BACKGROUND: This article describes the rationale and contents of an intervention program aimed at strengthening students' social relations in order to reduce dropout from vocational schools in Denmark. Taking its theoretical cue from the concept of 'social participation', a qualitative study...... additional qualitative interviews and four group interviews were conducted with students 16-25 years old. RESULTS: The qualitative data collection resulted in seven major themes to be addressed in the intervention: social relations, sole focus on professional skills, institutionalized individualization...

  17. Index-aware model order reduction methods applications to differential-algebraic equations

    CERN Document Server

    Banagaaya, N; Schilders, W H A

    2016-01-01

    The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.

  18. Strategies for Reduced-Order Models in Uncertainty Quantification of Complex Turbulent Dynamical Systems

    Science.gov (United States)

    Qi, Di

    applied in the training phase for calibrating model errors to achieve optimal imperfect model parameters; and total statistical energy dynamics are introduced to improve the model sensitivity in the prediction phase especially when strong external perturbations are exerted. The validity of reduced-order models for predicting statistical responses and intermittency is demonstrated on a series of instructive models with increasing complexity, including the stochastic triad model, the Lorenz '96 model, and models for barotropic and baroclinic turbulence. The skillful low-order modeling methods developed here should also be useful for other applications such as efficient algorithms for data assimilation.

  19. Higher-Order Semi-Implicit Projection Methods

    Energy Technology Data Exchange (ETDEWEB)

    Minion, M L

    2001-09-06

    A semi-implicit form of the method of spectral deferred corrections is applied to the solution of the incompressible Navier-Stokes equations. A methodology for constructing semi-implicit projection methods with arbitrarily high order of temporal accuracy in both the velocity and pressure is presented. Three variations of projection methods are discussed which differ in the manner in which the auxiliary velocity and the pressure are calculated. The presentation will make clear that project methods in general need not be viewed as fractional step methods as is often the practice. Two simple numerical examples re used to demonstrate fourth-order accuracy in time for an implementation of each variation of projection method.

  20. A high-order SPH method by introducing inverse kernels

    Directory of Open Access Journals (Sweden)

    Le Fang

    2017-02-01

    Full Text Available The smoothed particle hydrodynamics (SPH method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square (LS and Moving-Least-Square (MLS methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.

  1. DETERMINING ENERGY SAVINGS IN BUILDINGS USING THE REDUCING COSTS METHOD

    OpenAIRE

    STAN IVAN F.E.; MIRCEA I

    2015-01-01

    The paper is structured in four parts. The first part presents the importance of thermal insulation for buildings energy economy and some insulation properties. In the second part of the paper it is described the reducing cost method to determine the energy savings. The third part of the paper includes an analysis and a comparison for an exterior wall provided with different thicknesses of insulation layer in order to determine the average savings cost. The last par...

  2. Experimental verifications of a structural damage identification technique using reduced order finite-element model

    Science.gov (United States)

    Li, Rui; Zhou, Li; Yang, Jann N.

    2010-04-01

    An objective of the structural health monitoring system is to identify the state of the structure and to detect the damage when it occurs. Analysis techniques for the damage identification of structures, based on vibration data measured from sensors, have received considerable attention. Recently, a new damage tracking technique, referred to as the adaptive quadratic sum-square error (AQSSE) technique, has been proposed, and simulation studies demonstrated that the AQSSE technique is quite effective in identifying structural damages. In this paper, the adaptive quadratic sumsquare error (AQSSE) along with the reduced-order finite-element method is proposed to identify the damages of complex structures. Experimental tests were conducted to verify the capability of the proposed damage detection approach. A series of experimental tests were performed using a scaled cantilever beam subject to the white noise and sinusoidal excitations. The capability of the proposed reduced-order finite-element based adaptive quadratic sum-square error (AQSSE) method in detecting the structural damage is demonstrated by the experimental results.

  3. Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

    Science.gov (United States)

    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.

  4. Static aeroelastic analysis including geometric nonlinearities based on reduced order model

    Directory of Open Access Journals (Sweden)

    Changchuan Xie

    2017-04-01

    Full Text Available This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM. The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM. Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

  5. Multilevel Fast Multipole Method for Higher Order Discretizations

    DEFF Research Database (Denmark)

    Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

    2014-01-01

    The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....

  6. Reduced-order LPV model of flexible wind turbines from high fidelity aeroelastic codes

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Sønderby, Ivan Bergquist; Hansen, Morten Hartvig

    2013-01-01

    Linear aeroelastic models used for stability analysis of wind turbines are commonly of very high order. These high-order models are generally not suitable for control analysis and synthesis. This paper presents a methodology to obtain a reduced-order linear parameter varying (LPV) model from a se...

  7. New high order FDTD method to solve EMC problems

    Directory of Open Access Journals (Sweden)

    N. Deymier

    2015-10-01

    Full Text Available In electromagnetic compatibility (EMC context, we are interested in developing new ac- curate methods to solve efficiently and accurately Maxwell’s equations in the time domain. Indeed, usual methods such as FDTD or FVTD present im- portant dissipative and/or dispersive errors which prevent to obtain a good numerical approximation of the physical solution for a given industrial scene unless we use a mesh with a very small cell size. To avoid this problem, schemes like the Discontinuous Galerkin (DG method, based on higher order spa- tial approximations, have been introduced and stud- ied on unstructured meshes. However the cost of this kind of method can become prohibitive accord- ing to the mesh used. In this paper, we first present a higher order spatial approximation method on carte- sian meshes. It is based on a finite element ap- proach and recovers at the order 1 the well-known Yee’s schema. Next, to deal with EMC problem, a non-oriented thin wire formalism is proposed for this method. Finally, several examples are given to present the benefits of this new method by compar- ison with both Yee’s schema and DG approaches.

  8. Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling

    KAUST Repository

    Ruzziconi, Laura

    2013-06-10

    We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.

  9. Hybrid RANS-LES using high order numerical methods

    Science.gov (United States)

    Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael

    2017-11-01

    Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

  10. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    Liu, Dayan

    2015-02-01

    This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

  11. Linear multistep method for solution of second order initial value ...

    African Journals Online (AJOL)

    Linear multistep method for solution of second order initial value problems of ordinary differential equations: a truncation error approach. M O Udo, G A Olayi, R A Ademiluyi. Abstract. No Abstract. Global Journal of Mathematical Sciences Vol. 6 (2) 2007: pp. 119-126. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT

  12. High-Order CESE Methods for Solving Hyperbolic PDEs (Preprint)

    Science.gov (United States)

    2011-05-03

    system of coupled hyperbolic PDE’s with arbitrarily high-order con- vergence . Numerical results show that the extended algorithm can achieve higher...Velocity- Stress Equations for Waves in Solids of Hexagonal Symmetry Solved by the Space-Time CESE Method. ASME Journal of Vibration and Acoustics, 133 (2

  13. A second order Rosenbrock method applied to photochemical dispersion problems

    NARCIS (Netherlands)

    J.G. Verwer (Jan); E.J. Spee (Edwin); J.G. Blom (Joke); W. Hundsdorfer (Willem)

    1997-01-01

    textabstractA 2nd-order, L-stable Rosenbrock method from the field of stiff ordinary differential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective and turbulent diffusive transport. Partial differential equation problems of this type occur

  14. An alternative method for order tracking using autopower spectrum

    Directory of Open Access Journals (Sweden)

    Guido R Guercioni

    2015-11-01

    Full Text Available Order tracking is a method of analysis used by engineers in the diagnosis of rotating machinery. In many applications, order analysis of non-stationary signals is required. The direct extraction of the amplitude information from the short-time Fourier transform may lead to inaccurate vibration-level estimation in the case of fast changes in the signal frequency content. This article discusses spectral smearing, which is the main reason of the problem, and its sensitivity to the characteristics of the signal (frequency and amplitude variations and to the input parameters of discrete Fourier transform analysis (window size and type. Through the years, many different approaches to perform order analysis have been developed; this article introduces a novel method for order tracking based on the short-time Fourier transform, which applies a compensation of the smearing effect based on an invariant information contained in autopower spectrum. The limitations and capabilities of the proposed method with respect to other existing techniques are discussed: considering the accuracy of the results, low requirements of computational resources, and ease of implementation, this method proves a valid alternative to currently used techniques.

  15. ORIGINAL ARTICLE Sixth Order Stable Central Difference Method ...

    African Journals Online (AJOL)

    quantum mechanics, plasticity, chemical- reaction theory, aerodynamics, plasma ... Department of Mathematics, Jimma University, Jimma ...... sixth-order stable central difference method, has been presented for solving self-adjoint singularly perturbed two point boundary value problems. Three model examples are given to ...

  16. Staggered-Grid Finite Difference Method with Variable-Order Accuracy for Porous Media

    Directory of Open Access Journals (Sweden)

    Jinghuai Gao

    2013-01-01

    Full Text Available The numerical modeling of wave field in porous media generally requires more computation time than that of acoustic or elastic media. Usually used finite difference methods adopt finite difference operators with fixed-order accuracy to calculate space derivatives for a heterogeneous medium. A finite difference scheme with variable-order accuracy for acoustic wave equation has been proposed to reduce the computation time. In this paper, we develop this scheme for wave equations in porous media based on dispersion relation with high-order staggered-grid finite difference (SFD method. High-order finite difference operators are adopted for low-velocity regions, and low-order finite difference operators are adopted for high-velocity regions. Dispersion analysis and modeling results demonstrate that the proposed SFD method can decrease computational costs without reducing accuracy.

  17. High order integral equation method for diffraction gratings.

    Science.gov (United States)

    Lu, Wangtao; Lu, Ya Yan

    2012-05-01

    Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasi-periodic Green's functions. The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method in Wu and Lu [J. Opt. Soc. Am. A 26, 2444 (2009)], [J. Opt. Soc. Am. A 28, 1191 (2011)] is a recently developed integral equation method that avoids the quasi-periodic Green's functions and is relatively easy to implement. In this paper, we present a number of improvements for this method, including a revised formulation that is more stable numerically, and more accurate methods for computing tangential derivatives along material interfaces and for matching boundary conditions with the homogeneous top and bottom regions. Numerical examples indicate that the improved BIE-NtD map method achieves a high order of accuracy for in-plane and conical diffractions of dielectric gratings. © 2012 Optical Society of America

  18. Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

    KAUST Repository

    Parsani, Matteo

    2012-01-01

    Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.

  19. Identification of fractional order systems using modulating functions method

    KAUST Repository

    Liu, Dayan

    2013-06-01

    The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

  20. Effect of reducing agents in tuning the third-order optical nonlinearity and optical limiting behavior of reduced graphene oxide

    Science.gov (United States)

    Muruganandi, G.; Saravanan, M.; Vinitha, G.; Jessie Raj, M. B.; Sabari Girisun, T. C.

    2017-05-01

    Reduced graphene oxide (rGO) was prepared by reduction method using various reductants like hydrazine, sodium borohydride and ascorbic acid. XRD and Raman analysis confirmed the effective removal of functional groups in GO. SEM revealed that rGO consists of thin crumpled and disordered sheets closely associated with each other. Blue shift in UV-absorption maxima was due to weak interlayer coupling between the layers of rGO. Third order NLO properties of dispersed rGO were measured by Z-scan technique (532 nm, 50 mW). Both GO and rGO possess self defocusing, saturable absorption and optical limiting behavior. The nonlinear component of refractive index, absorption coefficient and optical susceptibility were found to be 10-8 cm2/W, 10-3 cm/W and 10-6 esu respectively. Tunability of NLO coefficients with altering functional groups upon rGO was achieved. rGO prepared using hydrazine with high NLO coefficient and excellent durability, signify the scope of utilizing them as optical limiters.

  1. Adaptively trained reduced-order model for acceleration of oscillatory flow simulations

    CSIR Research Space (South Africa)

    Oxtoby, Oliver F

    2012-07-01

    Full Text Available We present an adaptively trained Reduced-Order Model (ROM) to dramatically speed up flow simulations of an oscillatory nature. Such repetitive flowfields are frequently encountered in fluid-structure interaction modelling, aeroelastic flutter being...

  2. Novel Reduced Order in Time Models for Problems in Nonlinear Aeroelasticity Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Research is proposed for the development and implementation of state of the art, reduced order models for problems in nonlinear aeroelasticity. Highly efficient and...

  3. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

    Science.gov (United States)

    Shah, A A; Xing, W W; Triantafyllidis, V

    2017-04-01

    In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

  4. Plant factory: A new method for reducing carbon emissions

    Science.gov (United States)

    Zhang, Rong; Liu, Tong; Ma, Jianshe

    2017-03-01

    In recent years, climate change has become a focus issue all over the world. Many scientific studies have confirmed the relationship between the emission of greenhouse gas such as carbon dioxide and global climate change. Reducing the emission of greenhouse gas is an effective way to solve the problem of climate change. This paper presents a new method for reducing carbon emissions: using the photosynthesis of plants to achieve carbon fixation in plant factory. In order to verify the feasibility of this method, we built a closed artificial light plant factory adopting LED lighting to conduct the experiment of carbon dioxide enrichment. The results shows that the production of the plants increased by 20%-25% and the plants fixed a considerable amount of carbon dioxide by increasing the concentration of carbon dioxide in the environment to 1000 ppm.

  5. A new reduced-order observer design for the synchronization of Lorenz systems

    Energy Technology Data Exchange (ETDEWEB)

    Martinez-Guerra, R. [Departamento de Control Automatico, CINVESTAV-IPN, AP 14-740, CP 07360, Mexico, DF (Mexico)] e-mail: rguerra@ctrl.cinvestav.mx; Cruz-Victoria, J.C. [Departamento de Control Automatico, CINVESTAV-IPN, AP 14-740, CP 07360, Mexico, DF (Mexico); Gonzalez-Galan, R. [Departamento de Control Automatico, CINVESTAV-IPN, AP 14-740, CP 07360, Mexico, DF (Mexico); Aguilar-Lopez, R. [Departamento de Energia, UAM-Azcapotzalco, 02200 (Mexico)

    2006-04-01

    In this paper we tackle the synchronization of Lorenz system problem using a new proportional reduced-order observer design in the algebraic and differential setting. We prove the asymptotic stability of the resulting error system and by means of algebraic manipulations we obtain the estimates of the current states (master system), the construction of a proportional reduced-order observer is the main ingredient in our approach. Finally, we present a simulation to illustrate the effectiveness of the suggested approach.

  6. Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method

    Directory of Open Access Journals (Sweden)

    M. Mechee

    2013-01-01

    Full Text Available Runge-Kutta-Nyström (RKN method is adapted for solving the special second order delay differential equations (DDEs. The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.

  7. A General Method for Designing Fractional Order PID Controller

    Directory of Open Access Journals (Sweden)

    Marzieh Safaei

    2013-01-01

    Full Text Available The idea of using fractional order calculus in control became apparent when this kind of calculus was accepted as a powerful tool in many applications. This resulted in a new generation of PID controller called fractional order PID Controller, named as Controller. controller is more flexible and provides a better response with larger stability region as compared with standard PID controller. This paper presents a simple and reliable method for finding the family of controllers. The required calculations are done in frequency domain based on frequency response of the system and the stability region is specified in the parameters space. This method can be used for time-delay systems and, more generally, for any system with no transfer function.

  8. International Conference on Spectral and High-Order Methods

    CERN Document Server

    Dumont, Ney; Hesthaven, Jan

    2017-01-01

    This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

  9. A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

    Science.gov (United States)

    Si, Gang-Quan; Sun, Zhi-Yong; Zhang, Yan-Bin

    2011-08-01

    This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By introducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.

  10. Fuzzy Critical Path Method Based on Lexicographic Ordering

    Directory of Open Access Journals (Sweden)

    Phani Bushan Rao P

    2012-01-01

    Full Text Available The Critical Path Method (CPM is useful for planning and control of complex projects. The CPM identifies the critical activities in the critical path of an activity network. The successful implementation of CPM requires the availability of clear determined time duration for each activity. However, in practical situations this requirement is usually hard to fulfil since many of activities will be executed for the first time. Hence, there is always uncertainty about the time durations of activities in the network planning.  This has led to the development of fuzzy CPM.  In this paper, we use a Lexicographic ordering method for ranking fuzzy numbers to a critical path method in a fuzzy project network, where the duration time of each activity is represented by a trapezoidal fuzzy number. The proposed method is compared with fuzzy CPM based on different ranking methods of fuzzy numbers. The comparison reveals that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path.   This new method is simple in calculating fuzzy critical path than many methods proposed so far in literature.  

  11. Delay generation methods with reduced memory requirements

    DEFF Research Database (Denmark)

    Tomov, Borislav Gueorguiev; Jensen, Jørgen Arendt

    2003-01-01

    Modern diagnostic ultrasound beamformers require delay information for each sample along the image lines. In order to avoid storing large amounts of focusing data, delay generation techniques have to be used. In connection with developing a compact beamformer architecture, recursive algorithms we...

  12. Effect of Under-Resolved Grids on High Order Methods

    Science.gov (United States)

    Yee, H. C.; Sjoegreen, B.; Mansour, Nagi (Technical Monitor)

    2001-01-01

    There has been much discussion on verification and validation processes for establishing the credibility of CFD simulations. Since the early 1990s, many of the aeronautical and mechanical engineering related reference journals mandated that any accepted articles in numerical simulations (without known solutions to compared with) need to perform a minimum of one level of grid refinement and time step reduction. Due to the difficulty in analysis, the effect of under-resolved grids and the nonlinear behavior of available spatial discretizations, are scarcely discussed in the literature. Here, an under-resolved numerical simulation is one where the grid spacing being used is too coarse to resolve the smallest physically relevant scales of the chosen continuum governing equations that are of interest to the numerical modeler. With the advent of new developments in fourth-order or higher spatial schemes, it has become common to regard high order schemes as more accurate, reliable and require less grid points. The danger comes when one tries to perform computations with the coarsest grid possible while still hoping to maintain numerical results sufficiently accurate for complex flows, and especially, data-limited problems. On one hand, high order methods when applies to highly coupled multidimensional complex nonlinear problems might have different stability, convergence and reliability behavior than their well studied low order counterparts, especially for nonlinear schemes such as TVD, MUSCL with limiters, ENO, WENO and discrete Galerkin. On the other hand, high order methods involve more operation counts and systematic grid convergence study can be time consuming and prohibitively expansive. At the same time it is difficult to fully understand or categorize the different nonlinear behavior of finite discretizations, especially at the limits of under-resolution when different types of bifurcation phenomena might occur, depending on the combination of grid spacings, time

  13. Methods and framework for visualizing higher-order finite elements.

    Science.gov (United States)

    Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh

    2006-01-01

    The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the

  14. DETERMINING ENERGY SAVINGS IN BUILDINGS USING THE REDUCING COSTS METHOD

    Directory of Open Access Journals (Sweden)

    STAN IVAN F.E.

    2015-03-01

    Full Text Available The paper is structured in four parts. The first part presents the importance of thermal insulation for buildings energy economy and some insulation properties. In the second part of the paper it is described the reducing cost method to determine the energy savings. The third part of the paper includes an analysis and a comparison for an exterior wall provided with different thicknesses of insulation layer in order to determine the average savings cost. The last part presents conclusions and discussion.

  15. Methods of reducing vehicle aerodynamic drag

    Energy Technology Data Exchange (ETDEWEB)

    Sirenko V.; Rohatgi U.

    2012-07-08

    A small scale model (length 1710 mm) of General Motor SUV was built and tested in the wind tunnel for expected wind conditions and road clearance. Two passive devices, rear screen which is plate behind the car and rear fairing where the end of the car is aerodynamically extended, were incorporated in the model and tested in the wind tunnel for different wind conditions. The conclusion is that rear screen could reduce drag up to 6.5% and rear fairing can reduce the drag by 26%. There were additional tests for front edging and rear vortex generators. The results for drag reduction were mixed. It should be noted that there are aesthetic and practical considerations that may allow only partial implementation of these or any drag reduction options.

  16. Effectiveness of Provider Education Followed by Computerized Provider Order Entry Alerts in Reducing Inappropriate Red Blood Cell Transfusion

    Directory of Open Access Journals (Sweden)

    Vijay M. Patel

    2016-01-01

    Full Text Available To reduce the rate of inappropriate red blood cell transfusion, a provider education program, followed by alerts in the computerized provider order entry system (CPOE, was established to encourage AABB transfusion guidelines. Metrics were established for nonemergent inpatient transfusions. Service lines with high order volume were targeted with formal education regarding AABB 2012 transfusion guidelines. Transfusion orders were reviewed in real time with email communications sent to ordering providers falling outside of AABB recommendations. After 12 months of provider education, alerts were activated in CPOE. With provider education alone, the incidence of pretransfusion hemoglobin levels greater than 8 g/dL decreased from 16.64% to 6.36%, posttransfusion hemoglobin levels greater than 10 g/dL from 14.03% to 3.78%, and number of nonemergent two-unit red blood cell orders from 45.26% to 22.66%. Red blood cell utilization decreased by 13%. No additional significant reduction in nonemergent two-unit orders was observed with CPOE alerts. Provider education, an effective and low-cost method, should be considered as a first-line method for reducing inappropriate red blood cell transfusion rates in stable adult inpatients. Alerts in the computerized order entry system did not significantly lower the percentage of two-unit red blood cells orders but may help to maintain educational efforts.

  17. Performance of Several High Order Numerical Methods for Supersonic Combustion

    Science.gov (United States)

    Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)

    2001-01-01

    The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.

  18. Stirling Analysis Comparison of Commercial vs. High-Order Methods

    Science.gov (United States)

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

    2007-01-01

    Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/ proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's Compact scheme and Dyson s Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model although sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

  19. Stirling Analysis Comparison of Commercial Versus High-Order Methods

    Science.gov (United States)

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

    2005-01-01

    Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's compact scheme and Dyson's Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model with sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

  20. High-order finite element methods for cardiac monodomain simulations

    Directory of Open Access Journals (Sweden)

    Kevin P Vincent

    2015-08-01

    Full Text Available Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

  1. High-order finite element methods for cardiac monodomain simulations

    Science.gov (United States)

    Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.

    2015-01-01

    Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783

  2. A Modified AH-FDTD Unconditionally Stable Method Based on High-Order Algorithm

    Directory of Open Access Journals (Sweden)

    Zheng Pan

    2017-01-01

    Full Text Available The unconditionally stable method, Associated-Hermite FDTD, has attracted more and more attentions in computational electromagnetic for its time-frequency compact property. Because of the fewer orders of AH basis needed in signal reconstruction, the computational efficiency can be improved further. In order to further improve the accuracy of the traditional AH-FDTD, a high-order algorithm is introduced. Using this method, the dispersion error induced by the space grid can be reduced, which makes it possible to set coarser grid. The simulation results show that, on the condition of coarse grid, the waveforms obtained from the proposed method are matched well with the analytic result, and the accuracy of the proposed method is higher than the traditional AH-FDTD. And the efficiency of the proposed method is higher than the traditional FDTD method in analysing 2D waveguide problems with fine-structure.

  3. Solution of higher order boundary value problems by spline methods

    Science.gov (United States)

    Chaurasia, Anju; Srivastava, P. C.; Gupta, Yogesh

    2017-10-01

    Spline solution of Boundary Value Problems has received much attention in recent years. It has proven to be a powerful tool due to the ease of use and quality of results. This paper concerns with the survey of methods that try to approximate the solution of higher order BVPs using various spline functions. The purpose of this article is to thrash out the problems as well as conclusions, reached by the numerous authors in the related field. We critically assess many important relevant papers, published in reputed journals during last six years.

  4. Kernel methods for interpretable machine learning of order parameters

    Science.gov (United States)

    Ponte, Pedro; Melko, Roger G.

    2017-11-01

    Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of supervised learning has come from employing neural networks as classifiers. Although very powerful, such algorithms suffer from a lack of interpretability, which is usually desired in scientific applications in order to associate learned features with physical phenomena. In this paper, we explore support vector machines (SVMs), which are a class of supervised kernel methods that provide interpretable decision functions. We find that SVMs can learn the mathematical form of physical discriminators, such as order parameters and Hamiltonian constraints, for a set of two-dimensional spin models: the ferromagnetic Ising model, a conserved-order-parameter Ising model, and the Ising gauge theory. The ability of SVMs to provide interpretable classification highlights their potential for automating feature detection in both synthetic and experimental data sets for condensed matter and other many-body systems.

  5. Rad-Hydro with a High-Order, Low-Order Method

    Energy Technology Data Exchange (ETDEWEB)

    Wollaber, Allan Benton [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Park, HyeongKae [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lowrie, Robert Byron [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rauenzahn, Rick M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Cleveland, Mathew Allen [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-08-04

    Moment-based acceleration via the development of “high-order, low-order” (HO-LO) algorithms has provided substantial accuracy and efficiency enhancements for solutions of the nonlinear, thermal radiative transfer equations by CCS-2 and T-3 staff members. Accuracy enhancements over traditional, linearized methods are obtained by solving a nonlinear, timeimplicit HO-LO system via a Jacobian-free Newton Krylov procedure. This also prevents the appearance of non-physical maximum principle violations (“temperature spikes”) associated with linearization. Efficiency enhancements are obtained in part by removing “effective scattering” from the linearized system. In this highlight, we summarize recent work in which we formally extended the HO-LO radiation algorithm to include operator-split radiation-hydrodynamics.

  6. Variable-order rotated staggered-grid method for elastic-wave forward modeling

    Science.gov (United States)

    Wang, Wei-Zhong; Hu, Tian-Yue; Lu, Xue-Mei; Qin, Zhen; Li, Yan-Dong; Zhang, Yan

    2015-09-01

    Numerical simulations of a seismic wavefield are important to analyze seismic wave propagation. Elastic-wave equations are used in data simulation for modeling migration and imaging. In elastic wavefield numerical modeling, the rotated staggered-grid method (RSM) is a modification of the standard staggered-grid method (SSM). The variable-order method is based on the method of variable-length spatial operators and wavefield propagation, and it calculates the real dispersion error by adapting different finite-difference orders to different velocities. In this study, the variable-order rotated staggered-grid method (VRSM) is developed after applying the variable-order method to RSM to solve the numerical dispersion problem of RSM in low-velocity regions and reduce the computation cost. Moreover, based on theoretical dispersion and the real dispersion error of wave propagation calculated with the wave separation method, the application of the original method is extended from acoustic to shear waves, and the calculation is modified from theoretical to time-varying values. A layered model and an overthrust model are used to demonstrate the applicability of VRSM. We also evaluate the order distribution, wave propagation, and computation time. The results suggest that the VRSM order distribution is reasonable and VRSM produces high-precision results with a minimal computation cost.

  7. Fourth-order stable central difference method for self-adjoint ...

    African Journals Online (AJOL)

    In this paper, fourth order stable central difference method is presented for solving self-adjoint singular perturbation problems for small values of perturbation parameter, ε . First, the given differential equation was reduced to its conventional form and then it was transformed into linear system of algebraic equations in the ...

  8. Error estimation and adaptive order nodal method for solving multidimensional transport problems

    Energy Technology Data Exchange (ETDEWEB)

    Zamonsky, O.M.; Gho, C.J. [Bariloche Atomic Center, Rio Negro (Argentina). Instituto Balseiro; Azmy, Y.Y. [Oak Ridge National Lab., TN (United States)

    1998-01-01

    The authors propose a modification of the Arbitrarily High Order Transport Nodal method whereby they solve each node and each direction using different expansion order. With this feature and a previously proposed a posteriori error estimator they develop an adaptive order scheme to automatically improve the accuracy of the solution of the transport equation. They implemented the modified nodal method, the error estimator and the adaptive order scheme into a discrete-ordinates code for solving monoenergetic, fixed source, isotropic scattering problems in two-dimensional Cartesian geometry. They solve two test problems with large homogeneous regions to test the adaptive order scheme. The results show that using the adaptive process the storage requirements are reduced while preserving the accuracy of the results.

  9. An error bound for a discrete reduced order model of a linear multivariable system

    Science.gov (United States)

    Al-Saggaf, Ubaid M.; Franklin, Gene F.

    1987-01-01

    The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

  10. An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

    KAUST Repository

    Xu, Tiantian

    2014-08-17

    Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

  11. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    Energy Technology Data Exchange (ETDEWEB)

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

    2016-09-15

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  12. Reduced-Order Observer Model for Antiaircraft Artillery (AAA) Tracker Response

    Science.gov (United States)

    1979-08-01

    basic concept of this research and for many valuable discussions. 2. TABLE OF CONTENTS Section Page I INTRODUCTION 6 II REDUCED-ORDER OBSERVER MODEL...stochastic part of the gunner model. These randomness sources include the modelling error, the observation error, the neuromotor noise, etc. Mathema

  13. A Fuel-Sensitive Reduced-Order Model (ROM) for Piston Engine Scaling Analysis

    Science.gov (United States)

    2017-09-29

    single-cylinder moving piston case near top dead center at diesel - engine conditions. The ROM provides a real-time engineering analytical tool for liquid...length scaling that may be used toward optimizing engine performance . 15. SUBJECT TERMS reduced-order model, ROM, engine scaling, spray... diesel engine ................................... 20 Approved for public release; distribution is unlimited. 1 1. Introduction A central

  14. Modified reduced order observer based linear active disturbance rejection control for TITO systems.

    Science.gov (United States)

    Pawar, S N; Chile, R H; Patre, B M

    2017-11-01

    This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  15. Identification of reduced-order model for an aeroelastic system from flutter test data

    Directory of Open Access Journals (Sweden)

    Wei Tang

    2017-02-01

    Full Text Available Recently, flutter active control using linear parameter varying (LPV framework has attracted a lot of attention. LPV control synthesis usually generates controllers that are at least of the same order as the aeroelastic models. Therefore, the reduced-order model is required by synthesis for avoidance of large computation cost and high-order controller. This paper proposes a new procedure for generation of accurate reduced-order linear time-invariant (LTI models by using system identification from flutter testing data. The proposed approach is in two steps. The well-known poly-reference least squares complex frequency (p-LSCF algorithm is firstly employed for modal parameter identification from frequency response measurement. After parameter identification, the dominant physical modes are determined by clear stabilization diagrams and clustering technique. In the second step, with prior knowledge of physical poles, the improved frequency-domain maximum likelihood (ML estimator is presented for building accurate reduced-order model. Before ML estimation, an improved subspace identification considering the poles constraint is also proposed for initializing the iterative procedure. Finally, the performance of the proposed procedure is validated by real flight flutter test data.

  16. An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators.

    Science.gov (United States)

    Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Atherton, Derek P

    2016-05-01

    This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications. Copyright © 2016 ISA. All rights reserved.

  17. Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2011-01-01

    Full Text Available We have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs. An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.

  18. Diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ODEs

    Science.gov (United States)

    Ismail, Fudziah; Salih, Mohammed M.

    2014-06-01

    In this paper we derived a new diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ordinary differential equation. The stability polynomial of the method is obtained and the stability region is presented. A set of problems are tested upon and numerical results proved that the method is more accurate compared to other well known methods in the scientific literature.

  19. Reduced Order Model Implementation in the Risk-Informed Safety Margin Characterization Toolkit

    Energy Technology Data Exchange (ETDEWEB)

    Mandelli, Diego [Idaho National Lab. (INL), Idaho Falls, ID (United States); Smith, Curtis L. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Alfonsi, Andrea [Idaho National Lab. (INL), Idaho Falls, ID (United States); Rabiti, Cristian [Idaho National Lab. (INL), Idaho Falls, ID (United States); Cogliati, Joshua J. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Talbot, Paul W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Rinaldi, Ivan [Idaho National Lab. (INL), Idaho Falls, ID (United States); Maljovec, Dan [Idaho National Lab. (INL), Idaho Falls, ID (United States); Wang, Bei [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pascucci, Valerio [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhao, Haihua [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2015-09-01

    The RISMC project aims to develop new advanced simulation-based tools to perform Probabilistic Risk Analysis (PRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermo-hydraulic behavior of the reactor primary and secondary systems but also external events temporal evolution and components/system ageing. Thus, this is not only a multi-physics problem but also a multi-scale problem (both spatial, µm-mm-m, and temporal, ms-s-minutes-years). As part of the RISMC PRA approach, a large amount of computationally expensive simulation runs are required. An important aspect is that even though computational power is regularly growing, the overall computational cost of a RISMC analysis may be not viable for certain cases. A solution that is being evaluated is the use of reduce order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RICM analysis computational cost by decreasing the number of simulations runs to perform and employ surrogate models instead of the actual simulation codes. This report focuses on the use of reduced order modeling techniques that can be applied to any RISMC analysis to generate, analyze and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (µs instead of hours/days). We apply reduced order and surrogate modeling techniques to several RISMC types of analyses using RAVEN and RELAP-7 and show the advantages that can be gained.

  20. Weighted graph based ordering techniques for preconditioned conjugate gradient methods

    Science.gov (United States)

    Clift, Simon S.; Tang, Wei-Pai

    1994-01-01

    We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

  1. Ordered Boolean List (OBL): reducing the footprint for evaluating Boolean expressions.

    Science.gov (United States)

    Rossignac, Jaroslaw Jarek

    2011-09-01

    An Expanded Boolean Expression (EBE) does not contain any XOR or EQUAL operators. The occurrence of each variable is a different literal. We provide a linear time algorithm that converts an EBE of n literals into a logically equivalent Ordered Boolean List (OBL) and show how to use the OBL to evaluate the EBE in n steps and O(log log n) space, if the values of the literals are each read once in the order prescribed by the OBL. (An evaluation workspace of 5 bits suffices for all EBEs of up to six billion literals.) The primary application is the SIMD architecture, where the same EBE is evaluated in parallel for different input vectors when rendering solid models on the GPU directly from their Constructive Solid Geometry (CSG) representation. We compare OBL to the Reduced Ordered Binary Decision Diagram (ROBDD) and suggest possible applications of OBL to logic verification and to circuit design.

  2. Low-dimensional reduced-order models for statistical response and uncertainty quantification: Barotropic turbulence with topography

    Science.gov (United States)

    Qi, Di; Majda, Andrew J.

    2017-03-01

    A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty to changes in forcing in a barotropic turbulent system with topography involving interactions between small-scale motions and a large-scale mean flow. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model parameters. Statistical theories about a Gaussian invariant measure and the exact statistical energy equations are also developed for the truncated barotropic equations that can be used to improve the imperfect model prediction skill. A stringent paradigm model of 57 degrees of freedom is used to display the feasibility of the reduced-order methods. This simple model creates large-scale zonal mean flow shifting directions from westward to eastward jets with an abrupt change in amplitude when perturbations are applied, and prototype blocked and unblocked patterns can be generated in this simple model similar to the real natural system. Principal statistical responses in mean and variance can be captured by the reduced-order models with desirable accuracy and efficiency with only 3 resolved modes. An even more challenging regime with non-Gaussian equilibrium statistics using the fluctuation equations is also tested in the reduced-order models with accurate prediction using the first 5 resolved modes. These reduced-order models also show potential for uncertainty quantification and prediction in more complex realistic geophysical turbulent dynamical systems.

  3. Using the Electronic Medical Record to Reduce Unnecessary Ordering of Coagulation Studies for Patients with Chest Pain

    Directory of Open Access Journals (Sweden)

    Jeremiah S. Hinson

    2017-02-01

    Full Text Available Introduction: Our goal was to reduce ordering of coagulation studies in the emergency department (ED that have no added value for patients presenting with chest pain. We hypothesized this could be achieved via implementation of a stopgap measure in the electronic medical record (EMR. Methods: We used a pre and post quasi-experimental study design to evaluate the impact of an EMRbased intervention on coagulation study ordering for patients with chest pain. A simple interactive prompt was incorporated into the EMR of our ED that required clinicians to indicate whether patients were on anticoagulation therapy prior to completion of orders for coagulation studies. Coagulation order frequency was measured via detailed review of randomly sampled encounters during two-month periods before and after intervention. We classified existing orders as clinically indicated or non-value added. Order frequencies were calculated as percentages, and we assessed differences between groups by chi-square analysis. Results: Pre-intervention, 73.8% (76/103 of patients with chest pain had coagulation studies ordered, of which 67.1% (51/76 were non-value added. Post-intervention, 38.5% (40/104 of patients with chest pain had coagulation studies ordered, of which 60% (24/40 were non-value added. There was an absolute reduction of 35.3% (95% confidence interval [CI]: 22.7%, 48.0% in the total ordering of coagulation studies and 26.4% (95% CI: 13.8%, 39.0% in non-value added order placement. Conclusion: Simple EMR-based interactive prompts can serve as effective deterrents to indiscriminate ordering of diagnostic studies. [West J Emerg Med. 2017;18(2267-269.

  4. The discrete ordered median problem models and solution methods

    CERN Document Server

    Domínguez-Marín, Patricia

    2003-01-01

    This is the first book about the discrete ordered median problem (DOMP), which unifies many classical and new facility location problems Several exact and heuristic approaches are developed in this book in order to solve the DOMP Audience The book is suitable for researchers in location theory, and graduate students in combinatorial optimization

  5. The Development of High Order Methods for Real World Applications

    Science.gov (United States)

    2015-12-03

    three-stage 3rd order Runge-Kutta scheme Gottlieb and Shu [43] is used as the temporal discretization. Here we give a brief description. Rewrite the...Science and Engineering. Springer Berlin Heidelberg, pp. 47–95. [43] Gottlieb , S., Shu, C.-W., 2011. Strong stability-preserving high-order time dis

  6. Package Equivalent Reactor Networks as Reduced Order Models for Use with CAPE-OPEN Compliant Simulation

    Energy Technology Data Exchange (ETDEWEB)

    Meeks, E.; Chou, C. -P.; Garratt, T.

    2013-03-31

    Engineering simulations of coal gasifiers are typically performed using computational fluid dynamics (CFD) software, where a 3-D representation of the gasifier equipment is used to model the fluid flow in the gasifier and source terms from the coal gasification process are captured using discrete-phase model source terms. Simulations using this approach can be very time consuming, making it difficult to imbed such models into overall system simulations for plant design and optimization. For such system-level designs, process flowsheet software is typically used, such as Aspen Plus® [1], where each component where each component is modeled using a reduced-order model. For advanced power-generation systems, such as integrated gasifier/gas-turbine combined-cycle systems (IGCC), the critical components determining overall process efficiency and emissions are usually the gasifier and combustor. Providing more accurate and more computationally efficient reduced-order models for these components, then, enables much more effective plant-level design optimization and design for control. Based on the CHEMKIN-PRO and ENERGICO software, we have developed an automated methodology for generating an advanced form of reduced-order model for gasifiers and combustors. The reducedorder model offers representation of key unit operations in flowsheet simulations, while allowing simulation that is fast enough to be used in iterative flowsheet calculations. Using high-fidelity fluiddynamics models as input, Reaction Design’s ENERGICO® [2] software can automatically extract equivalent reactor networks (ERNs) from a CFD solution. For the advanced reduced-order concept, we introduce into the ERN a much more detailed kinetics model than can be included practically in the CFD simulation. The state-of-the-art chemistry solver technology within CHEMKIN-PRO allows that to be accomplished while still maintaining a very fast model turn-around time. In this way, the ERN becomes the basis for

  7. Adaptive Higher-Order Methods for Problems in Elastodynamics

    National Research Council Canada - National Science Library

    Oden, J

    2000-01-01

    .... Two significant classes of new methods were developed, analyzed, and implemented: 1) the so-called hp-Cloud Method, a variant of the meshfree methods built on partitions of unity generated by traditional finite elements...

  8. Multi-Level Reduced Order Modeling Equipped with Probabilistic Error Bounds

    Science.gov (United States)

    Abdo, Mohammad Gamal Mohammad Mostafa

    model parameters, responses, or state variables, are projected onto lower dimensional subspaces, referred to as the "active subspaces", which are selected to capture a user-defined portion of the snapshots variations. Once determined, the ROM model application involves constraining the variables to the active subspaces. In doing so, the contribution from the variables discarded components can be estimated using a fundamental theorem from random matrix theory which has its roots in Dixon's theory, developed in 1983. This theory was initially presented for linear matrix operators. The thesis extends this theorem's results to allow reduction of general smooth nonlinear operators. The result is an approach by which the adequacy of a given active subspace determined using a given set of snapshots, generated either using the full high fidelity model, or other models with lower fidelity, can be assessed, which provides insight to the analyst on the type of snapshots required to reach a reduction that can satisfy user-defined preset tolerance limits on the reduction errors. Reactor physics calculations are employed as a test bed for the proposed developments. The focus will be on reducing the effective dimensionality of the various data streams such as the cross-section data and the neutron flux. The developed methods will be applied to representative assembly level calculations, where the size of the cross-section and flux spaces are typically large, as required by downstream core calculations, in order to capture the broad range of conditions expected during reactor operation. (Abstract shortened by ProQuest.).

  9. Reduced Order Models for Decision Analysis and Upscaling of Aquifer Heterogeneity

    Science.gov (United States)

    Vesselinov, V. V.; O'Malley, D.; Alexandrov, B.; Moore, B.

    2016-12-01

    Model-based analyses such as uncertainty quantification, sensitivity analysis, and decision support using complex physics models with numerous model parameters and typically require a huge number of model evaluations (on order of 106). Furthermore, model simulations of complex physics may require substantial computational time. For example, accounting for simultaneously occurring physical processes such as fluid flow and biogeochemical reactions in heterogeneous porous medium may require days of wall-clock computational time. To address these issues, we have developed a methodology for reduced order modeling, which couples support vector regression (SVR), genetic algorithms (GA) and artificial and convolutional neural network (ANN/CNN). SVR is applied to predict the model behavior within prior uncertainty ranges associated with the model parameters. ANN and CNN procedures are applied to upscale heterogeneity of the porous medium. In the upscaling process, fine-scale high-resolution models of heterogeneity are applied to inform coarse-resolution models which have improved computational efficiency while capturing the impact of fine-scale effects at the course scale of interest. These techniques are tested independently on a series of synthetic problems. We also present a decision analysis related to contaminant remediation where the developed reduced order models are applied to reproduce groundwater flow and contaminant transport in a synthetic heterogeneous aquifer. The decision analysis is performed using Bayesian-Information-Gap Decision Theory which is implemented as part of the MADS framework (https://github.com/madsjulia/Mads.jl).

  10. Homotopy Continuation Method of Arbitrary Order of Convergence ...

    Indian Academy of Sciences (India)

    Most importantly, the method does not need any prior knowledge of the initial guess. A property which avoids the critical situations between divergent and very slow convergent solutions that may exist in other numerical methods which depend on initial guess. Computational Package for digital implementation of the method ...

  11. A Metric on the Space of kth-order reduced Phylogenetic Networks.

    Science.gov (United States)

    Wang, Juan; Guo, Maozu

    2017-06-09

    Phylogenetic networks can be used to describe the evolutionary history of species which experience a certain number of reticulate events, and represent conflicts in phylogenetic trees that may be due to inadequacies of the evolutionary model used in the construction of the trees. Measuring the dissimilarity between two phylogenetic networks is at the heart of our understanding of the evolutionary history of species. This paper proposes a new metric, i.e. kth-distance, for the space of kth-order reduced phylogenetic networks that can be calculated in polynomial time in the size of the compared networks.

  12. Computational Benefits Using an Advanced Concatenation Scheme Based on Reduced Order Models for RF Structures

    CERN Document Server

    Heller, Johann; Van Rienen, Ursula; 10.1016/j.phpro.2015.11.060

    2015-01-01

    The computation of electromagnetic fields and parameters derived thereof for lossless radio frequency (RF) structures filled with isotropic media is an important task for the design and operation of particle accelerators. Unfortunately, these computations are often highly demanding with regard to computational effort. The entire computational demand of the problem can be reduced using decomposition schemes in order to solve the field problems on standard workstations. This paper presents one of the first detailed comparisons between the recently proposed state-space concatenation approach (SSC) and a direct computation for an accelerator cavity with coupler-elements that break the rotational symmetry.

  13. Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

    Science.gov (United States)

    Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

    2017-03-01

    Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Methods to determine mechanical properties in order to grade roundwood

    NARCIS (Netherlands)

    Gard, W.F.; Vries, P. de; Lanvin, J.D.

    1998-01-01

    Roundwood as a construction material is becoming more and more interesting to users. The use of roundwood with small diameters is not optimised in terms of value. Using roundwood in construction increases the value of the wood and may open new opportunities for construction design. In order to use

  15. Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N A; Sjogreen, B

    2012-03-26

    second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a

  16. A reduced polynomial chaos expansion method for the stochastic ...

    Indian Academy of Sciences (India)

    The stochastic finite element analysis of elliptic type partial differential equations is considered. A reduced method of the spectral stochastic finite element method using polynomial chaos is proposed. The method is based on the spectral decomposition of the deterministic system matrix. The reduction is achieved by ...

  17. An efficient higher-order PML in WLP-FDTD method for time reversed wave simulation

    Science.gov (United States)

    Wei, Xiao-Kun; Shao, Wei; Ou, Haiyan; Wang, Bing-Zhong

    2016-09-01

    Derived from a stretched coordinate formulation, a higher-order complex frequency shifted (CFS) perfectly matched layer (PML) is proposed for the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials (WLPs). The higher-order PML is implemented with an auxiliary differential equation (ADE) approach. In order to further improve absorbing performance, the parameter values of stretching functions in the higher-order PML are optimized by the multi-objective genetic algorithm (MOGA). The optimal solutions can be chosen from the Pareto front for trading-off between two independent objectives. It is shown in a numerical test that the higher-order PML is efficient in terms of attenuating propagating waves and reducing late time reflections. Moreover, the higher-order PML can be placed very close to the wall when analyzing the channel characteristics of time reversal (TR) waves in a multipath indoor environment. Numerical examples of TR wave propagation demonstrate the availability of the proposed method.

  18. Some Uniform Order Block Methods for the Solution of First Order ...

    African Journals Online (AJOL)

    The block suggested approach is self-starting and produce parallel solution of the ordinary differential equations (ODES) which minimizes the cost of computation compared to other variants. Both block methods at k=3 and k=2 converges to the exact solutions with the two Numerical examples tested with this approach.

  19. A reduced-order representation of the Schrödinger equation

    Directory of Open Access Journals (Sweden)

    Ming-C. Cheng

    2016-09-01

    Full Text Available A reduced-order-based representation of the Schrödinger equation is investigated for electron wave functions in semiconductor nanostructures. In this representation, the Schrödinger equation is projected onto an eigenspace described by a small number of basis functions that are generated from the proper orthogonal decomposition (POD. The approach substantially reduces the numerical degrees of freedom (DOF’s needed to numerically solve the Schrödinger equation for the wave functions and eigenstate energies in a quantum structure and offers an accurate solution as detailed as the direct numerical simulation of the Schrödinger equation. To develop such an approach, numerical data accounting for parametric variations of the system are used to perform decomposition in order to generate the POD eigenvalues and eigenvectors for the system. This approach is applied to develop POD models for single and multiple quantum well structure. Errors resulting from the approach are examined in detail associated with the selected numerical DOF’s of the POD model and quality of data used for generation of the POD eigenvalues and basis functions. This study investigates the fundamental concepts of the POD approach to the Schrödinger equation and paves a way toward developing an efficient modeling methodology for large-scale multi-block simulation of quantum nanostructures.

  20. Reduced-order modellin for high-pressure transient flow of hydrogen-natural gas mixture

    Science.gov (United States)

    Agaie, Baba G.; Khan, Ilyas; Alshomrani, Ali Saleh; Alqahtani, Aisha M.

    2017-05-01

    In this paper the transient flow of hydrogen compressed-natural gas (HCNG) mixture which is also referred to as hydrogen-natural gas mixture in a pipeline is numerically computed using the reduced-order modelling technique. The study on transient conditions is important because the pipeline flows are normally in the unsteady state due to the sudden opening and closure of control valves, but most of the existing studies only analyse the flow in the steady-state conditions. The mathematical model consists in a set of non-linear conservation forms of partial differential equations. The objective of this paper is to improve the accuracy in the prediction of the HCNG transient flow parameters using the Reduced-Order Modelling (ROM). The ROM technique has been successfully used in single-gas and aerodynamic flow problems, the gas mixture has not been done using the ROM. The study is based on the velocity change created by the operation of the valves upstream and downstream the pipeline. Results on the flow characteristics, namely the pressure, density, celerity and mass flux are based on variations of the mixing ratio and valve reaction and actuation time; the ROM computational time cost advantage are also presented.

  1. Estimating unmeasured invasive EEG signals using a reduced-order observer.

    Science.gov (United States)

    Gunnarsdottir, Kristin M; Li, Adam; Bulacio, Juan; Gonzalez-Martinez, Jorge; Sarma, Sridevi V

    2017-07-01

    Epilepsy affects around 50 million people worldwide. Over 30% of patients are drug-resistant where the only treatment may be surgical resection of the epileptogenic zone (EZ), the region of the brain that generates seizures. Identification of the EZ is often based on invasive EEG recordings. As such, surgical outcome relies heavily on precise and dense placement of EEG electrodes into the brain. Despite large brain regions being removed, success rates barely reach 65%. This gives rise to the "missing electrode problem", where clinicians want to know what neural activity looks like between sparsely implanted electrodes. Solving this problem will enable more accurate localization of the EZ. In this paper, we demonstrate the first steps towards developing a computational platform to estimate neural activity at the "missing electrodes" using a reduced-order observer from control theory. Specifically, we constructed a sequence of discrete time Linear Time-Invariant (LTI) models using the available EEG data from two epilepsy patients. Then, we used the models to simulate EEG data and remove selected signals ("missing" states) from the simulated data set. Finally, we used a reduced-order observer to estimate the signals of these "missing" states and evaluated performance by comparing the observer estimates to the simulated EEG time series.

  2. Photoswitchable method for the ordered attachment of proteins to surfaces

    Science.gov (United States)

    Camarero, Julio A.; De Yoreo, James J.; Kwon, Youngeun

    2010-04-20

    Described herein is a method for the attachment of proteins to any solid support with control over the orientation of the attachment. The method is extremely efficient, not requiring the previous purification of the protein to be attached, and can be activated by UV-light. Spatially addressable arrays of multiple protein components can be generated by using standard photolithographic techniques.

  3. On the scaling of entropy viscosity in high order methods

    OpenAIRE

    Kornelus, Adeline; Appelö, Daniel

    2017-01-01

    In this work, we outline the entropy viscosity method and discuss how the choice of scaling influences the size of viscosity for a simple shock problem. We present examples to illustrate the performance of the entropy viscosity method under two distinct scalings.

  4. High order numerical methods for myxobacteria pattern formation

    OpenAIRE

    Glavan, Ana Maria

    2015-01-01

    Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal clock regulating them, and from contact signaling during bacterial collisions. Our main interest in this research is the numerical approximation with high order accuracy in space of the solutions of mathematical models proposed for myxobacteria rippling. We r...

  5. Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order

    KAUST Repository

    Hadjimichael, Yiannis

    2013-07-23

    We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.

  6. Reduced-order molecular-dynamics model for polystyrene by equivalent-structure coarse graining.

    Science.gov (United States)

    Srivastava, Anand; Ghosh, Somnath

    2012-02-01

    This paper develops a reduced-order equivalent-structure based model for polystyrene in a rigid body molecular dynamics framework. In general, a coarse-grained model for polymers is obtained by replacing a group of chemically connected atoms by an effective particle and deriving a coarse-grained interaction potential that reproduces the structure and dynamics at the desired length and time scale. In the current model, a detailed (~16 atoms) polystyrene monomer referred to as basic structural element (BSE) is replaced by an equivalent model with spherical backbone particles and an ellipsoidal particle that represents the styrene sidegroup. The governing principals of this homogenization is based on the mass, centroid, angular momentum, and energy equivalence between the detailed and the proposed reduced-order model. The bonded interactions parameters are readily obtained in the optimization of the equivalent structure from the detailed representation. The nonbonded interactions are treated separately. In order to capture the stereochemistry of the polystyrene molecule, an anisotropic biaxial nonbonded interaction potential function known as RE-squared (RE2) interaction has been used between pairs of ellipsoidal and/or spherical particles in the system. The required calibration of the nonbonded parameters is carried out by matching with the experimental density and the local structure using radial distribution function. This homogenization process scales up the modeling system size significantly as the higher frequency motions like -C-H- vibrations and sidegroup movements are suppressed. The accuracy of the model is established by comparing fine-scale simulation with explicit representations.

  7. Reduced-Order Models for Load Management in the Power Grid

    Science.gov (United States)

    Alizadeh, Mahnoosh

    In recent years, considerable research efforts have been directed towards designing control schemes that can leverage the inherent flexibility of electricity demand that is not tapped into in today's electricity markets. It is expected that these control schemes will be carried out by for-profit entities referred to as aggregators that operate at the edge of the power grid network. While the aggregator control problem is receiving much attention, more high-level questions of how these aggregators should plan their market participation, interact with the main grid and with each other, remain rather understudied. Answering these questions requires a large-scale model for the aggregate flexibility that can be harnessed from the a population of customers, particularly for residences and small businesses. The contribution of this thesis towards this goal is divided into three parts: In Chapter 3, a reduced-order model for a large population of heterogeneous appliances is provided by clustering load profiles that share similar degrees of freedom together. The use of such reduced-order model for system planning and optimal market decision making requires a foresighted approximation of the number of appliances that will join each cluster. Thus, Chapter 4 provides a systematic framework to generate such forecasts for the case of Electric Vehicles, based on real-world battery charging data. While these two chapters set aside the economic side that is naturally involved with participation in demand response programs and mainly focus on the control problem, Chapter 5 is dedicated to the study of optimal pricing mechanisms in order to recruit heterogeneous customers in a demand response program in which an aggregator can directly manage their appliances' load under their specified preferences. Prices are proportional to the wholesale market savings that can result from each recruitment event.

  8. Reduced Order Modeling for Prediction and Control of Large-Scale Systems.

    Energy Technology Data Exchange (ETDEWEB)

    Kalashnikova, Irina [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Mathematics; Arunajatesan, Srinivasan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Aerosciences Dept.; Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Aerosciences Dept.; van Bloemen Waanders, Bart Gustaaf [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Uncertainty Quantification and Optimization Dept.; Fike, Jeffrey A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Component Science and Mechanics Dept.

    2014-05-01

    This report describes work performed from June 2012 through May 2014 as a part of a Sandia Early Career Laboratory Directed Research and Development (LDRD) project led by the first author. The objective of the project is to investigate methods for building stable and efficient proper orthogonal decomposition (POD)/Galerkin reduced order models (ROMs): models derived from a sequence of high-fidelity simulations but having a much lower computational cost. Since they are, by construction, small and fast, ROMs can enable real-time simulations of complex systems for onthe- spot analysis, control and decision-making in the presence of uncertainty. Of particular interest to Sandia is the use of ROMs for the quantification of the compressible captive-carry environment, simulated for the design and qualification of nuclear weapons systems. It is an unfortunate reality that many ROM techniques are computationally intractable or lack an a priori stability guarantee for compressible flows. For this reason, this LDRD project focuses on the development of techniques for building provably stable projection-based ROMs. Model reduction approaches based on continuous as well as discrete projection are considered. In the first part of this report, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. The key idea is to apply a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. It is shown that, for many PDE systems including the linearized compressible Euler and linearized compressible Navier-Stokes equations, the desired transformation is induced by a special inner product, termed the “symmetry inner product”. Attention is then turned to nonlinear conservation laws. A new transformation and corresponding energy-based inner product for the full nonlinear compressible Navier

  9. Second derivative multistep method for solving first-order ordinary differential equations

    Science.gov (United States)

    Turki, Mohammed Yousif; Ismail, Fudziah; Senu, Norazak; Ibrahim, Zarina Bibi

    2016-06-01

    In this paper, a new second derivative multistep method was constructed to solve first order ordinary differential equations (ODEs). In particular, we used the new method as a corrector method and 5-steps Adam's Bashforth method as a predictor method to solve first order (ODEs). Numerical results were compared with the existing methods which clearly showed the efficiency of the new method.

  10. Nonlinear Parameter-Varying AeroServoElastic Reduced Order Model for Aerostructural Sensing and Control Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...

  11. A Reduced Order Model of the Linearized Incompressible Navier-Strokes Equations for the Sensor/Actuator Placement Problem

    Science.gov (United States)

    Allan, Brian G.

    2000-01-01

    A reduced order modeling approach of the Navier-Stokes equations is presented for the design of a distributed optimal feedback kernel. This approach is based oil a Krylov subspace method where significant modes of the flow are captured in the model This model is then used in all optimal feedback control design where sensing and actuation is performed oil tile entire flow field. This control design approach yields all optimal feedback kernel which provides insight into the placement of sensors and actuators in the flow field. As all evaluation of this approach, a two-dimensional shear layer and driven cavity flow are investigated.

  12. Origin of how steam rockets can reduce space transport cost by orders of magnitude

    Science.gov (United States)

    Zuppero, Anthony; Larson, Thomas K.; Schnitzler, Bruce G.; Werner, James E.; Rice, John W.; Hill, Thomas J.; Richins, William D.; Parlier, Lynn

    1999-01-01

    A brief sketch shows the origin of why and how thermal rocket propulsion has the unique potential to dramatically reduce the cost of space transportation for most inner solar system missions of interest. Orders of magnitude reduction in cost are apparently possible when compared to all processes requiring electrolysis for the production of rocket fuels or propellants and to all electric propulsion systems. An order of magnitude advantage can be attributed to rocket propellant tank factors associated with storing water propellant, compared to cryogenic liquids. An order of magnitude can also be attributed to the simplicity of the extraction and processing of ice on the lunar surface, into an easily stored, non-cryogenic rocket propellant (water). A nuclear heated thermal rocket can deliver thousands of times its mass to Low Earth Orbit from the Lunar surface, providing the equivalent to orders of magnitude drop in launch cost for mass in Earth orbit. Mass includes water ice. These cost reductions depend (exponentially) on the mission delta-v requirements being less than about 6 km/s, or about 3 times the specific velocity of steam rockets (2 km/s, from Isp 200 sec). Such missions include: from the lunar surface to Low Lunar Orbit, (LLO), from LLO to lunar escape, from Low Earth Orbit (LEO) to Geosynchronous Orbit (GEO), from LEO to Earth Escape, from LEO to Mars Transfer Orbit, from LLO to GEO, missions returning payloads from about 10% of the periodic comets using propulsive capture to orbits around Earth itself, and fast, 100 day missions from Lunar Escape to Mars. All the assertions depend entirely and completely on the existence of abundant, nearly pure ice at the permanently dark North and South Poles of the Moon.

  13. Origin of how steam rockets can reduce space transport cost by orders of magnitude

    Energy Technology Data Exchange (ETDEWEB)

    Zuppero, A.; Larson, T.K.; Schnitzler, B.G.; Rice, J.W.; Hill, T.J.; Richins, W.D.; Parlier, L. [Lockheed Martin Idaho Technologies, Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415 (United States); Werner, J.E. [Department of Energy, Idaho Field Office, Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415 (United States)

    1999-01-01

    A brief sketch shows the origin of why and how thermal rocket propulsion has the unique potential to dramatically reduce the cost of space transportation for most inner solar system missions of interest. Orders of magnitude reduction in cost are apparently possible when compared to all processes requiring electrolysis for the production of rocket fuels or propellants and to all electric propulsion systems. An order of magnitude advantage can be attributed to rocket propellant tank factors associated with storing water propellant, compared to cryogenic liquids. An order of magnitude can also be attributed to the simplicity of the extraction and processing of ice on the lunar surface, into an easily stored, non-cryogenic rocket propellant (water). A nuclear heated thermal rocket can deliver thousands of times its mass to Low Earth Orbit from the Lunar surface, providing the equivalent to orders of magnitude drop in launch cost for mass in Earth orbit. Mass includes water ice. These cost reductions depend (exponentially) on the mission delta-v requirements being less than about 6 km/s, or about 3 times the specific velocity of steam rockets (2 km/s, from Isp 200 sec). Such missions include: from the lunar surface to Low Lunar Orbit, (LLO), from LLO to lunar escape, from Low Earth Orbit (LEO) to Geosynchronous Orbit (GEO), from LEO to Earth Escape, from LEO to Mars Transfer Orbit, from LLO to GEO, missions returning payloads from about 10{percent} of the periodic comets using propulsive capture to orbits around Earth itself, and fast, 100 day missions from Lunar Escape to Mars. All the assertions depend entirely and completely on the existence of abundant, nearly pure ice at the permanently dark North and South Poles of the Moon. {copyright} {ital 1999 American Institute of Physics.}

  14. Implicit sampling combined with reduced order modeling for the inversion of vadose zone hydrological data

    Science.gov (United States)

    Liu, Yaning; Pau, George Shu Heng; Finsterle, Stefan

    2017-11-01

    Bayesian inverse modeling techniques are computationally expensive because many forward simulations are needed when sampling the posterior distribution of the parameters. In this paper, we combine the implicit sampling method and generalized polynomial chaos expansion (gPCE) to significantly reduce the computational cost of performing Bayesian inverse modeling. There are three steps in this approach: (1) find the maximizer of the likelihood function using deterministic approaches; (2) construct a gPCE-based surrogate model using the results from a limited number of forward simulations; and (3) efficiently sample the posterior distribution of the parameters using implicit sampling method. The cost of constructing the gPCE-based surrogate model is further decreased by using sparse Bayesian learning to reduce the number of gPCE coefficients that have to be determined. We demonstrate the approach for a synthetic ponded infiltration experiment simulated with TOUGH2. The surrogate model is highly accurate with mean relative error that is method or a Markov chain Monte Carlo method utilizing the full model.

  15. Reduced-Order Monte Carlo Modeling of Radiation Transport in Random Media

    Science.gov (United States)

    Olson, Aaron

    The ability to perform radiation transport computations in stochastic media is essential for predictive capabilities in applications such as weather modeling, radiation shielding involving non-homogeneous materials, atmospheric radiation transport computations, and transport in plasma-air structures. Due to the random nature of such media, it is often not clear how to model or otherwise compute on many forms of stochastic media. Several approaches to evaluation of transport quantities for some stochastic media exist, though such approaches often either yield considerable error or are quite computationally expensive. We model stochastic media using the Karhunen-Loeve (KL) expansion, seek to improve efficiency through use of stochastic collocation (SC), and provide higher-order information of output values using the polynomial chaos expansion (PCE). We study and demonstrate method convergence and apply the new methods to both spatially continuous and spatially discontinuous stochastic media. New methods are shown to produce accurate solutions for reasonable computational cost for several problem when compared with existing solution methods. Spatially random media are modeled using transformations of the Gaussian-distributed KL expansion-continuous random media with a lognormal transformation and discontinuous random media with a Nataf transformation. Each transformation preserves second-order statistics for the quantity-atom density or material index, respectively-being modeled. The Nystrom method facilitates numerical solution of the KL eigenvalues and eigenvectors, and a variety of methods are investigated for sampling KL eigenfunctions as a function of solved eigenvectors. The infinite KL expansion is truncated to a finite number of terms each containing a random variable, and material realizations are created by either randomly or deterministically sampling from the random variables. Deterministic sampling is performed with either isotropic or anisotropic

  16. High-order adaptive methods for parabolic systems

    Science.gov (United States)

    Adjerid, S.; Flaherty, J. E.; Moore, P. K.; Wang, Y. J.

    1992-11-01

    We consider the adaptive solution of parabolic partial differential systems in one and two space dimensions by finite element procedures that automatically refine and coarsen computational meshes, vary the degree of the piecewise polynomial basis and, in one dimension, move the computational mesh. Two-dimensional meshes of triangular, quadrilateral, or a mixture of triangular and quadrilateral elements are generated using a finite quadtree procedure that is also used for data management. A posteriori estimates, used to control adaptive enrichment, are generated from the hierarchical polynomial basis. Temporal integration, within a method-of-lines framework, uses either backward difference methods or a variant of the singly implicit Runge-Kutta (SIRK) methods. A high-level user interface facilitates use of the adaptive software.

  17. Homotopy Continuation Method of Arbitrary Order of Convergence ...

    Indian Academy of Sciences (India)

    putational Package for digital implementation of the method is given and is applied to many case studies. Key words. Homotopy method—hyperbolic Kepler's equation—initial ..... from this inequality and the known equation tanh. (. G. 2. ) = √ e − 1 e + 1 tan. ( ν. 2. ) , we get using equation (1.1) Table 1, which shows some ...

  18. Fourth order compact finite difference method for solving singularly ...

    African Journals Online (AJOL)

    A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...

  19. Fourth Order Compact Finite Difference Method for Solving ...

    African Journals Online (AJOL)

    fasika

    A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...

  20. Qualitatively stability of nonstandard 2-stage explicit Runge-Kutta methods of order two

    Science.gov (United States)

    Khalsaraei, M. M.; Khodadosti, F.

    2016-02-01

    When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Nonstandard finite differences (NSFDs) schemes can improve the accuracy and reduce computational costs of traditional finite difference schemes. In addition NSFDs produce numerical solutions which also exhibit essential properties of solution. In this paper, a class of nonstandard 2-stage Runge-Kutta methods of order two (we call it nonstandard RK2) is considered. The preservation of some qualitative properties by this class of methods are discussed. In order to illustrate our results, we provide some numerical examples.

  1. Selected methods for reducing hazards of spontaneous coal oxidation

    Energy Technology Data Exchange (ETDEWEB)

    Skalicka, J.; Vydra, J.

    1988-01-01

    Discusses methods of preventing coal spontaneous combustion in underground mines. Injection methods and the spraying of inhibiting compounds are comparatively evaluated: injection is aimed at reducing air flow from a ventilation system to a center of spontaneous combustion; spraying reduces the active surface of coal exposed to oxidation. Injection of polyurethane foam and urea-formaldehyde foam is described. Spraying coal with the following compounds is discussed: a mixture of bentonite with calcium chloride, a mixture of water solution of water glass and limestone dust, the Plamor mixture developed by the Bratislava Technical University, the Neoxiplast mixture on the basis of acrylates. Combined use of injection methods, spraying inhibiting mixtures and reducing air access is discussed. Effects of mining schemes without leaving support pillars and reducing coal losses on hazards of coal spontaneous combustion are discussed. 2 refs.

  2. Nonlinear Acoustic Response of an Aircraft Fuselage Sidewall Structure by a Reduced-Order Analysis

    Science.gov (United States)

    Przekop, Adam; Rizzi, Stephen A.; Groen, David S.

    2006-01-01

    A reduced-order nonlinear analysis of a structurally complex aircraft fuselage sidewall panel is undertaken to explore issues associated with application of such analyses to practical structures. Of primary interest is the trade-off between computational efficiency and accuracy. An approach to modal basis selection is offered based upon the modal participation in the linear regime. The nonlinear static response to a uniform pressure loading and nonlinear random response to a uniformly distributed acoustic loading are computed. Comparisons of the static response with a nonlinear static solution in physical degrees-of-freedom demonstrate the efficacy of the approach taken for modal basis selection. Changes in the modal participation as a function of static and random loading levels suggest a means for improvement in the basis selection.

  3. Fast and efficient evaluation of gravitational waveforms via reduced-order spline interpolation

    CERN Document Server

    Galley, Chad R

    2016-01-01

    Numerical simulations of merging black hole binaries produce the most accurate gravitational waveforms. The availability of hundreds of these numerical relativity (NR) waveforms, often containing many higher spherical harmonic modes, allows one to study many aspects of gravitational waves. Amongst these are the response of data analysis pipelines, the calibration of semi-analytical models, the building of reduced-order surrogates, the estimation of the parameters of detected gravitational waves, and the composition of public catalogs of NR waveform data. The large number of generated NR waveforms consequently requires efficient data storage and handling, especially since many more waveforms will be generated at an increased rate in the forthcoming years. In addition, gravitational wave data analyses often require the NR waveforms to be interpolated and uniformly resampled at high sampling rates. Previously, this resulted in very large data files (up to $\\sim$ several GB) in memory-intensive operations, which ...

  4. Physically-Based Reduced Order Modelling of a Uni-Axial Polysilicon MEMS Accelerometer

    Science.gov (United States)

    Ghisi, Aldo; Mariani, Stefano; Corigliano, Alberto; Zerbini, Sarah

    2012-01-01

    In this paper, the mechanical response of a commercial off-the-shelf, uni-axial polysilicon MEMS accelerometer subject to drops is numerically investigated. To speed up the calculations, a simplified physically-based (beams and plate), two degrees of freedom model of the movable parts of the sensor is adopted. The capability and the accuracy of the model are assessed against three-dimensional finite element simulations, and against outcomes of experiments on instrumented samples. It is shown that the reduced order model provides accurate outcomes as for the system dynamics. To also get rather accurate results in terms of stress fields within regions that are prone to fail upon high-g shocks, a correction factor is proposed by accounting for the local stress amplification induced by re-entrant corners. PMID:23202031

  5. Physically-Based Reduced Order Modelling of a Uni-Axial Polysilicon MEMS Accelerometer

    Directory of Open Access Journals (Sweden)

    Sarah Zerbini

    2012-10-01

    Full Text Available In this paper, the mechanical response of a commercial off-the-shelf, uni-axial polysilicon MEMS accelerometer subject to drops is numerically investigated. To speed up the calculations, a simplified physically-based (beams and plate, two degrees of freedom model of the movable parts of the sensor is adopted. The capability and the accuracy of the model are assessed against three-dimensional finite element simulations, and against outcomes of experiments on instrumented samples. It is shown that the reduced order model provides accurate outcomes as for the system dynamics. To also get rather accurate results in terms of stress fields within regions that are prone to fail upon high-g shocks, a correction factor is proposed by accounting for the local stress amplification induced by re-entrant corners.

  6. A reduced order model to analytically infer atmospheric CO2 concentration from stomatal and climate data

    Science.gov (United States)

    Konrad, Wilfried; Katul, Gabriel; Roth-Nebelsick, Anita; Grein, Michaela

    2017-06-01

    To address questions related to the acceleration or deceleration of the global hydrological cycle or links between the carbon and water cycles over land, reliable data for past climatic conditions based on proxies are required. In particular, the reconstruction of palaeoatmospheric CO2 content (Ca) is needed to assist the separation of natural from anthropogenic Ca variability and to explore phase relations between Ca and air temperature Ta time series. Both Ta and Ca are needed to fingerprint anthropogenic signatures in vapor pressure deficit, a major driver used to explain acceleration or deceleration phases in the global hydrological cycle. Current approaches to Ca reconstruction rely on a robust inverse correlation between measured stomatal density in leaves (ν) of many plant taxa and Ca. There are two methods that exploit this correlation: The first uses calibration curves obtained from extant species assumed to represent the fossil taxa, thereby restricting the suitable taxa to those existing today. The second is a hybrid eco-hydrological/physiological approach that determines Ca with the aid of systems of equations based on quasi-instantaneous leaf-gas exchange theories and fossil stomatal data collected along with other measured leaf anatomical traits and parameters. In this contribution, a reduced order model (ROM) is proposed that derives Ca from a single equation incorporating the aforementioned stomatal data, basic climate (e.g. temperature), estimated biochemical parameters of assimilation and isotope data. The usage of the ROM is then illustrated by applying it to isotopic and anatomical measurements from three extant species. The ROM derivation is based on a balance between the biochemical demand and atmospheric supply of CO2 that leads to an explicit expression linking stomatal conductance to internal CO2 concentration (Ci) and Ca. The resulting expression of stomatal conductance from the carbon economy of the leaf is then equated to another

  7. Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

    Energy Technology Data Exchange (ETDEWEB)

    Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.u, E-mail: rsuarez@ucu.edu.u [Universidad Catolica del Uruguay, Montevideo (Uruguay). Fac. de Ingenieria y Tecnologias. Dept. de Matematica; Ministerio de Industria, Energia y Mineria, Montevideo (Uruguay). Direccion General de Secretaria

    2011-07-01

    One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)

  8. Reducing vibration transfer from power plants by active methods

    Science.gov (United States)

    Kiryukhin, A. V.; Milman, O. O.; Ptakhin, A. V.

    2017-12-01

    The possibility of applying the methods of active damping of vibration and pressure pulsations for reducing their transfer from power plants into the environment, the seating, and the industrial premises are considered. The results of experimental works implemented by the authors on the active broadband damping of vibration and dynamic forces after shock-absorption up to 15 dB in the frequency band up to 150 Hz, of water pressure pulsations in the pipeline up to 20 dB in the frequency band up to 600 Hz, and of spatial low-frequency air noise indoors of a diesel generator at discrete frequency up to 20 dB are presented. It is shown that a reduction of vibration transfer through a vibration-isolating junction (expansion joints) of pipelines with liquid is the most complicated and has hardly been developed so far. This problem is essential for vibration isolation of power equipment from the seating and the environment through pipelines with water and steam in the power and transport engineering, shipbuilding, and in oil and gas pipelines in pumping stations. For improving efficiency, reducing the energy consumption, and decreasing the overall dimensions of equipment, it is advisable to combine the work of an active system with passive damping means, the use of which is not always sufficient. The executive component of the systems of active damping should be placed behind the vibration isolators (expansion joints). It is shown that the existence of working medium and connection of vibration with pressure pulsations in existing designs of pipeline expansion joints lead to growth of vibration stiffness of the expansion joint with the environment by two and more orders as compared with the static stiffness and makes difficulties for using the active methods. For active damping of vibration transfer through expansion joints of pipelines with a liquid, it is necessary to develop expansion joint structures with minimal connection of vibrations and pulsations and minimal

  9. On High-Order Upwind Methods for Advection

    Science.gov (United States)

    Huynh, Hung T.

    2017-01-01

    Scheme III (piecewise linear) and V (piecewise parabolic) of Van Leer are shown to yield identical solutions provided the initial conditions are chosen in an appropriate manner. This result is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The result also shows a key connection between the approaches of discontinuous and continuous representations.

  10. Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes.

    Science.gov (United States)

    Marchesseau, S; Delingette, H; Sermesant, M; Cabrera-Lozoya, R; Tobon-Gomez, C; Moireau, P; Figueras i Ventura, R M; Lekadir, K; Hernandez, A; Garreau, M; Donal, E; Leclercq, C; Duckett, S G; Rhode, K; Rinaldi, C A; Frangi, A F; Razavi, R; Chapelle, D; Ayache, N

    2013-10-01

    Patient-specific cardiac modeling can help in understanding pathophysiology and therapy planning. However it requires to combine functional and anatomical data in order to build accurate models and to personalize the model geometry, kinematics, electrophysiology and mechanics. Personalizing the electromechanical coupling from medical images is a challenging task. We use the Bestel-Clément-Sorine (BCS) electromechanical model of the heart, which provides reasonable accuracy with a reasonable number of parameters (14 for each ventricle) compared to the available clinical data at the organ level. We propose a personalization strategy from cine MRI data in two steps. We first estimate global parameters with an automatic calibration algorithm based on the Unscented Transform which allows to initialize the parameters while matching the volume and pressure curves. In a second step we locally personalize the contractilities of all AHA (American Heart Association) zones of the left ventricle using the reduced order unscented Kalman filtering on Regional Volumes. This personalization strategy was validated synthetically and tested successfully on eight healthy and three pathological cases. Copyright © 2013 Elsevier B.V. All rights reserved.

  11. A high order regularisation method for solving the Poisson equation and selected applications using vortex methods

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm

    A regularisation method for solving the Poisson equation using Green’s functions is presented.The method is shown to obtain a convergence rate which corresponds to the design of the regularised Green’s function and a spectral-like convergence rate is obtained using a spectrally ideal regularisation....... It is shown that the regularised Poisson solver can be extended to handle mixed periodic and free-space boundary conditions. This is done by solving the equation spectrally in the periodic directions which yields a modified Helmholtz equation for the free-space directions which in turn is solved by deriving...... the appropriate regularised Green’s functions. Using an analogy to the particle-particle particle-mesh method, a framework for calculating multi-resolution solutions using local refinement patches is presented. The regularised Poisson solver is shown to maintain a high order converging solution for different...

  12. A non-linear reduced order methodology applicable to boiling water reactor stability analysis

    Energy Technology Data Exchange (ETDEWEB)

    Prill, Dennis Paul

    2013-12-06

    Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

  13. Lattice Boltzmann flow simulations with applications of reduced order modeling techniques

    KAUST Repository

    Brown, Donald

    2014-01-01

    With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.

  14. The solution of Riccati type differential equation by means of variable order variable stepsize backward difference method

    Directory of Open Access Journals (Sweden)

    Ahmad Fadly Nurullah b. Rasedee

    2016-06-01

    Full Text Available In this article a variable order variable step size technique in backwards difference form is used to solve nonlinear Riccati differential equations directly. The method proposed requires calculating the integration coefficients only once at the beginning, in contrast to current divided difference methods which calculate integration coefficients at every step change. Numerical results will show that the variable order variable step size technique reduces computational cost in terms of total steps without effecting accuracy.

  15. A second-order unconstrained optimization method for canonical-ensemble density-functional methods.

    Science.gov (United States)

    Nygaard, Cecilie R; Olsen, Jeppe

    2013-03-07

    A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.

  16. Calibration of aero-structural reduced order models using full-field experimental measurements

    Science.gov (United States)

    Perez, R.; Bartram, G.; Beberniss, T.; Wiebe, R.; Spottswood, S. M.

    2017-03-01

    The structural response of hypersonic aircraft panels is a multi-disciplinary problem, where the nonlinear structural dynamics, aerodynamics, and heat transfer models are coupled. A clear understanding of the impact of high-speed flow effects on the structural response, and the potential influence of the structure on the local environment, is needed in order to prevent the design of overly-conservative structures, a common problem in past hypersonic programs. The current work investigates these challenges from a structures perspective. To this end, the first part of this investigation looks at the modeling of the response of a rectangular panel to an external heating source (thermo-structural coupling) where the temperature effect on the structure is obtained from forward looking infrared (FLIR) measurements and the displacement via 3D-digital image correlation (DIC). The second part of the study uses data from a previous series of wind-tunnel experiments, performed to investigate the response of a compliant panel to the effects of high-speed flow, to train a pressure surrogate model. In this case, the panel aero-loading is obtained from fast-response pressure sensitive paint (PSP) measurements, both directly and from the pressure surrogate model. The result of this investigation is the use of full-field experimental measurements to update the structural model and train a computational efficient model of the loading environment. The use of reduced order models, informed by these full-field physical measurements, is a significant step toward the development of accurate simulation models of complex structures that are computationally tractable.

  17. Reduced-Order Biogeochemical Flux Model for High-Resolution Multi-Scale Biophysical Simulations

    Science.gov (United States)

    Smith, Katherine; Hamlington, Peter; Pinardi, Nadia; Zavatarelli, Marco

    2017-04-01

    Biogeochemical tracers and their interactions with upper ocean physical processes such as submesoscale circulations and small-scale turbulence are critical for understanding the role of the ocean in the global carbon cycle. These interactions can cause small-scale spatial and temporal heterogeneity in tracer distributions that can, in turn, greatly affect carbon exchange rates between the atmosphere and interior ocean. For this reason, it is important to take into account small-scale biophysical interactions when modeling the global carbon cycle. However, explicitly resolving these interactions in an earth system model (ESM) is currently infeasible due to the enormous associated computational cost. As a result, understanding and subsequently parameterizing how these small-scale heterogeneous distributions develop and how they relate to larger resolved scales is critical for obtaining improved predictions of carbon exchange rates in ESMs. In order to address this need, we have developed the reduced-order, 17 state variable Biogeochemical Flux Model (BFM-17) that follows the chemical functional group approach, which allows for non-Redfield stoichiometric ratios and the exchange of matter through units of carbon, nitrate, and phosphate. This model captures the behavior of open-ocean biogeochemical systems without substantially increasing computational cost, thus allowing the model to be combined with computationally-intensive, fully three-dimensional, non-hydrostatic large eddy simulations (LES). In this talk, we couple BFM-17 with the Princeton Ocean Model and show good agreement between predicted monthly-averaged results and Bermuda testbed area field data (including the Bermuda-Atlantic Time-series Study and Bermuda Testbed Mooring). Through these tests, we demonstrate the capability of BFM-17 to accurately model open-ocean biochemistry. Additionally, we discuss the use of BFM-17 within a multi-scale LES framework and outline how this will further our understanding

  18. High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2012-09-20

    The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered

  19. Methods of extending lower order problems to higher order problems in the context of smallest eigenvalue comparisons

    Directory of Open Access Journals (Sweden)

    J. Neugebauer

    2011-12-01

    Full Text Available The theory of $u_{0}$-positive operators with respect to a cone in a Banach space is applied to the linear differential equations $u^{(4}+\\lambda_{1} p(xu=0$ and $u^{(4}+\\lambda_{2} q(xu=0$, $0\\leq x\\leq 1$, with each satisfying the boundary conditions $u(0=u^{\\prime}(r=u^{\\prime \\prime}(r=u^{\\prime \\prime \\prime}(1=0$, $0order problem using two different methods. One method involves finding sign conditions for the Green's function for $-u^{(n}=0$ satisfying the higher order boundary conditions, and the other involves making a substitution that allows us to work with a variation of the fourth order problem.

  20. Assessment of probability density function based on POD reduced-order model for ensemble-based data assimilation

    Energy Technology Data Exchange (ETDEWEB)

    Kikuchi, Ryota; Misaka, Takashi; Obayashi, Shigeru, E-mail: rkikuchi@edge.ifs.tohoku.ac.jp [Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577 (Japan)

    2015-10-15

    An integrated method of a proper orthogonal decomposition based reduced-order model (ROM) and data assimilation is proposed for the real-time prediction of an unsteady flow field. In this paper, a particle filter (PF) and an ensemble Kalman filter (EnKF) are compared for data assimilation and the difference in the predicted flow fields is evaluated focusing on the probability density function (PDF) of the model variables. The proposed method is demonstrated using identical twin experiments of an unsteady flow field around a circular cylinder at the Reynolds number of 1000. The PF and EnKF are employed to estimate temporal coefficients of the ROM based on the observed velocity components in the wake of the circular cylinder. The prediction accuracy of ROM-PF is significantly better than that of ROM-EnKF due to the flexibility of PF for representing a PDF compared to EnKF. Furthermore, the proposed method reproduces the unsteady flow field several orders faster than the reference numerical simulation based on the Navier–Stokes equations. (paper)

  1. Reducing waste generation and radiation exposure by analytical method modification

    Energy Technology Data Exchange (ETDEWEB)

    Ekechukwu, A.A.

    1996-10-01

    The primary goal of an analytical support laboratory has traditionally been to provide accurate data in a timely and cost effective fashion. Added to this goal is now the need to provide the same high quality data while generating as little waste as possible. At the Savannah River Technology Center (SRTC), we have modified and reengineered several methods to decrease generated waste and hence reduce radiation exposure. These method changes involved improving detection limits (which decreased the amount of sample required for analysis), decreasing reaction and analysis time, decreasing the size of experimental set-ups, recycling spent solvent and reagents, and replacing some methods. These changes had the additional benefits of reducing employee radiation exposure and exposure to hazardous chemicals. In all cases, the precision, accuracy, and detection limits were equal to or better than the replaced method. Most of the changes required little or no expenditure of funds. This paper describes these changes and discusses some of their applications.

  2. Semi-automatic reduced order models from expert-defined transients

    Science.gov (United States)

    Class, Andreas; Prill, Dennis

    2013-11-01

    Boiling water reactors (BWRs) not only show growing power oscillations at high-power low-flow conditions but also amplitude limited oscillations with temporal flow reversal. Methodologies, applicable in the non-linear regime, allow insight into the physical mechanisms behind BWR dynamics. The proposed methodology exploits relevant simulation data computed by an expert choice of transient. Proper orthogonal modes are extracted and serve as Ansatz functions within a spectral approach, yielding a reduced order model (ROM). Required steps to achieve reliable and numerical stable ROMs are discussed, i.e. mean value handling, inner product choice, variational formulation of derivatives and boundary conditions.Two strongly non-linear systems are analyzed: The tubular reactor, including Arrhenius reaction and heat losses, yields sensitive response on transient boundary conditions. A simple natural convection loop is considered due to its dynamical similarities to BWRs. It exhibits bifurcations resulting in limit cycles. The presented POD-ROM methodology reproduces dynamics with a small number of spectral modes and reaches appreciable accuracy. Funded by AREVA GmbH.

  3. A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound

    Science.gov (United States)

    Kreider, Wayne; Crum, Lawrence A.; Bailey, Michael R.; Sapozhnikov, Oleg A.

    2011-01-01

    Cavitation often occurs in therapeutic applications of medical ultrasound such as shock-wave lithotripsy (SWL) and high-intensity focused ultrasound (HIFU). Because cavitation bubbles can affect an intended treatment, it is important to understand the dynamics of bubbles in this context. The relevant context includes very high acoustic pressures and frequencies as well as elevated temperatures. Relative to much of the prior research on cavitation and bubble dynamics, such conditions are unique. To address the relevant physics, a reduced-order model of a single, spherical bubble is proposed that incorporates phase change at the liquid-gas interface as well as heat and mass transport in both phases. Based on the energy lost during the inertial collapse and rebound of a millimeter-sized bubble, experimental observations were used to tune and test model predictions. In addition, benchmarks from the published literature were used to assess various aspects of model performance. Benchmark comparisons demonstrate that the model captures the basic physics of phase change and diffusive transport, while it is quantitatively sensitive to specific model assumptions and implementation details. Given its performance and numerical stability, the model can be used to explore bubble behaviors across a broad parameter space relevant to therapeutic ultrasound. PMID:22088026

  4. Energy balance and mass conservation in reduced order models of fluid flows

    Science.gov (United States)

    Mohebujjaman, Muhammad; Rebholz, Leo G.; Xie, Xuping; Iliescu, Traian

    2017-10-01

    In this paper, we investigate theoretically and computationally the conservation properties of reduced order models (ROMs) for fluid flows. Specifically, we investigate whether the ROMs satisfy the same (or similar) energy balance and mass conservation as those satisfied by the Navier-Stokes equations. All of our theoretical findings are illustrated and tested in numerical simulations of a 2D flow past a circular cylinder at a Reynolds number Re = 100. First, we investigate the ROM energy balance. We show that using the snapshot average for the centering trajectory (which is a popular treatment of nonhomogeneous boundary conditions in ROMs) yields an incorrect energy balance. Then, we propose a new approach, in which we replace the snapshot average with the Stokes extension. Theoretically, the Stokes extension produces an accurate energy balance. Numerically, the Stokes extension yields more accurate results than the standard snapshot average, especially for longer time intervals. Our second contribution centers around ROM mass conservation. We consider ROMs created using two types of finite elements: the standard Taylor-Hood (TH) element, which satisfies the mass conservation weakly, and the Scott-Vogelius (SV) element, which satisfies the mass conservation pointwise. Theoretically, the error estimates for the SV-ROM are sharper than those for the TH-ROM. Numerically, the SV-ROM yields significantly more accurate results, especially for coarser meshes and longer time intervals.

  5. A reduced order aerothermodynamic modeling framework for hypersonic vehicles based on surrogate and POD

    Directory of Open Access Journals (Sweden)

    Chen Xin

    2015-10-01

    Full Text Available Aerothermoelasticity is one of the key technologies for hypersonic vehicles. Accurate and efficient computation of the aerothermodynamics is one of the primary challenges for hypersonic aerothermoelastic analysis. Aimed at solving the shortcomings of engineering calculation, computation fluid dynamics (CFD and experimental investigation, a reduced order modeling (ROM framework for aerothermodynamics based on CFD predictions using an enhanced algorithm of fast maximin Latin hypercube design is developed. Both proper orthogonal decomposition (POD and surrogate are considered and compared to construct ROMs. Two surrogate approaches named Kriging and optimized radial basis function (ORBF are utilized to construct ROMs. Furthermore, an enhanced algorithm of fast maximin Latin hypercube design is proposed, which proves to be helpful to improve the precisions of ROMs. Test results for the three-dimensional aerothermodynamic over a hypersonic surface indicate that: the ROMs precision based on Kriging is better than that by ORBF, ROMs based on Kriging are marginally more accurate than ROMs based on POD-Kriging. In a word, the ROM framework for hypersonic aerothermodynamics has good precision and efficiency.

  6. A Deep Learning based Approach to Reduced Order Modeling of Fluids using LSTM Neural Networks

    Science.gov (United States)

    Mohan, Arvind; Gaitonde, Datta

    2017-11-01

    Reduced Order Modeling (ROM) can be used as surrogates to prohibitively expensive simulations to model flow behavior for long time periods. ROM is predicated on extracting dominant spatio-temporal features of the flow from CFD or experimental datasets. We explore ROM development with a deep learning approach, which comprises of learning functional relationships between different variables in large datasets for predictive modeling. Although deep learning and related artificial intelligence based predictive modeling techniques have shown varied success in other fields, such approaches are in their initial stages of application to fluid dynamics. Here, we explore the application of the Long Short Term Memory (LSTM) neural network to sequential data, specifically to predict the time coefficients of Proper Orthogonal Decomposition (POD) modes of the flow for future timesteps, by training it on data at previous timesteps. The approach is demonstrated by constructing ROMs of several canonical flows. Additionally, we show that statistical estimates of stationarity in the training data can indicate a priori how amenable a given flow-field is to this approach. Finally, the potential and limitations of deep learning based ROM approaches will be elucidated and further developments discussed.

  7. Towards reduced order modelling for predicting the dynamics of coherent vorticity structures within wind turbine wakes.

    Science.gov (United States)

    Debnath, M; Santoni, C; Leonardi, S; Iungo, G V

    2017-04-13

    The dynamics of the velocity field resulting from the interaction between the atmospheric boundary layer and a wind turbine array can affect significantly the performance of a wind power plant and the durability of wind turbines. In this work, dynamics in wind turbine wakes and instabilities of helicoidal tip vortices are detected and characterized through modal decomposition techniques. The dataset under examination consists of snapshots of the velocity field obtained from large-eddy simulations (LES) of an isolated wind turbine, for which aerodynamic forcing exerted by the turbine blades on the atmospheric boundary layer is mimicked through the actuator line model. Particular attention is paid to the interaction between the downstream evolution of the helicoidal tip vortices and the alternate vortex shedding from the turbine tower. The LES dataset is interrogated through different modal decomposition techniques, such as proper orthogonal decomposition and dynamic mode decomposition. The dominant wake dynamics are selected for the formulation of a reduced order model, which consists in a linear time-marching algorithm where temporal evolution of flow dynamics is obtained from the previous temporal realization multiplied by a time-invariant operator.This article is part of the themed issue 'Wind energy in complex terrains'. © 2017 The Author(s).

  8. Household methods to reduce {sup 137}Cs contents of mushrooms

    Energy Technology Data Exchange (ETDEWEB)

    Kostiainen, E. [Radiation and Nuclear Safety Authority - STUK, Helsinki (Finland)

    2005-09-15

    High radiocaesium contents in different species of mushrooms have been observed in areas contaminated by radiocaesium deposition after the Chernobyl accident in 1986. There has been no significant reduction in the {sup 137}Cs contents of mushrooms during the past ten years, besides via radioactive decay. The internal radiation dose received via mushrooms can be reduced by processing mushrooms before consumption. Various household methods were studied to find out their efficiency to reduce {sup 137}Cs contents of mushrooms. The methods tested were the same as normally used in cooking. The tests were made for the species of edible mushrooms widely consumed. The retention factors for the treatments tested were in most cases 0.2-0.3. The efficiency of treatments in reducing the {sup 137}Cs contents increased with larger water volumes and prolonged treatment times.

  9. Effectiveness Of Self-Efficacy Strategies As Methods Of Reducing ...

    African Journals Online (AJOL)

    Effectiveness Of Self-Efficacy Strategies As Methods Of Reducing Test Anxiety Of Student Nurses In Ogbomoso North Local Government Area, Oyo State, Nigeria. ... Also, it was found that test anxiety when not properly managed has a significant negative effect on academic performance of students and that there are ...

  10. Method to reduce dislocation density in silicon using stress

    Science.gov (United States)

    Buonassisi, Anthony; Bertoni, Mariana; Argon, Ali; Castellanos, Sergio; Fecych, Alexandria; Powell, Douglas; Vogl, Michelle

    2013-03-05

    A crystalline material structure with reduced dislocation density and method of producing same is provided. The crystalline material structure is annealed at temperatures above the brittle-to-ductile transition temperature of the crystalline material structure. One or more stress elements are formed on the crystalline material structure so as to annihilate dislocations or to move them into less harmful locations.

  11. Reduced Order Model-Based Prediction of the Nonlinear Geometric Response of a Panel Under Thermal, Aerodynamic, and Acoustic Loads

    Science.gov (United States)

    Matney, Andrew

    This paper addresses some aspects of the development of fully coupled thermal-structural reduced order modeling of planned hypersonic vehicles. A general framework for the construction of the structural and thermal basis is presented and demonstrated on a representative panel considered in prior investigations. The thermal reduced order model is first developed using basis functions derived from appropriate conduction eigenvalue problems. The modal amplitudes are the solution of the governing equation, which is nonlinear due to the presence of radiation and temperature dependent capacitance and conductance matrices, and the predicted displacement field is validated using published data. A structural reduced order model was developed by first selecting normal modes of the system and then constructing associated dual modes for the capturing of nonlinear inplane displacements. This isothermal model was validated by comparison with full finite element results (Nastran) in static and dynamic loading environments. The coupling of this nonlinear structural reduced order model with the thermal reduced order model is next considered. Displacement-induced thermal modes are constructed in order to account for the effect that structural deflections will have on the thermal problem. This coupling also requires the enrichment of the structural basis to model the elastic deformations that may be produced consistently with the thermal reduced order model. The validation of the combined structural-thermal reduced order model is carried out with pure mechanical loads, pure thermal loads, and combined mechanical-thermal excitations. Such comparisons are performed here on static solutions with temperature increases up to 2200F and pressures up to 3 psi for which the maximum displacements are of the order of 3 thicknesses. The reduced order model predicted results agree well with the full order finite element predictions in all of these various cases. A fully coupled analysis was

  12. Finite element method for neutron transport. 7. Completely boundary-free maximum principle for the first-order Boltzmann equation

    Energy Technology Data Exchange (ETDEWEB)

    Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Establishment. Process Technology and Safety Directorate)

    1983-01-01

    A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour.

  13. Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

    OpenAIRE

    Stein, David B.; Guy, Robert D; Thomases, Becca

    2015-01-01

    The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given sm...

  14. A Class of Optimal-Order Zero-Finding Methods Using Derivative Evaluations

    Science.gov (United States)

    1975-06-01

    order, x1 = x(tn + h) + 0(h ) , so our nonlinear Runge-Kutta method has order three by the usual definition of order ( Henrici [62]). Similarly...mmmmmmim ll!,IW!.lnl|ll,|HMIIl.pilwmpiW, . 14, Henrici 162] Henrici , P., "Discrete variable methods in or- dinary differential equations", Wiley

  15. Development of a Reduced-Order Three-Dimensional Flow Model for Thermal Mixing and Stratification Simulation during Reactor Transients

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Rui

    2017-09-03

    Mixing, thermal-stratification, and mass transport phenomena in large pools or enclosures play major roles for the safety of reactor systems. Depending on the fidelity requirement and computational resources, various modeling methods, from the 0-D perfect mixing model to 3-D Computational Fluid Dynamics (CFD) models, are available. Each is associated with its own advantages and shortcomings. It is very desirable to develop an advanced and efficient thermal mixing and stratification modeling capability embedded in a modern system analysis code to improve the accuracy of reactor safety analyses and to reduce modeling uncertainties. An advanced system analysis tool, SAM, is being developed at Argonne National Laboratory for advanced non-LWR reactor safety analysis. While SAM is being developed as a system-level modeling and simulation tool, a reduced-order three-dimensional module is under development to model the multi-dimensional flow and thermal mixing and stratification in large enclosures of reactor systems. This paper provides an overview of the three-dimensional finite element flow model in SAM, including the governing equations, stabilization scheme, and solution methods. Additionally, several verification and validation tests are presented, including lid-driven cavity flow, natural convection inside a cavity, laminar flow in a channel of parallel plates. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the developed 3-D fluid model can perform very well for a wide range of flow problems.

  16. On the parameters identification of the Duffing's system by means of a reduced order observer

    Energy Technology Data Exchange (ETDEWEB)

    Mendoza-Camargo, Juan [CINVESTAV-IPN, Departamento de Control Automatico, Av. IPN 2508, A.P. 14740, Mexico, D.F. 07360 (Mexico); Aguilar-Iban-tilde ez, Carlos [CIC-IPN, Av. Juan de Dios Batiz s/n Esq. Manuel Othon de M., Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, A.P. 75476, Mexico, D.F. 07700 (Mexico)]. E-mail: caguilar@cic.ipn.mx; Martinez-Guerra, Rafael [CINVESTAV-IPN, Departamento de Control Automatico, Av. IPN 2508, A.P. 14740, Mexico, D.F. 07360 (Mexico)]. E-mail: rguerra@ctrl.cinvestav.mx; Garrido-Moctezuma, Ruben [CINVESTAV-IPN, Departamento de Control Automatico, Av. IPN 2508, A.P. 14740, Mexico, D.F. 07360 (Mexico)

    2004-10-25

    An on-line procedure for recovering the unknown parameters set of the Duffing's oscillator by means of a reduced order proportional integral observer is presented in this Letter. First, it is shown that the oscillator has the properties of being algebraically observable and algebraically identifiable with respect to a well-chosen output (which turns out to be the oscillator's position). Therefore, an extended differential parametrization of the output and its time derivatives can be obtained. This extended differential parametrization has the necessary information to estimate the output time derivatives and to recover the unknown parameters. The numerical implementation of this method is easily accomplished in a digital computer.

  17. Methods for Engineering Sulfate Reducing Bacteria of the Genus Desulfovibrio

    Energy Technology Data Exchange (ETDEWEB)

    Chhabra, Swapnil R; Keller, Kimberly L.; Wall, Judy D.

    2011-03-15

    Sulfate reducing bacteria are physiologically important given their nearly ubiquitous presence and have important applications in the areas of bioremediation and bioenergy. This chapter provides details on the steps used for homologous-recombination mediated chromosomal manipulation of Desulfovibrio vulgaris Hildenborough, a well-studied sulfate reducer. More specifically, we focus on the implementation of a 'parts' based approach for suicide vector assembly, important aspects of anaerobic culturing, choices for antibiotic selection, electroporation-based DNA transformation, as well as tools for screening and verifying genetically modified constructs. These methods, which in principle may be extended to other sulfate-reducing bacteria, are applicable for functional genomics investigations, as well as metabolic engineering manipulations.

  18. The Theoretical Foundation of Reduced Basis Methods (Preprint)

    Science.gov (United States)

    2016-01-01

    priori convergence theory for reduced- basis approximations of single-parametric elliptic partial differential equations , J. Sci. Comput., 17(2002), pp... elliptic partial differential equations , C. R. Acad. Sci., Paris, Ser. I, Math., 335(2002), pp. 289–294. (Cited on pp. 20, 21) [23] Y. MADAY, B. STAMM... elliptic coercive partial differential equations Ñ applica- tion to transport and continuum mechanics, Arch. Comput Method E, 15(2008), pp. 229–275

  19. Reduced Exergy Method for Heat-Electricity Cost Allocation in Combined Heat and Power Plants

    Directory of Open Access Journals (Sweden)

    Xue-min Ye

    2003-12-01

    Full Text Available Abstract: Although the cost allocation method does not change the total benefits of CHP, the use of various cost allocation methods generally results in significant differences in costs allocated for CHP products. In order to overcome the inadequacy of existing cost allocating methods in theory and in practice, according to the different roles of anergy and exergy in heat supply process of CHP plant, the reduced exergy method for cost allocation is formulated by introducing the concepts of the available anergy and reduced exergy. The contribution of the available anergy is expressed with a user factor, which can reflect different utilization for different practical conditions. Some practical conditions for typical CHP units are computed and compared with existing methods. Calculations show that the cost allocation by using the reduced exergy model is more rational and practical than those by using existing models in terms of embodying the physical meaning.

  20. Higher-order finite-difference methods for partial differential equations

    OpenAIRE

    Cheema, Tasleem Akhter

    1997-01-01

    This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University. This thesis develops two families of numerical methods, based upon rational approximations having distinct real poles, for solving first- and second-order parabolic/ hyperbolic partial differential equations. These methods are thirdand fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods first- and second-order spatial derivatives are ...

  1. High-Order Unsteady Heat Transfer with the Harmonic Balance Method

    Science.gov (United States)

    Knapke, Robert David

    accurately and efficiently simulating the unsteady heat transfer in turbomachinery flows. The HB and CHT methods are developed within a framework that uses a high-order Discontinuous Galerkin (DG) spatial discretization and a versatile Chimera overset scheme. The implemented HB method is fully linearized, allowing the use of an efficient Quasi-Newton solver. The HB equations are coupled within a linear system that includes the linearized HB pseudo-spectral operator. Phase lag and relative motion interfaces are included, hence the computational domain of multistage turbomachinery simulations is reduced to one passage per blade row. Modeling turbulent flows is achieved with the Spalart-Allmaras turbulence model. A strongly coupled CHT method is introduced. The solid and fluid domains are both discretized with the DG method. The fluid to solid interface enforces a consistent wall temperature and heat flux. The Harmonic Balance method, the Conjugate Heat Transfer method, and the Spalart-Allmaras turbulence model are independently verified using a series of test cases. In addition, CHT on curved 3D geometries is performed for the first time. Lastly, unsteady heat transfer is simulated using the combination of the HB and CHT methods. These test cases demonstrate the fast convergence and accurate modeling of the implemented methods. This work provides the basis for the accurate and efficient simulation of turbomachinery flows.

  2. From homotopy perturbation technique to reduced order model for multiparametric modal analysis of large finite element models

    Science.gov (United States)

    Massa, F.; Turpin, I.; Tison, T.

    2017-11-01

    The paper focuses on the definition of a reduced order model for linear modal analysis. The aim is to supply a suitable mathematical alternative tool compatible for multiparametric analysis of large finite element model considering numerous variable parameters, numerous mode shapes and significant levels of variation. The initial full eigenvalue problem is so replaced by a reduced one considering an efficient projection basis. To build it, we propose to combine homotopy transformation and perturbation technique for each parameter direction to define a reduced order model compatible with the design space. Finally, a complete finite element application highlights the capabilities of the proposal in terms of precision and computational time.

  3. Methods for compressible fluid simulation on GPUs using high-order finite differences

    Science.gov (United States)

    Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer

    2017-08-01

    We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

  4. Nonlinear AeroServoElastic Reduced Order Model for Active Structural Control Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall goal of the proposed effort is to develop and demonstrate rigorous model order reduction (MOR) technologies to automatically generate fully coupled,...

  5. Executive Order 13513---federal leadership on reducing text messaging while driving

    Science.gov (United States)

    2009-10-01

    Presidential Executive Order establishing a Federal Government-wide prohibition on the use of text messaging while driving on official business or while using Government-supplied equipment. This policy also extends to cover Federal contractors and co...

  6. Effect of Information Security Management in Automotive Supply Chains to Reduce appetite Boosting Orders

    OpenAIRE

    Manijeh Teimori

    2014-01-01

    The purpose of this study was to evaluate the impact of supply chain management, information security, Iran's auto industry is doing hide Strengthen accountability orders. With these two issues in the study of literature, various factors were identified with the help of factor analysis, factors were determined in the automotive industry. Furthermore, the correlation analysis, how the ISMS impact on supply chains has been Strengthen accountability orders. Studies of the impact of various aspec...

  7. A Method to Reduce Non-Nominal Troposphere Error

    Science.gov (United States)

    Wang, Zhipeng; Xin, Pumin; Li, Rui; Wang, Shujing

    2017-01-01

    Under abnormal troposphere, Ground-Based Augmentation System (GBAS) is unable to eliminate troposphere delay, resulting in non-nominal troposphere error. This paper analyzes the troposphere meteorological data of eight International GNSS Monitoring Assessment System (iGMAS) stations and 10 International GNSS Service (IGS) stations in China and records the most serious conditions during 2015 and 2016. Simulations show that the average increase in Vertical Protection Level (VPL) of all visible satellites under non-nominal troposphere is 2.32 m and that more satellites increase the VPL. To improve GBAS integrity, this paper proposes a satellite selection method to reduce the non-nominal troposphere error. First, the number of satellites in the optimal subset is determined to be 16 based on the relationship among VPL, non-nominal troposphere error and satellite geometry. Second, the distributions of the optimal satellites are determined. Finally, optimal satellites are selected in different elevation ranges. Results show that the average VPL increase caused by non-nominal troposphere error is 1.15 m using the proposed method. Compared with the brute method and greedy method, the running rate of the proposed method is improved by 390.91% and 111.65%, respectively. In summary, the proposed method balances the satellite geometry and non-nominal troposphere error while minimizing the VPL and improving the running rate. PMID:28758983

  8. Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Wen Zhou

    2014-01-01

    Full Text Available We present a third-order method for solving the systems of nonlinear equations. This method is a Newton-type scheme with the vector extrapolation. We establish the local and semilocal convergence of this method. Numerical results show that the composite method is more robust and efficient than a number of Newton-type methods with the other vector extrapolations.

  9. Solving eighth-order boundary value problems using differential transformation method

    Science.gov (United States)

    Hussin, Che Haziqah Che; Mandangan, Arif

    2014-12-01

    In this study, we solved linear and nonlinear eighth-order boundary value problems using Differential Transformation Method. Then we calculate the error of DTM and compare the results with other methods such as modified application of the variational iteration method (MVAM), homotopy perturbation method (HPM) and modified Adomian decomposition method (MADM). We compared the errors of each method with exact solutions. We provided several numerical examples in order to show the accuracy and efficiency of present method. The results showed that the DTM is more accurate in comparison with those obtained by other methods.

  10. Usage of the Reduced Basis Method and High-Performance Simulations in Geosciences

    Science.gov (United States)

    Degen, Denise; Veroy, Karen; Wellmann, Florian

    2017-04-01

    The field of Computational Geosciences often encounters the "curse" of dimensionality, since it aims at analyzing complex coupled processes over a large domain in space and time. These high-dimensional problems are computationally intensive, requiring High-Performance Computing infrastructures. However, constructing parallelized problems is often not trivial. Therefore, we present a software implementation within the Multiphysics Object-Orientated Simulation Environment (MOOSE) offering a built-in parallelization. Even with the computational potential of High-Performance Computers, it may be prohibitive to perform model calibrations or inversions for a reasonably large number of parameters, since the geoscientific forward simulations can be very demanding. Hence, one desires a method reducing the dimensionality of the problem while retaining the accuracy within a certain tolerance. Considering model order reduction techniques is a way to achieve this. We present the Reduced Basis (RB) Method being such a Model Order Reduction Technique aiming at considerably reducing the number of degrees of freedom. We show how the reduction in the dimension results in a significant speed-up, which in turn allows one to perform sensitivity analyses and parameter estimations, to analyze more complicated structures, or to obtain results in real-time. In order to demonstrate the powerful combination of the Reduced Basis Method and High-Performance Computing, we investigate the method's of scalability and parallel efficiency, two measurements for the performance of clusters by using the example of a geothermal conduction problem.

  11. Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method

    Science.gov (United States)

    Hodges, Dewey H.; Rutkowski, Michael J.

    1981-01-01

    The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.

  12. Endocardial botulinum toxin injection into ganglionated plexi in order to reduce atrial fibrillation inducibility

    Directory of Open Access Journals (Sweden)

    А. Г. Стрельников

    2016-01-01

    Full Text Available Objective. Prior animal studies suggest that botulinum toxin injection into the epicardial fat pads can suppress atrial fibrillation (AF inducibility. The purpose of the present study was to assess the efficacy and safety of endocardial botulinum toxin injection into epicardial fat pads and intramyocardial left atrial ganglionated plexi (GP for preventing AF.Methods. Twenty-four dogs were separated into 3 groups: endocardial approach for botulinum toxin (Xeomin, Germany injection into epicardial fat pads and intramyocardial GPs; endocardial approach for placebo injection (0.9% normal saline; control 1; n = 8 and epicardial approach for botulinum toxin injection (control 2; n = 8.Results. A mean of 6.9±1.7 intramyocardial injections (10 U/0.2 mL at each and 3 injections (50 U/1 mL at each were administered into each site exhibiting a positive vagal response and into each epicardial fat pad in all groups (p>0.05 between groups.The injections of botulinum toxin demonstrated dramatic prolongation of ERP in all PV-atrial junctions. This effect correlated with less pronounced ERP shortening in response to vagal nerve stimulation. Suppression of AF inducibility was observed at 7 days after endocardial botulinum toxin injections. The level of AF inducibility was: at 7 days – 57% (p<0.001 vs placebo; p<0.001 vs baseline; at 14 days – 61% (p<0.001 vs placebo; p<0.001 vs baseline; at 1 month – 38% (p<0.001 vs placebo; p<0.001 vs baseline; at 3 months – 23% (p = 0.003; p = 0.06 vs baseline. There were no differences between botulinum groups (p>0.05 for all. The effect of AF suppression disappeared at 3 months. No procedure-related complications occurred.Conclusion. Botulinum toxin injection into intramyocardial GPs and epicardial fat pads by an endocardial approach is feasible and safe. It provides complete removal of cardiac vagal responses and reliably reduces vulnerability to atrial fibrillation.

  13. Two Embedded Pairs of Runge-Kutta Type Methods for Direct Solution of Special Fourth-Order Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    Kasim Hussain

    2015-01-01

    Full Text Available We present two pairs of embedded Runge-Kutta type methods for direct solution of fourth-order ordinary differential equations (ODEs of the form y(iv=f(x,y denoted as RKFD methods. The first pair, which we will call RKFD5(4, has orders 5 and 4, and the second one has orders 6 and 5 and we will call it RKFD6(5. The techniques used in the derivation of the methods are that the higher order methods are very precise and the lower order methods give the best error estimate. Based on these pairs, we have developed variable step codes and we have used them to solve a set of special fourth-order problems. Numerical results show the robustness and the efficiency of the new RKFD pairs as compared with the well-known embedded Runge-Kutta pairs in the scientific literature after reducing the problems into a system of first-order ordinary differential equations (ODEs and solving them.

  14. An alternative method of determining the neutrino mass ordering in reactor neutrino experiments

    Directory of Open Access Journals (Sweden)

    S.M. Bilenky

    2017-09-01

    Full Text Available We discuss a novel alternative method of determining the neutrino mass ordering in medium baseline experiments with reactor antineutrinos. Results on the potential sensitivity of the new method are also presented.

  15. An alternative method of determining the neutrino mass ordering in reactor neutrino experiments

    Science.gov (United States)

    Bilenky, S. M.; Capozzi, F.; Petcov, S. T.

    2017-09-01

    We discuss a novel alternative method of determining the neutrino mass ordering in medium baseline experiments with reactor antineutrinos. Results on the potential sensitivity of the new method are also presented.

  16. Estimation method for mathematical expectation of continuous variable upon ordered sample

    OpenAIRE

    Domchenkov, O. A.

    2014-01-01

    Method for estimation of mathematical expectation of a continuous variable based on analysis of the ordered sample is proposed. The method admits the estimation class propagation on nonlinear estimation classes.

  17. Innovative Development of Kernel-Based Reduced-Order Models for Predicting LCO Onset Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Reducing uncertainty in the prediction of limit cycle oscillations (LCO) and other nonlinear aeroservoelastic phenomena is critical to flight safety. To do so...

  18. Turbine and method for reducing shock losses in a turbine

    Science.gov (United States)

    Ristau, Neil

    2015-09-01

    A turbine includes a rotor and a casing that circumferentially surrounds at least a portion of the rotor. The rotor and the casing at least partially define a gas path through the turbine. A last stage of rotating blades is circumferentially arranged around the rotor and includes a downstream swept portion radially outward from the rotor. A method for reducing shock losses in a turbine includes removing a last stage of rotating blades circumferentially arranged around a rotor and replacing the last stage of rotating blades with rotating blades having a downstream swept portion radially outward from the rotor.

  19. Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method

    Directory of Open Access Journals (Sweden)

    Mustafa Inc

    2014-01-01

    Full Text Available We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions. These results have been compared with the results that are obtained by variational iteration method (VIM, homotopy perturbation method (HPM, Adomian decomposition method (ADM, variation of parameters method (VPM, and homotopy analysis method (HAM. Obtained results show that our method is very effective.

  20. Monotone method for Riemann-Liouville multi-order fractional differential systems

    Directory of Open Access Journals (Sweden)

    Zachary Denton

    2016-01-01

    Full Text Available In this paper we develop the monotone method for nonlinear multi-order \\(N\\-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders \\(q_i\\ where \\(0 \\lt q_i \\lt 1\\. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.

  1. Methods to reduce mercury pollution in small gold mining operations

    Directory of Open Access Journals (Sweden)

    Pantoja-Timarán, F.

    2005-06-01

    Full Text Available The use of mercury for gold beneficiation is still a current practice in small mining operations, mainly in underdeveloped countries, due to the low investment required and necessity of easy to operate systems. But the lack of basic protections makes unavoidable the high pollution of water streams, soils, and in fact, human bodies. Some improvements have been done at site like that related to the removal of the mercury from the amalgam, that usually was done in the open air and now have been changed to the utilization of artisan iron retorts which considerably reduce the emissions of mercury vapors to the atmosphere, but there are still high losses of mercury into the waste solids or tailings coming from the amalgamation process (nearly most of the total weight of the ore treated. In order to reduce the mercury losses into the tailings from the process, this research work has been based in the use of cheap systems, available to the isolated miners, to proof that it is feasible to get an important reduction of the losses and the pollution. The procedure has been accomplished by means of washing the ores with alkaline or detergent agents, together with the use of activated mercury purified by electrowinning in a simple device, easily manufactured in site by the own workers. It is also proven herewith that controlling the time of amalgamation and the total amount of mercury used could reduce the total pollution, and in addition, the gold recovery would be improved. This investigation reports the possibility of a reduction of mercury losses down to 2.4 g per 100 g of gold produced (case of rich ores like La Bruja, with gold recovery up to 94 %; and 8,6 g per 100 g of gold produced (from ores with average grades like La Gruesa, and gold recoveries in the range of 92 %. All that is about 20 to 100 times lower than data reported in current bibliography. The introduction of a previous step of the ore concentration in shaking tables, decreases the total

  2. Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Gustavo Fernández-Torres

    2013-01-01

    Full Text Available We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.

  3. Reduced basis methods for partial differential equations an introduction

    CERN Document Server

    Quarteroni, Alfio; Negri, Federico

    2016-01-01

    This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization.  The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures.  More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis.  The whole mathematical presentation is made more stimulating by the use of representative examp...

  4. Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method

    Science.gov (United States)

    Hayashi, Masahito

    We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.

  5. Verification of higher-order discontinuous Galerkin method for hexahedral elements

    NARCIS (Netherlands)

    Ozdemir, H.; Hagmeijer, Rob; Hoeijmakers, Hendrik Willem Marie

    2005-01-01

    A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing

  6. High-order evolving surface finite element method for parabolic problems on evolving surfaces

    OpenAIRE

    Kovács, Balázs

    2016-01-01

    High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order versions of geometric approximation errors and perturbation error estimates and by the careful error analysis of a modified Ritz map. Furthermore, convergence of full discretisations using backward difference formulae and implicit Runge-Kutta methods are als...

  7. Immersed boundary smooth extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

    Science.gov (United States)

    Stein, David B.; Guy, Robert D.; Thomases, Becca

    2016-01-01

    The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.

  8. Comparison of Dijkstra's algorithm and dynamic programming method in finding shortest path for order picker in a warehouse

    Science.gov (United States)

    Nordin, Noraimi Azlin Mohd; Omar, Mohd; Sharif, S. Sarifah Radiah

    2017-04-01

    Companies are looking forward to improve their productivity within their warehouse operations and distribution centres. In a typical warehouse operation, order picking contributes more than half percentage of the operating costs. Order picking is a benchmark in measuring the performance and productivity improvement of any warehouse management. Solving order picking problem is crucial in reducing response time and waiting time of a customer in receiving his demands. To reduce the response time, proper routing for picking orders is vital. Moreover, in production line, it is vital to always make sure the supplies arrive on time. Hence, a sample routing network will be applied on EP Manufacturing Berhad (EPMB) as a case study. The Dijkstra's algorithm and Dynamic Programming method are applied to find the shortest distance for an order picker in order picking. The results show that the Dynamic programming method is a simple yet competent approach in finding the shortest distance to pick an order that is applicable in a warehouse within a short time period.

  9. Segment scheduling method for reducing 360° video streaming latency

    Science.gov (United States)

    Gudumasu, Srinivas; Asbun, Eduardo; He, Yong; Ye, Yan

    2017-09-01

    360° video is an emerging new format in the media industry enabled by the growing availability of virtual reality devices. It provides the viewer a new sense of presence and immersion. Compared to conventional rectilinear video (2D or 3D), 360° video poses a new and difficult set of engineering challenges on video processing and delivery. Enabling comfortable and immersive user experience requires very high video quality and very low latency, while the large video file size poses a challenge to delivering 360° video in a quality manner at scale. Conventionally, 360° video represented in equirectangular or other projection formats can be encoded as a single standards-compliant bitstream using existing video codecs such as H.264/AVC or H.265/HEVC. Such method usually needs very high bandwidth to provide an immersive user experience. While at the client side, much of such high bandwidth and the computational power used to decode the video are wasted because the user only watches a small portion (i.e., viewport) of the entire picture. Viewport dependent 360°video processing and delivery approaches spend more bandwidth on the viewport than on non-viewports and are therefore able to reduce the overall transmission bandwidth. This paper proposes a dual buffer segment scheduling algorithm for viewport adaptive streaming methods to reduce latency when switching between high quality viewports in 360° video streaming. The approach decouples the scheduling of viewport segments and non-viewport segments to ensure the viewport segment requested matches the latest user head orientation. A base layer buffer stores all lower quality segments, and a viewport buffer stores high quality viewport segments corresponding to the most recent viewer's head orientation. The scheduling scheme determines viewport requesting time based on the buffer status and the head orientation. This paper also discusses how to deploy the proposed scheduling design for various viewport adaptive video

  10. First-order Convex Optimization Methods for Signal and Image Processing

    DEFF Research Database (Denmark)

    Jensen, Tobias Lindstrøm

    2012-01-01

    In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple...

  11. Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Muhammad Aslam Noor

    2006-12-01

    Full Text Available We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.

  12. Optimal sixteenth order convergent method based on quasi-Hermite interpolation for computing roots.

    Science.gov (United States)

    Zafar, Fiza; Hussain, Nawab; Fatimah, Zirwah; Kharal, Athar

    2014-01-01

    We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.

  13. Three-step iterative methods with eighth-order convergence for solving nonlinear equations

    Directory of Open Access Journals (Sweden)

    Mashallah Matinfar

    2013-01-01

    Full Text Available A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.

  14. Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots

    Science.gov (United States)

    Hussain, Nawab; Fatimah, Zirwah

    2014-01-01

    We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method. PMID:25197701

  15. Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

    Science.gov (United States)

    Fink, P. W.; Wilton, D. R.; Dobbins, J. A.

    2002-01-01

    In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required

  16. Embedded ICT technology on sprayers in order to reduce water pollution; the Aware project

    OpenAIRE

    2009-01-01

    International audience; Various routes exist to reduce water pollution due to pesticide spray drift: decision aid systems for spraying when necessary, a better tuning of sprayers and more precise spraying combinations involving a sprayer and its nozzles, an active matter and an adjuvant. In the European project Aware, supported by a LIFE Environment program, the interest of ICT technologies is demonstrated at the different stages of the spraying process: before, during and after spraying. The...

  17. Quantifying and Trading Off the Benefits of Reducing Order and Shipping Times

    National Research Council Canada - National Science Library

    Zimmerman, Dennis

    1997-01-01

    ... be generated by a reduction in retail levels. Working with the costs from distribution-oriented initiatives developed by the DLA Operations Research Office, the tradeoff analysis generated a method for determining when routine requisitions...

  18. Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes

    Science.gov (United States)

    2013-01-01

    flutter analysis. In order to transform the Volterra equations to discrete time, Clancy and Rugh55 looked at the identifica- tion of Volterra series kernels...for discrete-time polynomial systems. This extension of the Volterra and convolution integrals to discrete time paved the way for its further...The unit impulse is the derivative of the unit step, so integration by parts yields y (t) = f (t)H (0) + ∫ t 0 f (τ)h (t− τ) dτ (2.4) Equations 2.3

  19. A high order multi-resolution solver for the Poisson equation with application to vortex methods

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Spietz, Henrik Juul; Walther, Jens Honore

    A high order method is presented for solving the Poisson equation subject to mixed free-space and periodic boundary conditions by using fast Fourier transforms (FFT). The high order convergence is achieved by deriving mollified Green’s functions from a high order regularization function which...... provides a correspondingly smooth solution to the Poisson equation.The high order regularization function may be obtained analogous to the approximate deconvolution method used in turbulence models and strongly relates to deblurring algorithms used in image processing. At first we show that the regularized...

  20. Non-asymptotic fractional order differentiators via an algebraic parametric method

    KAUST Repository

    Liu, Dayan

    2012-08-01

    Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

  1. Synchronization of variable-order fractional financial system via active control method

    Science.gov (United States)

    Xu, Yufeng; He, Zhimin

    2013-06-01

    In this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.

  2. Chaos control and function projective synchronization of fractional-order systems through the backstepping method

    Science.gov (United States)

    Das, S.; Yadav, V. K.

    2016-10-01

    We study the chaos control and the function projective synchronization of a fractional-order T-system and Lorenz chaotic system using the backstepping method. Based on stability theory, we consider the condition for the local stability of nonlinear three-dimensional commensurate fractional-order system. Using the feedback control method, we control the chaos in the considered fractional-order T-system. We simulate the function projective synchronization between the fractional-order T-system and Lorenz system numerically using MATLAB and depict the results with plots.

  3. Reduced-Order Dynamic Modeling, Fouling Detection, and Optimal Control of Solar-Powered Direct Contact Membrane Distillation

    KAUST Repository

    Karam, Ayman M.

    2016-12-01

    Membrane Distillation (MD) is an emerging sustainable desalination technique. While MD has many advantages and can be powered by solar thermal energy, its main drawback is the low water production rate. However, the MD process has not been fully optimized in terms of its manipulated and controlled variables. This is largely due to the lack of adequate dynamic models to study and simulate the process. In addition, MD is prone to membrane fouling, which is a fault that degrades the performance of the MD process. This work has three contributions to address these challenges. First, we derive a mathematical model of Direct Contact Membrane Distillation (DCMD), which is the building block for the next parts. Then, the proposed model is extended to account for membrane fouling and an observer-based fouling detection method is developed. Finally, various control strategies are implemented to optimize the performance of the DCMD solar-powered process. In part one, a reduced-order dynamic model of DCMD is developed based on lumped capacitance method and electrical analogy to thermal systems. The result is an electrical equivalent thermal network to the DCMD process, which is modeled by a system of nonlinear differential algebraic equations (DAEs). This model predicts the water-vapor flux and the temperature distribution along the module length. Experimental data is collected to validate the steady-state and dynamic responses of the proposed model, with great agreement demonstrated in both. The second part proposes an extension of the model to account for membrane fouling. An adaptive observer for DAE systems is developed and convergence proof is presented. A method for membrane fouling detection is then proposed based on adaptive observers. Simulation results demonstrate the performance of the membrane fouling detection method. Finally, an optimization problem is formulated to maximize the process efficiency of a solar-powered DCMD. The adapted method is known as Extremum

  4. Proposed method of reducing ground vibration from delay blasting

    Energy Technology Data Exchange (ETDEWEB)

    Coursen, D.L. [Dynatec Explosives Consultants, Inc., Espanola, NM (United States)

    1995-12-31

    In the proposed method, the charges are elongated and arranged in one or more arrays. The orientation of each charge in an array, its velocity of propagation of explosion, and the velocity of propagation of vibration in the formation are such that, at an outlying location where vibration is to be reduced, the onset of vibration from the explosion of the first negligibly small increment of each charge arrives a finite time before that from the explosion of the last negligibly small increment of that charge. The charges of each array are fired in accurately-timed sequence, with the times between initiations chosen so that, at the outlying location, the onset of vibration from the explosion of the last small increment of each charge, except the last charge, arrives a negligibly small increment of time before the onset of vibration from the explosion of the first negligibly small increment of the succeeding charge. With such timing, vibration may be reduced at the widest range of locations by tilting the boreholes so that the terminal end of each charge is directly above or below the terminal end of the succeeding charge. With the proposed method, vibration can be expected to decrease with increasing charge length, decreasing velocity of propagation of explosion, increasing number of charges per array, decreasing reverberation time, increasing precision of initiation timing, and increasing homogeneity of the rock. Computer modeling of the resulting vibration from single arrays having a total duration of explosion longer than the reverberation time shows a starting transient and an ending transient with little or no vibration between them. For patterns containing more than one array, the modeling indicates that the recommended timing between arrays can largely eliminate the vibration from the starting and ending transients as well when they are dominated by a single frequency.

  5. Reduced order feedback control equations for linear time and frequency domain analysis

    Science.gov (United States)

    Frisch, H. P.

    1981-01-01

    An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized.

  6. Reducing variety in product solution spaces of engineer-to-order companies: The case of Novenco A/S

    DEFF Research Database (Denmark)

    Haug, Anders; Hvam, Lars; Mortensen, Niels Henrik

    2013-01-01

    by eliminating the product variety that do not create customer value. However, for Engineer-to-Order (ETO) companies, elimination of variety is particularly challenging, since it is about reducing variety in a complex product solution space, rather than just eliminating already produced product variants...

  7. On the definition of the spin-free cumulant of the second-order reduced density matrix

    Science.gov (United States)

    Lain, Luis; Torre, Alicia; Bochicchio, Roberto

    2002-09-01

    This note deals with the appropriate definition for the spin-free cumulant of the second-order reduced density matrix. Our approach leads to a direct derivation of one of the proposals reported by Kutzelnigg and Mukherjee [J. Chem. Phys. 116, 4787 (2002)] and it points out its suitability.

  8. Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Purba, Victor [University of Minnesota; Jafarpour, Saber [University of California Santa-Barbara; Bullo, Francesco [University of California Santa-Barbara; Dhople, Sairaj V. [University of Minnesota

    2017-08-21

    Next-generation power networks will contain large numbers of grid-connected inverters satisfying a significant fraction of system load. Since each inverter model has a relatively large number of dynamic states, it is impractical to analyze complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model with lumped parameters for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. We show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as any individual inverter in the system. Numerical simulations validate the reduced-order model.

  9. Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Purba, Victor [University of Minnesota; Jafarpour, Saber [University of California, Santa Barbara; Bullo, Francesco [University of California, Santa Barbara; Dhople, Sairaj [University of Minnesota

    2017-08-31

    Given that next-generation infrastructures will contain large numbers of grid-connected inverters and these interfaces will be satisfying a growing fraction of system load, it is imperative to analyze the impacts of power electronics on such systems. However, since each inverter model has a relatively large number of dynamic states, it would be impractical to execute complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. That is, we show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as an individual inverter in the paralleled system. Numerical simulations validate the reduced-order models.

  10. Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

    KAUST Repository

    Abdulle, Assyr

    2013-01-01

    We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

  11. Simulation of vesicle using level set method solved by high order finite element

    Directory of Open Access Journals (Sweden)

    Doyeux Vincent

    2013-01-01

    Full Text Available We present a numerical method to simulate vesicles in fluid flows. This method consists of writing all the properties of the membrane as interfacial forces between two fluids. The main advantage of this approach is that the vesicle and the fluid models may be decoupled easily. A level set method has been implemented to track the interface. Finite element discretization has been used with arbitrarily high order polynomial approximation. Several polynomial orders have been tested in order to get a better accuracy. A validation on equilibrium shapes and “tank treading” motion of vesicle have been presented.

  12. A Novel High Order Time Domain Vector Finite Element Method for the Simulation of Electromagnetic Devices

    Energy Technology Data Exchange (ETDEWEB)

    Rieben, Robert N. [Univ. of California, Davis, CA (United States)

    2004-01-01

    The goal of this dissertation is two-fold. The first part concerns the development of a numerical method for solving Maxwell's equations on unstructured hexahedral grids that employs both high order spatial and high order temporal discretizations. The second part involves the use of this method as a computational tool to perform high fidelity simulations of various electromagnetic devices such as optical transmission lines and photonic crystal structures to yield a level of accuracy that has previously been computationally cost prohibitive. This work is based on the initial research of Daniel White who developed a provably stable, charge and energy conserving method for solving Maxwell's equations in the time domain that is second order accurate in both space and time. The research presented here has involved the generalization of this procedure to higher order methods. High order methods are capable of yielding far more accurate numerical results for certain problems when compared to corresponding h-refined first order methods , and often times at a significant reduction in total computational cost. The first half of this dissertation presents the method as well as the necessary mathematics required for its derivation. The second half addresses the implementation of the method in a parallel computational environment, its validation using benchmark problems, and finally its use in large scale numerical simulations of electromagnetic transmission devices.

  13. Data mining of Ti-Al semi-empirical parameters for developing reduced order models

    Energy Technology Data Exchange (ETDEWEB)

    Broderick, Scott R. [Department of Materials Science and Engineering and Institute for Combinatorial Discovery, Iowa State University, Ames, IA 50011 (United States); Aourag, Hafid [Department of Physics, University Abou Bakr Belkaid, Tlemcen 13000 (Algeria); Rajan, Krishna, E-mail: krajan@iastate.ed [Department of Materials Science and Engineering and Institute for Combinatorial Discovery, Iowa State University, Ames, IA 50011 (United States)

    2011-05-15

    A focus of materials design is determining the minimum amount of information necessary to fully describe a system, thus reducing the number of empirical results required and simplifying the data analysis. Screening descriptors calculated through a semi-empirical model, we demonstrate how an informatics-based analysis can be used to address this issue with no prior assumptions. We have developed a unique approach for identifying the minimum number of descriptors necessary to capture all the information of a system. Using Ti-Al alloys of varying compositions and crystal chemistries as the test bed, 5 of the 21 original descriptors from electronic structure calculations are found to capture all the information from the calculation, thereby reducing the structure-chemistry-property search space. Additionally, by combining electronic structure calculations with data mining, we classify the systems by chemistries and structures, based on the electronic structure inputs, and thereby rank the impact of change in chemistry and crystal structure on the electronic structure. -- Research Highlights: {yields} We developed an informatics-based methodology to minimize the necessary information. {yields} We applied this methodology to descriptors from semi-empirical calculations. {yields} We developed a validation approach for maintaining information from screening. {yields} We classified intermetallics and identified patterns of composition and structure.

  14. Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

    Directory of Open Access Journals (Sweden)

    Gang Chen

    2012-01-01

    Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

  15. Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

    Science.gov (United States)

    Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

    2018-02-01

    We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

  16. New modification of Laplace decomposition method for seventh order KdV equation

    Science.gov (United States)

    Kashkari, B. S.; Bakodah, H. O.

    2013-10-01

    In this paper, we develop a new modification of Laplace decomposition method for solving the seventh order KdV equations. The numerical results show that the method converges rapidly and compared with the Adomian decomposition method. The conservation properties of solution are examined by calculating the first three invariants.

  17. A Reduced Order Model of Force Displacement Curves for the Failure of Mechanical Bolts in Tension.

    Energy Technology Data Exchange (ETDEWEB)

    Moore, Keegan J. [Univ. of Illinois, Urbana-Champaign, IL (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Brake, Matthew Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-12-01

    Assembled mechanical systems often contain a large number of bolted connections. These bolted connections (joints) are integral aspects of the load path for structural dynamics, and, consequently, are paramount for calculating a structure's stiffness and energy dissipation prop- erties. However, analysts have not found the optimal method to model appropriately these bolted joints. The complexity of the screw geometry causes issues when generating a mesh of the model. This report will explore different approaches to model a screw-substrate connec- tion. Model parameters such as mesh continuity, node alignment, wedge angles, and thread to body element size ratios are examined. The results of this study will give analysts a better understanding of the influences of these parameters and will aide in finding the optimal method to model bolted connections.

  18. Coupling order release methods with autonomous control methods – an assessment of potentials by literature review and discrete event simulation

    Directory of Open Access Journals (Sweden)

    Sebastian Grundstein

    2015-01-01

    Full Text Available Production planning and control faces increasing uncertainty, dynamics and complexity. Autonomous control methods proved themselves as a promising approach for coping with these challenges. However, there is a lack of knowledge regarding the interaction between autonomous control and precedent functions of production planning and control. In particular, up to now previous research has paid no attention to the influence of order release methods on the efficiency of autonomous control methods. Thereby, many researchers over the last decades provided evidence that the order release function has great influence on the logistic objective achievement in conventional production systems. Therefore, this paper examines the influence of order release methods on the efficiency of autonomous control methods by both theoretic evaluation and discrete event simulation. The simulation results indicate an overall high influence. Moreover, the logistic performance differs considerably depending on the implemented order release methods and the combinations of order release methods with autonomous control methods. The findings highlight demand for further research in this field.

  19. Using the Electronic Medical Record to Reduce Unnecessary Ordering of Coagulation Studies for Patients with Chest Pain.

    Science.gov (United States)

    Hinson, Jeremiah S; Mistry, Binoy; Hsieh, Yu-Hsiang; Risko, Nicholas; Scordino, David; Paziana, Karolina; Peterson, Susan; Omron, Rodney

    2017-02-01

    Our goal was to reduce ordering of coagulation studies in the emergency department (ED) that have no added value for patients presenting with chest pain. We hypothesized this could be achieved via implementation of a stopgap measure in the electronic medical record (EMR). We used a pre and post quasi-experimental study design to evaluate the impact of an EMR-based intervention on coagulation study ordering for patients with chest pain. A simple interactive prompt was incorporated into the EMR of our ED that required clinicians to indicate whether patients were on anticoagulation therapy prior to completion of orders for coagulation studies. Coagulation order frequency was measured via detailed review of randomly sampled encounters during two-month periods before and after intervention. We classified existing orders as clinically indicated or non-value added. Order frequencies were calculated as percentages, and we assessed differences between groups by chi-square analysis. Pre-intervention, 73.8% (76/103) of patients with chest pain had coagulation studies ordered, of which 67.1% (51/76) were non-value added. Post-intervention, 38.5% (40/104) of patients with chest pain had coagulation studies ordered, of which 60% (24/40) were non-value added. There was an absolute reduction of 35.3% (95% confidence interval [CI]: 22.7%, 48.0%) in the total ordering of coagulation studies and 26.4% (95% CI: 13.8%, 39.0%) in non-value added order placement. Simple EMR-based interactive prompts can serve as effective deterrents to indiscriminate ordering of diagnostic studies.

  20. R-Stable Embedded DIRKN Method of Orders 4(3) for Solving ...

    African Journals Online (AJOL)

    DIRKN) methods of orders 4(3) for the numerical solution of the special second order initial value problems (IVPs) of the differential equation y¢ = f (x, y) possessing oscillatory solutions. The motivation for this work comes from the fact that not ...

  1. Aligning Order Picking Methods, Incentive Systems, and Regulatory Focus to Increase Performance

    NARCIS (Netherlands)

    de Vries, J.; de Koster, R.; Stam, D.

    2016-01-01

    A controlled field experiment investigates order picking performance in terms of productivity. We examined three manual picker-to-parts order picking methods (parallel, zone, and dynamic zone picking) under two different incentive systems (competition-based vs. cooperation-based) for pickers with

  2. Aligning order picking methods, incentive systems, and regulatory focus to increase performance

    NARCIS (Netherlands)

    J. de Vries (Jelle); M.B.M. de Koster (René); D.A. Stam (Daan)

    2015-01-01

    textabstractA unique controlled field experiment investigates order picking performance (in terms of productivity and quality). We examined three manual picker-to-parts order picking methods (parallel, zone, and dynamic zone picking) under two different incentive systems (competition- based versus

  3. Galerkin. methods for even-order parabolic. equations in one space variable

    NARCIS (Netherlands)

    M. Bakker (Miente)

    1982-01-01

    textabstractFor parabolic equations in one space variable with a strongly coercive self-adjoint $2m$th order spatial operator, a $k$th degree Faedo-Galerkin method is developed which has local convergence of order $2(k + 1 - m)$ at the knots for the first $m - 1$ spatial derivatives and, if $k \\geqq

  4. Method for reducing CO2, CO, NOX, and SOx emissions

    Science.gov (United States)

    Lee, James Weifu; Li, Rongfu

    2002-01-01

    Industrial combustion facilities are integrated with greenhouse gas-solidifying fertilizer production reactions so that CO.sub.2, CO, NO.sub.x, and SO.sub.x emissions can be converted prior to emission into carbonate-containing fertilizers, mainly NH.sub.4 HCO.sub.3 and/or (NH.sub.2).sub.2 CO, plus a small fraction of NH.sub.4 NO.sub.3 and (NH.sub.4).sub.2 SO.sub.4. The invention enhances sequestration of CO.sub.2 into soil and the earth subsurface, reduces N0.sub.3.sup.- contamination of surface and groundwater, and stimulates photosynthetic fixation of CO.sub.2 from the atmosphere. The method for converting CO.sub.2, CO, NO.sub.x, and SO.sub.x emissions into fertilizers includes the step of collecting these materials from the emissions of industrial combustion facilities such as fossil fuel-powered energy sources and transporting the emissions to a reactor. In the reactor, the CO.sub.2, CO, N.sub.2, SO.sub.x, and/or NO.sub.x are converted into carbonate-containing fertilizers using H.sub.2, CH.sub.4, or NH.sub.3. The carbonate-containing fertilizers are then applied to soil and green plants to (1) sequester inorganic carbon into soil and subsoil earth layers by enhanced carbonation of groundwater and the earth minerals, (2) reduce the environmental problem of NO.sub.3.sup.- runoff by substituting for ammonium nitrate fertilizer, and (3) stimulate photosynthetic fixation of CO.sub.2 from the atmosphere by the fertilization effect of the carbonate-containing fertilizers.

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

    Science.gov (United States)

    Meldi, M.; Poux, A.

    2017-10-01

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

  6. Higher-order multi-resolution topology optimization using the finite cell method

    DEFF Research Database (Denmark)

    Groen, Jeroen Peter; Langelaar, Matthijs; Sigmund, Ole

    2017-01-01

    This article presents a detailed study on the potential and limitations of performing higher-order multi-resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high-contrast topologies, a length-scale is applied on the solution using filter methods....... This reduction is caused by exploiting the decoupling of density and analysis mesh, and by condensing the higher-order modes out of the stiffness matrix....

  7. Accelerated Extra-Gradient Descent: A Novel Accelerated First-Order Method

    OpenAIRE

    Diakonikolas, Jelena; Orecchia, Lorenzo

    2018-01-01

    We provide a novel accelerated first-order method that achieves the asymptotically optimal convergence rate for smooth functions in the first-order oracle model. To this day, Nesterov's Accelerated Gradient Descent (AGD) and variations thereof were the only methods achieving acceleration in this standard blackbox model. In contrast, our algorithm is significantly different from AGD, as it relies on a predictor-corrector approach similar to that used by Mirror-Prox [Nemirovski, 2004] and Extra...

  8. How can we strengthen students' social relations in order to reduce school dropout?

    DEFF Research Database (Denmark)

    Ingholt, Liselotte; Sørensen, Betina Bang; Andersen, Susan

    2015-01-01

    on ethnographic methods, including 22 qualitative interviews with students 17-19 years old and fieldwork with participant observations at four vocational schools over 40 days, including informal interviews and discussion meetings with managers, teachers, counselors and students. As part of the fieldwork, four......, importance of the introduction period, physical surroundings and schedules, tobacco and cannabis use and communication about drug use. The program addressing these themes incorporates suggestions that are meant to improve how teachers welcome new students, to enable greater integration of social...... and educational activities and to enhance the capacity of teachers and counselors to deal with drug use problems among students. CONCLUSION: The development of new intervention programs might benefit from adopting a theoretical and methodological perspective that enables a closer exploration of the everyday...

  9. Back-stepping active disturbance rejection control design for integrated missile guidance and control system via reduced-order ESO.

    Science.gov (United States)

    Xingling, Shao; Honglun, Wang

    2015-07-01

    This paper proposes a novel composite integrated guidance and control (IGC) law for missile intercepting against unknown maneuvering target with multiple uncertainties and control constraint. First, by using back-stepping technique, the proposed IGC law design is separated into guidance loop and control loop. The unknown target maneuvers and variations of aerodynamics parameters in guidance and control loop are viewed as uncertainties, which are estimated and compensated by designed model-assisted reduced-order extended state observer (ESO). Second, based on the principle of active disturbance rejection control (ADRC), enhanced feedback linearization (FL) based control law is implemented for the IGC model using the estimates generated by reduced-order ESO. In addition, performance analysis and comparisons between ESO and reduced-order ESO are examined. Nonlinear tracking differentiator is employed to construct the derivative of virtual control command in the control loop. Third, the closed-loop stability for the considered system is established. Finally, the effectiveness of the proposed IGC law in enhanced interception performance such as smooth interception course, improved robustness against multiple uncertainties as well as reduced control consumption during initial phase are demonstrated through simulations. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  10. Determination of the optimal amount of nitrous oxide injected into the engine in order to reduce emissions

    Directory of Open Access Journals (Sweden)

    M Ghari

    2015-09-01

    Full Text Available Introduction: Nowadays the number of motor vehicles in large and small cities is growing. Increasing the number of motor vehicles leads to serious increase of the amount of environmental pollution and daily fuel consumption. Motor vehicle emissions that are known as the most air polluting emissions cause 50-90 percent of air pollution. With large increasd in the number of motor vehicles and their emissions todays, many researchers have investigated engine optimization in order to reduce emissions of motor vehicles. But due to the lack of affordable changes in the physical structure of the engine, it is not possible to create major changes in the amount of engine exhaust. Hence, in order to improve engine performance and reduce emissions, a lot of research has been carried out on changes in the fuel and engine inlet air. So, in this study a new method has been proposed and tested in order to detect changes in the charactristics of emissions. So, the effects of enriched nitrous oxide gas on the exhaust emissions of a spark-injection engine were investigated. In this way, a certain amount of Nitrous Oxide (N2O gas was mixed with the engine inlet air (with concentration of 0, 4, 8, 12 and 16 percent and it was injected to the engine. Then its effect was studied on emission parameters at various engine rotational speeds. Then, by using genetic algorithm, the optimal values of N2O concentration and engine rotational speed were determined to reach the minimum emission parameters. Materials and Methods: To measure the engine emission parameters including CO, CO2, HC and NOx, the expriments were conducted after preparing a system to inject inlet air with different percentages of N2O into an Otto engine (model: M13NI. In this study, the randomized complete block design was used to investigate the effect of N2O concentration (five levels and engine rotational speed (three levels on exhauste emission parameters. Each expriment was replicated 9 times. For

  11. Refrigeration arrangement and methods for reducing charge migration

    Science.gov (United States)

    Litch, Andrew D.; Wu, Guolian

    2017-04-11

    A refrigerator appliance including a refrigerant circuit between a condenser, an evaporator, and a compressor that includes two conduits and pressure reducing devices arranged in parallel between the evaporator and the condenser. The appliance also includes a valve system to direct refrigerant through one, both or none of the conduits and pressure reducing devices, and a heat exchanging member in thermal contact with either one pressure reducing device, or one conduit between the pressure reducing device and the valve system.

  12. Solving New Fourth-Order Emden-Fowler-Type Equations by the Adomian Decomposition Method

    Science.gov (United States)

    Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng

    2015-03-01

    In this article, we extend the second-order Emden-Fowler equation to three new fourth-order Emden-Fowler type equations. We show that the singular point at x = 0, and hence the shape factor, may appear in more than one term of the equation. We solve the developed singular fourth-order equations by using the systematic Adomian decomposition method. We corroborate this work by studying several fourth-order Emden-Fowler type examples including linear and nonlinear cases.

  13. Application of adomian decomposition method for singularly perturbed fourth order boundary value problems

    Science.gov (United States)

    Deniz, Sinan; Bildik, Necdet

    2016-06-01

    In this paper, we use Adomian Decomposition Method (ADM) to solve the singularly perturbed fourth order boundary value problem. In order to make the calculation process easier, first the given problem is transformed into a system of two second order ODEs, with suitable boundary conditions. Numerical illustrations are given to prove the effectiveness and applicability of this method in solving these kinds of problems. Obtained results shows that this technique provides a sequence of functions which converges rapidly to the accurate solution of the problems.

  14. Higher-order schemes for the Laplace transformation method for parabolic problems

    KAUST Repository

    Douglas, C.

    2011-01-01

    In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.

  15. Aperture-Tolerant, Chemical-Based Methods to Reduce Channeling

    Energy Technology Data Exchange (ETDEWEB)

    Randall S. Seright

    2007-09-30

    This final technical progress report describes work performed from October 1, 2004, through May 16, 2007, for the project, 'Aperture-Tolerant, Chemical-Based Methods to Reduce Channeling'. We explored the potential of pore-filling gels for reducing excess water production from both fractured and unfractured production wells. Several gel formulations were identified that met the requirements--i.e., providing water residual resistance factors greater than 2,000 and ultimate oil residual resistance factors (F{sub rro}) of 2 or less. Significant oil throughput was required to achieve low F{sub rro} values, suggesting that gelant penetration into porous rock must be small (a few feet or less) for existing pore-filling gels to provide effective disproportionate permeability reduction. Compared with adsorbed polymers and weak gels, strong pore-filling gels can provide greater reliability and behavior that is insensitive to the initial rock permeability. Guidance is provided on where relative-permeability-modification/disproportionate-permeability-reduction treatments can be successfully applied for use in either oil or gas production wells. When properly designed and executed, these treatments can be successfully applied to a limited range of oilfield excessive-water-production problems. We examined whether gel rheology can explain behavior during extrusion through fractures. The rheology behavior of the gels tested showed a strong parallel to the results obtained from previous gel extrusion experiments. However, for a given aperture (fracture width or plate-plate separation), the pressure gradients measured during the gel extrusion experiments were much higher than anticipated from rheology measurements. Extensive experiments established that wall slip and first normal stress difference were not responsible for the pressure gradient discrepancy. To explain the discrepancy, we noted that the aperture for gel flow (for mobile gel wormholing through concentrated

  16. Nonlinear reduced order models for fluids systems using extended dynamic mode decomposition

    Science.gov (United States)

    Dawson, Scott; Rowley, Clarence

    2015-11-01

    The development of techniques that can extract simple, accurate, and computationally tractable models from fluids data is of importance for enhanced prediction, control, and fundamental understanding of such systems. Modeling approaches can take the form of identifying modes upon which to project the governing equations (e.g., Galerkin projection onto a set of POD modes), or in determining (or calibrating) the temporal dynamics from data, such as in dynamic mode decomposition (DMD), or various modifications to Galerkin projection. Here, we demonstrate that choosing appropriate observables (such as linear and quadratic monomials of POD coefficients) can allow for nonlinear behavior to be accurately captured using the recently proposed extended DMD algorithm. For cylinder wake data spanning the transient and vortex shedding limit cycle regimes, the identified nonlinear models show significant improvement in accuracy and robustness over standard DMD and Galerkin projection. Compared to traditional DMD, this approach should also allow for a better global approximation of the Koopman operator for the dynamical system. We make connections with other related model identification algorithms, and additionally investigate the performance of the method upon spatially sparse and noisy data. This work was supported by the Air Force Office of Scientific Research, under award No. FA9550-12-1-0075.

  17. High-throughput DNA sequencing errors are reduced by orders of magnitude using circle sequencing

    Science.gov (United States)

    Lou, Dianne I.; Hussmann, Jeffrey A.; McBee, Ross M.; Acevedo, Ashley; Andino, Raul; Press, William H.; Sawyer, Sara L.

    2013-01-01

    A major limitation of high-throughput DNA sequencing is the high rate of erroneous base calls produced. For instance, Illumina sequencing machines produce errors at a rate of ∼0.1–1 × 10−2 per base sequenced. These technologies typically produce billions of base calls per experiment, translating to millions of errors. We have developed a unique library preparation strategy, “circle sequencing,” which allows for robust downstream computational correction of these errors. In this strategy, DNA templates are circularized, copied multiple times in tandem with a rolling circle polymerase, and then sequenced on any high-throughput sequencing machine. Each read produced is computationally processed to obtain a consensus sequence of all linked copies of the original molecule. Physically linking the copies ensures that each copy is independently derived from the original molecule and allows for efficient formation of consensus sequences. The circle-sequencing protocol precedes standard library preparations and is therefore suitable for a broad range of sequencing applications. We tested our method using the Illumina MiSeq platform and obtained errors in our processed sequencing reads at a rate as low as 7.6 × 10−6 per base sequenced, dramatically improving the error rate of Illumina sequencing and putting error on par with low-throughput, but highly accurate, Sanger sequencing. Circle sequencing also had substantially higher efficiency and lower cost than existing barcode-based schemes for correcting sequencing errors. PMID:24243955

  18. First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

    Science.gov (United States)

    Mazaheri, Alireza; Nishikawa, Hiroaki

    2014-01-01

    A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

  19. High-Order Ghost-Fluid Method for Compressible Flow in Complex Geometry

    Science.gov (United States)

    Al Marouf, Mohamad; Samtaney, Ravi

    2014-11-01

    We present a high-order embedded boundary method for numerical solutions of the Compressible Navier Stokes (CNS) equations in arbitrary domains. A high-order ghost fluid method based on the PDEs multidimensional extrapolation approach of Aslam (J. Comput. Phys. 2003) is utilized to extrapolate the solution across the fluid-solid interface to impose boundary conditions. A fourth order accurate numerical time integration for the CNS is achieved by fourth order Runge-Kutta scheme, and a fourth order conservative finite volume scheme by McCorquodale & Colella (Comm. in App. Math. & Comput. Sci. 2011) is used to evaluate the fluxes. Resolution at the embedded boundary and high gradient regions is accomplished by applying block-structured adaptive mesh refinement. A number of numerical examples with different Reynolds number for a low Mach number flow over an airfoil and circular cylinder will be presented. Supported by OCRF-CRG grant at KAUST.

  20. Overlay control methodology comparison: field-by-field and high-order methods

    Science.gov (United States)

    Huang, Chun-Yen; Chiu, Chui-Fu; Wu, Wen-Bin; Shih, Chiang-Lin; Huang, Chin-Chou Kevin; Huang, Healthy; Choi, DongSub; Pierson, Bill; Robinson, John C.

    2012-03-01

    Overlay control in advanced integrated circuit (IC) manufacturing is becoming one of the leading lithographic challenges in the 3x and 2x nm process nodes. Production overlay control can no longer meet the stringent emerging requirements based on linear composite wafer and field models with sampling of 10 to 20 fields and 4 to 5 sites per field, which was the industry standard for many years. Methods that have emerged include overlay metrology in many or all fields, including the high order field model method called high order control (HOC), and field by field control (FxFc) methods also called correction per exposure. The HOC and FxFc methods were initially introduced as relatively infrequent scanner qualification activities meant to supplement linear production schemes. More recently, however, it is clear that production control is also requiring intense sampling, similar high order and FxFc methods. The added control benefits of high order and FxFc overlay methods need to be balanced with the increased metrology requirements, however, without putting material at risk. Of critical importance is the proper control of edge fields, which requires intensive sampling in order to minimize signatures. In this study we compare various methods of overlay control including the performance levels that can be achieved.

  1. APPLICATION OF THE CRAIG-BAMPTON MODEL ORDER REDUCTION METHOD TO A COMPOSITE STRUCTURE: MAC AND XOR

    Directory of Open Access Journals (Sweden)

    Humberto Peredo Fuentes

    2014-04-01

    Full Text Available The Craig-Bampton model order reduction (CBMOR method based on the Rayleigh-Ritz approach is applied to dynamic behavior simulation of a composite structure in order to verify the method’s feasibility and accuracy. The principle of this method is to represent a coupled component model based on the mass, damping and stiffness matrices. The methodology consists of a finite element model based on the classical laminate theory (CLT, a design of experiment to improve the modal assurance criteria (MAC and experimental results in order to validate the reduced model based on CBMOR method and substructures (super-elements. Experimental modal analysis has been performed using a scanner laser Doppler vibrometer (SLDV in order to assess the quality of the finite element models. The MAC and cross orthogonality MAC (XOR values are computed to verify the eigenfrequencies and eigenvectors. This approach demonstrates the feasibility of using CBMOR for composite structures. The example is prepared and solved with MSC/NASTRAN SOL103. The design of experiments (DOE method has been applied in order to identify the critical parameters and thus obtain high MAC values.

  2. Hybrid High-Order methods for finite deformations of hyperelastic materials

    Science.gov (United States)

    Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

    2018-01-01

    We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

  3. Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

    Directory of Open Access Journals (Sweden)

    Seng-Kin Lao

    2014-01-01

    Full Text Available A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.

  4. High Order Adjoint Derivatives using ESDIRK Methods for Oil Reservoir Production Optimization

    DEFF Research Database (Denmark)

    Capolei, Andrea; Stenby, Erling Halfdan; Jørgensen, John Bagterp

    2012-01-01

    In production optimization, computation of the gradients is the computationally expensive step. We improve the computational efficiency of such algorithms by improving the gradient computation using high-order ESDIRK (Explicit Singly Diagonally Implicit Runge-Kutta) temporal integration methods...... and continuous adjoints . The high order integration scheme allows larger time steps and therefore faster solution times. We compare gradient computation by the continuous adjoint method to the discrete adjoint method and the finite-difference method. The methods are implemented for a two phase flow reservoir...... the time steps are controlled in a certain range, the continuous adjoint method produces gradients sufficiently accurate for the optimization algorithm and somewhat faster than the discrete adjoint method....

  5. A homotopy perturbation method for fractional-order advection-diffusion-reaction boundary-value problems

    NARCIS (Netherlands)

    Ateş, I.; Zegeling, P. A.|info:eu-repo/dai/nl/073634433

    2017-01-01

    In this paper we describe the application of the homotopy perturbation method (HPM) to two-point boundary-value problems with fractional-order derivatives of Caputo-type. We show that HPM is equivalent to the semi-analytical Adomian decomposition method when applied to a class of nonlinear

  6. A Simple Method for Estimation of Parameters in First order Systems

    DEFF Research Database (Denmark)

    Niemann, Hans Henrik; Miklos, Robert

    2014-01-01

    A simple method for estimation of parameters in first order systems with time delays is presented in this paper. The parameter estimation approach is based on a step response for the open loop system. It is shown that the estimation method does not require a complete step response, only a part of...

  7. New true fourth-order accurate scalar beam propagation methods for both TE and TM polarization

    NARCIS (Netherlands)

    Stoffer, Remco; Bollerman, P.A.A.J.; Hoekstra, Hugo; van Groesen, Embrecht W.C.; van Beckum, F.P.H.

    1999-01-01

    New 2D scalar beam propagation methods for both TE and TM polarization are presented. Both second- and fourth-order accurate schemes, in the lateral stepsize, are shown. The methods use uniform discretization and can handle arbitrary positions of interfaces between materials with different

  8. Newton's method for stochastic differential equations and its probabilistic second-order error estimate

    Directory of Open Access Journals (Sweden)

    Kazuo Amano

    2012-01-01

    Full Text Available Kawabata and Yamada [5] proposed an implicit Newton's method for nonlinear stochastic differential equations and proved its convergence. Later Amano [2] gave an explicit formulation of method and showed its direct error estimate. In this article, we prove a probabilistic second-order error estimate which has been an open problem since 1991.

  9. Modulating functions method for parameters estimation in the fifth order KdV equation

    KAUST Repository

    Asiri, Sharefa M.

    2017-07-25

    In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a system of linear algebraic equations of the unknowns. The statistical properties of the modulating functions solution are described in this paper. In addition, guidelines for choosing the number of modulating functions, which is an important design parameter, are provided. The effectiveness and robustness of the proposed method are shown through numerical simulations in both noise-free and noisy cases.

  10. An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

    Directory of Open Access Journals (Sweden)

    Fairouz Zouyed

    2015-01-01

    Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

  11. High Performance Reduced Order Models for Wind Turbines with Full-Scale Converters Applied on Grid Interconnection Studies

    Directory of Open Access Journals (Sweden)

    Heverton A. Pereira

    2014-11-01

    Full Text Available Wind power has achieved technological evolution, and Grid Code (GC requirements forced wind industry consolidation in the last three decades. However, more studies are necessary to understand how the dynamics inherent in this energy source interact with the power system. Traditional energy production usually contains few high power unit generators; however, Wind Power Plants (WPPs consist of dozens or hundreds of low-power units. Time domain simulations of WPPs may take too much time if detailed models are considered in such studies. This work discusses reduced order models used in interconnection studies of synchronous machines with full converter technology. The performance of all models is evaluated based on time domain simulations in the Simulink/MATLAB environment. A detailed model is described, and four reduced order models are compared using the performance index, Normalized Integral of Absolute Error (NIAE. Models are analyzed during wind speed variations and balanced voltage dip. During faults, WPPs must be able to supply reactive power to the grid, and this characteristic is analyzed. Using the proposed performance index, it is possible to conclude if a reduced order model is suitable to represent the WPPs dynamics on grid studies.

  12. Identification of the reduced order models of a BWR reactor; Identificacion de modelos de orden reducido de un reactor BWR

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez S, A. [UNAM, Laboratorio de Analisis de Ingenieria de Reactores Nucleares, DEPFI, Campus Morelos, en IMTA Jiutepec, Morelos (Mexico)]. e-mail: augusto@correo.unam.mx

    2004-07-01

    The present work has as objective to analyze the relative stability of a BWR type reactor. It is analyzed that so adaptive it turns out to identify the parameters of a model of reduced order so that this it reproduces a condition of given uncertainty. This will take of a real fact happened in the La Salle plant under certain operation conditions of power and flow of coolant. The parametric identification is carried out by means of an algorithm of recursive least square and an Output Error model (Output Error), measuring the output power of the reactor when the instability is present, and considering that it is produced by a change in the reactivity of the system in the same way that a sign of type step. Also it is carried out an analytic comparison of the relative stability, analyzing two types of answers: the original answer of the uncertainty of the reactor vs. the obtained response identifying the parameters of the model of reduced order, reaching the conclusion that it is very viable to adapt a model of reduced order to study the stability of a reactor, under the only condition to consider that the dynamics of the reactivity is of step type. (Author)

  13. A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

    Science.gov (United States)

    Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

    2018-01-01

    In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

  14. A bundle with a preformatted medical order sheet and an introductory course to reduce prescription errors in neonates.

    Science.gov (United States)

    Palmero, David; Di Paolo, Ermindo R; Beauport, Lydie; Pannatier, André; Tolsa, Jean-François

    2016-01-01

    The objective of this study was to assess whether the introduction of a new preformatted medical order sheet coupled with an introductory course affected prescription quality and the frequency of errors during the prescription stage in a neonatal intensive care unit (NICU). Two-phase observational study consisting of two consecutive 4-month phases: pre-intervention (phase 0) and post-intervention (phase I) conducted in an 11-bed NICU in a Swiss university hospital. Interventions consisted of the introduction of a new preformatted medical order sheet with explicit information supplied, coupled with a staff introductory course on appropriate prescription and medication errors. The main outcomes measured were formal aspects of prescription and frequency and nature of prescription errors. Eighty-three and 81 patients were included in phase 0 and phase I, respectively. A total of 505 handwritten prescriptions in phase 0 and 525 in phase I were analysed. The rate of prescription errors decreased significantly from 28.9% in phase 0 to 13.5% in phase I (p prescriptions decreased from 44.2 to 25.7 and 8.5 to 3.2% (p prescriptions and reduce medication errors. Medication errors are frequent in NICUs and prescription is one of the most critical steps. CPOE reduce prescription errors, but their implementation is not available everywhere. Preformatted medical order sheet coupled with an introductory course decrease medication errors in a NICU. Preformatted medical order sheet is an inexpensive and readily implemented alternative to CPOE.

  15. Improved first-order uncertainty method for water-quality modeling

    Science.gov (United States)

    Melching, C.S.; Anmangandla, S.

    1992-01-01

    Uncertainties are unavoidable in water-quality modeling and subsequent management decisions. Monte Carlo simulation and first-order uncertainty analysis (involving linearization at central values of the uncertain variables) have been frequently used to estimate probability distributions for water-quality model output due to their simplicity. Each method has its drawbacks: Monte Carlo simulation's is mainly computational time; and first-order analysis are mainly questions of accuracy and representativeness, especially for nonlinear systems and extreme conditions. An improved (advanced) first-order method is presented, where the linearization point varies to match the output level whose exceedance probability is sought. The advanced first-order method is tested on the Streeter-Phelps equation to estimate the probability distribution of critical dissolved-oxygen deficit and critical dissolved oxygen using two hypothetical examples from the literature. The advanced first-order method provides a close approximation of the exceedance probability for the Streeter-Phelps model output estimated by Monte Carlo simulation using less computer time - by two orders of magnitude - regardless of the probability distributions assumed for the uncertain model parameters.

  16. An improved 2D MoF method by using high order derivatives

    Science.gov (United States)

    Chen, Xiang; Zhang, Xiong

    2017-11-01

    The MoF (Moment of Fluid) method is one of the most accurate approaches among various interface reconstruction algorithms. Alike other second order methods, the MoF method needs to solve an implicit optimization problem to obtain the optimal approximate interface, so an iteration process is inevitable under most circumstances. In order to solve the optimization efficiently, the properties of the objective function are worthy of studying. In 2D problems, the first order derivative has been deduced and applied in the previous researches. In this paper, the high order derivatives of the objective function are deduced on the convex polygon. We show that the nth (n ≥ 2) order derivatives are discontinuous, and the number of the discontinuous points is two times the number of the polygon edge. A rotation algorithm is proposed to successively calculate these discontinuous points, thus the target interval where the optimal solution is located can be determined. Since the high order derivatives of the objective function are continuous in the target interval, the iteration schemes based on high order derivatives can be used to improve the convergence rate. Moreover, when iterating in the target interval, the value of objective function and its derivatives can be directly updated without explicitly solving the volume conservation equation. The direct update makes a further improvement of the efficiency especially when the number of edges of the polygon is increasing. The Halley's method, which is based on the first three order derivatives, is applied as the iteration scheme in this paper and the numerical results indicate that the CPU time is about half of the previous method on the quadrilateral cell and is about one sixth on the decagon cell.

  17. International journal of computational fluid dynamics real-time prediction of unsteady flow based on POD reduced-order model and particle filter

    Science.gov (United States)

    Kikuchi, Ryota; Misaka, Takashi; Obayashi, Shigeru

    2016-04-01

    An integrated method consisting of a proper orthogonal decomposition (POD)-based reduced-order model (ROM) and a particle filter (PF) is proposed for real-time prediction of an unsteady flow field. The proposed method is validated using identical twin experiments of an unsteady flow field around a circular cylinder for Reynolds numbers of 100 and 1000. In this study, a PF is employed (ROM-PF) to modify the temporal coefficient of the ROM based on observation data because the prediction capability of the ROM alone is limited due to the stability issue. The proposed method reproduces the unsteady flow field several orders faster than a reference numerical simulation based on Navier-Stokes equations. Furthermore, the effects of parameters, related to observation and simulation, on the prediction accuracy are studied. Most of the energy modes of the unsteady flow field are captured, and it is possible to stably predict the long-term evolution with ROM-PF.

  18. Khater method for nonlinear Sharma Tasso-Olever (STO equation of fractional order

    Directory of Open Access Journals (Sweden)

    Sadaf Bibi

    Full Text Available In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering. Keywords: Khater method, Modified Riemann-Liouville derivative, Exact solutions, Fractional complex transform, Space-time fractional Sharma Tasso-Olever (STO equation

  19. Managing Variety in Configure-to-Order Products - An Operational Method

    DEFF Research Database (Denmark)

    Myrodia, Anna; Hvam, Lars

    2014-01-01

    is to develop an operational method to analyze profitability of Configure-To-Order (CTO) products. The operational method consists of a four-step: analysis of product assortment, profitability analysis on configured products, market and competitor analysis and, product assortment scenarios analysis....... The proposed operational method is firstly developed based on both available literature and practitioners experience and subsequently tested on a company that produces CTO products. The results from this application are further discussed and opportunities for further research identified....

  20. A class of Steffensen type methods with optimal order of convergente

    OpenAIRE

    Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón

    2011-01-01

    In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a better approximation to the derivative of the given function. Each derivative-free member of the family requires only three evaluations of the given function per iteration. Therefore, this class of methods has efficiency index equal to 1.587. Kung and Traub conjectured that the ...

  1. A fourth order accurate adaptive mesh refinement method forpoisson's equation

    Energy Technology Data Exchange (ETDEWEB)

    Barad, Michael; Colella, Phillip

    2004-08-20

    We present a block-structured adaptive mesh refinement (AMR) method for computing solutions to Poisson's equation in two and three dimensions. It is based on a conservative, finite-volume formulation of the classical Mehrstellen methods. This is combined with finite volume AMR discretizations to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.

  2. Variational method for second-order properties in atoms and molecules

    Energy Technology Data Exchange (ETDEWEB)

    Bendazzoli, G.L. (Bologna Univ. (Italy)); Evangelisti, S. (Bologna Univ. (Italy). Ist. di Fisica); Fano, G.; Ortolani, F. (Bologna Univ. (Italy). Ist. di Fisica; Istituto Nazionale di Fisica Nucleare, Bologna (Italy))

    1980-02-11

    Second-order properties are computed by diagonalizing a perturbed Hamiltonian in a three-dimensional linear space L. The choice of the basis vectors generating L is suggested by the coupled perturbed Hartree-Fock (CPHF) method. A test numerical computation on the dipole polarizability of the H/sub 2/ molecule is presented. The method can be considered as an improvement of the CPHF method.

  3. High order aberrations calculation of a hexapole corrector using a differential algebra method

    Energy Technology Data Exchange (ETDEWEB)

    Kang, Yongfeng, E-mail: yfkang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Zhao, Jingyi, E-mail: jingyi.zhao@foxmail.com [School of Science, Chang’an University, Xi’an 710064 (China); Tang, Tiantong [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China)

    2017-02-21

    A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.

  4. Governor Design for a Hydropower Plant with an Upstream Surge Tank by GA-Based Fuzzy Reduced-Order Sliding Mode

    Directory of Open Access Journals (Sweden)

    Chang Xu

    2015-11-01

    Full Text Available This paper investigates governor design by reduced-order sliding mode for a hydropower plant with an upstream surge tank. The governing system is made up of a tunnel, a surge tank, a penstock, a wicket gate and servomechanism, a governor, a hydro-turbine and a grid. Concerning the components of the governing system, their mathematic models are established. Then, these models are interconnected to simulate the governing system. From the viewpoint of state space in modern control theory, the governing system is partially observed, which challenges the governor design. By introducing an additional state variable, the control method of reduced-order sliding mode is proposed, where the governor design is based on a reduced-order governing system. Since the governor is applied to the original governing system, the system stability is analyzed by means of the small gain theorem. An genetic algorithm is employed to search a group of parameters of the predefined sliding surface, and a fuzzy inference system is utilized to decrease the chattering problem. Some numerical simulations are illustrated to verify the feasibility and robustness of the control method.

  5. A Local Order Parameter-Based Method for Simulation of Free Energy Barriers in Crystal Nucleation.

    Science.gov (United States)

    Eslami, Hossein; Khanjari, Neda; Müller-Plathe, Florian

    2017-03-14

    While global order parameters have been widely used as reaction coordinates in nucleation and crystallization studies, their use in nucleation studies is claimed to have a serious drawback. In this work, a local order parameter is introduced as a local reaction coordinate to drive the simulation from the liquid phase to the solid phase and vice versa. This local order parameter holds information regarding the order in the first- and second-shell neighbors of a particle and has different well-defined values for local crystallites and disordered neighborhoods but is insensitive to the type of the crystal structure. The order parameter is employed in metadynamics simulations to calculate the solid-liquid phase equilibria and free energy barrier to nucleation. Our results for repulsive soft spheres and the Lennard-Jones potential, LJ(12-6), reveal better-resolved solid and liquid basins compared with the case in which a global order parameter is used. It is also shown that the configuration space is sampled more efficiently in the present method, allowing a more accurate calculation of the free energy barrier and the solid-liquid interfacial free energy. Another feature of the present local order parameter-based method is that it is possible to apply the bias potential to regions of interest in the order parameter space, for example, on the largest nucleus in the case of nucleation studies. In the present scheme for metadynamics simulation of the nucleation in supercooled LJ(12-6) particles, unlike the cases in which global order parameters are employed, there is no need to have an estimate of the size of the critical nucleus and to refine the results with the results of umbrella sampling simulations. The barrier heights and the nucleation pathway obtained from this method agree very well with the results of former umbrella sampling simulations.

  6. Entropy Viscosity Method for High-Order Approximations of Conservation Laws

    KAUST Repository

    Guermond, J. L.

    2010-09-17

    A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

  7. Dynamics of a fractional-order simplified unified system based on the Adomian decomposition method

    Science.gov (United States)

    Xu, Yixin; Sun, Kehui; He, Shaobo; Zhang, Limin

    2016-06-01

    In this paper, the Adomian decomposition method (ADM) is applied to solve the fractional-order simplified unified system. The dynamics of the system is analyzed by means of the Lyapunov exponent spectrum, bifurcations, chaotic attractor, power spectrum and maximum Lyapunov exponent diagram. Route to chaos by period doubling is observed. Chaos is found to exist in the system with order as low as 1.371. In addition, chaotic behaviors are studied with different dimensional order, and the results show that this system is chaotic when only the first or third dimension is fractional.

  8. Method of reducing the green density of a slip cast article

    Science.gov (United States)

    Mangels, John A. (Inventor); Dickie, Ray A. (Inventor)

    1985-01-01

    The method disclosed in this specification is one of reducing the green density of an article cast in a slip casting operation. The article is cast from a casting slip containing silicon metal particles, yttrium containing particles, and a small amount of a fluoride salt which is effective to suppress flocculation of the silicon metal particles by y.sup.+3 ions derived from the yttrium containing particles. The method is characterized by the following step. A small amount of compound which produces a cation which will partly flocculate the particles of silicon metal is added to the casting slip. The small amount of this compound is added so that when the casting slip is slip cast into a casting mold, the partly flocculated particles of silicon will interrupt an otherwise orderly packing of the particles of silicon and particles of yttrium. In this manner, the green density of the slip cast article is reduced and the article may be more easily nitrided.

  9. A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Mohammed AL-Smadi

    2014-01-01

    Full Text Available The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.

  10. Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es

    2009-01-15

    A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

  11. A novel auto-tuning method for fractional order PI/PD controllers.

    Science.gov (United States)

    De Keyser, Robin; Muresan, Cristina I; Ionescu, Clara M

    2016-05-01

    Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Methods for globally treating silica optics to reduce optical damage

    Science.gov (United States)

    Miller, Philip Edward; Suratwala, Tayyab Ishaq; Bude, Jeffrey Devin; Shen, Nan; Steele, William Augustus; Laurence, Ted Alfred; Feit, Michael Dennis; Wong, Lana Louie

    2012-11-20

    A method for preventing damage caused by high intensity light sources to optical components includes annealing the optical component for a predetermined period. Another method includes etching the optical component in an etchant including fluoride and bi-fluoride ions. The method also includes ultrasonically agitating the etching solution during the process followed by rinsing of the optical component in a rinse bath.

  13. The Adapted Ordering Method for Lie algebras and superalgebras and their generalizations

    Energy Technology Data Exchange (ETDEWEB)

    Gato-Rivera, Beatriz [Instituto de Matematicas y Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); NIKHEF-H, Kruislaan 409, NL-1098 SJ Amsterdam (Netherlands)

    2008-02-01

    In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows us to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this paper we present the Adapted Ordering Method for general Lie algebras and superalgebras and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N = 2 and Ramond N = 1 superconformal algebras.

  14. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Directory of Open Access Journals (Sweden)

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  15. A ROBUST ARBITRARILY HIGH ORDER TRANSPORT METHOD OF THE CHARACTERISTIC TYPE FOR UNSTRUCTURED TETRAHEDRAL GRIDS

    Energy Technology Data Exchange (ETDEWEB)

    R. M. Ferrer; Y. Y. Azmy

    2009-05-01

    We present a robust arbitrarily high order transport method of the characteristic type for unstructured tetrahedral grids. Previously encountered difficulties have been addressed through the reformulation of the method based on coordinate transformations, evaluation of the moments balance relation as a linear system of equations involving the expansion coefficients of the projected basis, and the asymptotic expansion of the integral kernels in the thin cell limit. The proper choice of basis functions for the high-order spatial expansion of the solution is discussed and its effect on problems involving scattering discussed. Numerical tests are presented to illustrate the beneficial effect of these improvements, and the improved robustness they yield.

  16. An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

    KAUST Repository

    Cockburn, Bernardo

    2008-12-20

    We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.

  17. Application of Computational Intelligence in Order to Develop Hybrid Orbit Propagation Methods

    Directory of Open Access Journals (Sweden)

    Iván Pérez

    2013-01-01

    Full Text Available We present a new approach in astrodynamics and celestial mechanics fields, called hybrid perturbation theory. A hybrid perturbation theory combines an integrating technique, general perturbation theory or special perturbation theory or semianalytical method, with a forecasting technique, statistical time series model or computational intelligence method. This combination permits an increase in the accuracy of the integrating technique, through the modeling of higher-order terms and other external forces not considered in the integrating technique. In this paper, neural networks have been used as time series forecasters in order to help two economic general perturbation theories describe the motion of an orbiter only perturbed by the Earth’s oblateness.

  18. Solution of the first order linear fuzzy differential equations by some reliable methods

    Directory of Open Access Journals (Sweden)

    Mojtaba Ghanbari

    2012-10-01

    Full Text Available Fuzzy differential equations are used in modeling problems in science and engineering. For instance, it is known that the knowledge of dynamical systems modeled by ordinary differential equations is often incomplete or vague. While, fuzzy differential equations represent a proper way to model dynamical systems under uncertainty and vagueness. In this paper, two methods for solving first order linear fuzzy differential equations under generalized differentiability are proposed and compared. These methods are variational iteration method (VIM and Adomian decomposition method (ADM. The comparison of the exact solutions with solutions obtained by VIM and ADM are in details. The comparison shows that solutions are excellent agreement.

  19. Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations

    Directory of Open Access Journals (Sweden)

    C. Ünlü

    2013-01-01

    Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.

  20. Improved processing methods to reduce the total cyanide content of ...

    African Journals Online (AJOL)

    WHO amendments (10 mg HCN equivalent per kilogram flour), if the initial cyanide level of roots did not exceed 200 mg/kg d.w. Actually, the initial maximum total cyanide content was confirmed to be fundamental in order to obtain safe products ...

  1. Energy stable and high-order-accurate finite difference methods on staggered grids

    Science.gov (United States)

    O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

    2017-10-01

    For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

  2. Numerical solution of first order initial value problem using quartic spline method

    Science.gov (United States)

    Ala'yed, Osama; Ying, Teh Yuan; Saaban, Azizan

    2015-12-01

    Any first order initial value problem can be integrated numerically by discretizing the interval of integration into a number of subintervals, either with equally distributed grid points or non-equally distributed grid points. Hence, as the integration advances, the numerical solutions at the grid points are calculated and being known. However, the numerical solutions between the grid points remain unknown. This will form difficulty to individuals who wish to study a particular solution which may not fall on the grid points. Therefore, some sorts of interpolation techniques are needed to deal with such difficulty. Spline interpolation technique remains as a well known approach to approximate the numerical solution of a first order initial value problem, not only at the grid points but also everywhere between the grid points. In this short article, a new quartic spline method has been derived to obtain the numerical solution for first order initial value problem. The key idea of the derivation is to treat the third derivative of the quartic spline function to be a linear polynomial, and obtain the quartic spline function with undetermined coefficients after three integrations. The new quartic spline function is ready to be used when all unknown coefficients are found. We also described an algorithm for the new quartic spline method when used to obtain the numerical solution of any first order initial value problem. Two test problems have been used for numerical experimentations purposes. Numerical results seem to indicate that the new quartic spline method is reliable in solving first order initial value problem. We have compared the numerical results generated by the new quartic spline method with those obtained from an existing spline method. Both methods are found to have comparable accuracy.

  3. Progress Report on SAM Reduced-Order Model Development for Thermal Stratification and Mixing during Reactor Transients

    Energy Technology Data Exchange (ETDEWEB)

    Hu, R. [Argonne National Lab. (ANL), Argonne, IL (United States)

    2017-09-01

    This report documents the initial progress on the reduced-order flow model developments in SAM for thermal stratification and mixing modeling. Two different modeling approaches are pursued. The first one is based on one-dimensional fluid equations with additional terms accounting for the thermal mixing from both flow circulations and turbulent mixing. The second approach is based on three-dimensional coarse-grid CFD approach, in which the full three-dimensional fluid conservation equations are modeled with closure models to account for the effects of turbulence.

  4. A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

    Energy Technology Data Exchange (ETDEWEB)

    Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com [Universidad Politécnica de Tlaxcala Av. Universidad Politecnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico); Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx [Departamento de Control Automático CINVESTAV-IPN, A.P. 14-740, D.F., México C.P. 07360 (Mexico); Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx [Universidad Politécnica de Tlaxcala Av. Universidad Politécnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico)

    2015-10-15

    This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

  5. A new time–space domain high-order finite-difference method for the acoustic wave equation

    KAUST Repository

    Liu, Yang

    2009-12-01

    A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

  6. Characterization method of unusual second-order-harmonic generation based on vortex transformation

    Science.gov (United States)

    Zhang, Chaojin; Wu, Erheng; Gu, Mingliang; Hu, Zhengfeng; Liu, Chengpu

    2017-09-01

    When a few-cycle laser beam nonresonantly propagates through an inversion-symmetric medium, beyond the usual odd-order harmonics in the transmission spectra, a well-defined spectral peak at twice the incident laser central frequency is disclosed [T. Tritschler et al., Phys. Rev. Lett. 90, 217404 (2003), 10.1103/PhysRevLett.90.217404]. Beyond the characterization method via the rf measurement of its carrier-envelope phase dependence, here a more direct mode of characterization is proposed by means of vortex transformation where a few-cycle vortex laser is adopted instead: One can easily clarify its origin as an usual third-order harmonic that appears to be a second-order harmonic, based on the criteria that the topological charge number of harmonics is directly proportional to its harmonic order.

  7. Improved processing methods to reduce the total cyanide content of ...

    African Journals Online (AJOL)

    PierGuido

    2013-05-08

    May 8, 2013 ... The identification of highly effective procedures that reduce the cyanogens contained in cassava roots which require no sophisticated equipment, and can readily be adopted by subsistence farmers is of tremendous importance. This study, which used cassava root samples collected in Burundi, included.

  8. Methods for Reducing the Energy Consumption of Mobile Broadband Networks

    DEFF Research Database (Denmark)

    Micallef, Gilbert

    2010-01-01

    Up until recently, very little consideration has been given towards reducing the energy consumption of the networks supporting mobile communication. This has now become an important issue since with the predicted boost in traffic, network operators are required to upgrade and extend their networks...

  9. Comparison of Three Methods to Reduce Student Procrastination in PSI.

    Science.gov (United States)

    Lamwers, Linda L.; And Others

    While self-pacing may appear to be an ideal solution to problems stemming from individual differences in academic skill levels among college students, students in Personalized System of Instruction (PSI) courses may tend to procrastinate. Three course contingencies were studied for their effectiveness in reducing student procrastination and…

  10. Higher order analytical nodal methods in response-matrix formulation for the multigroup neutron diffusion equations

    Energy Technology Data Exchange (ETDEWEB)

    Guessous, N. E-mail: guessous_najib@hotmail.com; Akhmouch, M

    2002-10-01

    A higher analytical nodal method for the multigroup neutron diffusion equations, based on the transverse integration procedure, is presented. The discrete 1D equations are cast with the interface partial current techniques in response matrix formalism. The remaining Legendre coefficients of the transverse leakage moment are determined exactly in terms of the different neutron flux moments order in the reference node. In the weighted balance equations, the transverse leakage moments are linearly written in terms of the partial currents, facial and centered fluxes moments. The self-consistent is guaranteed. Furthermore, as the order k increase the neutronic balance in each node and the copulate between the adjacent cell are reinforced. The convergence order in L{sup 2}-norm is of O(h{sup k+3-{delta}k{sub 0}}) under smooth assumptions. The efficacy of the method is showed for 2D-PWR, 2D-IAEA LWR and 2D-LMFBR benchmark problems.

  11. High-order time-splitting Hermite and Fourier spectral methods

    Science.gov (United States)

    Thalhammer, Mechthild; Caliari, Marco; Neuhauser, Christof

    2009-02-01

    In this paper, we are concerned with the numerical solution of the time-dependent Gross-Pitaevskii Equation (GPE) involving a quasi-harmonic potential. Primarily, we consider discretisations that are based on spectral methods in space and higher-order exponential operator splitting methods in time. The resulting methods are favourable in view of accuracy and efficiency; moreover, geometric properties of the equation such as particle number and energy conservation are well captured. Regarding the spatial discretisation of the GPE, we consider two approaches. In the unbounded domain, we employ a spectral decomposition of the solution into Hermite basis functions; on the other hand, restricting the equation to a sufficiently large bounded domain, Fourier techniques are applicable. For the time integration of the GPE, we study various exponential operator splitting methods of convergence orders two, four, and six. Our main objective is to provide accuracy and efficiency comparisons of exponential operator splitting Fourier and Hermite pseudospectral methods for the time evolution of the GPE. Furthermore, we illustrate the effectiveness of higher-order time-splitting methods compared to standard integrators in a long-term integration.

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

    Science.gov (United States)

    Song, Junqiang; Leng, Hongze; Lu, Fengshun

    2014-01-01

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

  13. Higher-order multi-resolution topology optimization using the finite cell method

    NARCIS (Netherlands)

    Groen, J.P.; Langelaar, M.; Sigmund, O; Ruess, M.

    2017-01-01

    This article presents a detailed study on the potential and limitations of performing higher-order multi-resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high-contrast topologies, a length-scale is applied on the solution using filter

  14. First Order Linear Homogeneous Fuzzy Ordinary Differential Equation Based on Lagrange Multiplier Method

    Directory of Open Access Journals (Sweden)

    Sankar Prasad Mondal

    2013-11-01

    Full Text Available In this paper the First Order Linear Fuzzy Ordinary Differential Equations are described. Here coefficients and /or initial condition of said differential equation are taken as the Generalized Triangular Fuzzy Numbers (GTFNs.The solution procedure of this Fuzzy Differential Equation is developed by Lagrange Multiplier Method. An imprecise barometric pressure problem is described.

  15. A family of block methods for special second order initial value ...

    African Journals Online (AJOL)

    In this paper, efforts are directed towards generating a 2-block 2-point numerical method for solving the special second order initial value problems of the form Y\\'\\' = F(X, Y), Y(0) = YO, Y\\'(0) = YOO .. The scheme so developed, is in the same line of thought as Shampine and Watts (1969, 1972) [9]; Chu and Hamltion (1987) ...

  16. Application of the cluster variation method to ordering in an interstitital solid solution

    DEFF Research Database (Denmark)

    Pekelharing, Marjon I.; Böttger, Amarante; Somers, Marcel A. J.

    1999-01-01

    The tetrahedron approximation of the cluster variation method (CVM) was applied to describe the ordering on the fcc interstitial sublattice of gamma-Fe[N] and gamma'-Fe4N1-x. A Lennard-Jones potential was used to describe the dominantly strain-induced interactions, caused by misfitting of the N a...

  17. Probabilistic modelling of combined sewer overflow using the First Order Reliability Method

    DEFF Research Database (Denmark)

    Thorndahl, Søren; Schaarup-Jensen, Kjeld; Jensen, Jacob Birk

    2007-01-01

    uncertainties on an application of the commercial urban drainage model MOUSE combined with the probabilistic First Order Reliability Method (FORM). Applying statistical characteristics on several years of rainfall, it is possible to derive a parameterization of the rainfall input and the failure probability...

  18. Probabilistic Modelling of Combined Sewer Overflow Using the First Order Reliability Method

    DEFF Research Database (Denmark)

    Thorndahl, Søren; Schaarup-Jensen, Kjeld; Jensen, Jacob Birk

    2008-01-01

    uncertainties on an application of the commercial urban drainage model MOUSE combined with the probabilistic First Order Reliability Method (FORM). Applying statistical characteristics on several years of rainfall, it is possible to derive a parameterization of the rainfall input and the failure probability...

  19. Uniform Order Zero- Stable K-Step Block Methods For Initial Value ...

    African Journals Online (AJOL)

    ... successive steps movement at a time (block steps). Numerical examples are given to illustrate the performance of the new procedures. Keywords: Zero stability, Hybrid, k–step, Block methods, first order initial value problem. Journal of the Nigerian Association of Mathematical Physics, Volume 20 (March, 2012), pp 65 – 74 ...

  20. Algorithms and software for total variation image reconstruction via first-order methods

    DEFF Research Database (Denmark)

    Dahl, Joahim; Hansen, Per Christian; Jensen, Søren Holdt

    2010-01-01

    This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov's first-order methods, tailored to the image processing applications in such a way that...

  1. A region-based multiple testing method for hypotheses ordered in space or time

    NARCIS (Netherlands)

    Meijer, R.J.; Krebs, T.J.; Goeman, J.J.

    2015-01-01

    Abstract We present a multiple testing method for hypotheses that are ordered in space or time. Given such hypotheses, the elementary hypotheses as well as regions of consecutive hypotheses are of interest. These region hypotheses not only have intrinsic meaning but testing them also has the

  2. A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows

    Science.gov (United States)

    Zhou, Qiang; Fan, Liang-Shih

    2014-07-01

    A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding

  3. Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

    Energy Technology Data Exchange (ETDEWEB)

    Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)

    2013-09-15

    Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.

  4. Model's sparse representation based on reduced mixed GMsFE basis methods

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn [Institute of Mathematics, Hunan University, Changsha 410082 (China); Li, Qiuqi, E-mail: qiuqili@hnu.edu.cn [College of Mathematics and Econometrics, Hunan University, Changsha 410082 (China)

    2017-06-01

    In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in

  5. Comparison of the methods for discrete approximation of the fractional-order operator

    Directory of Open Access Journals (Sweden)

    Zborovjan Martin

    2003-12-01

    Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.

  6. Analysis of some methods for reduced rank Gaussian process regression

    DEFF Research Database (Denmark)

    Quinonero-Candela, J.; Rasmussen, Carl Edward

    2005-01-01

    proliferation of a number of cost-effective approximations to GPs, both for classification and for regression. In this paper we analyze one popular approximation to GPs for regression: the reduced rank approximation. While generally GPs are equivalent to infinite linear models, we show that Reduced Rank......While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent...... Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning...

  7. Higher-Order Equation-of-Motion Coupled-Cluster Methods for Ionization Processes

    Energy Technology Data Exchange (ETDEWEB)

    Kamiya, Muneaki; Hirata, So

    2006-08-21

    Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both {alpha} and {beta} and ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N{sub 2} and CO (with the ambiguity due to finite basis sets eliminated by extrapolation) has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV. However, these errors can be systematically reduced to tenths or even hundredths of an eV by IP-EOM-CCSDT or CCSDTQ. Comparison of spectroscopic parameters of the FH{sup +} and NH{sup +} radicals between IP-EOM-CC and experiments has also underscored the importance of higher-order IP-EOM-CC treatments. For instance, the harmonic frequencies of the {tilde A} {sup 2}{Sigma}{sup -} state of NH{sup +}+ are predicted to be 1285, 1723, and 1705 cm{sup -1} by IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively, as compared to the observed value of 1707 cm{sup -1}. The small adiabatic energy separation (observed 0.04 eV) between the {tilde X} {sup 2}II and {tilde a} {sup 4}{sigma}{sup -} states of NH{sup +} also requires IP-EOM-CCSDTQ for a quantitative

  8. A simplified fractional order impedance model and parameter identification method for lithium-ion batteries

    Science.gov (United States)

    Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing

    2017-01-01

    Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405

  9. A Preconditioning Technique for First-Order Primal-Dual Splitting Method in Convex Optimization

    Directory of Open Access Journals (Sweden)

    Meng Wen

    2017-01-01

    Full Text Available We introduce a preconditioning technique for the first-order primal-dual splitting method. The primal-dual splitting method offers a very general framework for solving a large class of optimization problems arising in image processing. The key idea of the preconditioning technique is that the constant iterative parameters are updated self-adaptively in the iteration process. We also give a simple and easy way to choose the diagonal preconditioners while the convergence of the iterative algorithm is maintained. The efficiency of the proposed method is demonstrated on an image denoising problem. Numerical results show that the preconditioned iterative algorithm performs better than the original one.

  10. Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

    Directory of Open Access Journals (Sweden)

    Iryna Komashynska

    2014-01-01

    Full Text Available We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.

  11. A method for simultaneously counterbalancing condition order and assignment of stimulus materials to conditions.

    Science.gov (United States)

    Zeelenberg, René; Pecher, Diane

    2015-03-01

    Counterbalanced designs are frequently used in the behavioral sciences. Studies often counterbalance either the order in which conditions are presented in the experiment or the assignment of stimulus materials to conditions. Occasionally, researchers need to simultaneously counterbalance both condition order and stimulus assignment to conditions. Lewis (1989; Behavior Research Methods, Instruments, & Computers 25:414-415, 1993) presented a method for constructing Latin squares that fulfill these requirements. The resulting Latin squares counterbalance immediate sequential effects, but not remote sequential effects. Here, we present a new method for generating Latin squares that simultaneously counterbalance both immediate and remote sequential effects and assignment of stimuli to conditions. An Appendix is provided to facilitate implementation of these Latin square designs.

  12. Implementation of an optimal first-order method for strongly convex total variation regularization

    DEFF Research Database (Denmark)

    Jensen, Tobias Lindstrøm; Jørgensen, Jakob Heide; Hansen, Per Christian

    2012-01-01

    We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to μ-strongly convex objective functions with L-Lipschitz continuous gradient...... parameter μ for solving ill-conditioned problems to high accuracy, in comparison with an optimal method for non-strongly convex problems and a first-order method with Barzilai-Borwein step size selection........ In the framework of Nesterov both μ and L are assumed known—an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient μ and L during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss...

  13. A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    Sufia Zulfa Ahmad

    2016-01-01

    Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

  14. A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

    Science.gov (United States)

    Bilyeu, David

    This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For

  15. Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

    Science.gov (United States)

    Merrikh-Bayat, Farshad

    2011-04-01

    One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

  16. Exploring Ce3+/Ce4+ cation ordering in reduced ceria nanoparticles using interionic-potential and density-functional calculations.

    Science.gov (United States)

    Migani, Annapaola; Neyman, Konstantin M; Illas, Francesc; Bromley, Stefan T

    2009-08-14

    The performance of atomistic calculations using interionic potentials has been examined in detail with respect to the structures and energetic stabilities of ten configurational isomers (i.e., distinct Ce3+/Ce4+ cationic orderings) of a low energy octahedral ceria nanoparticle Ce19O32. The outcome of these calculations is compared with the results of corresponding density-functional (DF) calculations employing local and gradient corrected functionals with an additional corrective onsite Coulombic interaction applied to the f-electrons (i.e., LDA+U and GGA+U, respectively). Strikingly similar relative energy ordering of the isomers and atomic scale structural trends (e.g., cation-cation distances) are obtained in both the DF and interionic-potential calculations. The surprisingly good agreement between the DF electronic structure calculations and the relatively simple classical potentials is not found to be due to a single dominant interaction type but is due to a sensitive balance between long range electrostatics and local bonding contributions to the energy. Considering the relatively high computational cost and technical difficulty involved in obtaining charge-localized electronic solutions for reduced ceria using DF calculations, the use of interionic potentials for rapid and reliable preselection of the most stable Ce3+/Ce4+ cationic orderings is of considerable benefit.

  17. Optimized Computerized Order Entry can Reduce Errors in Electronic Prescriptions and Associated Pharmacy Calls to Clarify (CTC).

    Science.gov (United States)

    Patel, Jaimin; Ogletree, Richard; Sutterfield, Allison; Pace, John C; Lahr, Laurene

    2016-01-01

    After implementation of a system-wide EMR within our university system, e-prescribing is now commonplace. The authors conducted a study to assess whether optimization of computerized provider order entry (CPOE) can reduce errors in these electronically transmitted prescriptions and would require less frequent interventions from pharmacists, in particular the need for them to "call to clarify" (CTC) details of particular prescriptions. Secondary analysis based on cost assumptions was preformed to presume cost differences before and after optimization changes. In order to generate complete, error-free prescriptions, optimization changes were implemented in the form of in line validation messages. These messages were generated if (1) an order did not specify a provider or pharmacy; (2) the DEA requirements were not met; (3) character limits were exceeded in patient sig or demographics or (4) administration instructions had breaks or had both discrete and free text elements. Retrospectively, prescriptions were randomly selected from a nine month period before and after implementing changes. These prescriptions were analyzed by a pharmacist and a nurse to identify types of errors that would require a CTC to a prescribing provider. Errors were compared statistically to determine effectiveness of changes pre and post optimization. A total of 602 prescriptions were analyzed; 301 before changes and 301 after changes. Of these prescriptions, 20.27% had errors before changes and 12.96% had errors after changes. The decline in the error rate was considered statistically significant for pprescriptions for pharmacist and physician time-cost estimates combined. Implementing optimization changes to the CPOE resulted in a reduction in error rate requiring pharmacist CTC. This study identifies effective optimization changes for electronic prescribing that can reduce prescribing errors and may result in cost saving.

  18. A Further Indication of the Self-Ordering Capacity of Water Via the Droplet Evaporation Method

    Directory of Open Access Journals (Sweden)

    Igor Jerman

    2014-10-01

    Full Text Available The droplet evaporation method (DEM is increasingly used for assessing various characteristics of water. In our research we tried to use DEM to detect a possible self-ordering capability of (spring water that would be similar to the already found and described autothixotropic phenomenon, namely increasing order of non-distilled water subject to aging. The output of DEM is a droplet remnant pattern (DRP. For analysis of DRP images we used a specially developed computer program that does the frequency distribution analysis of certain parameters of the images. The results of experiments demonstrated statistically significant differences in both aging of water as well as in the glass exposed surface/volume ratio of the aged water. The most important result supporting the self-ordering character of water was found in an increasing dependence between two analyzed parameters: distance and frequency, at the peak frequency. As the result concerns mostly aging and shows increasing order it further corroborates other findings concerning increasing order by aging. Such further confirmation of self-ordering capacity of water is not important only for physical chemistry, but also for biology.

  19. High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

    KAUST Repository

    Abdulle, Assyr

    2012-01-01

    © 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

  20. Surface sterilization method for reducing microbial contamination of ...

    African Journals Online (AJOL)

    An effective disinfection method for strawberry (Fragaria x ananassa Duch.) cv. Senga Sengana micropropagation using runner tips and nodal segments as explants was developed. The explants were surface sterilized with different sterilants for different durations. The present studies on the effect of different regimes of ...

  1. Managing concrete bridges: Methods for reducing costs and user inconveniences

    DEFF Research Database (Denmark)

    Goltermann, Per

    2005-01-01

    The paper presents experiences from modern bridge maintenance management, which has been forced to develop new and cost-efficient approaches in order to cope with the increase in overall deterioration of the aging bridge stock, the growing requirements to accessibility and the decreasing budgets....... These approaches are focused on cost reductions, but must as well lead to a reduction of the user inconveniences (traffic delays, noise, dust) and to a reduction of the environmental impact. These approaches can be based on an assessment of the structures safety, which incorporates the inaccuracies...... in the condition assessments, the models and the predictions in the strategies and the cost estimations. This may lead to increased inspection frequencies, detailed simulations, monitoring and testing to be used as alternatives to extensive repairs, rehabilitations or strengthening. The approaches will in other...

  2. Spectrophotometric determination of chlorthalidone in pharmaceutical formulations using different order derivative methods

    Directory of Open Access Journals (Sweden)

    Narmeen S. Abdullah

    2017-05-01

    Full Text Available Simple, repaid and accurate zero-, first- and second-order derivative spectrophotometric methods have been developed for determination of chlorthalidone (CLT in commercially available tablets. Normal spectrophotometric scan (zero order shows maximum absorbance at 276 nm in methanol solution and a good linearity in the range of 10.0–75.0 μg/mL. Linear relations using first (D1 and second (D2 order derivative methods were obtained at 278 and 288 nm for D1 and 286 and 292 nm for D2.The calibration curves were constructed in the range of 1.0–25.0 μg/mL for D1 (R = 0.998 and D2 (R = 0.999. Different analytical validations were determined (accuracy, precision, specificity, recovery, stability and robustness to demonstrate its suitability for routine quality control labs. All the developed methods were successfully applied to a tablet formulation and the results were compared statistically with each other and with those obtained by the HPLC reference method.

  3. Compositional modeling of three-phase flow with gravity using higher-order finite element methods

    KAUST Repository

    Moortgat, Joachim

    2011-05-11

    A wide range of applications in subsurface flow involve water, a nonaqueous phase liquid (NAPL) or oil, and a gas phase, such as air or CO2. The numerical simulation of such processes is computationally challenging and requires accurate compositional modeling of three-phase flow in porous media. In this work, we simulate for the first time three-phase compositional flow using higher-order finite element methods. Gravity poses complications in modeling multiphase processes because it drives countercurrent flow among phases. To resolve this issue, we propose a new method for the upwinding of three-phase mobilities. Numerical examples, related to enhanced oil recovery and carbon sequestration, are presented to illustrate the capabilities of the proposed algorithm. We pay special attention to challenges associated with gravitational instabilities and take into account compressibility and various phase behavior effects, including swelling, viscosity changes, and vaporization. We find that the proposed higher-order method can capture sharp solution discontinuities, yielding accurate predictions of phase boundaries arising in computational three-phase flow. This work sets the stage for a broad extension of the higher-order methods for numerical simulation of three-phase flow for complex geometries and processes.

  4. A Robust Control Method for Q-S Synchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems

    Directory of Open Access Journals (Sweden)

    Adel Ouannas

    2015-01-01

    Full Text Available A robust control approach is presented to study the problem of Q-S synchronization between Integer-order and fractional-order chaotic systems with different dimensions. Based on Laplace transformation and stability theory of linear integer-order dynamical systems, a new control law is proposed to guarantee the Q-S synchronization between n-dimensional integer-order master system and m-dimensional fractional-order slave system. This paper provides further contribution to the topic of Q-S chaos synchronization between integer-order and fractional-order systems and introduces a general control scheme that can be applied to wide classes of chaotic and hyperchaotic systems. Illustrative example and numerical simulations are used to show the effectiveness of the proposed method.

  5. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

    Directory of Open Access Journals (Sweden)

    Huan-Yu Bi

    2015-09-01

    Full Text Available The Principle of Maximum Conformality (PMC eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I; the other, more recent, method (PMC-II uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e− and the Higgs partial width Γ(H→bb¯. Both methods lead to the same resummed (‘conformal’ series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  6. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

    Science.gov (United States)

    Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

    2015-09-01

    The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Γ (H → b b bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi }-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  7. Numerical simulation of the second-order Stokes theory using finite difference method

    Directory of Open Access Journals (Sweden)

    M.A. Maâtoug

    2016-09-01

    Full Text Available The nonlinear water waves problem is of great importance because, according to the mechanical modeling of this problem, a relationship exists between the potential flow and pressure exerted by water waves. The difficulty of this problem comes not only from the fact that the kinematic and dynamic conditions are nonlinear in relation to the velocity potential, but especially because they are applied at an unknown and variable free surface. To overcome this difficulty, Stokes used an approach consisting of perturbations series around the still water level to develop a nonlinear theory. This paper deals with computation of the second-order Stokes theory in order to simulate the potential flow and the surface elevation and then to deduct the pressure loads. The Crank–Nicholson scheme and the finite difference method are used. The modeling accuracy was proved and is of order two in time and in space. Some computational results are presented and discussed.

  8. Methods to reduce production of oil sands mature fine tailings

    Energy Technology Data Exchange (ETDEWEB)

    Ozum, B. [Apex Engineering Inc., Edmonton, AB (Canada); Scott, J.D. [Alberta Univ., Edmonton, AB (Canada)

    2010-07-01

    This paper discussed experimental findings regarding the use of alternative extraction additives in the Clark Hot Water Bitumen Extraction (CHWBE) process to improve the geotechnical characteristics of the tailings and the salinity of the recycled release water. It also discussed results regarding the production of non-segregating tailings (NST) from the blend of cyclone underflow and thickener underflow using either calcium oxide (CaO) or CaO and carbon dioxide (CO{sub 2}) as additives. Sodium hydroxide (NaOH) is currently used in CHWBE to increase extraction efficiency, but this additive also creates tailings with poor settling and consolidation properties and high salinity in the recycled release water. The use of CaO for adjusting pH, ozone (O{sub 3}) for producing surfactants from bitumen asphaltenes, and biodiesel as surfactant additives were found to increase the efficiency of the extraction process, produce tailings with friendlier geotechnical properties, and eliminate saline concentrations in the recycled release water. The use of the described alternative extraction additives and the NST production processes has the potential to reduce the environmental impacts of oil sands plants, potentially providing a solution to the problems associated with Low Temperature Extraction and Consolidated Tailings processes. The solubility of CaO and O{sub 3} as a function of temperature could potentially allow the extraction temperature to be reduced. O{sub 3} was found to work better as an oxidant to produce surfactants from bitumen when the ore-slurry is first treated with CaO. Study on a larger scale is required. 23 refs., 7 tabs., 7 figs.

  9. System and methods for reducing harmonic distortion in electrical converters

    Energy Technology Data Exchange (ETDEWEB)

    Kajouke, Lateef A; Perisic, Milun; Ransom, Ray M

    2013-12-03

    Systems and methods are provided for delivering energy using an energy conversion module. An exemplary method for delivering energy from an input interface to an output interface using an energy converison module coupled between the input interface and the output interface comprises the steps of determining an input voltage reference for the input interface based on a desired output voltage and a measured voltage and the output interface, determining a duty cycle control value based on a ratio of the input voltage reference and the measured voltage, operating one or more switching elements of the energy conversion module to deliver energy from the input interface to the output interface to the output interface with a duty cycle influenced by the dute cycle control value.

  10. System Response Analysis and Model Order Reduction, Using Conventional Method, Bond Graph Technique and Genetic Programming

    Directory of Open Access Journals (Sweden)

    Lubna Moin

    2009-04-01

    Full Text Available This research paper basically explores and compares the different modeling and analysis techniques and than it also explores the model order reduction approach and significance. The traditional modeling and simulation techniques for dynamic systems are generally adequate for single-domain systems only, but the Bond Graph technique provides new strategies for reliable solutions of multi-domain system. They are also used for analyzing linear and non linear dynamic production system, artificial intelligence, image processing, robotics and industrial automation. This paper describes a unique technique of generating the Genetic design from the tree structured transfer function obtained from Bond Graph. This research work combines bond graphs for model representation with Genetic programming for exploring different ideas on design space tree structured transfer function result from replacing typical bond graph element with their impedance equivalent specifying impedance lows for Bond Graph multiport. This tree structured form thus obtained from Bond Graph is applied for generating the Genetic Tree. Application studies will identify key issues and importance for advancing this approach towards becoming on effective and efficient design tool for synthesizing design for Electrical system. In the first phase, the system is modeled using Bond Graph technique. Its system response and transfer function with conventional and Bond Graph method is analyzed and then a approach towards model order reduction is observed. The suggested algorithm and other known modern model order reduction techniques are applied to a 11th order high pass filter [1], with different approach. The model order reduction technique developed in this paper has least reduction errors and secondly the final model retains structural information. The system response and the stability analysis of the system transfer function taken by conventional and by Bond Graph method is compared and

  11. Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede

    2004-01-01

    This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...... matrix converter model. Regulated Order Extended Luenberger Observer (ROELO) is employed to bring better response in the whole speed operation range and a method to select the observer gain is presented. Experimental results are shown to illustrate the performance of the proposed system...

  12. FIRST-ORDER ULTRAVIOLET DERIVATIVE SPECTROPHOTOMETRIC METHODS FOR DETERMINATION OF RESERPINE IN ANTIHYPERTENSION TABLET

    Directory of Open Access Journals (Sweden)

    Latifah K Darusman

    2012-12-01

    Full Text Available A new ultraviolet derivative spectrophotometry (UVDS method has been developed for determination of reserpine in antihypertension tablets. A first-order UVDS based on the measurement of the distance between peaks to baseline (DZ at the wavelength of 312 nm was used. Evaluation of analytical performance showed that accuracy as percentage recovery was 99.18-101.13%, precision expressed as relative standard deviation (RSD was 1.91% and linear correlation was also obtained 0.9998 in the range of 10-50 µg/mL. Estimation of limit of detection and limit of quantitation was 0.8868 µg/mL and 2.6874 µg/mL, respectively. As a reference method, HPLC methods from United States Pharmacopiea (USP were used. Commercially tablets available were analyzed by the two methods. The content of reserpine in tablets was found 0.2260±0.0033 mg by UVDS and 0.2301±0.0051 mg by the USP methods. The result obtained from the two methods was compared statistically using F-test and t-test and showed no significant differences between the variance and mean values of the two methods at 95% confidence level. This method was faster, easier, low cost and gave result as well as the reference method published by USP.

  13. Level set methods for detonation shock dynamics using high-order finite elements

    Energy Technology Data Exchange (ETDEWEB)

    Dobrev, V. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Grogan, F. C. [Univ. of California, San Diego, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, T. V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, R [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Tomov, V. Z. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2017-05-26

    Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two- and three-dimensional benchmark problems as well as applications to DSD.

  14. Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

    Directory of Open Access Journals (Sweden)

    Sankar Prasad Mondal

    2016-06-01

    Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

  15. Performance of First- and Second-Order Methods for L1-Regularized Least Squares Problems

    OpenAIRE

    Fountoulakis, Kimon; Gondzio, Jacek

    2015-01-01

    We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously defined generator is presented which allows control of the dimensions, the conditioning and the sparsity of the problem. The generator has very low memory requirements and scales well with the dimensions of the problem.

  16. A finite difference method for nonlinear parabolic-elliptic systems of second order partial differential equations

    OpenAIRE

    Marian Malec; Lucjan Sapa

    2007-01-01

    This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in \\(\\mathbf{R}^{1+n}\\). A suitable finite difference scheme is constructed. It is proved that the scheme has a unique sol...

  17. Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs

    Directory of Open Access Journals (Sweden)

    Hala Kamal

    2017-11-01

    Full Text Available Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows for one to extract partial information and gives an alternative to classical graph approach.

  18. 10th International Conference on Spectral and High-Order Methods

    CERN Document Server

    Berzins, Martin; Hesthaven, Jan

    2015-01-01

    The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area.  The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.

  19. Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Asma Ali Elbeleze

    2014-01-01

    Full Text Available We are concerned here with singular partial differential equations of fractional order (FSPDEs. The variational iteration method (VIM is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.

  20. Radial basis function methods for the Rosenau equation and other higher order PDEs

    OpenAIRE

    Safdari-Vaighani, Ali; Larsson, Elisabeth; Heryudono, Alfa

    2017-01-01

    Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can provide high order convergence, they are not more complicated for problems with many space dimensions and they allow for local refinement. The aim of this paper is to show that the solution of the Rosenau equation, as an example of an initial-boundary valu...

  1. A 3D Unstructured Mesh Euler Solver Based on the Fourth-Order CESE Method

    Science.gov (United States)

    2013-06-01

    hyperplane in every BCE associated with the current cell (j, n) and then take the sum of all integrations . For a tetrahedral mesh each cell has four...conservation in space and time without using a one-dimensional Riemann solver, (ii) genuinely multi-dimensional treatment without dimensional splitting (iii...of the original second-order CESE method, including: (i) flux conservation in space and time without using a one-dimensional Riemann solver, (ii

  2. Sensitivity Weaknesses in Application of some Statistical Distribution in First Order Reliability Methods

    DEFF Research Database (Denmark)

    Sørensen, John Dalsgaard; Enevoldsen, I.

    1993-01-01

    a stochastic variable is modelled by an asymmetrical density function. For lognormally, Gumbel and Weibull distributed stochastic variables it is shown for which combinations of the/3-point, the expected value and standard deviation the weakness can occur. In relation to practical application the behaviour...... is probably rather infrequent. A simple example is shown as illustration and to exemplify that for second order reliability methods and for exact calculations of the probability of failure this behaviour is much more infrequent....

  3. Error analysis of Newmark's method for the second order equation with inhomogeneous term

    Energy Technology Data Exchange (ETDEWEB)

    Chiba, F.; Kako, T. [Department of Computer Science, University of Electro-Communications, Tokyo (Japan)

    2000-06-01

    For the second order time evolution equation with a general dissipation term, we introduce a recurrence relation of Newmark's method. Deriving an energy inequality from this relation, we consider the stability and the convergence criteria of Newmark's method. We treat a dissipation term under the assumption that the coefficient-damping matrix is constant in time and non-negative. We can relax however the assumptions for the dissipation and the rigidity matrices to be arbitrary symmetric matrices. (author)

  4. Local convergence of a fifth convergence order method in Banach space

    Directory of Open Access Journals (Sweden)

    Ioannis K. Argyros

    2017-07-01

    Full Text Available We provide a local convergence analysis for a fifth convergence order method to find a solution of a nonlinear equation in a Banach space. In our paper the sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative. Previous works use conditions reaching up to the fourth Fréchet-derivative. This way, the applicability of these methods is extended under weaker conditions and less computational cost for the Lipschitz constants appearing in the convergence analysis. Numerical examples are also given in this paper.

  5. Experimental Methods in Reduced-gravity Soldering Research

    Science.gov (United States)

    Pettegrew, Richard D.; Struk, Peter M.; Watson, John K.; Haylett, Daniel R.

    2002-01-01

    The National Center for Microgravity Research, NASA Glenn Research Center, and NASA Johnson Space Center are conducting an experimental program to explore the influence of reduced gravity environments on the soldering process. An improved understanding of the effects of the acceleration environment is important to application of soldering during current and future human space missions. Solder joint characteristics that are being considered include solder fillet geometry, porosity, and microstructural features. Both through-hole and surface mounted devices are being investigated. This paper focuses on the experimental methodology employed in this project and the results of macroscopic sample examination. The specific soldering process, sample configurations, materials, and equipment were selected to be consistent with those currently on-orbit. Other apparatus was incorporated to meet requirements imposed by operation onboard NASA's KC-135 research aircraft and instrumentation was provided to monitor both the atmospheric and acceleration environments. The contingent of test operators was selected to include both highly skilled technicians and less skilled individuals to provide a population cross-section that would be representative of the skill mix that might be encountered in space mission crews.

  6. Ordered and ultrathin reduced graphene oxide LB films as hole injection layers for organic light-emitting diode.

    Science.gov (United States)

    Yang, Yajie; Yang, Xiaojie; Yang, Wenyao; Li, Shibin; Xu, Jianhua; Jiang, Yadong

    2014-01-01

    In this paper, we demonstrated the utilization of reduced graphene oxide (RGO) Langmuir-Blodgett (LB) films as high performance hole injection layer in organic light-emitting diode (OLED). By using LB technique, the well-ordered and thickness-controlled RGO sheets are incorporated between the organic active layer and the transparent conducting indium tin oxide (ITO), leading to an increase of recombination between electrons and holes. Due to the dramatic increase of hole carrier injection efficiency in RGO LB layer, the device luminance performance is greatly enhanced comparable to devices fabricated with spin-coating RGO and a commercial conducting polymer PEDOT:PSS as the hole transport layer. Furthermore, our results indicate that RGO LB films could be an excellent alternative to commercial PEDOT:PSS as the effective hole transport and electron blocking layer in light-emitting diode devices.

  7. Validation and application of an high-order spectral difference method for flow induced noise simulation

    KAUST Repository

    Parsani, Matteo

    2011-09-01

    The main goal of this paper is to develop an efficient numerical algorithm to compute the radiated far field noise provided by an unsteady flow field from bodies in arbitrary motion. The method computes a turbulent flow field in the near fields using a high-order spectral difference method coupled with large-eddy simulation approach. The unsteady equations are solved by advancing in time using a second-order backward difference formulae scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lowerupper symmetric GaussSeidel algorithm. In the second step, the method calculates the far field sound pressure based on the acoustic source information provided by the first step simulation. The method is based on the Ffowcs WilliamsHawkings approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases. The test cases used are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 10 3 and M = 0.15 and a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5. In order to show the application of the numerical method in industrial cases and to assess its capability for sound field simulation, a three-dimensional turbulent flow in a muffler at Re = 4.665 × 10 4 and M = 0.05 has been chosen as a third test case. The flow results show good agreement with numerical and experimental reference solutions. Comparison of the computed noise results with those of reference solutions also shows that the numerical approach predicts noise accurately. © 2011 IMACS.

  8. Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\\mathrm{curl}}$-Conforming High Order Finite Element Methods

    KAUST Repository

    Janssen, Bärbel

    2011-01-01

    A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method\\'s convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.

  9. Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters

    Science.gov (United States)

    Yee, H. C.; Sandham, N. D.; Djomehri, M. J.

    1998-01-01

    An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

  10. Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

    Science.gov (United States)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.

    2004-01-01

    A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of

  11. Development of a Reduced-Order Model for Reacting Gas-Solids Flow using Proper Orthogonal Decomposition

    Energy Technology Data Exchange (ETDEWEB)

    McDaniel, Dwayne; Dulikravich, George; Cizmas, Paul

    2017-11-27

    This report summarizes the objectives, tasks and accomplishments made during the three year duration of this research project. The report presents the results obtained by applying advanced computational techniques to develop reduced-order models (ROMs) in the case of reacting multiphase flows based on high fidelity numerical simulation of gas-solids flow structures in risers and vertical columns obtained by the Multiphase Flow with Interphase eXchanges (MFIX) software. The research includes a numerical investigation of reacting and non-reacting gas-solids flow systems and computational analysis that will involve model development to accelerate the scale-up process for the design of fluidization systems by providing accurate solutions that match the full-scale models. The computational work contributes to the development of a methodology for obtaining ROMs that is applicable to the system of gas-solid flows. Finally, the validity of the developed ROMs is evaluated by comparing the results against those obtained using the MFIX code. Additionally, the robustness of existing POD-based ROMs for multiphase flows is improved by avoiding non-physical solutions of the gas void fraction and ensuring that the reduced kinetics models used for reactive flows in fluidized beds are thermodynamically consistent.

  12. Methods to reduce prescribing errors in elderly patients with multimorbidity

    Directory of Open Access Journals (Sweden)

    Lavan AH

    2016-06-01

    challenge is to design, build, validate, and test by clinical trials suitably versatile and efficient software engines that can reliably and swiftly perform complex medication reviews in older multimorbid people. The European Union-funded SENATOR and OPERAM clinical trials commencing in 2016 will examine the impact of customized software engines in reducing medication-related morbidity, avoidable excess cost, and rehospitalization in older multimorbid people. Keywords: prescribing errors, multimorbidity, aged

  13. First-order derivative UV spectrophotometric method for simultaneous measurement of delapril and manidipine in tablets.

    Science.gov (United States)

    Todeschini, Vítor; Barden, Amanda Thomas; Sfair, Leticia Lenz; da Silva Sangoi, Maximiliano; Volpato, Nadia Maria

    2013-01-01

    A first-order derivative spectrophotometric (1D-UV) method was developed and validated for simultaneous determination of delapril (DEL) and manidipine (MAN) in tablets. The 1D-UV spectra were obtained using change lambda = 4.0 nm and wavelength set at 228 nm for DEL and 246 nm for MAN. The method was validated in accordance with the ICH requirements, involving the specificity, linearity, precision, accuracy, robustness and limits of detection and quantitation. The method showed high specificity in the presence of two drugs and formulation excipients and was linear over the concentration range of 18-54 microg mL(-1) (r2 = 0.9994) for DEL and 6-18 microg mL(-1) (r2 = 0.9981) for MAN with adequate results for the precision (< or = 1.47%) and accuracy (98.98% for DEL and 100.50% for MAN). Moreover, the method proved to be robust by a Plackett-Burman experimental design evaluation. The proposed 'D-UV method was successfully applied for simultaneous analysis of DEL and MAN in tablets and can be used as alternative green method to separation techniques. The results were compared with the validated liquid chromatography, capillary electrophoresis and liquid chromatography-tandem mass spectrometry methods, showing non-significant difference.

  14. A hybrid metaheuristic method to optimize the order of the sequences in continuous-casting

    Directory of Open Access Journals (Sweden)

    Achraf Touil

    2016-06-01

    Full Text Available In this paper, we propose a hybrid metaheuristic algorithm to maximize the production and to minimize the processing time in the steel-making and continuous casting (SCC by optimizing the order of the sequences where a sequence is a group of jobs with the same chemical characteristics. Based on the work Bellabdaoui and Teghem (2006 [Bellabdaoui, A., & Teghem, J. (2006. A mixed-integer linear programming model for the continuous casting planning. International Journal of Production Economics, 104(2, 260-270.], a mixed integer linear programming for scheduling steelmaking continuous casting production is presented to minimize the makespan. The order of the sequences in continuous casting is assumed to be fixed. The main contribution is to analyze an additional way to determine the optimal order of sequences. A hybrid method based on simulated annealing and genetic algorithm restricted by a tabu list (SA-GA-TL is addressed to obtain the optimal order. After parameter tuning of the proposed algorithm, it is tested on different instances using a.NET application and the commercial software solver Cplex v12.5. These results are compared with those obtained by SA-TL (simulated annealing restricted by tabu list.

  15. Method proposition to set the pallet positions designated to fractioned picking orders in a warehouse

    Directory of Open Access Journals (Sweden)

    Caroline Morito Pereira

    2016-11-01

    Full Text Available Storage processes have acquired great importance in the modern supply chain, which demands better performance by warehouses in organizing goods in order to achieve high utilization of physical space and to facilitate the movement of materials. Sizing the storage area and organizing items strategically in storage positions ensures better efficiency in picking processes and customer service. In this context, this study aims to propose a method for defining the positions of pallets assigned to fractioned picking orders in a warehouse according to criteria based on popularity and turnover of the products. This method will be presented in a case study, and the pallets will be positioned in the warehouse in accordance with the results obtained. The gains in terms of order picking productivity and optimization of storage positions will then be measured. Research in this area has grown rapidly in recent years, but the combination of sizing items and classifying these items has not been closely explored. Thus, it is believed that the results could contribute to future research, bridging academic researchers and warehouse professionals.

  16. High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids

    Science.gov (United States)

    Jacobs, G. B.; Hesthaven, J. S.

    2006-05-01

    We present a high-order particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas dynamics. The core of the algorithm utilizes an unstructured grid discontinuous Galerkin Maxwell field solver combining high-order accuracy with geometric flexibility. We introduce algorithms in the Lagrangian framework that preserve the favorable properties of the field solver in the PIC solver. Fast full-order interpolation and effective search algorithms are used for tracking individual particles on the general grid and smooth particle shape functions are introduced to ensure low noise in the charge and current density. A pre-computed levelset distance function is employed to represent the geometry and facilitates complex particle-boundary interaction. To enforce charge conservation we consider two different techniques, one based on projection and one on hyperbolic cleaning. Both are found to work well, although the latter is found be too expensive when used with explicit time integration. Examples of simple plasma phenomena, e.g., plasma waves, instabilities, and Landau damping are shown to agree well with theoretical predictions and/or results found by other computational methods. We also discuss generic well known problems such as numerical Cherenkov radiation and grid heating before presenting a few two-dimensional tests, showing the potential of the current method to handle fully relativistic plasma dynamics in complex geometries.

  17. A finite difference method for nonlinear parabolic-elliptic systems of second order partial differential equations

    Directory of Open Access Journals (Sweden)

    Marian Malec

    2007-01-01

    Full Text Available This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations and the other of the elliptic type (equations with a parameter in a cube in \\(\\mathbf{R}^{1+n}\\. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.

  18. A novel method for identifying the order of interference using phase-shifting digital holography.

    Science.gov (United States)

    Sokkar, T Z N; El-Farahaty, K A; Ramadan, W A; Wahba, H H; Raslan, M I; Hamza, A A

    2016-04-01

    In this paper, we introduced a mathematical method for measuring the optical path length differences (OPDs), which is suitable for large OPD values where the fringes connections are difficult to detect. The proposed method is based on varying the width of the fringes, without changing the wavelength of the used coherent source. Also, in this work, we discussed the need for such method in off-axis phase-shifting digital holography. Low-resolution off-axis holograms failed to detect the correct interference order. In general, off-axis phase-shifting digital holography is limited by the resolution of the captured holograms. The results obtained using our proposed technique were compared to the results obtained using off-axis phase-shifting digital holograms and conventional two-beam interferometry. Holograms were given for illustration. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.

  19. Estimation of ibuprofen and famotidine in tablets by second order derivative spectrophotometery method

    Directory of Open Access Journals (Sweden)

    Dimal A. Shah

    2017-02-01

    Full Text Available A simple and accurate method for the analysis of ibuprofen (IBU and famotidine (FAM in their combined dosage form was developed using second order derivative spectrophotometery. IBU and FAM were quantified using second derivative responses at 272.8 nm and 290 nm in the spectra of their solutions in methanol. The calibration curves were linear in the concentration range of 100–600 μg/mL for IBU and 5–25 μg/mL for FAM. The method was validated and found to be accurate and precise. Developed method was successfully applied for the estimation of IBU and FAM in their combined dosage form.

  20. Optimized Signaling Method for High-Speed Transmission Channels with Higher Order Transfer Function

    Science.gov (United States)

    Ševčík, Břetislav; Brančík, Lubomír; Kubíček, Michal

    2017-08-01

    In this paper, the selected results from testing of optimized CMOS friendly signaling method for high-speed communications over cables and printed circuit boards (PCBs) are presented and discussed. The proposed signaling scheme uses modified concept of pulse width modulated (PWM) signal which enables to better equalize significant channel losses during data high-speed transmission. Thus, the very effective signaling method to overcome losses in transmission channels with higher order transfer function, typical for long cables and multilayer PCBs, is clearly analyzed in the time and frequency domain. Experimental results of the measurements include the performance comparison of conventional PWM scheme and clearly show the great potential of the modified signaling method for use in low power CMOS friendly equalization circuits, commonly considered in modern communication standards as PCI-Express, SATA or in Multi-gigabit SerDes interconnects.

  1. A comparison of different methods to implement higher order derivatives of density functionals

    Energy Technology Data Exchange (ETDEWEB)

    van Dam, Hubertus J.J. [Brookhaven National Lab. (BNL), Upton, NY (United States)

    2016-05-18

    Density functional theory is the dominant approach in electronic structure methods today. To calculate properties higher order derivatives of the density functionals are required. These derivatives might be implemented manually,by automatic differentiation, or by symbolic algebra programs. Different authors have cited different reasons for using the particular method of their choice. This paper presents work where all three approaches were used and the strengths and weaknesses of each approach are considered. It is found that all three methods produce code that is suffficiently performanted for practical applications, despite the fact that our symbolic algebra generated code and our automatic differentiation code still have scope for significant optimization. The automatic differentiation approach is the best option for producing readable and maintainable code.

  2. Noise reducing small aggregate exposed method; Obei no teisoon concrete hoso (shoryukei kotsuzai roshutsu koho)

    Energy Technology Data Exchange (ETDEWEB)

    Noda, E. [Japan Highway Public Corp., Tokyo (Japan). Technical Lab.

    1996-04-10

    The technique for noise reduction of the concrete pavements indicated in the title and its development process in Austria is presented on the basis of the published literature survey and the visit to the working sites where the technique is applied, and some works achieved by the method in United States and England in addition to Austria are described. First of all, the working method with which the mortar surface is scraped away in order to expose crushed coarse aggregates of 8 to 4 mm in diameter consisting the sublayer is defined and its principle of reducing the noise generated from the tyre vibration and the air pumping is introduced. Then, the measured noise level and the sliding resistance of the pavement achieved by this method is compared with those of conventional asphalt pavement. In addition, the developing process of the working technique of this method as well as improvement in the choice of retarding and curing agents in Austria are described, together with the outline of standards for concrete materials and pavement in this country. Further, the work achievement, the pavement structure, the working method, results of the noise measurement in the said 3 countries are tabulated. Lastly, some items to be examined during the construction are indicated referring to the real working cases and questions arising from the application of this technique to Japan are pointed out. 11 refs., 27 figs., 9 tabs.

  3. Fourth-Order Method for Numerical Integration of Age- and Size-Structured Population Models

    Energy Technology Data Exchange (ETDEWEB)

    Iannelli, M; Kostova, T; Milner, F A

    2008-01-08

    In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.

  4. Stable and high order accurate difference methods for the elastic wave equation in discontinuous media

    KAUST Repository

    Duru, Kenneth

    2014-12-01

    © 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.

  5. Recursion method for the quasiparticle structure of a single vortex with induced magnetic order

    DEFF Research Database (Denmark)

    Udby, L.; Andersen, B.M.; Hedegård, P.

    2006-01-01

    . Furthermore, we study the low-energy quasiparticle structure when magnetic vortices operate as pinning centers for surrounding unidirectional spin density waves (stripes). We calculate the Fourier transformed LDOS and show how the energy dependence of relevant Fourier components can be used to determine...... the nature of the magnetic field-induced order, and predict field-induced LDOS features that can be tested by future scanning tunneling microscopy experiments.......We use a real-space recursion method to calculate the local density of states (LDOS) within a model that contains both d-wave superconducting and antiferromagnetic order. We focus on the LDOS in the superconducting phase near single vortices with either normal or antiferromagnetic cores...

  6. Density of states for systems with multiple order parameters: a constrained Wang-Landau method

    Science.gov (United States)

    Chan, Chor-Hoi; Brown, Gregory; Rikvold, Per Arne

    2017-11-01

    A macroscopically constrained Wang-Landau Monte Carlo method was recently proposed to calculate the joint density of states (DOS) for systems with multiple order parameters. Here we demonstrate results for a nearest-neighbor Ising antiferromagnet with ferromagnetic long-range interactions (a model spin-crossover material). Its two relevant order parameters are the magnetization M and the staggered magnetization M s. The joint DOS, g(E, M, M s) where E is the total system energy, is calculated for zero external field and long-range interaction strength, and then obtained for arbitrary values of these two field-like model parameters by a simple transformation of E. Illustrations are shown for several parameter sets.

  7. REGULAR METHOD FOR SYNTHESIS OF BASIC BENT-SQUARES OF RANDOM ORDER

    Directory of Open Access Journals (Sweden)

    A. V. Sokolov

    2016-01-01

    Full Text Available The paper is devoted to the class construction of the most non-linear Boolean bent-functions of any length N = 2k (k = 2, 4, 6…, on the basis of their spectral representation – Agievich bent squares. These perfect algebraic constructions are used as a basis to build many new cryptographic primitives, such as generators of pseudo-random key sequences, crypto graphic S-boxes, etc. Bent-functions also find their application in the construction of C-codes in the systems with code division multiple access (CDMA to provide the lowest possible value of Peak-to-Average Power Ratio (PAPR k = 1, as well as for the construction of error-correcting codes and systems of orthogonal biphasic signals. All the numerous applications of bent-functions relate to the theory of their synthesis. However, regular methods for complete class synthesis of bent-functions of any length N = 2k are currently unknown. The paper proposes a regular synthesis method for the basic Agievich bent squares of any order n, based on a regular operator of dyadic shift. Classification for a complete set of spectral vectors of lengths (l = 8, 16, … based on a criterion of the maximum absolute value and set of absolute values of spectral components has been carried out in the paper. It has been shown that any spectral vector can be a basis for building bent squares. Results of the synthesis for the Agievich bent squares of order n = 8 have been generalized and it has been revealed that there are only 3 basic bent squares for this order, while the other 5 can be obtained with help the operation of step-cyclic shift. All the basic bent squares of order n = 16 have been synthesized that allows to construct the bent-functions of length N = 256. The obtained basic bent squares can be used either for direct synthesis of bent-functions and their practical application or for further research in order to synthesize new structures of bent squares of orders n = 16, 32, 64, …

  8. Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101 (China); Badal, José, E-mail: badal@unizar.es [Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain)

    2017-05-01

    The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational

  9. A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

    KAUST Repository

    Efendiev, Yalchin R.

    2015-08-01

    We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

  10. A numerical study of the second-order wave excitation of ship springing by a higher-order boundary element method

    Directory of Open Access Journals (Sweden)

    Yan-Lin Shao

    2014-12-01

    Full Text Available This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.

  11. Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

    Science.gov (United States)

    Chen, Tianheng; Shu, Chi-Wang

    2017-09-01

    It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and Shu (1994) [39]) and symmetric hyperbolic systems (Hou and Liu (2007) [36]), in any space dimension and for any triangulations. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantly more difficult to design DG methods to satisfy entropy inequalities for a non-square convex entropy, and/or when the integration is approximated by a numerical quadrature. In this paper, we develop a unified framework for designing high order DG methods which will satisfy entropy inequalities for any given single convex entropy, through suitable numerical quadrature which is specific to this given entropy. Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws. For the one-dimensional case, our numerical quadrature is based on the methodology established in Carpenter et al. (2014) [5] and Gassner (2013) [19]. The main ingredients are summation-by-parts (SBP) operators derived from Legendre Gauss-Lobatto quadrature, the entropy conservative flux within elements, and the entropy stable flux at element interfaces. We then generalize the scheme to two-dimensional triangular meshes by constructing SBP operators on triangles based on a special quadrature rule. A local discontinuous Galerkin (LDG) type treatment is also incorporated to achieve the generalization to convection-diffusion equations. Extensive numerical experiments are performed to validate the accuracy and shock capturing efficacy of these entropy stable DG methods.

  12. Stochastic Order Redshift Technique (SORT): a simple, efficient and robust method to improve cosmological redshift measurements

    Science.gov (United States)

    Tejos, Nicolas; Rodríguez-Puebla, Aldo; Primack, Joel R.

    2018-01-01

    We present a simple, efficient and robust approach to improve cosmological redshift measurements. The method is based on the presence of a reference sample for which a precise redshift number distribution (dN/dz) can be obtained for different pencil-beam-like sub-volumes within the original survey. For each sub-volume we then impose that: (i) the redshift number distribution of the uncertain redshift measurements matches the reference dN/dz corrected by their selection functions and (ii) the rank order in redshift of the original ensemble of uncertain measurements is preserved. The latter step is motivated by the fact that random variables drawn from Gaussian probability density functions (PDFs) of different means and arbitrarily large standard deviations satisfy stochastic ordering. We then repeat this simple algorithm for multiple arbitrary pencil-beam-like overlapping sub-volumes; in this manner, each uncertain measurement has multiple (non-independent) 'recovered' redshifts which can be used to estimate a new redshift PDF. We refer to this method as the Stochastic Order Redshift Technique (SORT). We have used a state-of-the-art N-body simulation to test the performance of SORT under simple assumptions and found that it can improve the quality of cosmological redshifts in a robust and efficient manner. Particularly, SORT redshifts (zsort) are able to recover the distinctive features of the so-called 'cosmic web' and can provide unbiased measurement of the two-point correlation function on scales ≳4 h-1Mpc. Given its simplicity, we envision that a method like SORT can be incorporated into more sophisticated algorithms aimed to exploit the full potential of large extragalactic photometric surveys.

  13. Method of applying single higher order polynomial basis function over multiple domains

    CSIR Research Space (South Africa)

    Lysko, AA

    2010-03-01

    Full Text Available . Derivation of the computational complexity in terms of oating point operations (FLOP) showed a possible speed gain nearly an order of the number of unknowns of direct MoM. 1. INTRODUCTION The process of numerical electromagnetic modeling may be split... functions. A special note needs to be made with regards to a comparison of the method proposed, to the characteristic basis functions [13]. The characteristic basis functions require to solve a set of 2 subdomain/local problems, thus permitting to flnd...

  14. The Second-Order Polarization Propagator Approximation (SOPPA) method coupled to the polarizable continuum model

    DEFF Research Database (Denmark)

    Eriksen, Janus Juul; Solanko, Lukasz Michal; Nåbo, Lina J.

    2014-01-01

    2) wave function coupled to PCM, we introduce dynamical PCM solvent effects only in the Random Phase Approximation (RPA) part of the SOPPA response equations while the static solvent contribution is kept in both the RPA terms as well as in the higher order correlation matrix components of the SOPPA...... response equations. By dynamic terms, we refer to contributions that describe a change in environmental polarization which, in turn, reflects a change in the core molecular charge distribution upon an electronic excitation. This new combination of methods is termed PCM-SOPPA/RPA. We apply this newly...

  15. Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

    Energy Technology Data Exchange (ETDEWEB)

    Iaroshenko, Oleksandr [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2016-09-01

    In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

  16. Computation of Nonlinear Backscattering Using a High-Order Numerical Method

    Science.gov (United States)

    Fibich, G.; Ilan, B.; Tsynkov, S.

    2001-01-01

    The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

  17. Adaptive grouping for the higher-order multilevel fast multipole method

    DEFF Research Database (Denmark)

    Borries, Oscar Peter; Jørgensen, Erik; Meincke, Peter

    2014-01-01

    functions. Results from both a uniformly and nonuniformly meshed scatterer are presented, showing how the technique is worthwhile even for regular meshes, and demonstrating that there is no loss of accuracy in spite of the large reduction in memory requirements and the relatively low computational cost.......An alternative parameter-free adaptive approach for the grouping of the basis function patterns in the multilevel fast multipole method is presented, yielding significant memory savings compared to the traditional Octree grouping for most discretizations, particularly when using higher-order basis...

  18. BICLUSTERING METHODS FOR RE-ORDERING DATA MATRICES IN SYSTEMS BIOLOGY, DRUG DISCOVERY AND TOXICOLOGY

    Directory of Open Access Journals (Sweden)

    Christodoulos A. Floudas

    2010-12-01

    Full Text Available Biclustering has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the ``best'' grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters. In the first part of the presentation, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric [1,2]. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. The performance of OREO is tested on several important data matrices arising in systems biology to validate the ability of the proposed method and compare it to existing biclustering and clustering methods. In the second part of the talk, we will focus on novel methods for clustering of data matrices that are very sparse [3]. These types of data matrices arise in drug discovery where the x- and y-axis of a data matrix can correspond to different functional groups for two distinct substituent sites on a molecular scaffold. Each possible x and y pair corresponds to a single molecule which can be synthesized and tested for a certain property, such as percent inhibition of a protein function. For even moderate size matrices, synthesizing and testing a small fraction of the molecules is labor intensive and not economically feasible. Thus, it is of paramount importance to have a reliable method for guiding the synthesis process to select molecules that have a high probability of success. In the second part of the presentation, we introduce a new strategy to enable efficient substituent reordering and descriptor-free property estimation. Our approach casts

  19. Multi-Model blending Method and Application on Reducing the uncertainty of Air Quality Models

    Science.gov (United States)

    Huang, Si; Zhang, Meng; Xie, Bao Guo; Du, Hui; Tang, Yu Jia; Lin, Jian; Yin, Wen Jun

    2017-04-01

    In this study, the linear regression method is used to blend multi-model forecasts to reduce the uncertainties in the air quality models. The PM2.5 forecast performance of three models (WRF-Chem, CAMx and CMAQ) are evaluated over Beijing city. In order to improve the forecast skill, the PM2.5 forecast concentration of the three models are combined by the linear regression method with different weight and equal weight. The results indicate that: (1) large differences exist among three numerical models, no individual model performs better than the other two models for all statistic indexes, such as accuracy, mean absolute error (MAE), mean bias and (MB), correlations coefficients. Overall, The MAE index of WRF-Chem is lower than that of other two models, whereas CMAQ has better tendency similarity with observation and CAMx performs better in level forecast accuracy. (2) Liner regression with equal weight presents poor performance in improving the PM2.5 forecast skill, neither correlation coefficients nor MAE of the blended forecast results is better than those of the individual model forecast. On the other hand, the linear regression method with different weight brings significant improvement of the PM2.5 forecast with an appropriate training length (12 days). The MAE of PM2.5 forecast over 13 national monitoring stations of Beijing is reduced by 20% 30% through non-equal weight linear regression method and the level accuracy increases significantly by 12%. Furthermore, the non-equal weight linear regression method can also improve the hit ratio of heavy pollution event forecast.

  20. A stochastic collocation method for the second order wave equation with a discontinuous random speed

    KAUST Repository

    Motamed, Mohammad

    2012-08-31

    In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.

  1. Two-photon or higher-order absorbing optical materials and methods of use

    Science.gov (United States)

    Marder, Seth (Inventor); Perry, Joseph (Inventor)

    2012-01-01

    Compositions capable of simultaneous two-photon absorption and higher order absorptivities are provided. Compounds having a donor-pi-donor or acceptor-pi-acceptor structure are of particular interest, where the donor is an electron donating group, acceptor is an electron accepting group, and pi is a pi bridge linking the donor and/or acceptor groups. The pi bridge may additionally be substituted with electron donating or withdrawing groups to alter the absorptive wavelength of the structure. Also disclosed are methods of generating an excited state of such compounds through optical stimulation with light using simultaneous absorption of photons of energies individually insufficient to achieve an excited state of the compound, but capable of doing so upon simultaneous absorption of two or more such photons. Applications employing such methods are also provided, including controlled polymerization achieved through focusing of the light source(s) used.

  2. Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

    Science.gov (United States)

    Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

    2002-01-01

    Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

  3. Assessment of reduced-order unscented Kalman filter for parameter identification in 1-dimensional blood flow models using experimental data.

    Science.gov (United States)

    Caiazzo, A; Caforio, Federica; Montecinos, Gino; Muller, Lucas O; Blanco, Pablo J; Toro, Eluterio F

    2016-10-25

    This work presents a detailed investigation of a parameter estimation approach on the basis of the reduced-order unscented Kalman filter (ROUKF) in the context of 1-dimensional blood flow models. In particular, the main aims of this study are (1) to investigate the effects of using real measurements versus synthetic data for the estimation procedure (i.e., numerical results of the same in silico model, perturbed with noise) and (2) to identify potential difficulties and limitations of the approach in clinically realistic applications to assess the applicability of the filter to such setups. For these purposes, the present numerical study is based on a recently published in vitro model of the arterial network, for which experimental flow and pressure measurements are available at few selected locations. To mimic clinically relevant situations, we focus on the estimation of terminal resistances and arterial wall parameters related to vessel mechanics (Young's modulus and wall thickness) using few experimental observations (at most a single pressure or flow measurement per vessel). In all cases, we first perform a theoretical identifiability analysis on the basis of the generalized sensitivity function, comparing then the results owith the ROUKF, using either synthetic or experimental data, to results obtained using reference parameters and to available measurements. Copyright © 2016 John Wiley & Sons, Ltd.

  4. Scaled Second Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods

    Energy Technology Data Exchange (ETDEWEB)

    Rhee, Young Min; Head-Gordon, Martin

    2007-02-01

    Two modifications of the perturbative doubles correction to configuration interaction with single substitutions (CIS(D)) are suggested, which are excited state analogs of ground state scaled second order Moeller-Plesset (MP2) methods. The first approach employs two parameters to scale the two spin components of the direct term of CIS(D), starting from the two-parameter spin-component scaled (SCS) MP2 ground state, and is termed SCS-CIS(D). An efficient resolution-of-the-identity (RI) implementation of this approach is described. The second approach employs a single parameter to scale only the opposite-spin direct term of CIS(D), starting from the one-parameter scaled opposite spin (SOS) MP2 ground state, and is called SOS-CIS(D). By utilizing auxiliary basis expansions and a Laplace transform, a fourth order algorithm for SOS-CIS(D) is described and implemented. The parameters describing SCS-CIS(D) and SOS-CIS(D) are optimized based on a training set including valence excitations of various organic molecules and Rydberg transitions of water and ammonia, and they significantly improve upon CIS(D) itself. The accuracy of the two methods is found to be comparable. This arises from a strong correlation between the same-spin and opposite-spin portions of the excitation energy terms. The methods are successfully applied to the zincbacteriochlorin-bacteriochlorin charge transfer transition, for which time-dependent density functional theory, with presently available exchange-correlation functionals, is known to fail. The methods are also successfully applied to describe various electronic transitions outside of the training set. The efficiency of SOS-CIS(D) and the auxiliary basis implementation of CIS(D) and SCS-CIS(D) are confirmed with a series of timing tests.

  5. A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids

    Energy Technology Data Exchange (ETDEWEB)

    Bungartz, H.J. [Technische Universitaet Muenchen (Germany)

    1996-12-31

    In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.

  6. A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Zhen Chen

    2017-03-01

    Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

  7. PWC-ICA: A Method for Stationary Ordered Blind Source Separation with Application to EEG.

    Science.gov (United States)

    Ball, Kenneth; Bigdely-Shamlo, Nima; Mullen, Tim; Robbins, Kay

    2016-01-01

    Independent component analysis (ICA) is a class of algorithms widely applied to separate sources in EEG data. Most ICA approaches use optimization criteria derived from temporal statistical independence and are invariant with respect to the actual ordering of individual observations. We propose a method of mapping real signals into a complex vector space that takes into account the temporal order of signals and enforces certain mixing stationarity constraints. The resulting procedure, which we call Pairwise Complex Independent Component Analysis (PWC-ICA), performs the ICA in a complex setting and then reinterprets the results in the original observation space. We examine the performance of our candidate approach relative to several existing ICA algorithms for the blind source separation (BSS) problem on both real and simulated EEG data. On simulated data, PWC-ICA is often capable of achieving a better solution to the BSS problem than AMICA, Extended Infomax, or FastICA. On real data, the dipole interpretations of the BSS solutions discovered by PWC-ICA are physically plausible, are competitive with existing ICA approaches, and may represent sources undiscovered by other ICA methods. In conjunction with this paper, the authors have released a MATLAB toolbox that performs PWC-ICA on real, vector-valued signals.

  8. Rigorous speckle simulation using surface integral equations and higher order boundary element method.

    Science.gov (United States)

    Fu, Liwei; Frenner, Karsten; Osten, Wolfgang

    2014-07-15

    The scattering of electromagnetic waves from rough surfaces has been actively studied for more than a century now because of its involvement in vast application areas. In the past two decades, great advances have been made by incorporating multiple scattering effects into analytical approaches. However, no model can yet be applied to surfaces with arbitrary roughness. It is also very difficult to study the cross-polarization, shadowing, or multiple scattering effects. In order to study more fundamentally the interaction of polarized light with more general rough surfaces of general media, we have developed a rigorous numerical simulator to calculate the resulting speckle fields. The full Maxwell equations were solved using surface integral equations combined with a boundary element method. The rough surface was discretized by higher order quadrilateral edge elements. The effective tangential electric and magnetic fields in each element in terms of 10 edges were first solved. The scattered electric and magnetic fields everywhere in space were then calculated correspondingly. One of the great advantages of such a simulator is that both the near and far fields can be calculated directly. Preliminary results of different kinds of metallic structures are presented, by which the advantages of the method are demonstrated.

  9. Enhanced higher-order interior-point method to minimise active power losses in electric energy systems

    Energy Technology Data Exchange (ETDEWEB)

    Rider, M.J.; Castro, C.A.; Garcia, A.V. [State University of Campinas (Brazil). Electric Energy Systems Dept.; Paucar, V.L. [Federal University of Maranhao (Brazil). Electrical Engineering Dept.

    2004-07-01

    A method for computing the minimum active power loss in competitive electric power markets is proposed. The active power loss minimisation problem is formulated as an optimal power flow (OPF) with equality and inequality nonlinear constraints which take into account the power system security. The OPF has been solved using the multiple predictor-corrector interior-point method (MPC) of the family of higher-order interior-point methods, enhanced with a procedure for step-length computation during Newton iterations. The utilisation of the proposed enhanced MPC leads to convergence with a smaller number of iterations and better computational times than some results reported in the literature. An efficient computation of the primal and dual step-sizes is capable of reducing the primal and dual objective function errors, respectively, assuring continuously decreasing errors during the iterations of the interior-point method procedure. The proposed method has been simulated for several IEEF- test systems and two real systems including a 464 bus configuration of the interconnected Peruvian power system, and a 2256 bus scenario of the South-Southeast interconnected Brazilian system. Results of the tests have shown that the convergence is facilitated and the number of iterations may be small. (author)

  10. Some methods of increasing the density of metal in order to increase him corrosion resistance

    Science.gov (United States)

    Chumanov, I. V.; Anikeev, A. N.; Sergeev, D. V.; Maltseva, A. N.

    2017-11-01

    Methods to increase the density of metal in order to increase its corrosion resistance in an aggressive environment are examined in the article. Two steel grades, differing in the content of alloying elements, increasing the resistance to corrosion are selected for the manufacture of experimental metallic materials. Two technologies are chosen as methods for increasing the density, and as a result, corrosion resistance, of the experimental materials obtained: the first is electroslag remelting with rotation of the consumable electrode, the second is centrifugal casting with modification. The microstructure of the metal becomes more homogeneous, the degree of metal refining from non-metallic inclusions increases, the rate of crystallization during metal smelting by the ESR method increases with rotation of the consumable electrode. When ingots are produced by the method of centrifugal casting, they are modified with dispersed WC and TiC particles, which increases the crystallization rate, increases the metal density, corrosion and mechanical properties. The evaluation of their corrosion resistance with the help of the autoclaved test complex “Cortest” is made after obtaining ingots by various technologies.

  11. A Stable-Matching-Based User Linking Method with User Preference Order

    Directory of Open Access Journals (Sweden)

    Xuzhong Wang

    2017-01-01

    Full Text Available With the development of social networks, more and more users choose to use multiple accounts from different networks to meet their needs. Linking a particular user’s multiple accounts not only can improve user’s experience of the net-services such as recommender system, but also plays a significant role in network security. However, multiple accounts of the same user are often not directly linked to each other, and further, the privacy policy provided by the service provider makes it harder to find accounts for a particular user. In this paper, we propose a stable-matching-based method with user preference order for the problem of low accuracy of user linking in cross-media sparse data. Different from the traditional way which just calculates the similarity of accounts, we take full account of the mutual influence among multiple accounts by regarding different networks as bilateral (multilateral market and user linking as a stable matching problem in such a market. Based on the combination of Game-Theoretic Machine Learning and Pairwise, a novel user linking method has been proposed. The experiment shows that our method has a 21.6% improvement in accuracy compared with the traditional linking method and a further increase of about 7.8% after adding the prior knowledge.

  12. Evaluation of linear, inviscid, viscous, and reduced-order modelling aeroelastic solutions of the AGARD 445.6 wing using root locus analysis

    Science.gov (United States)

    Silva, Walter A.; Chwalowski, Pawel; Perry, Boyd, III

    2014-03-01

    Reduced-order modelling (ROM) methods are applied to the Computational Fluid Dynamics (CFD)-based aeroelastic analysis of the AGARD 445.6 wing in order to gain insight regarding well-known discrepancies between the aeroelastic analyses and the experimental results. The results presented include aeroelastic solutions using the inviscid Computational Aeroelasticity Programme-Transonic Small Disturbance (CAP-TSD) code and the FUN3D code (Euler and Navier-Stokes). Full CFD aeroelastic solutions and ROM aeroelastic solutions, computed at several Mach numbers, are presented in the form of root locus plots in order to better reveal the aeroelastic root migrations with increasing dynamic pressure. Important conclusions are drawn from these results including the ability of the linear CAP-TSD code to accurately predict the entire experimental flutter boundary (repeat of analyses performed in the 1980s), that the Euler solutions at supersonic conditions indicate that the third mode is always unstable, and that the FUN3D Navier-Stokes solutions stabilize the unstable third mode seen in the Euler solutions.

  13. Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

    Directory of Open Access Journals (Sweden)

    Navnit Jha

    2014-04-01

    Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

  14. Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

    Science.gov (United States)

    Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

    2017-05-01

    The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational

  15. Reduced-Order Model for Leakage Through an Open Wellbore from the Reservoir due to Carbon Dioxide Injection

    Energy Technology Data Exchange (ETDEWEB)

    Pan, Lehua [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oldenburg, Curtis M. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2017-07-26

    Potential CO2 leakage through existing open wellbores is one of the most significant hazards that need to be addressed in geologic carbon sequestration (GCS) projects. In the framework of the National Risk Assessment Partnership (NRAP) which requires fast computations for uncertainty analysis, rigorous simulation of the coupled wellbore-reservoir system is not practical. We have developed a 7,200-point look-up table reduced-order model (ROM) for estimating the potential leakage rate up open wellbores in response to CO2 injection nearby. The ROM is based on coupled simulations using T2Well/ECO2H which was run repeatedly for representative conditions relevant to NRAP to create a look-up table response-surface ROM. The ROM applies to a wellbore that fully penetrates a 20-m thick reservoir that is used for CO2 storage. The radially symmetric reservoir is assumed to have initially uniform pressure, temperature, gas saturation, and brine salinity, and it is assumed these conditions are held constant at the far-field boundary (100 m away from the wellbore). In such a system, the leakage can quickly reach quasi-steady state. The ROM table can be used to estimate both the free-phase CO2 and brine leakage rates through an open well as a function of wellbore and reservoir conditions. Results show that injection-induced pressure and reservoir gas saturation play important roles in controlling leakage. Caution must be used in the application of this ROM because well leakage is formally transient and the ROM lookup table was populated using quasi-steady simulation output after 1000 time steps which may correspond to different physical times for the various parameter combinations of the coupled wellbore-reservoir system.

  16. High order vector mode coupling mechanism based on mode matching method

    Science.gov (United States)

    Zhang, Zhishen; Gan, Jiulin; Heng, Xiaobo; Li, Muqiao; Li, Jiong; Xu, Shanhui; Yang, Zhongmin

    2017-06-01

    The high order vector mode (HOVM) coupling mechanism is investigated based on the mode matching method (MMM). In the case of strong HOVM coupling where the weakly guiding approximation fails, conventional coupling analysis methods become invalid due to the asynchronous coupling feature of the horizontal and vertical polarization components of HOVM. The MMM, which uses the interference of the local eigenmodes instead of the assumptive modes to simulate the light propagation, is adopted as a more efficient analysis method for investigating HOVM coupling processes, especially for strong coupling situations. The rules of the optimal coupling length, coupling efficiency, and mode purity in microfiber directional coupler are firstly quantitatively analyzed and summarized. Different from the specific input modes, some special new modes would be excited at the output through the strong HOVM coupling process. The analysis of HOVM coupling mechanism based on MMM could provide precise and accurate design guidance for HOVM directional coupler and mode converter, which are believed to be fundamental devices for multi-mode communication applications.

  17. Fabrication of ordered bulk heterojunction organic photovoltaic cells using nanopatterning and electrohydrodynamic spray deposition methods.

    Science.gov (United States)

    Park, Sung-Eun; Kim, Sehwan; Kim, Kangmin; Joe, Hang-Eun; Jung, Buyoung; Kim, Eunkyoung; Kim, Woochul; Min, Byung-Kwon; Hwang, Jungho

    2012-12-21

    Organic photovoltaic cells with an ordered heterojunction (OHJ) active layer are expected to show increased performance. In the study described here, OHJ cells were fabricated using a combination of nanoimprinting and electrohydrodynamic (EHD) spray deposition methods. After an electron donor material was nanoimprinted with a PDMS stamp (valley width: 230 nm, period: 590 nm) duplicated from a Si nanomold, an electron acceptor material was deposited onto the nanoimprinted donor layer using an EHD spray deposition method. The donor-acceptor interface layer was observed by obtaining cross-sectional images with a focused ion beam (FIB) microscope. The photocurrent generation performance of the OHJ cells was evaluated with the current density-voltage curve under air mass (AM) 1.5 conditions. It was found that the surface morphology of the electron acceptor layer affected the current and voltage outputs of the photovoltaic cells. When an electron acceptor layer with a smooth thin (250 nm above the valley of the electron donor layer) surface morphology was obtained, power conversion efficiency was as high as 0.55%. The electrohydrodynamic spray deposition method used to produce OHJ photovoltaic cells provides a means for the adoption of large area, high throughput processes.

  18. Presenting a Multi Objective Model for Supplier Selection in Order to Reduce Green House Gas Emission under Uncertion Demand

    Directory of Open Access Journals (Sweden)

    Habibollah Mohamadi

    2014-08-01

    Full Text Available Recently, much attention has been given to Stochastic demand due to uncertainty in the real -world. In the literature, decision-making models and suppliers' selection do not often consider inventory management as part of shopping problems. On the other hand, the environmental sustainability of a supply chain depends on the shopping strategy of the supply chain members. The supplier selection plays an important role in the green chain. In this paper, a multi-objective nonlinear integer programming model for selecting a set of supplier considering Stochastic demand is proposed. while the cost of purchasing include the total cost, holding and stock out costs, rejected units, units have been delivered sooner, and total green house gas emissions are minimized, while the obtained total score from the supplier assessment process is maximized. It is assumed, the purchaser provides the different products from the number predetermined supplier to a with Stochastic demand and the uniform probability distribution function. The product price depends on the order quantity for each product line is intended. Multi-objective models using known methods, such as Lp-metric has become an objective function and then uses genetic algorithms and simulated annealing meta-heuristic is solved.

  19. Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter

    Energy Technology Data Exchange (ETDEWEB)

    Stetzel, KD; Aldrich, LL; Trimboli, MS; Plett, GL

    2015-03-15

    This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables. (C) 2014 Elsevier B.V. All rights reserved.

  20. Nonlinear fractional order proportion-integral-derivative active disturbance rejection control method design for hypersonic vehicle attitude control

    Science.gov (United States)

    Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang

    2015-06-01

    Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.

  1. A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell–Whitehead–Segel equation

    Directory of Open Access Journals (Sweden)

    A. Saravanan

    2013-10-01

    Full Text Available In this paper, we will carry out a comparative study between the reduced differential transform method and the Adomian decomposition method. This is been achieved by handling the Newell–Whitehead–Segel equation. Two numerical examples have also been carried out to validate and demonstrate efficiency of the two methods. Furthermost, it is shown that the reduced differential transform method has an advantage over the Adomian decomposition method that it takes less time to solve the nonlinear problems without using the Adomian polynomials.

  2. Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

    Energy Technology Data Exchange (ETDEWEB)

    Fraysse, F., E-mail: francois.fraysse@rs2n.eu [RS2N, St. Zacharie (France); E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid (Spain); Redondo, C.; Rubio, G.; Valero, E. [E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid (Spain)

    2016-12-01

    This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.

  3. Efficient design of a truss beam by applying first order optimization method

    Science.gov (United States)

    Fedorik, Filip

    2013-10-01

    Applications of optimization procedures in structural designs are widely discussed problems, which are caused by currently still-increasing demands on structures. Using of optimization methods in efficient designs passes through great development, especially in duplicate production where even small savings might lead to considerable reduction of total costs. The presented paper deals with application and analysis of the First Order optimization technique, which is implemented in the Design Optimization module that uses the main features of multi-physical FEM program ANSYS, in steel truss-beam design. Constraints of the design are stated by EN 1993 Eurocode 3, for uniform compression forces in compression members and tensile resistance moments in tension members. Furthermore, a minimum frequency of the first natural modal shape of the structure is determined. The aim of the solution is minimizing the weight of the structure by changing members' cross-section properties.

  4. Optimization of accelerator parameters using normal form methods on high-order transfer maps

    Energy Technology Data Exchange (ETDEWEB)

    Snopok, Pavel [Michigan State Univ., East Lansing, MI (United States)

    2007-05-01

    Methods of analysis of the dynamics of ensembles of charged particles in collider rings are developed. The following problems are posed and solved using normal form transformations and other methods of perturbative nonlinear dynamics: (1) Optimization of the Tevatron dynamics: (a) Skew quadrupole correction of the dynamics of particles in the Tevatron in the presence of the systematic skew quadrupole errors in dipoles; (b) Calculation of the nonlinear tune shift with amplitude based on the results of measurements and the linear lattice information; (2) Optimization of the Muon Collider storage ring: (a) Computation and optimization of the dynamic aperture of the Muon Collider 50 x 50 GeV storage ring using higher order correctors; (b) 750 x 750 GeV Muon Collider storage ring lattice design matching the Tevatron footprint. The normal form coordinates have a very important advantage over the particle optical coordinates: if the transformation can be carried out successfully (general restrictions for that are not much stronger than the typical restrictions imposed on the behavior of the particles in the accelerator) then the motion in the new coordinates has a very clean representation allowing to extract more information about the dynamics of particles, and they are very convenient for the purposes of visualization. All the problem formulations include the derivation of the objective functions, which are later used in the optimization process using various optimization algorithms. Algorithms used to solve the problems are specific to collider rings, and applicable to similar problems arising on other machines of the same type. The details of the long-term behavior of the systems are studied to ensure the their stability for the desired number of turns. The algorithm of the normal form transformation is of great value for such problems as it gives much extra information about the disturbing factors. In addition to the fact that the dynamics of particles is represented

  5. Second order Method for Solving 3D Elasticity Equations with Complex Interfaces

    Science.gov (United States)

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

    2015-01-01

    Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422

  6. Adaptive Mesh Refinement and High Order Geometrical Moment Method for the Simulation of Polydisperse Evaporating Sprays

    Directory of Open Access Journals (Sweden)

    Essadki Mohamed

    2016-09-01

    Full Text Available Predictive simulation of liquid fuel injection in automotive engines has become a major challenge for science and applications. The key issue in order to properly predict various combustion regimes and pollutant formation is to accurately describe the interaction between the carrier gaseous phase and the polydisperse evaporating spray produced through atomization. For this purpose, we rely on the EMSM (Eulerian Multi-Size Moment Eulerian polydisperse model. It is based on a high order moment method in size, with a maximization of entropy technique in order to provide a smooth reconstruction of the distribution, derived from a Williams-Boltzmann mesoscopic model under the monokinetic assumption [O. Emre (2014 PhD Thesis, École Centrale Paris; O. Emre, R.O. Fox, M. Massot, S. Chaisemartin, S. Jay, F. Laurent (2014 Flow, Turbulence and Combustion 93, 689-722; O. Emre, D. Kah, S. Jay, Q.-H. Tran, A. Velghe, S. de Chaisemartin, F. Laurent, M. Massot (2015 Atomization Sprays 25, 189-254; D. Kah, F. Laurent, M. Massot, S. Jay (2012 J. Comput. Phys. 231, 394-422; D. Kah, O. Emre, Q.-H. Tran, S. de Chaisemartin, S. Jay, F. Laurent, M. Massot (2015 Int. J. Multiphase Flows 71, 38-65; A. Vié, F. Laurent, M. Massot (2013 J. Comp. Phys. 237, 277-310]. The present contribution relies on a major extension of this model [M. Essadki, S. de Chaisemartin, F. Laurent, A. Larat, M. Massot (2016 Submitted to SIAM J. Appl. Math.], with the aim of building a unified approach and coupling with a separated phases model describing the dynamics and atomization of the interface near the injector. The novelty is to be found in terms of modeling, numerical schemes and implementation. A new high order moment approach is introduced using fractional moments in surface, which can be related to geometrical quantities of the gas-liquid interface. We also provide a novel algorithm for an accurate resolution of the evaporation. Adaptive mesh refinement properly scaling on massively

  7. Correlations between preparation methods, structural features and electrochemical Li-storage behavior of reduced graphene oxide.

    Science.gov (United States)

    Sonia, Farjana J; Kalita, Hemen; Aslam, M; Mukhopadhyay, Amartya

    2017-08-10

    Wide differences in the structural features of graphenic carbon, especially in the case of reduced graphene oxides (rGO), are expected to have considerable impacts on the properties, thus leading to significant scatter and poor understanding/prediction of their performances for various applications, including as electrode materials for electrochemical Li-storage. In this context, the present work develops a comprehensive understanding (via thorough experimentation, including in situ X-ray diffraction studies, and analysis) on the effects of graphene oxide (GO) reduction methods/conditions on the structural features (mainly 'graphenic' ordering) and concomitant influences of the same on electrochemical Li-storage behavior. 'Moderately oxidized' GO (O/C ∼0.41) was reduced via three different methods, viz., (i) using hydrazine hydrate vapor at room temperature (rGO-H; O/C ∼0.23), (ii) thermal reduction by annealing at just 500 °C (rGO-A; O/C ∼0.20) and (iii) hydrazine treatment, followed by the same annealing treatment (rGO-HA; O/C ∼0.17). Raman spectroscopy, in situ X-ray diffraction recorded during annealing and high resolution TEM imaging indicate that while GO and rGO-H had considerable defect contents [I(D)/I(G) ∼1.4 for rGO-H], including a very non-uniform interlayer spacing (varying between 3.1 and 3.6 Å), the 500 °C annealed rGO-A and rGO-HA had significantly reduced defect contents [I(D)/I(G) ∼0.6] and near-perfect 'graphenic' ordering with a uniform interlayer spacing of ∼3.35 Å. Despite the nanoscaled dimensions, defect structures, especially the non-uniform interlayer spacing, resulted in relatively poor reversible Li-capacity and rate capability for the non-annealed rGO-H, even in comparison to the bulk graphitic carbon. By contrast, the annealed rGOs, especially the rGO-HA, not only possessed a superior reversible Li-capacity of ∼450 mA h g -1 (at C/20), but also exhibited a significantly improved rate capability (even compared to

  8. Hybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations

    KAUST Repository

    AbouEisha, Hassan M.

    2016-06-02

    In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.

  9. Reduced Differential Transform Method for Exact Solution of Parabolic and Hyperbolic Partial Differential Equations

    OpenAIRE

    Giriraj MEHTI

    2017-01-01

    Aim of the paper is to obtain solution of parabolic, elliptical and coupled partial differential equation using Reduced Differential Transform Method (RDTM). The results are compared with solution obtained by other methods. It is observed that RDTM is easy to implement, accurate and efficient. It reduces volume of computation and save time.

  10. Reduced Differential Transform Method for Exact Solution of Parabolic and Hyperbolic Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Giriraj MEHTI

    2017-04-01

    Full Text Available Aim of the paper is to obtain solution of parabolic, elliptical and coupled partial differential equation using Reduced Differential Transform Method (RDTM. The results are compared with solution obtained by other methods. It is observed that RDTM is easy to implement, accurate and efficient. It reduces volume of computation and save time.

  11. Modified Inverse First Order Reliability Method (I-FORM) for Predicting Extreme Sea States.

    Energy Technology Data Exchange (ETDEWEB)

    Eckert-Gallup, Aubrey Celia; Sallaberry, Cedric Jean-Marie; Dallman, Ann Renee; Neary, Vincent Sinclair

    2014-09-01

    Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulation s as a part of the stand ard current practice for designing marine structure s to survive extreme sea states. Such environmental contours are characterized by combinations of significant wave height ( ) and energy period ( ) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first - order reliability method (IFORM) i s standard design practice for generating environmental contours. In this paper, the traditional appli cation of the IFORM to generating environmental contours representing extreme sea states is described in detail and its merits and drawbacks are assessed. The application of additional methods for analyzing sea state data including the use of principal component analysis (PCA) to create an uncorrelated representation of the data under consideration is proposed. A reexamination of the components of the IFORM application to the problem at hand including the use of new distribution fitting techniques are shown to contribute to the development of more accurate a nd reasonable representations of extreme sea states for use in survivability analysis for marine struc tures. Keywords: In verse FORM, Principal Component Analysis , Environmental Contours, Extreme Sea State Characteri zation, Wave Energy Converters

  12. 3 CFR 13513 - Executive Order 13513 of October 1, 2009. Federal Leadership on Reducing Text Messaging While...

    Science.gov (United States)

    2010-01-01

    ... consultation with the Administrator of General Services and the Director of the Office of Personnel Management... action pursuant to this order. Sec. 6. Definitions. (a) The term “agency” as used in this order means an...” or “Text Messaging” means reading from or entering data into any handheld or other electronic device...

  13. A high-order CESE scheme with a new divergence-free method for MHD numerical simulation

    Science.gov (United States)

    Yang, Yun; Feng, Xue-Shang; Jiang, Chao-Wei

    2017-11-01

    In this paper, we give a high-order space-time conservation element and solution element (CESE) method with a most compact stencil for magneto-hydrodynamics (MHD) equations. This is the first study to extend the second-order CESE scheme to a high order for MHD equations. In the CESE method, the conservative variables and their spatial derivatives are regarded as the independent marching quantities, making the CESE method significantly different from the finite difference method (FDM) and finite volume method (FVM). To utilize the characteristics of the CESE method to the maximum extent possible, our proposed method based on the least-squares method fundamentally keeps the magnetic field divergence-free. The results of some test examples indicate that this new method is very efficient.

  14. Numerical solutions and solitary wave solutions of fractional KDV equations using modified fractional reduced differential transform method

    Science.gov (United States)

    Saha Ray, S.

    2013-12-01

    In this paper, the modified fractional reduced differential transform method (MFRDTM) has been proposed and it is implemented for solving fractional KdV (Korteweg-de Vries) equations. The fractional derivatives are described in the Caputo sense. In this paper, the reduced differential transform method is modified to be easily employed to solve wide kinds of nonlinear fractional differential equations. In this new approach, the nonlinear term is replaced by its Adomian polynomials. Thus the nonlinear initial-value problem can be easily solved with less computational effort. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of the solutions, several fractional KdV equations with different types of nonlinearities are considered. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional KdV equations.

  15. Two efficient reliable methods for solving fractional fifth order modified Sawada–Kotera equation appearing in mathematical physics

    Directory of Open Access Journals (Sweden)

    S. Saha Ray

    2016-09-01

    Full Text Available The present paper deals with two reliable efficient methods viz. tanh-sech method and modified Kudryashov method, which are used to solve time-fractional nonlinear evolution equation. For delineating the legitimacy of proposed methods, we employ it to the time-fractional fifth-order modified Sawada–Kotera equations. As a consequence, we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada–Kotera equation. We have also presented the numerical simulations for time-fractional fifth-order modified Sawada–Kotera equation by means of three dimensional plots.

  16. Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

    Science.gov (United States)

    Pazner, Will; Persson, Per-Olof

    2018-02-01

    In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

  17. Business risks, functions, methods of assessment and ways to reduce risk

    Directory of Open Access Journals (Sweden)

    A.V. Mihalchuk

    2015-06-01

    Full Text Available For successful existence in a market economy entrepreneur have to take bold actions, and this increases the risk. The article describes the concept of entrepreneurship and business risk, positive and negative aspects of functions of risk in business. Therefore, it is necessary to assess the risk properly and be able to manage it to achieve the most effective results in the market. In market conditions the problem of assessing and accounting market becomes independent theoretical and practical significance as an important component of the theory and practice of management. Risk - a key element of business activities. Development of risk situations can lead to both the occurrence of adverse effects (losses, lost profits, and positive results for a company in the form of increased profit. This article describes: the concept of entrepreneurship, risk and business risks, characteristic of positive and negative aspects of risk functions in business, methods of assessment and risk reduction, shows formulae and examples you can use to assess risk in an enterprise. Analyzing already established methods of risk assessment a number of rules were proposed in order to reduce business risk.

  18. [Papanicolau smears: reducing the false negative rate by improving the method].

    Science.gov (United States)

    Biran, Galya; Levy, Tally

    2004-03-01

    Screening for cervical carcinoma precursors by Papanicolau (Pap) smears diminishes the incidence of cervical cancer in screened populations. The Pap smear test has a considerable rate of false negatives and in order to improve its efficiency and sensitivity several types of technologies were developed, two of which are discussed in this review. One entails measures for collecting cells from the cervix into a liquid medium and preparing single layer smears from these cells. Using this method, a thin and clean smear is obtained, in comparison to the regular Pap smear. The liquid-based test improves sample adequacy and increases the diagnostic accuracy of low-grade and high-grade squamous intraepithelial lesions. The second type of technology is computerized deciphering of cervical smears, which are prepared either by the regular method or using the previously mentioned thin smear. the computerized deciphering is based on structural measurements of cells via an instrument that is programmed to differentiate between cellular components, thus categorizing the smears into those which are normal and those that require further evaluation by a cytopathologist. Alternatively the computer can display the most abnormal cells in the smear to the cytopathologist. In this manner, the workload of the cytopathologist is reduced while the test efficiency and sensitivity are increased.

  19. Stochastic Self-Consistent Second-Order Green's Function Method for Correlation Energies of Large Electronic Systems.

    Science.gov (United States)

    Neuhauser, Daniel; Baer, Roi; Zgid, Dominika

    2017-11-14

    The second-order Matsubara Green's function method (GF2) is a robust temperature-dependent quantum chemistry approach, extending beyond the random-phase approximation. However, until now the scope of GF2 applications was quite limited as they require computer resources that rise steeply with system size. In each step of the self-consistent GF2 calculation there are two parts: estimating of the self-energy from the previous step's Green's function and updating the Green's function from the self-energy. The first part formally scales as the fifth power of the system size, while the second has a much gentler cubic scaling. Here, we develop a stochastic approach to GF2 (sGF2), which reduces the fifth power scaling of the first step to merely quadratic, leaving the overall sGF2 scaling as cubic. We apply the method to linear hydrogen chains with up to 1000 electrons, showing that the approach is numerically stable, efficient, and accurate. The stochastic errors are very small, on the order of 0.1% or less of the correlation energy for large systems, with only a moderate computational effort. The first iteration of GF2 is an MP2 calculation that is done in linear scaling; hence we obtain an extremely fast stochastic MP2 (sMP2) method as a byproduct. While here we consider finite systems with large band gaps where at low temperatures effects are negligible, the sGF2 formalism is temperature dependent and general and can be applied to finite or periodic systems with small gaps at finite temperatures.

  20. Using fractional order method to generalize strengthening generating operator buffer operator and weakening buffer operator

    OpenAIRE

    Wu, L.; Liu, S.; Yang, Yingjie

    2016-01-01

    Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases.